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We live in a time when science – and even physics – books are regularly seen on the best-seller lists, while registration for science – and physics – classes are on the decline. What is it that the publishing industry knows that our educational system does not?

One word: humanity.

Again and again we see that this is a mistake. Even business schools are learning this lesson.

To teach the history of the nineteenth century and not mention James Clark Maxwell and the mastery of electricity is nothing short of an intellectual perversion, for nothing that happened in the nineteenth century was as lasting and important as this event. Truly, few events in the secular history of man can rival this.

 

1) Mysteries

Light and energy, gravity and inertia; these are material mysteries. We cannot explain them.

A mystery is not the same as a puzzle. A puzzle can be figured out. A mystery, in the religious sense, cannot. A mystery cannot be figured out, because it defies figuring.

We are accustomed to talking about spiritual mysteries. We accept that the spiritual world cannot be explained, since all explanations are rooted in the material world, all language being built on metaphor – images of material things and experiences. Thus we gladly accept the fact that science can never speak to religious matters, simply because religious matters are not of the “material” category. And vice-versa. Thus, we are happy to accept the obvious fact that to make a statement about the existence or non-existence of God is by definition to make a non-scientific statement.

Fine. We are OK with that. God is safe from scientists (thank goodness).

But that science can no longer speak to material matters is quite something else indeed. We are not as easy with that. And yet here we are in the 21st century, where we now suspect that 96% of the mass and energy in the universe is of a type not explainable by our current physics. The vast majority of the cosmos is beyond the scope of the laws of physics we know. Most of reality is invisible, undetectable, unknown, and unexplained.

Moreover, the 4% that we think we know, we don’t know all that well. We have measurements, but no real good explanations. When physicists try to explain the meaning of the equations that “describe” the material universe, they get into disputes with one another that are so interminable, that they have long since given up such attempts at such explanations, leaving this pursuit to the philosophers.

Yes, science has given up.

So here we sit, with no explanation of light, no explanation of gravity, no explanation for inertia, no explanation of the strong force. Worse yet, the hardest of the hard sciences tell us without equivocation: there can be no explanation. This, of all things, being an essential law upon which all of physics – the Mother of all Scientific Knowledge – is built.

2) Known knowns

The Greeks have different words for knowledge. There is propositional knowledge, or knowledge-that, and there is procedural knowledge, or knowledge-how.

Knowing-that is called  episteme. The study (logy) of  episteme is called epistemology.

Knowing-how is what Plato called techne, or skill. This is where the word, technology comes from. Technology and Epistemology are two ways of knowing. We have an abundance of one, while the other remains so elusive and mysterious that science has abandoned it.

For example, we “know-that” light travels at a certain speed, has certain energies, etc. But to this very day, we have no explanation for how it does what it does. In other words, we have a lot of “know-that”, or epistemological, information about light. But we have very little “know-how”, or technical, mechanical information about light. We do not understand the mechanism by which it operates.

Again, we do not “know how” light works. We simply “know that” it does. We know that it does X, Y, and Z when A, B, and C are present.

We have literally taken lightening out of the sky and made it to sing, yet in a very real sense, we have no real knowledge of it all.

3) Known Unknowns

Here is a video of Feynman talking about his discovery of inertia when he was a child. He asks his father for an explanation, but his father, having a “deep” understanding, said that no one knows why things have inertia. We only know that they do.

Socrates understood that he did not “know” much. This is wisdom. That there is still so much that we do not know, cannot know, in this world; this is sublime.

Here is another video of Feynman talking about what it is that we ask when we ask why.

4) Physics reaches the brink

So, we know that light has certain properties, and we know that light does this and does that under certain conditions – we just don’t know how. Moreover, as Richard Feynman has remarked, science has long ago given up (yes, science has given up) the attempt to discover how light works.

This question is a matter of philosophy and religion now. Why? Because the “how” question has no material (Newtonian) answer. Which is to say the rules of logic – of cause and effect – do not apply, therefore, “explanations” fail, simply because to explain something is to use the rules of logic to show the causes and effects. But in the quantum world, current principles tell us that we cannot know these things – not because we are not clever enough, but because they are true mysteries.

One might still like to ask: “How does it work? What is the mechanism behind the law?” No one has found any machinery behind the law. No one can “explain” any more than we have just “explained.” No one will give you a deeper representation of the situation. We have no ideas about a more basic mechanism from which these results can be deduced.

Truly, we have reached the brink of the knowable.

We would like to emphasize a very important difference between classical and quantum mechanics. We have been talking about the probability that an electron will arrive in a given circumstance. We have implied that in our experimental arrangement (or even in the best possible one) it would be impossible to predict exactly what would happen. We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes! Physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible, that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step, but no one has seen a way to avoid it.

The Newtonian, material, (know-that) world is but a puzzle. The quantum (know-how) world, in contrast, is a true mystery in the religious sense of the word. And yet the Newtonian, material world is made up – everywhere and in all parts – of the quantum. In other words, the quantum world IS the material world! All of physics, every phenomenon in the history of the universe from the Big Bang to my lunch break yesterday can be explained with the QED, which is a mathematical framework that describes the interaction of photons with electrons. When it comes to the material world, this is all there is. This is the sum of the smallest to the largest and all the in-between. This explanation is science’s greatest achievement. But it is all “know-that” and no “know-how”. Even worse, at it’s very core is this fact: that it is ultimately an unsolvable mystery. The “know-how” is un-knowable.

Here is a video of Feynman talking about this.

The problem he is discussing is the problem you encounter when you come to the end of language. All language is metaphor. Which is to say that our words use material objects as maps to concepts and meaning. It has always been so. But with particle physics, we have no corresponding material experiences with which to map the concepts of what is happening. We have equations but no words.

We have the theory right but we haven’t got the pictures that will go with the theory. Is that because we haven’t caught on to the right pictures, or is it because there aren’t any right pictures?

Feynman goes on to suggest that only by immersing oneself in the quantum world for prolonged periods of time can the student attain an instinct for such an unfamiliar realm for which there is no language or images from which to draw explanations. This is the philosophy of “efficient practice precedes the theory of it.” This is reminiscent, not so much of physics, as it is of religious mysticism. In fact, this is the very same mechanism behind many religious rituals dating back through antiquity and further. Philosophy until Aristotle was a practice, a way of life, more than a mere intellectual exercise. Religious experience was precisely the experience Feynman describes. It is the experience of that for which we have no words. The experience of the immaterial.

The modern enlightened intellectual may find him or herself far removed from such mystical, religious practices. But we have come full circle. Once again, to understand the mysteries of this world, we come back to the silence that transcends words. Psychologists have defined this mystical experience as “flow“. Athletes call it being in the “zone”. Religion simply calls it God, or Nirvana, or Enlightenment. These may not all be the same experience, per se, but they are the same kind of experience.

And this is the way of Feynman, master of the secrets of light. Like a Zen master, or Christian mystic, more than a physicist, he suggests that the only way to understand light is through something that can best be described as transcendent.

Thus, studying particle physics brings the student to the same place that the religious mystics find themselves: to experience that  which is beyond words, beyond the material world, beyond cause and effect, beyond binary logic. The Greeks had a word for this kind of knowledge too, they called it gnosis, or knowledge of the spiritual.

The same thing happens when we try to “know-how” gravity works. And with so many other mysteries in our lives. Not only can science not explain the spiritual, it cannot even adequately explain the material. Whether you are studying science, or religion, you will inevitably come to the end of words, the end of pictures, and be confronted with the brink.

Crossing the brink is what Kierkegaard describes as making a leap of faith. It is the point at which you can go no further unless you let go of what some may call “reason”. But science is pure reason, you declare! Yes, but logic dictates that a material object can only be in one place or another. However, Science now tells us that light is a particle and yet is always in more than one location at a time. Good bye logic. Beyond this point you are no longer needed. All who enter here leave Science behind. There is but one way through the Mystery. Welcome to the brink.

Further examples and explanations:

Again, here is Feynman explaining the “know-that”, which physicist possess vs the “know-how”, which they do not.

Once again, here he explains the difference between knowing the name of something and knowing the theory of something.

Ernest Rutherford once made the comment that “all science is either physics or stamp collecting.” Well, even physicists are stamp collectors now.

 

Key concepts:

Interference Patterns

Defraction and Refraction

Information Theory

QED

Holograms take advantage of some pretty amazing physics. For example, on a piece of holographic film, the entire image is recorded on every piece of the film. You can cut up the film into as many pieces as you like and it will still reproduce the full image that was recorded on it. Imagine if your DVD worked this way!

If you make a hologram of a magnifying glass, the image of the magnifying glass produced by the hologram will magnify other parts of the hologram!

So how the heck does it do that? Is holographic film some magic technology? Not at all. It turns out, however, that Light is. Holographic film “records” the interference patterns that light waves make when they cross each other.

This is actually an old technology. We have been manipulating light in this way with radio for many decades now.

see: Carrier waves and Information waves.

To understand how this works, we first need to discuss the mechanics of what happens when light reflects off of an object.

The Miracle Known as the Reflection of Light

The problem with miracles, sometimes, is that we give them such unimpressive names, like “reflection”.

When a “beam of light” shines on a reflective object, the object first “absorbs” the light, chews on it for a bit, and then it either “sends it back” out into the world, or swallows it.

It all depends on the atomic structure of the object and the motion (energy) of the electrons. Either way, in the case of a reflective material, light is being trasformed into matter and then transformed back into light.

So, the photons are absorbed by the electrons, causing them to wiggle, and thus increasing the atom’s energy. Two things can happen from here: If the electron is “loosely” connected (outer shell electrons), it will speed up enough to emit a photon back out. This is the reflection of light.

If the electron is tightly connected (inner shell electrons), it cannot wiggle freely enough to emit the photon back out (due to friction) but it does wiggle as much as it can. This wiggling, combined with the friction o being more tightly “packed” causes the atom to vibrate, producing heat. This is the absorption of light.

Notice, however, that what we call absorption is just a special case of reflection, because as we know, heat is a form of invisible radiation. The light is still “reflected”, we just can’t see all of it!

In other words, the light is absorbed, filtered through the object and reflected back out, but we only see certain portions (colors) of what is filtered back out because some of what comes back out is in the form of infrared (heat) radiation, which is invisible to the human eye.

Color is an atomic fingerprint

Color is a fundamental property – of atoms. Let me say this again: color is not a property of light, but of matter. This is one of those very deep statements that sinks in further and further as understanding deepens. We don’t talk in this way, because we are lazy and have more important things to do, but if we slow down and get precise, we can see the cold, hard facts at work – and they are miraculous!

Few ideas get me as excited as this idea of the unity of matter and light. After all, light does not just originate from empty space. It originates – from matter!

All matter radiates light all the time.

Yes, this includes you and your radiating nose and ears, but before we go down that path, lets finish this description of reflection.

Here comes a big aha moment…

There is a very deep-seated sort of identity between electrons and photons.

So I like to think of color, not as an object simply reflecting light, but as an object emitting light. It is the same mechanism, but the concept of reflection does not fully denote the facts.

Light becomes matter and then matter converts itself back to light. This is quite amazing. We call this miracle, “the reflection of light.” But understanding the mechanics of what has happened will help us to understand holograms.

Making a Hologram

if we take a beam of light and split it into 2, with the first beam directed to a piece of film and the second beam directed to an object and then to the same piece of film so that we end up with both beams meeting on the piece of film then we have recorded the information of a light beam and embedded the information of an object together in such a way as to produce a hologram.

Information Theory

We were in the process of describing how an object filters light like a crystal. We said that color reveals the atomic structure of the object that produces, or “reflects” it. This is why we can tell what stars are made of. By analyzing the wavelength of the light any object filters back to the observer, we can deduce the atomic structure of the object.

I already introduced the concept of matter chewing on a photon and spitting it back out and I suggested that this “new” photon encodes some sort of information about the object that can be retrieved from the photon.

This is a powerful idea. It leads us down the road to ideas about quantum bits of data and how the events of the universe can be understood in terms of quantum mechanical computation of quantum bits of information.

But that is a story for another post.

Right now, we are focused on understanding how a hologram works and why on earth would someone claim that the universe has some sort of holographic “properties”. What could all of this possibly mean?

One of the difficulties I had in understanding a hologram is the fact that the image is not recorded on the film: it is RECREATED from the film.

Interference

When two “beams of light” cross paths (Ghostbusters reference goes here) they create interference patterns (think of two waves in a lake moving toward each other). If these interference patterns are recorded on film, the image of

see also:

The Black Hole War

Computing the Universe

Here comes a big aha moment…

There is a very deep-seated sort of identity between electrons and photons.

So I like to think of color, not as an object simply reflecting light, but as an object emitting light. It is the same mechanism, but the concept of reflection does not fully denote the facts.

Light becomes matter and then matter converts itself back to light. This is quite amazing. We call this miracle, “the reflection of light.” But understanding the mechanics of what has happened will help us to understand holograms.

 

This is the interpretation of Quantum Mechanics that you DONT hear about (the one that actually makes sense).
http://en.wikipedia.org/wiki/De_Broglie-Bohm_theory

The “standard” interpretation is the “Copenhagen Interpretation” put forward by the Zen-minded Neils Bohr (Einstein and he had many heated arguments over this)
http://en.wikipedia.org/wiki/Copenhagen_interpretation

The problem here is that the mathematical models are not mechanical explanations. This is always glossed over entirely. Feynam was a genius because he was able to visualize and instead of dealing with long, difficult equations, he made pictures – the Feynman diagrams – to make the mathematics easier to do. It was a visual shortcut. In vector math, you can add vector arrows by putting one arrow on the end of another arrow, thus what was a difficult equation turns into a simple geometric diagram of arrows that is very intuitive.

The problem is that this is a model of the mathematics, NOT the physical mechanism at work in the world.

Here is an example of this. Calculating your bank account savings rate:

Finding a logarithm, you may recall, is the inverse action of raising some base number to an exponent. Which is to say that “finding the log” is to “find the exponent” that was raised on some base number.

log10 x = y (which is read as “y is the logarithm of x to base 10″).
The inverse of this statement is the exponential form, 10^y = x.

If we say “10^2 = 100″, then the inverse is  “log10 100 = 2″.

Exponential functions and logs are all about how GROWTH relates to TIME. In these formulas, the “y” and the “2″ are the time component. The “x” and the “100″ are the growth component. Let’s look again:

log10 100 = y (how much TIME until 10 grows to 100?)
10^2 = x (how much GROWTH will 10 produce after 2 time units?)

Let’s take a shortcut from logs to natural logs, where the relationship to time is more direct because natural logs are based on the transcendental number e, which in turn, is about continuous growth. Natural log is referenced with the term “ln” and the natural log of 1 is zero.

ln(1)=0

Awesome. What does this mean? How much TIME until my investment grows to itself? Answer? Zero. My investment is itself already. Similarly, the formula, ln(2)=x is asking the question, “how long until my investment doubles?

Ok so what does ln(.5)=x mean?

We can calculate this, and interpret the calculation as meaning that to “grow” by half, you just need to go “backwards in time” for a while until your something has “grown” in half. Whatever that “while” turns out to be, equals x.

The point…

If our interpretation of log10 100 = y is how much time until 10 grows to 100, which is a valid interpretation, then we are forced to interpret ln(.5)=10 as meaning that we have to go backwards in time for 10 units to lose half our investment.

The math has no problem with this, but we do. Because it does not make sense in the real, actual world. The formula is valid, and useful. But we need a better interpretation.

This has happened many times in the history of mathematics. Our interpretations have had to change. Zero. Negative numbers. Irrational Numbers. Imaginary Numbers. Transcendental Numbers. Trans-infinite Numbers. Each of these caused a re-mapping in our brains of Number itself. Imaginary Numbers are the best example. These numbers can not represent any “thing” in our world like the number “3″ can represent. And yet they are an extremely useful, and necessary number for solving all sorts of real world engineering and physics problems!

There was very real difficulty in explaining these numbers, interpreting them. Finally, in a turn of irony, we find a useful picture with Descartes’ own analytical geometry – the x and y coordinate system. Unitl the Imaginary numbers, we always visualized numbers as little dots on a “line”. In other words, we thought of Number in only one dimension. Descartes coined the term “imaginary number” as a derision against them, but it was his system that allows us to visualize these numbers properly: as two-dimensional numbers: literally, numbers that have “jumped off the line”. Thus there are so many more imaginary numbers than real numbers that the imaginary numbers make the real numbers look rather insignificant in comparison.

The lesson here is that these entities were derided and chastised and labeled “imaginary” at the time, simply because we lacked any interpretation that made sense with which to explain them to ourselves.

This is the current situation with Quantum Mechanics. It is in want of a better interpretation. The formulas work great. What they mean, we just don’t know. So we say that particles go backwards in time, simply because we have to say something. As far as the equations are concerned, this is “accurate”. But these equations are simply mathematical descriptions just like the log equation above. The equations of quantum mechanics do not describe any physical thing any more than the ln(.5)=10 describes the path my money takes through time to cut itself in half. They simply calculate where a particle is probably going to be. HOW it gets there is a total mystery. A TOTAL mystery.

Everyone misses this. But if you listen to Feynman, he is very clear about it. The physicists know this, deep down. They just allow the fallacy because it allows them to get on with their work.

The truth is that we have no explanation for what a photon is, what it looks like, or how it does what it does. We cannot explain this any more than we can explain what causes inertia gravity, or mass.

The most basic fundamental forces in the universe are still far beyond our comprehension.

 

It is common to think that objects attract each other by their gravitational force. That is to say that most people have this idea that a massive body like the earth pulls on other massive bodies like the moon through some invisible force that we call gravity. When we imagine this, we imagine perhaps an invisible force field or beam that stretches from the earth to the moon, but this is not what is happening.

The earth does not pull on the moon and the moon does not pull on the earth. There is no force emanating from the earth or the moon. There is only space. And space touches everything. It pushes on everything. (This is what is called inertia?) And matter pulls back on space. In fact, matter comes from space. Matter is inertial mass energy that has condensed out of the vacuum energy of empty space.

But before we go there, lets go back to space pushing on matter and matter pulling on space. When enough matter gets together it pulls on space very hard and the more concentrated that matter is, the more focused is its pulling of space. This pulling of space bends space, and when space bends, it moves (accelerates) the matter that is floating within it.

We think of space as empty, but it is not. Space is a physical thing. It touches everything and everything touches it. Matter deforms space, stretching it, and this stretching is what makes other objects seem to travel in curved trajectories, but they don’t. They are traveling on straight lines across a curved surface.

A picture is worth a thousand words, so check out this video of differential geometry to see it.

http://opinionator.blogs.nytimes.com/2010/03/21/think-globally/?ref=opinion

 

related post: fire

Heat and Light

I always get confused when thinking of infrared radiation and heat. I tend to think of these as the same, but they are not. This post is a refresher course for me for when I start to have trouble with these concepts…

Heat is not a substance, nor is it a form of energy, strictly speaking. Rather, it is the transfer of energy. More specifically, it is the transfer of kinetic energy. More specifically still, heat is the mechanism by which the transfer of molecular motion travels from a faster moving thing to a slower moving thing.

Here are the official definitions…

In modern terms, heat is concisely defined as energy in transit. Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of the first to enunciate a modern definition of “heat”. In short, Maxwell outlined four stipulations on the definition of heat. One, it is “something which may be transferred from one body to another”, as per the second law of thermodynamics. Two, it can be spoken of as a “measurable quantity”, and thus treated mathematically like other measurable quantities. Three, it “can not be treated as a substance”; for it may be transformed into something which is not a substance, e.g. mechanical work. Lastly, it is “one of the forms of energy”. Similar such modern, succinct definitions of heat are as follows:

  • In a thermodynamic sense, heat is never regarded as being stored within a body. Like work, it exists only as energy in transit from one body to another; in thermodynamic terminology, between a system and its surroundings. When energy in the form of heat is added to a system, it is stored not as heat, but as kinetic and potential energy of the atoms and molecules making up the system.[4]
  • The noun heat is defined only during the process of energy transfer by conduction or radiation.[5]
  • Heat is defined as any spontaneous flow of energy from one object to another, caused by a difference in temperature between the objects.[6]
  • Heat may be defined as energy in transit from a high-temperature object to a lower-temperature object.[7]
  • Heat as an interaction between two closed systems without exchange of work is a pure heat interaction when the two systems, initially isolated and in a stable equilibrium, are placed in contact. The energy exchanged between the two systems is then called heat.[8]
  • Heat is a form of energy possessed by a substance by virtue of the vibrational movement, i.e. kinetic energy, of its molecules or atoms.[9] The kinetic energy and heat may formally be equivalent, but they are not identical.

So, back to infrared radiation…

Is infrared radiation and heat the same thing? Moreover, if we understand IR as part of the electromagnetic spectrum, could we say that heat is therefore EM radiation, like light?

Infrared radiation IS a form of heat. That is, IR will transfer kinetic energy, and this transfer of kinetic energy is what we call “heat.”

What does this mean? Well, it means that the range of frequencies in the spectrum of electromagnetic radiation that we refer to as “infrared” are such that they transfer kinetic energy (motion).

The first question that arises when we state things this way, is: do other frequencies in the spectrum of electromagnetic radiation transfer kinetic energy as well, and why or why not?

The answer is no. The other frequencies in the spectrum of electromagnetic radiation do NOT transfer kinetic energy. But why?

Because of wave harmonics.

Infrared radiation can be felt. It is (invisible) Light that warms the skin. When we get close to the stove, a fire, or feel our skin warming on a sunny day, we are experiencing the effects of the same infrared radiation. This is why I tend to think of heat and light as the same thing. Because this particular Light warms the skin. But note that this is true only of the light in the lower (less energetic, longer wavelength) part of the visible portion of the spectrum – at the red end. Notice that this is the lower (energetic) end of the visible portion of the spectrum. We cannot “feel” the light in the even lower, longer (radio) ranges or the much higher, shorter, more energetic (gamma) range. From this we can see that although IR warms the skin, and IR is Light, not all “Light: warms the skin. Radio waves do not warm the skin and gamma rays do not warm the skin. This fact confounded scientists for centuries (hint: it should confound you, too. If it doesn’t, stop here and explain why this is so – the answer, by the way, was given in the previous paragraph).

Another way of observing the above is to notice that increasing the energy level (kinetic energy) of the Light, does not increase the heating effect of the Light on an object.

But why?

Let me say that again, more precisely:

Infrared radiation (red Light) from the sun transfers kinetic energy (heat) from the sun to our skin. Ultraviolet radiation (purple Light) from the sun does not. But UV Light is more “energetic”. The question, then is: Why is it not “hotter?”

Definitions

-Heat vs heat transfer – are these the same? From the wikipedia definition above, heat is the transfer of kinetic energy, so it is misleading to speak of the transfer of the transfer of something. What we are doing is confusing kinetic energy with heat when we start to make this kind of distinction between the thing and the transfer of the thing. In this case, the thing in question is atomic and molecular motion.

-Kinetic energy is this motion – the wiggling of atoms and molecules – and heat is the passing on of this “motion” from one object to another. Both kinetic energy and heat increase as the wiggling of atoms and molecules increase, but heat increases only to the extent that this increase in wiggling (kinetic energy) causes an increase in wiggling elsewhere (to another object).

-Temperature is the measurement of the amount of this wiggling (kinetic energy). This wiggling sounds familiar, for Light is itself a wiggle. So why is it that the UV wiggle does not increase the wiggle (temperature) in our skin as much as the IR wiggle? Why does Light with more kinetic energy not produce more heat? Why is the kinetic energy of this Light not transferred?

-Wave harmonics

The wiggle of IR reinforces the wiggle in the molecules of our skin, sort of like how microwave Light reinforces the wiggle in the polarized water molecule.

The key is that the wiggle is best transferred when the speed (temperature, or kinetic energy – referred to as “color” in the visible spectrum) of the wiggling matches between the source of the radiation (Light) and the receiver of the radiation. Another way of saying this is this is that IR is a particular speed (wavelegth) of Light that makes molecules wiggle. Sometimes, this particular (range of) wavelength of Light is called “heat waves,” “radiation,” and/or “infrared radiation.”

In all of these cases, we are referring to Light (electromagnetic radiation) of a certain range (the infrared range), which is to say of a certain wavelength, or “energy.” It just so happens that this particular range of wavelengths, or energy, harmonizes with molecules and increases their ever present wiggling.

So, the wiggling is kinetic energy and certain frequencies of Light transfers this wiggling to molecules. But other frequencies do not. This is why it is not the Light that is the heat, but that some Light can transfer its kinetic energy (wiggle) to objects. This form of Light is called infrared radiation, or heat waves.

But why is that only certain frequencies of Light make this transfer? Why don’t higher frequency wavelengths transfer more heat, and lower less?

Harmonics. Infrared radiation (the lower energy Light in this example) wiggles at a similar speed (temperature) as the molecules in our skin. Therefore, the wiggling in the Light and the wiggling in our skin can harmonize such that the wavelengths of the Light and the wavelengths of our skin add to each other.

Wavelengths of skin? Yes, whenever an electron moves it generates electromagnetic waves in the field that permeates the universe (I like to refer to all EM as Light, but traditionally people speak of light as a particular range of EM, just as IR (heat radiation) is another particular range of EM ). Another way of saying this is that when an electron moves, it emits Light. Light behaves as a wave such that two waves can cancel or reinforce. When we feel our skin get hot from the Light of the sun, what is happening is that the Light that is emanating from our skin and the Light that is penetrating our skin from the sun, reinforce. In other words, we shine brighter, hotter.

We shine? Yes, everything in the universe (except dark matter) emits Light (EM) because everything in the universe wiggles and every electron that wiggles creates ripples in the electromagnetic field which permeates the entire universe. These ripples are called electromagnetic radiation, or Light, as I have described.

[Additionally, not only does all non-dark matter radiate Light, but all non-dark matter in the universe radiates the entire spectrum of Light. Right now, your nose is emitting radio waves and gamma rays and everything in between. However, each piece of matter in the universe has a peak radiation frequency. That is to say that the wavelength of light that your nose is most strongly emitting falls somewhere between radio and gamma. more on this here]

So the upshot of all of this is that infrared radiation transfers its wiggle to molecules because it wiggles with a wavelength that is in a certain range that the molecules respond to. This is why higher energy Light from the sun (like UV Light) does not transfer heat to our skin – the harmonics are not right. UV Light is, in a sense, invisible to our skin in the same way it is invisible to our eyes. It wiggles too fast for our skin to “see” or “hear”

The Wiggle is All

It is interesting to note that the transfer of wiggles is a concept that applies to every event and phenomena of the universe. All of our senses are merely ways that the wiggles of the universe are transferred to our bodies, whether the source of the wiggle be described as Light (molecular wiggles felt by our eyes), sound (molecular wiggles felt by our ears), taste (molecular wiggles felt by our tongue), smell (molecular wiggles felt by our nose), or touch (molecular wiggles felt by our bodies). In each of these phenomena, kinetic energy is passed from one object to another through physical touch.

This is an interesting concept to keep in mind, particularly when thinking of forces (post on forces coming soon).

Everything that happens in the universe, every interaction, is a form of one thing touching another. There is no such thing as force. Not the way we tend to think of it: as something separated from, independent of, matter. Force and matter are the same phenomenon, like space and gravity. Einstein showed that gravity is not some force that acts in space, but that gravity is space itself. Likewise with electromagnetic radiation. Light is not something that moves through space; rather, it is the movement of space itself.

These are difficult abstractions to work through, but the movement of physics in the twentieth century has progressively stripped down our distinctions such that it is nearly impossible to draw a line between matter and space and energy at all. At the deepest level, we have seen the equivalence of these. To those who would challenge the idea that the concept of all the forces can be reduced to material interactions may want to refer to Richard Feynman’s theory of Quantum Electrodynamics, the most successful, most throughly tested, and most empirically accurate theory of the physical universe ever conceived by man. It is the pinnacle of scientific thought, and of science itself. It is hard to overstate the facts, but I will leave off here by pointing out to the reader that it is this theory that describes the forces as the exchange of sub-atomic, virtual particles between one another. As such, inertia itself is transferred. And that’s all. Should we ever conceive or grasp what inertia is we will have perhaps finally understood the universe in its essence.

[side note: the transfer of something from one body to another? Does that sound familiar?]

Now, you may say that this is all metaphorical, to say that this thing is actually another, and you would be absolutely right. Metaphor is exactly that: an expression that equates two seemingly different things. In other words, mathematics. The equations of physics that describe the universe are metaphors that tell us that this equals that. E=MC2 is the mathematical metaphor that tells is that matter IS energy. We know that space is not separate from time, and yet we speak of time as if it flows through space. This is not correct. Neither is it correct to speak of light and radio as if these are two different phenomena. They are not. One just has more kinetic energy but they are, in fact, the same phenomena. The joy of physics and mathematics – and religious contemplation – is merely the joy in discovering the multifaceted unification of the variety of experiences and phenomena in the universe. In the religious sense, this experience begins with the discovery that you are not your mind; it is the discovery that to experience your true self is to experience the ever present communion with God. The progress of physics thus mirrors the progress of the spirituality that grows only by seeing the ever more connectedness of the universe as one vast, single multifaceted phenomenon. This should not come as a surprise, for both of these journeys are of men and the journeys of men have but one end.

But wait, we started this meditation on heat and light by distinguishing them and declaring that they are not the same phenomenon. And surely taste and sight are not the same phenomenon. Well, yes and no. In the same way that red and blue are not the same, that is. But there is another sense in which red and blue are the same. That is to say, that they are of the same nature. The larger point in this meditation is really about levels of abstraction. We can go in either direction and make distinctions between red and blue, or we can go in the other direction and draw them together under one classification. In either case, these are just abstractions, or ways of thinking about these phenomena.

Thus the idea of the grand, singular, multifaceted phenomenon, aka, The Universe. After all, seen from a perspective outside of time, every event and phenomena in the history of the universe can be seen as a single event – in the mind of God, for example.

But now we have wandered far off the topic, so this will have to continue in another post.

See you then.

  • Heat is the transfer of energy between substances of different temperatures.
 

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

And yet it just won’t go away:
I feel it and cannot understand it;
cannot hold on to it;
nor yet forget it;
and if I grasp it wholly
I cannot measure it!

–Richard Wagner

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I do not know it – it is without name – it is a word unsaid,
It is not in any dictionary, utterance, symbol.

There is that in me – I do not know what it is – but I know it is in me.

–Walt Whitman Leaves of Grass

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

And it’s hard to explain how I feel;
It don’t go in words but I know that it’s real.
I can be moving or I can be still,
But still is still moving to me.

–Willie Nelson

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

And where we had thought to find an abomination,
we shall find a God; where we had thought to slay another,
we shall slay ourselves; where we had thought to travel outward,
we shall come to the center of our own existence;
where we we had thought to be alone,
we shall be with all the world.

–Joseph Campbell, A Hero with a Thousand Faces

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Now that lilacs are in bloom
she has a bowl of lilacs in her room
and twists one in her fingers while she talks.

“Ah, my friend, you do not know, you do not know
what life is, you who hold it in your hands”;
(slowly twisting the lilac stalks)

“You let it flow from you, you let it flow,
and youth is cruel, and has no remorse
and smiles at situations which it cannot see.”

I smile, of course,
and go on drinking tea.

–T.S. Eliot, Portrait of a Woman

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I am moved by fancies that are curled
around these fingers, and cling;
the notion of some infinitely gentle
infinitely suffering thing.

–T.S. Eliot, Preludes

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A flower grows
and blooms and dies
and sometimes is touched
by butterflies.

– PBT

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Take this kiss upon the brow!
and, in parting from you now,
thus much let me avow -
you are not wrong, who deem
that my days have been a dream;
yet if hope has flown away
in a night or in a day,
in a vision, or in none,
is it therefore the less gone?
All that we see or seem
is but a dream within a dream.

I stand amid the roar
of a surf-tormented shore,
and I hold in my hand
grains of the golden sand -
how few! yet how they creep
through my fingers to the deep,
while I weep – while I weep!
O God! Can I not grasp
them with a tighter clasp?
O God! Can I not save
one from the pitiless wave?
Is all that we see or seem
but a dream within a dream?

– Edgar Allen Poe

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

We had passed through an initiation
like that of the Tibetan ascetic,
who staggers half dead from a trance,
where he has seen himself eaten
alive and has not yet learned that
the eater was himself.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The battle between the manifest world
and the ancestral darkness
at the end of all things

the too great power of divinity

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

because in my head, frothy red
more interesting than the words she said
“I cannot say, I cannot say,
these things like little white wings
that carry and bring
yet have no speech
and cannot sing.

The dancing lightness
of sunshine washes (us) clean

– PBT

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

I know the cries that cry for all
I’ve known one well enough
to know them all

I know the despair of half-empty streets
under a half-empty moon
that lingers at half past three
in the half-dead, mid afternoon

I know where a yellow wildflower grows
through a half inch crack in black cement

I wonder whether a yellow wildflower knows
it was born in a place it was never meant?

Can a yellow wildflower decide
in the left lane of a highway divide?

– PBT

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Another and another and another -
has anyone ever counted them?
Does anyone know;
The number of waves
in a single day -
rising to crescendo
then receding quietly away?

– PBT

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

 

Hawking: The Beginning of Time

Quantum theory introduces a new idea, that of imaginary time. Imaginary time may sound like science fiction, and it has been brought into Doctor Who. But nevertheless, it is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there’s another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time. – Hawking

The no boundary proposal, predicts that the universe would start at a single point, like the North Pole of the Earth. But this point wouldn’t be a singularity, like the Big Bang. Instead, it would be an ordinary point of space and time, like the North Pole is an ordinary point on the Earth, or so I’m told. I have not been there myself.

According to the no boundary proposal, the universe would have expanded in a smooth way from a single point. As it expanded, it would have borrowed energy from the gravitational field, to create matter. As any economist could have predicted, the result of all that borrowing, was inflation. The universe expanded and borrowed at an ever-increasing rate. Fortunately, the debt of gravitational energy will not have to be repaid until the end of the universe.

Someone is going to have to help me out on this one. To borrow energy from the gravitational field to create matter? Wow. I admit, I never thought of the E=MC2 equation in terms of matter being created out of pure energy. We are all familiar with the energy that is bound up in matter and the result of releasing that energy (nuclear explosion), but I never consider the force that did the reverse: to suck the contents of that explosion and compress it into the nucleus.

But that is another story. This post is about two things: imaginary time and how inflation creates space. “The universe expanded and borrowed…” Another way of saying the universe expanded is to say more space was created. From where does this space come from?

If I am following correctly, Hawking is saying that gravity itself is the source of matter! What a reversal! I thought gravity was a property of matter, not its source. Can you conceive of gravity without matter? Interesting. Perhaps this “borrowing” explains why gravity is so weak?

 

~~~~~~~~~~~~~
The following is a collection of thoughts
on the Christian concept of contemplation by Thomas Merton.
~~~~~~~~~~~~~~~~

The solution to the problem of life is life itself. Life is not attained by reason and analysis but first of all by living.

Contemplation is life itself, fully awake, fully active, fully aware that it is alive. It is spiritual wonder. It is spontaneous awe at the sacredness of life, of being. It is gratitude for life, for awareness, and for being. It is a vivid realization of the fact that life and being in us proceed from an invisible, transcendent, and infinitely abundant Source. Contemplation is, above all, awareness of the reality of that Source. It knows the Source, obscurely, inexplicably, but with a certitude that goes beyond reason and beyond simple faith… It is a more profound depth of faith, a knowledge too deep to be grasped in images, in words, or even in clear concepts.

God is not simply the one Whom we reach when we are extended to our limits. He is, on the contrary, the ground and center of our existence, and though we may conceive ourselves as “going to” Him and reaching out to Him beyond the sphere of our everyday existence, we nevertheless start from Him and remain in Him as the very ground of our existence and reality.

The graduate level of learning is when one learns to sit still and be what one had become, which is what one does not know and does not need to know… One no longer seeks something else. One no longer seeks to be told by another who one is. One no longer demands assurance. But there is the whole infinite depth of what is remaining to be revealed. And it is not revealed to those who seek it from others.

Education in this sense means more than learning; and for such education, one is awarded no degree. One graduates by rising from the dead. Learning to be oneself means, therefore, learning to die in order to live. It means discovering in the ground of one’s being a “self” which is ultimate and indestructible, which not only survives the destruction of all other more superficial selves but finds its identity affirmed and clarified by their destruction.

The inmost self is naked.

The Christian is then not simply a man of good will, who commits himself to a certain set of beliefs, who has a definite dogmatic conception of the universe, of man, and of man’s reason for existing. He is not simply one who follows a moral code of brotherhood and benevolence with strong emphasis on certain rewards and punishments dealt out to the individual. Underlying Christianity is not simply a set of doctrines about God considered as dwelling remotely in heaven, and man struggling on earth, trying to appease a distant God by means of virtuous acts. On the contrary Christians themselves too often fail to realize that the infinite God is dwelling within them, so that He is in them and they are in Him. They remain unaware of the presence of the infinite source of being right in the midst of the world and of men. True Christian wisdom is therefore oriented to the experience of divine Light which is present in the world, the Light in Whom all things are, and which is nevertheless unknown to the world because no mind can see of grasp infinity.

This way of wisdom is no dream, no temptation and no evasion, for it is on the contrary a return to reality in its very root. It is not an escape from contradiction and confusion for it finds unity and clarity by plunging into the very midst of contradiction, by the acceptance of emptiness and suffering, by the renunciation of passions and obsessions with which the whole world is “on fire”. It does not withdraw from the fire. It is in the very heart of the fire, yet remains cool, because it has the gentleness and humility that come from self-abandonment, and hence does not seek to assert the illusion of the exterior self

Once a man has set foot on this way, there is no excuse for abandoning it, for to be actually on the way is to recognize without doubt or hesitation that only the way is fully real and that everything else is deception, except insofar as it may in some secret and hidden manner be connected with “the way.”

In the “prayer of the heart” we seek first of all the deepest ground of our identity in God. We do not reason about dogmas of faith, or “the mysteries.” We seek rather to gain a direct existential grasp, a personal experience of the deepest truths of life and faith, finding ourselves in God’s truth. Inner certainty depends of purification. The dark night rectifies our deepest intentions. In the silence of this “night of faith” [John of the Cross] we return to simplicity and sincerity of heart. We learn recollection which consists in listening for God’s will, in direct and simple attention to reality. Recollection is awareness of the unconditional. Prayer then means yearning for the simple presence of God, for a personal understanding of His word, for knowledge of His will and for the capacity to hear and obey Him.

Dread is an expression of our insecurity in this earthly life, a realization that we are never and can never be completely “sure” in the sense of possessing a definitive and established spiritual status. It means that we cannot any longer hope in ourselves, in our wisdom, our virtues, our fidelity. We see too clearly that all that is “ours” is nothing, and can completely fail us. In other words we no longer rely on what we “have,” what has been given by our past, what has been required. We are open to God and to His mercy in the inscrutable future and our trust in the emptiness where we will confront unforseen decisions. Only when we have descended in the dread to the center of our own nothingness, by His grace and His guidance, can we be led by Him, in His own time, to find Him in losing ourselves.

My Lord God, I have no idea where I am going. I do not see the road ahead of me. I cannot know for certain where it will end. Nor do I really know myself, and the fact I think I am following Your will does not mean that I am actually doing so. But I believe that the desire to please You does in fact please You. And I hope I have that desire in all that I am doing. I hope that I will never do anything apart from that desire. And I know that if I do this You will lead me by the right road, though I may know nothing about it. Therefore I will trust You always thought I may seem to be lost and in the shadow of death. I will not fear, for You are ever with me, and You will never leave me to face my perils alone.

The vocation to solitude is therefore at the same time a vocation to silence, poverty and emptiness. But the emptiness is for the sake of fullness: the purpose of the solitary life is, if you like, contemplation. But not contemplation in the pagan sense of an intellectual, esoteric enlightenment, achieved by ascetic technique. The contemplation of the Christian solitary is the awareness of the divine mercy transforming and elevating his own emptiness and turning it into the presence of perfect love, perfect fullness.

My life is a listening; His is a speaking. My salvation is to hear and respond. For this, my life must be silent. Hence, my silence is my salvation.

 

From the Good Math / Bad Math blog:

Throughout elementary and high school, I got awful marks in math. I always assumed I was just stupid in that way, which is perfectly possible. I also hated my teacher, so that didn’t help. A friend of mine got his PhD in math from Harvard before he was 25 (he is in his 40′s now) I was surprised the other week when I learned he isn’t particularly good at basic arithmetic etc. He said that’s not really what math is about. So my question is really for math fans/pros. What is math, really? I hear people throwing around phrases like “elegant” and “artistic” regarding math. I don’t understand how this can be. To me, math is add, subtract, etc. It is purely functional. Is there something you can compare it to so that I can understand?

So what is math? It’s really a great question, and not particularly an easy one to answer.

Interesting answers from the comments:

“that which can be known”

But math is not epistemology.

The word “mathematics” comes from the Greek μάθημα (máthēma), which means learning, study, science.

It seems to be that no one gets a phd in math because they love arithmetic. If this is true, or somewhat true, certain conclusions should follow…. Such as: Why should we hope to discover/support/develop future mathematicians in arithmetic classes? I would argue that we kill, not develop, our future mathematicians in these classes. The ones that survive surely do not outnumber the ones we destroy. And this is, I believe, the genesis of the reason for this article. People do not understand the beauty of math because we only expose it to those few who survive the boring, rote, uninspired ugliness of math for years and years, and who perhaps only discover the latent beauty of the subject by accident, long after so many other creative, energetic minds have gone elsewhere.

Math is just as much a part of the humanities as it is of the sciences. The history of the number sense, from the integers, to the irrationals and the imaginary and beyond is the history of human progress and should be taught as a part of Western Civilization 101. Likewise, Maxwell’s field equations are the crowning event of the 19th century and should be taught in every history book.

We make a fundamental error in thinking of math in terms of science merely.

more coming on this…

 

After reading the stories by the Great Author, a number of very learned, respected gentlemen declared that there was nothing in them. This was very concerning because on the one hand, these were, after all, learned gentlemen. Yet on the other hand, the stories were written by a Great Author.

Something, it would seem, had to give.

Nevertheless, it was hard to argue with the observation of the learned gentlemen. The stories themselves were in fact perhaps more impressive by what was not in them. It was almost as if something – the most important parts, perhaps – had been left out. As such, there was a pervasive sense that the stories were filled everywhere with blank spaces.

But this was precisely was what made the stories so great.

It was the comment of the Great Author, that he wanted “to write like Cezanne painted”, which helped me to see the stories in a new light, for I noticed one day that when you look at a certain Impressionist paintings, you will see colors that are not actually there. (It has been pointed out to me that the significance of Cezanne’s paintings is that he painted in broad strokes, not in details, but I mistakenly associated his style with another. I have left this error in the essay because it remains an apt image for reconciling the discrepancy alluded to above).

Cezanne (sic) had learned that by putting small dabs of complementary colors closely enough next to one another, the eye would mix these colors into a new color that is not actually there.

This reveals something very deep about the way we perceive reality. But in terms of the artist, the most immediate significance is simply this:

the true painting is finished, not on the canvas, but only in the viewers eye.

This may seem a mere cliche (if a tree falls in the woods…), and it is. But what a normal mind does with a cliche is perhaps quite different from what a genius might do. Thus the Great Author tried to do with his stories what Cezanne (sic) had done with his paintings.

In the end, I could not respond to the learned gentlemen who declared that there was nothing in these stories. After all, they were correct. I simply responded that I cared for these stories very deeply and we left it at that. But I was saddened that the learned gentlemen held such a view, for I could not but help to think that this criticism, rather than representing a failure of the author, represented a failure of the reader. And of that failure, there is no discussion possible. All one can say on the matter is whether one enjoyed the story or not.

Well, you may say that this is all a very highly subjective thing, and I would agree.

After all, this is the whole point of the matter.

related material:

How we see

 

Euler’s Identity Formula.

e

Gauss said that if the truth of this formula is not immediately apparent to you, you will never be a top notch mathematician.

Even for those of us who do not immediately see the truth of this formula, we can nevertheless recognize the breathtaking beauty of an equation that relates so many fundamentals: zero, one, addition, multiplication, exponents, pi, i, and e. Truly staggering!

~~~

Imaginary Numbers

imaginary

Proven to be very useful in engineering applications, yet whatever this number represents, it cannot be measured physically. Imaginary numbers are numbers that do not live on the number line! You will find them, however, on a number plane. Thus, these entities are simply numbers of higher dimension.

~~~

Alpha – the Fine Structure Constant

alphaeq

One of the fundamental physical constants in the universe: approximately 1/137. This is the number that determines  the strength of the electromagnetic force; it is related to the “gaps” between the electron’s orbital energies. If it were different, nothing in the universe would work the same: electrons would not orbit, there would be no differentiation between matter and radiation.

Therefore, this number controls the nature of the universe.

Alpha is strange in that it is a dimensionless constant, meaning it is just a number and not a measurement of length, energy, time, mass or any other dimension of physics, yet neither is it one of the mathematical constants.

Feynman said that all good physicists sit up at night worrying about alpha: “is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man.”

~~~

The Pythagorean Theorem

pythagorean1pythagorean2

New proofs are found for this equation every year.

“To this day, the theorem of Pythagoras remains the most important single theorem in the whole of mathematics.” – J. Bronowski The Ascent of Man

Misunderstood as a theorem about triangles, PT can actually apply to any shape, measure any distance. Any formula with a squared term is under its influence.

Here are some surprising uses of the Pythagorean Theorem

~~~

Newton’s Law of Universal Gravitation

newton_gravitation

This discovery was the culminating moment of the scientific revolution, Man’s closest glimpse into the Mind of God. It is said that the apple fell to Newton from the Tree of Knowledge in the Garden of Eden itself.

~~~

Maxwell’s Equations of electromagnetism

maxwell

10,000 years from now, these equations will be looked upon as the most significant event in the history of the 19th century. Did you learn about this in your history class?

~~~

Special Theory of Relativity

E = mc2

Matter and Energy are one and the same. Matter is Energy looped back upon itself, a snake biting its own tail.

~~~

General Theory of Relativity

einstein_general

This is the curvature of space-time. Unintuitive in the extreme, this equation represents a conquest of pure thought over pure experience. “The theory appeared to me then, and it still does, the greatest feat of human thinking” – Max Born

~~~

The Schwarzschild Radius

Schwarzschild

Given the mass of an object, This is the radius at which the object becomes dense enough to become a black hole

~~~

Schrodinger’s Equation

schrodinger

This is the basic equation of quantum theory. Mathematicians say it is as inexhaustible as mathematics itself.

~~~

The Black-Scholes Equation

black_scholes

This formula crashed Long Term Capital Management in the 1990′s. Despite this fact, Wall Street has been ever since in search of a formula that can eliminate risk. Each time they think they have found it, they haven’t.

~~~

excess_return_equation

This is the equation that tanked Enron in 2001.

~~~

The Gaussian Copula Formula

gaussian_copula

This Formula crashed Wall Street in 2008

 

Quantum Entanglement is THE mystery in physics. Entanglement is the thing that makes the quantum world, “different”. It is what is behind the two slit paradox. This is what Einstein called “spooky action at a distance.”

Of all the things in particle physics for which there are no explanations, entanglement is the biggest. If it weren’t demonstrably true, no one would be able to believe it. But physicists have already used entanglement to transport matter. Yes, like in Star Trek.

No, I am not kidding.

No one understands or can explain entanglement. It is very hard even to describe. Not being a mathematician, I still have trouble understanding the two-slit experiment in a satisfactory manner. It is hard for me to comprehend what they mean when they say “observe” a photon. If an atom were the size of a bus, then the kind of “observation” physicists do is crash a motorcycle into it, right? Surely we would not be surprised, after this event, to notice that we had “affected” the outcome. Duh. Yet this is what so many of these experiments seem to be saying. I am missing something there. I have not posted on the two slit experiment (yet). I am still looking for a better explanation.

I will say this: if the particle detector “collapses the wave function” then the particle detector, like the phosphorescent plate that records the pattern on the other side must be creating the particle, or causing the particle to condense, which may not be that mysterious. Instead of thinking of collapsing wave functions, think of water droplets condensing out of thin air. Maybe that will help. The particle-wave duality may be nothing more mysterious than the liquid-gas-solid trinity.The question then becomes: what is the mechanism that causes this condensation? I would think that the collapse is the result of some basic, atomic interaction such that the particle condenses out of its wave state quite readily when it meets matter and the whole mystery is based simply in this condensation process, which is not currently understood very well.

OK, so here is my attempt at explaining entanglement:

The story goes that a photon is fired into a crystal that splits the photon into two photons that are then entangled. The two photons shoot off in different directions. Photon A goes to detector A and photon B to detector B. The detectors can be any distance apart.

OK, here it goes: if you alter the orientation or spin or polarization, or whatever, of photon A, this will cause a change in photon B!

In other words, we have two separate objects that are connected in some mysterious way other than through space and time. In other words, they are connected, beyond space and time. Spooky action at a distance!

Now, I am sure there are all kinds of theories to explain this, but the most obvious one is that they are connected in some other dimension. I have not heard of such an explanation, but if you follow the logic, this seems a basic conclusion, unless for some other reason we cannot allow for “other” dimensions.

So that is what I am going with. It makes sense that the two photons, being derivatives of the original photon, are still one. It is only their “shadows” on the dimensions of space-time that are separate. Looked at in this way, it does not seem so strange, except it forces us to start adding dimensions to our perception of the universe. Yet this is hardly anything new.

This view is in line with the De Broglie/Bohm interpretation of quantum mechanics, which is opposed to the Copenhagen interpretation, put forth by Neils Bohr. As much as I like the mystical feel of the Copenhagen interpretation, I really think we will find that the De Broglie/Bohm interpretation – that there is yet something hidden from us that will explain all of this in a classical, cause and effect way. For example, a hidden dimension in which the photons are connected, non-locally.

This could also explain the two slit experiment. If there were “unseen” aspects to a photon such that we were in fact collapsing the wave function when we place detectors in one of the “paths” then this would explain why the interference patterns disappear, even when the detector is placed in one of the paths after the slits. We deduce that the photon goes through both slits, even though we can only ever “detect” that it goes in one or the other. This is the paradox of the two slit experiment. What we see happening does not match what we conclude must be happening, as the interference pattern clearly indicates. So you have a situation where what happened, happened undetected. So I posit that the photon does go through both slits, but that there is a “part” of the photon that we do not detect! And yet it seems this non-detection on our part has the effect of collapsing the wave function and removing the interference pattern.

I call this the Invisibility Principle, or maybe the Imaginary Principle. Apply the same technique that we use to understand complex numbers, and now imagine that the photon too has a “real” part and an “imaginary” part. Like with the complex number, which has literally jumped off the number line into another dimension of space, envision the photon likewise. If you imagine the electro-magnetic wave propagating at right angles to each other, you can imagine some other wave propagating at a right angle in a non-space dimension that we can’t detect. Of course, this may well be pure fantasy. It certainly is not founded in mathematical formulation. Wait, what? Strings? You say you do have the mathematical formulations for these extra dimensions? And a very strong theory that could unify the forces?

Hmmm.

 

I just read a very interesting article by Malcolm Gladwell. He is a very interesting author. He has written 3 books in the last few years, all best sellers. The Tipping Point, Blink, and Outliers and now has a book of his best articles from the New Yorker magazine called What The Dog Saw. His is my favorite kind of writing in that he seeks out the uncommon wisdom, the hidden connections in a story.

I read two of his articles on finance, and the one about Ceasar Milan, the Dog Whisperer in his latest collection. The first article on finance was about Enron. It turns out that Enron failed for the very same reason AIG did. They allowed MIT PhD physicists to make their financial decisions. These guys used very complex financial instruments that required mark to market accounting, which means that what they put in their books is what the estimated value of an investment will be in ten years, based on its current value. Their predections turned out to be wrong and the books in real life went bad.

The executives, when asked, admitted that they did not understand the deals, or the implications of the deals they were making. But they had confidence in the genius of the mathematical models and the wizards that explained them.

I was very intrigued to learn that Enron did not hide as much information as the media would lead you to believe. The transactions were so highly complex, however, that there were literally hundreds of thousands of financial and legal documents “disclosing” the details. They had these third party entities that would go between them and the bank for the purpose of making the loans seem less risky and for each of these transactions, the legal documents would be thousands of pages long. Enron had thousands of these third party entities set up, so the sheer amount of documents that were publicly disclosed were quite literally in the hundreds of thousands. But they were public, and it is on record at Harvard, where students reviewed Enron as a class exercise that they were able to use very standard accounting review methods and were able to determine that Enron was in trouble. This was way before the collapse. So we cannot say that the cause of the Enron debacle was a lack of information. The information was there. In fact, when the wall street journal did a similar review, they had to question the executives as part of the audit. The executives flew out to answer all questions. The WSJ concluded that enron was overvalued. This was before the collapse.

Now back to Gladwell.

Gladwell, goes on to discuss the difference between a puzzle and a mystery. Wow, that sounds familiar! But his defining difference is that a puzzle can be solved by finding the missing information. If this information is missing due to human malevolence or deception, we blame the person who was holding or hiding this information and the “crime” is solved. This works very well for solving puzzles. Mysteries, are quite different. In a mystery, it is not a lack of information that is the source of the problem, and it can even be too much information that is the problem. Gladwell says that failure to distinguish which TYPE of problem you have is disastrous, for these two different problems require very different solutions. If you misdiagnose, you can make the problem much worse.

Solving a puzzle requires more voices, more sources; solving a mystery often requires less voices, better ears. This is a common mistake in software development management. A development project is running late. The manager decides to double the number of engineers working on the project. This slows the project down. As the lines of communication grow exponentially with each new developer, progress slows.

The genius of open source development is in how it solves this problem. There are thousands of developers working on any given open source project, so how does the project not get mired down by the sheer weight of the overhead? The pieces of the project are designed to be orthogonal to each other, meaning perpendicular, at right angles. In software development, this means that if part C fails, it does not affect part A. A bad driver developed by a third party software vendor does not blue screen the operating system, for example.

OK, back to finance. the lesson is the lesson of the mystery. Of recognizing when the puzzle model solution is not appropriate. Think of our current crisis. They are trying to solve the problem as if it is a puzzle. It is not MORE regulation that is needed. It is the CORECT regulation.

Gladwell also notes that in the case of Enron and others, there is a very important element of overconfidence – this is what the third party entities are designed for: to give the banks more confidence of their loans.

But in that meeting where the executives flew in to talk to the wall street journal auditors, the MIT mathematicians were explaining why their models were so brilliant, and while they were admiring their own genius at being the masters of these complex entities, the auditors asked an interesting question. Who do you think is going to be elected President? The geniuses said it did not matter, then started to go back to their formulas, but the auditors interrupted. (Remember, Enron, is about energy, oil). The auditors asked, “One candidate is an environmentalist and the other an oil man. Do you not think that it will make a difference which gets elected?” The executives, deferring to their masters, looked to the mathematicians. The mathematicians blinked a couple of times. Then swallowed.

These complex mathematical models can be destroyed by the simplest assumption gone wrong. In Enron’s case it was simply a mis-prediction in the price of oil ten years out.

And yet there is nothing magical about seeing this. The IRS does not use mark to market accounting. They tax you when the purchase is made, when the money actually comes in. Thus, Enron paid no taxes for years and years, because the fact was always the same: They were not making money. There was nothing to tax. The hundreds of millions of dollars on their accounting books were from the start, imaginary. The IRS knew this. The investors should have known. It was not a lack of information that sank the ship. It was too much confidence. We let ourselves be dazzled by mathematicians and wizards.

It was the same mistake we made with Long Term Capital management 10 years earlier and the same mistake AIG made ten years later.

It is common sense that has gone perverse. Proof of this can be seen in the way the media, the financial gurus, Obama, and most others have treated the simple, common sense solutions of Paul Volker. His voice is almost alone the voice of common sense and reason in this current crisis. His advice is simply to separate hadge fund activity from banking. Let the hedge funds gamble in a sandbox. If they fail, they fail. Relocate them to Vegas, and let us get on with the business of banking. We can watch the neon flicker on and off from afar. Volker’s point is simple. Banking has become what it is not. Banking is not supposed to be short selling and derivative swaps. This is what hedging is. Gambling, in short, on the future value of paper. Until we learn the difference, as long as the hedge fund gurus are the presidents of our banks, this problem will not end.

Gladwell’s genius is in being able to see through the chaf, to the heart of the problem. Is it a puzzle, or a mystery? Too much information or too little? Are we a bank, or are we a hedge fund? You have to understand, philosophically, what a thing is, first and foremost. These are philosophical questions: it is the question socrates asked, “what IS it?” What IS a puzzle? What IS a mystery? What IS a bank? Get these answers wrong and nothing else that follows will be correct.

 

There is more.

Words are but a map, and by necessity, limited.

We have no words for what an atom is, no explanations for inertia, no mechanism for light, no description of energy.

Words are not adequate. They are not up to the task. They create paradox, the glaring evidence of their incompleteness.

If you but look closely you will find the broken edge of words and know that there is something beyond the crumbs of the last word; that even this final word is not the end.

Not by far.

This is the edge, the cracked precipice where the word falls silent. This is the brink. This is where we find ourselves when we stand in awe of the unknowable. If you want to experience God, you have to leave words behind.

This leaving behind is the task we face when we reach the brink. Close your eyes, silence your mind and you can experience that which words cannot say.

Nov 062009
 

From Walden:

Men sometimes speak as if the study of the classics would at length make way for more modern and practical studies; but the adventurous student will always study classics, in whatever language they may be written and however ancient they may be. For what are the classics but the noblest recorded thoughts of man?

We might as well omit to study Nature because she is old.

Books are the treasured wealth of the world and the fit inheritance of generations and nations.

The works of the great poets have never yet been read by mankind, for only great poets can read them. They have only been read as the multitude read the stars, at most astrologically, not astronomically. Most men have learned to read to serve a paltry convenience, as they have learned to cipher in order to keep accounts and not be cheated in trade; but of reading as a noble intellectual exercise they know little or nothing; yet this only is reading, in a high sense, not that which lulls us as a luxury and suffers the nobler faculties to sleep the while, but what we have to stand on tip-toe to read and devote our most alert and wakeful hours to.

Even the college-bred and so-called liberally educated men here and elsewhere have really little or no acquaintance with the English classics; and as for the recorded wisdom of mankind, the ancient classics and Bibles, which are accessible to all who will know of them, there are the feeblest efforts anywhere made to become acquainted with them.

A man, any man, will go considerably out of his way to pick up a silver dollar; but here are golden words, which the wisest men of antiquity have uttered, and whose worth the wise of every succeeding age have assured us of; — and yet we learn to read only as far as Easy Reading, the primers and class-books, and when we leave school, the “Little Reading,” and story-books, which are for boys and beginners; and our reading, our conversation and thinking, are all on a very low level, worthy only of pygmies and manikins.

I aspire to be acquainted with wiser men than this our Concord soil has produced, whose names are hardly known here. Or shall I hear the name of Plato and never read his book?

 

I sought the fount of fire in hollow reed
Hid privily, a measureless resource
For man, and mighty teacher of all arts

… and I purged
The glancing eye of fire, dim before,
And made its meaning plain. These are my works.

What thou wouldst learn I will make clear to thee,
Not weaving subtleties, but simple sooth
Unfolding as the mouth should speak to friends.
I am Prometheus, giver of fire to mortals.

Aeschylus, Prometheus Unbound

The Fireplace

When a piece of wood burns in a fire, it is not the wood that is “burning”. Not in the sense we might imagine. The hard material we think of when we think of wood is not what is giving off light. Rather, when the molecules of this hard wood stuff starts moving fast enough, they start to break apart.

This is what we see as smoke.

Smoke is the result of carbon materials being vaporized by friction. When wood, for example, has been vaporized in this way, it turns into black char. This is the hard stuff that remains after the wood has been converted to smoke. Actually, the wood has been converted to char + smoke.

So the equation for this is:

wood + friction = char + smoke.

[note: if you are wondering, friction is a result of, and consequence of, heat. Heat is nothing more than speed. Temperature is the (average) speed at which the molecules of a material are moving. This motion creates friction, which results in the release of photons from the disturbed atoms. We can feel the energy of these photons as heat, and see the radiation as infrared light. I have posted a meditation on light and heat here.]

wood + friction = char + smoke.

This can happen with no fire. But where there is smoke, often there is fire, right? Right, but it is not the fire that causes the smoke, but the smoke that causes the fire! The word, “cause” is being used loosely here. More accurately, we should say that it is not the fire that precedes the smoke, but the smoke that precedes the fire.

Ignition occurs when the gases in the smoke undergo a second chemical reaction. The carbon in the gaseous smoke combine (violently) with oxygen in the air. This chemical change creates more heat (because it is a strong, “violent” change) as the carbon-oxygen pair combine forcefully enough that the process “shines”. IN other words, the carbon and oxygen grab onto each other so hard that the motion of their grabbing each other releases visible photons. The marriage of carbon and oxygen is visible to us a shining that we call fire. This shining heat now creates a chain reaction, supplying the energy to keep the first reaction going (wood + heat = smoke + char) which creates more smoke, which is already hot enough that the carbon atoms bond with the oxygen in the air, and again, it is this process of the carbon bonding with oxygen that shines.

The carbon-oxygen reaction shines because it is such a forceful reaction that the heat that it produces is energetic enough to be part of the visible spectrum. Remember, heat radiation, like x ray radiation, and radio wave radiation, is all the same thing, just at different energies. What we see as visible light is just a certain slice, or range, of energies in this continuum of radiation from radio waves to gamma rays.

If our eyes had evolved such that we could see more of this range – say into the infrared energies – we would see each other “burning”, for our bodies continually radiate heat in the infrared range, just as “fire” radiates heat in the “visible” range. When soldiers wear infrared goggles at night, this is what they see: the light that is “burning” off of warm bodies.

In this sense, we are all on fire, as is everything in the universe.

Here is Richard Feyman describing fire. He points out that the substance of a tree is derive mostly from the air, not the ground and that when we burn wood, we are releasing the light of the sun that was put into the tree to begin with

The Sun

What we have described so far is a chemical reaction. Specifically, we have seen how visible light is produced in the form of heat radiation when a piece of wood decomposes to gas and the carbon in these gases combine with oxygen. This process produces visible light, and heat. The heat, if it is not extinguished, will keep these chemical reactions going for as long as there is carbon (in the wood) and oxygen (in the air).

Thus we say the reaction is self-sustaining.

Similarly, what happens in the sun is a self sustaining chain reaction. But it is not a chemical reaction. If we were to think of the sun in the way we think of wood burning, the first question we would run into is, “where is the carbon? Where is the oxygen? How does something burn in the vacuum of empty space, which has no air, and thus no oxygen, to burn?”

Well, it is well known that what happens on the Sun is a thermo-nuclear reaction involving the creation of helium from hydrogen. This is what we call nuclear fusion. And the by-products of this fusion is heat and light.

Fusion happens in the small, dense core of the sun. Thus in this chain reaction, the key component is not heat, but pressure. Pressure creates heat (via friction), but it is the pressure that drives the heat, and thus it is the pressure that keeps the chain reaction going. Well, one of the chain reactions, at least. When the hydrogen fuses, another chain reaction is created that, interestingly, counteracts the pressure reaction.

Therefore, you have two reactions going on: one creates an explosive, outward force while the other creates in implosive, inward force. This is why the sun does not simply fly apart from the billions of nuclear explosions that occur in its core every second.

Yes, I said billions of nuclear explosions that occur in its core every second.

So let’s look at this first chain reaction. Where does all this pressure come from? Oddly, it comes from the density of the core itself. The core of the sun was created when a huge cloud of hydrogen gas began to “collect”. This is odd, because gas does not like to collect. Gas likes to spread out. This is a paradox that has not been fully explained. If gas likes to spread out, what caused it to collect in the first place?

The Gravity Reaction

We know that gas spreads out through space, but what if space was curved? What if space even curved back in on itself? Well, we know that gravity does in fact bend space and we know that matter – even gas – has mass…

Do you see where this is going? Astronomers have concluded that there was so much gas that it bent space, creating a kind of crater, or hole, so deep that the gas could not help but to fall toward the center. Instead of spreading out, as gas is want to do, it started falling into the hole that it had itself created. This “hole” is known by the name of gravity. Despite what you have been told, gravity is not a force. It is not something apart from space, but an attribute of it. Gravity, as Einstein has so masterfully shown to us, is nothing more than those regions of space that are “bent”, “wrinkled”, or “curved.” In other words, gravity is just space itself. If space were a straight line, gravity is simply a bend in the very same line. When space bends, matter, which is always moving, changes direction. This change in direction is called acceleration and the observation and prediction that all matter accelerates in response to these bends, we call “the law of inertia.” Do not ask what causes the bending or why inertia makes matter accelerate, for no one knows. All we can do is observe what happens. No one knows how or why.

So this is what we have to imagine when we think of the hydrogen gas that formed the sun: that there was so much of it in a particular region of space, that it warped space so much that instead of escaping, the gas collected and compacted in on itself. It quite literally created a hole in space that it then proceeded to fall into.

This is amazing if you think about what you know about gas. Can you imagine releasing some helium in a room and seeing it rise up and collect itself into a disk or a sphere? Well this is what happened. In fact it is still happening. In our galaxy, a new sun is born every second.

Yes, I said in our galaxy a new sun is born every second.

The Light Reaction

So, this gravity reaction goes on and on – the more gas that falls into the hole, the deeper, and yet more compact the hole gets, causing more gas to fall in even as the “space” to “fall into” compresses. This process is self-perpetuating; as long as there is gas in the region the hole grows deeper and deeper, and, at the same time, more and more compact.

As this happens, the gas (hydrogen) gets more and more compact, more dense (and therefore hot, due to friction) until one day there is no more room to squeeze together. The gas molecules can’t even wiggle anymore. But the chain reaction continues; more and more gas squeezes into the hole. Eventually, the hydrogen atoms are being pushed into one another with so much pressure that the electrostatic force that keeps the nucleus of the atom intact, finally breaks.

Take a moment to think about this. This is the same electrostatic force we are familiar with. It is what makes our hair stand on end. We see its effects when we run a comb through our hair and see that the comb can disturb paper shreds like a magnet.

You may not realize it, but this force is unimaginably powerful, for when that comb moves those shreds of paper, we realize at the same time that the entire mass of the earth is trying to pull those shreds to itself. In other words, a few free electrons in that comb have the sheer power to overcome the gravitational pull of the entire earth.

The electrostatic force, in other words, is so much stronger than gravity that it takes hugely massive objects to equalize the force of but one single electron.

It is hard to stress the strength of the electrostatic force. If the proton was the size of a grain of sand, the radius of the electron’s orbit would be two miles.

Yes, I said if the proton was the size of a grain of sand, the radius of the electron’s orbit would be two miles!

Can you imagine anything the size of a grain of sand having that kind of power? And to hold something moving so fast as an electron? Think about that. The electron only wants one thing: to go go go at the speed limit of the universe in a straight line. But the proton has some serious mojo over that electron. The electrostatic force is unimaginably powerful stuff. It is so powerful, that despite the fact that enough gas has collected that it has actually bent the universe, the hydrogen proton remains intact. A giant gas cloud 100 million light years wide is crushing space in on itself and but for the sheer power of the electrostatic force, nothing has pushed its way past that single electron whizzing “two miles” around that grain of sand, our beloved hydrogen proton. Outer space itself is collapsing but the inner space between the electron and the proton holds. The electrostatic force pushes back as the universe itself collapses down upon it.

But even the electrostatic force has its limits. It is here, in the core of what is about to become a star where the electrostatic forces of the atom are defeated. The electron barrier surrounding the proton finally fails under the pressure of the curvature of space. Gravity has finally overcome the electron. When this happens, Light escapes from the proton itself in a great explosion that sets of a chain reaction of explosions that continues for tens of millions of years. All that pressure has unleashed something new in the universe.

Things fall apart; the center cannot hold;
Mere anarchy is loosed upon the world,
– Yeats, The Second Coming

Where there was darkness, now there is Light; where there was one kind of matter, now another.

Just as wood was chemically converted into char + smoke, our hydrogen atoms have now been converted into helium + Light. The universe is no longer dark.

This is called nuclear fusion.

In this instant atomic fusion, an elemental balance of nature is broken. In the next moment, a new balance of nature is struck. Protons and electrons form a new equilibrium as matter forms new matter and gives birth to Light.

Where we had one grain of sand, now we have two. And Light. Inside the atom, a new perimeter has been formed and new matter is born in the universe. Outside the atom, Light  – previously bound and hidden in the proton, now reveals itself.

Now, imagine that you are one of the atoms sitting next to the atom that was just broken. Suddenly, in addition to all the pressures being applied to your atomic walls by all the other atoms pushing up against you, now your next door neighbor has just exploded with a force so energetic even the electrostatic force of your impenetrable walls are helpless to withstand! And so there is another explosion, which causes another, and another…

This is the ultimate effect of the gravity chain reaction: the birth of a new chain reaction – The Light Reaction. In response to all the inward forces of the accumulating gas, now this violent, outward thrust from our grain of sand; this pulse of Light from the atom. The atoms in the core are now truly at war. Space is pushing in on them and finally, they are pushing back. E=MC2. Anarchy is loosed upon the world.

This new chain reaction of nuclear explosions lights up the heavens. This is the birth of a star, a series of explosions creating new matter + light in a process that is simply unstoppable. This continues until all the hydrogen is fused. Ultimately, this means billions of explosions per second for tens of billions of years – that’s how much gas we are talking about. Hey, it was enough to bend space, it takes a little while just to process its own explosion.

This is what is happening in the Sun – endless nuclear explosions. Again, this great outward thrust of the atom, generated from a great inward push of space. This is why the Sun does not simply fly apart. The pushing out and the pushing in are equalized.

Life

After careful examination, we see that the sun and all the stars are really atomic phenomena; we see that light is bound up in matter, and released by matter. In fact, what we find throughout all phenomena of the universe is simply this: that light is constantly being released and reabsorbed, whether in the proton, or the electron; whether in atomic or molecular reactions. In all cases, matter is being transformed into energy and that energy, Light, in turn, transforms the matter around it. This process of material transformation into Light, this “interaction of light with matter,” is all there is. All material phenomena in the universe from the big bang to the creation of this sentence is nothing more than this process of light escaping from and being absorbed again by matter. This is what is beneath all of physics and chemistry. We know of nothing in the universe that is not derived from this process of Light being transformed into matter and back to Light again. Think about that. You may think this is an overstatement, an exaggeration.

It.. is.. not. This is what we call physics. Welcome to the mystery.

So, in the atom, we find an equilibrium similar to what we have described as the two chain reactions in the sun: this tremendous force that is pushing outward, perfectly equalized by a tremendous force pulling inward. Matter and Energy are similarly related in an eternal dance, this equilibrium: matter as energy confined, energy chasing its tail, as it were.

When this tail-chasing of the energy within the atom is released – when what has been until now confined, is no longer..

From matter: light.

From light: life.

Yes, I said life.

The source of energy that makes all life possible is the photon that the sun releases, which falls to earth. Plants transform these photons into matter in a process called photosynthesis, then animals transform this matter back into photons through digestion, where the cells break the matter of the plants into pieces, which releases more photons, which the cells use to move and act and create more matter. In other words, the light from the sun literally becomes trapped in matter again through the photosynthesis of plants. This light is released again in the cell walls and used to move the cell parts around to create new matter and this is what life is: a highly sophisticated, complex, creative use of light.

Destruction, annihilation, death; then creation, release, birth.

The QED shows us that all material phenomena of the universe from the big bang to the creation of this sentence can be summed up by the physics of light interacting with matter. Which is to say light being emitted and absorbed by matter – again and again and again in infintely varied combinations.

Folks, that’s all there is. If we but understood how light, matter and space worked, we would have a theory of everything. For it is matter that bends space, which in turn, accelerates matter, which in turn creates light… and from light: life.

Mysteries

Gravity is the only force in the universe for which we have NO model to explain. We may not fully understand the true essence of the other forces (we have no theory to explain the mechanism of how light moves through the universe), but we know enough about them to play with them. Not so with gravity. It simply is. None of its secrets have been cracked. All we can do is observe how it behaves. We fare only slightly better with light, although it’s essential secret is so secret that physicists have declared that the workings of it fall outside the realm of physics. Literally. Physics has given up trying to explain light. For the physicist, explaining light is a religious, not scientific, feat.

Fire in the Sun?

To review: The difference between the fire in your fireplace and the “fire” of the sun is that one is a chemical reaction, and the other, an atomic reaction. The first is a rearrangement of molecules, the other a rearrangement of atoms. One reaction happens outside the nucleus as electrons rearrange (we call this chemistry), the other happens inside the nucleus as protons rearrange; we call this nuclear fusion.

related posts: heat and light

Richard Feynman explaining fire

 

This is the latest post I am working on for my blog. I am taking notes, writing down my thoughts as I read a book on the great virtues. This is a subject that I have not investigated much, but one which I am now very interested in. Again, I begin with the Greeks and already, I have re-discovered some profound insights, confirmed by the teachings of Jesus.

It tickles me to no end to make these “connections” between Reason and Faith, East and West, the Greeks and Jesus. The Greeks invented Reason as we know it – literally. The ancient voice of the Greeks IS the voice of Reason eternal. It is exciting to find in this voice the same truths we find in the East; the same voice we find from age to age, sage to sage and confirmed in Jesus’ s own teachings; I find it exhilarating when Reason and Faith come together. There is so much common perception otherwise in the world right now and I think this position is wrong. There is only one truth, Reason and Faith are both valid, so they cannot disagree on that truth in the end.

I will save that argument for another time, however. This is my first exploration of virtue. My studies of philosophy have always revolved around metaphysics and epistemology, so I am eager to finally get down and dirty with the more important questions of how to live the “good life”…

I have not yet been able to fully articulate my understanding, so some of the following needs further development to be philosophically tight, but here is an outline of the results that Plato reached on virtue:

Love is the alpha and omega of the virtues

1) If we but loved fully, we would we would be fully virtuous.

2) But we do not love fully

3) Because we are not born virtuous

4) But we can BECOME virtuous by ACTING virtuous

5) As we become virtuous, we necessarily love more fully because all virtue is derived from love.

6) The fullness of this love brings us to God

7) Therefore, there is a direct Path, a Way of living that will bring us to God.

… and it starts with acting polite.

Politeness, Morality, Love

Politeness is the seed of all virtue. Politeness is not itself a virtue, however, for the source of a thing cannot be the thing itself. We teach our children to “act” polite because they are too young to “be” virtuous. Thus it is with all virtue. We “act” as if we were virtuous and somehow this can transform us.

This was a big paradox for the Greeks: If we are not virtuous, how do we become virtuous? How do we practice “being” virtuous if we are not? The answer: by “acting” virtuous! A strange concept. What is this relationship of “acting” to “being” and can we really transform ourselves in this way?

Not only is the answer in the affirmative – yes, we can transform ourselves in this way – but moreover, this is the ONLY way we can transform ourselves. How else would we? What seems paradoxical, in the end, is the only thing that makes sense.

This line of reasoning (I have not presented it fully here) about the nature of the virtues ultimately leads Plato to a conclusion about love. He shows that all of the virtues are but remnant echos of love. This is quickly seen in the case of moral law.

Moral law demands of us to “act as though we loved”.

Morality is to love what politeness is to virtue. Morality, like all virtue, is a derivative of love. As such, we see that moral law is similarly related to love as are the rules of “acting” polite (that we enforce on children) related to “being” virtuous.

In other words, we “act” polite because we are NOT yet (fully) virtuous. Again, this “acting” that precedes “becoming”.

In exactly this way, we follow moral law because we do NOT (fully) love. For surely, if we DID love, we would need no law to command our very desire.

I think somewhere Jesus said, “Love, and do as you wish“. Jesus’ love frees us from the law, because this law is merely what we have (what we rely on) when we DON’T have love in its fullest. The demands of moral law command us when (and only when) our hearts have failed.

Thus, Love would extinguish the need for moral law. But in the absence of Love, the Law is a trustworthy guide, for Love is it’s source. And since no one other than Jesus loved fully in this sense, moral law is not extinguished.

Moral law obliges us to do what we would do simply out of love, if in fact we loved.

Thus we see how moral law (and all the virtues, ultimately) are derivatives of Love, and necessary only for our lack of Love.

Moral law demands of us to “act as though we loved.” Again, the acting. Once we are no longer acting, but being, then moral law can command nothing of us for nothing can command you to do what you already desire. This is also why the law could command nothing of Jesus, and it is why there is no way for Jesus to be in violation of the law, for love can never be immoral.

Moral law demands of us to “act as though we loved.” This is a revelation, for we see that if we DID indeed love, we would have no use of such a commandment. For then duty and desire would be one and the same (and not opposed).

This is so important! The Buddhists focused on this very opposition. They recognized it as the source of all suffering, and they were right. Again, Greek Reason, Christian Faith, and Eastern Mysticism agree.

I find this to be truly profound! First and foremost, that duty and desire are opposed because we lack the ability to live in a constant state of love is a powerful revelation. One of the tenets of all wise sages from the East and through the ages is to break the ego’s relentless desire for what is not and learn to simply love what is. This is nothing new to Jesus, of course, and more on that in a minute.

The other powerful revelation that this line of reasoning holds is that it is the total destruction of all relativist positions. Moral law is NOT just the rules that the weak have imposed on the strong to prevent the strong from using their strength to the disadvantage of the weak, as the opponents of moral law claim.

So let it be said here and now: Those who would oppose Moral Law, in fact, oppose Love.

I therefore challenge all my humanist brothers and sisters to wake up to their folly. Those of you that would stand against Moral Authority, you need to recognize that it is Love that you stand against.

Plato goes on to say that practicing virtue in this way, with discipline, we approach Love, and in it’s highest form this Love brings us to our own transcendence; to faith; to God…

Transcendence: From Acting to Becoming

When trying to define virtue, I like to think of Jesus. Similarly, when I think of what is meant by transcendence, I like to think of Jesus. If we knew someone who was transcendent (Jesus is a pretty good example), we would notice of them all the characteristics of virtue: politeness, fidelity, prudence, temperance, courage, justice, generosity, compassion, mercy, gratitude, humility, simplicity, tolerance, purity, gentleness, good faith, humor, and above all, love.

In our “acting” virtuous (lovingly) we move towards “being” virtuous (loving). If we were able to “become” we would have transcended. This is not possible, and yet it is what we are called to do. This seems a paradox, yet what is the alternative? There is nothing else that makes any sense.

We love, not to be loved; we love to love.

Love is the ultimate end, Aristotle’s unmoved mover, the source of all motion, energy and being. Thus we can say that we breathe to breathe, we dance to dance, we sing to sing. These need no explanation, no ulterior motive, for they are ultimate in themselves, done for themselves and nothing else. As such, these actions are transcendent for they exist in the purity of The Moment. This is Zen, what the some cultures call Flow. It is what musicians lose themselves in, what athletes experience as the Zone.

This is Transcendence itself, transcendence OF the Self. The loss of self, ego, desire, want, lack, suffering. All dissolved into The Moment. This is the promise and hope and experience of Love – not eros, but Joy, what the Greeks called philia, or deriving pleasure, or joy, from something.

Surely we have lost something in the language that we have but one word for Love any longer but surely we understand, deep in our soul, that a life lived in Love is a transcendent (selfless) one.

The Bravery Paradox

There is a saying that courage (a virtue) only comes after we do the thing we are scared to do. In other words, we have to “act” brave now, while we are still scared. The virtue of courage comes later – and ONLY later. Never does it work out that we get the courage before the fear. It is always the other way around. We have to pretend to be brave and the reward is that we get courage later. It is this way with all the virtues. We “act” first, then we “become”. Without the “acting” there is no “becoming” and our souls make no progress.

Notice that this “progress”, this acquiring of courage, requires there be that which we fear. Logic dictates a conclusion here: What would it mean if we were able to avoid that which we fear, for our entire lives? The consequences, as you can infer, would be disastrous for our souls.

This realization has the power to change everything we see in the world.

Now do we understand Socrates when he claims in the Gorgias that he would rather suffer injustice than do it? Yes, for doing an injustice harms the soul, whereas suffering injustice does not. Yes, we agree with Socrates, for suffering an injustice is an opportunity to practice a virtue, which itself frees the soul from suffering, whereas the reverse imprisons the soul in hatred.

Paradox, or Law of Nature? Courage comes after the fear, not before. We must be mindful of this in our daily lives, for

what would it mean if we were able to avoid that which we fear, for our entire lives? The consequences, as you can infer, would be disastrous for our souls.

Disastrous, for where else shall we have our practice? If we are not virtuous but for the practicing, where else shall we strengthen our souls? How sad would it be if no fear did we ever face such that no courage did we ever receive?

This idea, that by “acting”, we can willfully transform ourselves, is a powerful one. In the east, they call it Karma: act good now so that you become good later. In the Bible it is “reap what you sow.” In each case, we believe the self-evident truth of this for one reason alone: because we have glimpsed love, and we saw that it was good, and thus its derivatives must be good. This is Moral Law.

It is because we have loved, or experienced love at one time, that we are able to recognize the value, the truth, of this love and its derivative (morality), and thus we “act” as though we loved (morality) because to love, to be “in” love is universally recognized as “the good”. It is the prudent thing, always. To love. And it is because this value (of love, aka the good) is universal, that we prove that moral law is therefore not merely a cultural construct as the relativists would argue.

OK, so how do we do this acting?

We can see an example of what the practice of acting virtuously looks like in the writings of Marcus Aurelius, the only Roman Emporer who was also a philosopher. In his Meditations, he writes to himself:

“Put yourself in mind, every morning, that before that night you will meet with some meddlesome, ungrateful and abusive fellow, with some envious or unsociable churl. Remember that their perversity proceeds from ignorance of good and evil; and that since it has fallen to my share to understand the natural beauty of a good action and the deformity of an ill one; since I am satisfied that the disobliging person is of kin to me, our minds being both extracted from the Deity; since no man can do me a real injury because no man can force me to misbehave myself; I cannot therefore hate or be angry with one of my own nature and family. For we are all made for mutual assistance, no less than the parts of the body are for the service of the whole; whence it follows that clashing and opposition are utterly unnatural.


These words have had great impact on my life. Surely Jesus never had need for such self-reproaches for he was the one who loved fully. But for us, this is often the only way. It is very practical, as a method, at least. But more importantly, we can see from our vantage point the fact that Marcus was walking with Jesus (or vice versa), for it is Love, after all, that he was “practicing”. If we remind ourselves of this love, if we keep our eye on it, never lose site of it, we can live in it more and more.

This is the Way – of Reason and Faith both. This is Jesus. This is love your neighbor. This is to love as Jesus loved. This is the way to “becoming,” the way to “being,” the way of transcendence, the way to God. Every such act like the one above is an act of devotion to God. And this is what the Greek Philosophers, the inventors of Reason and Logic, taught. This is the Way of the East. This is what it means to “believe” in the Greek sense of the word, which actually means “commit” and “follow”. This is what Jesus asks of us, literally. In believing, committing to his Way, the Way of Love, we transcend to God.

As with Marcus, do we not also see how all of our suffering of all the petty, – and not so petty – evils of the world are but our soul’s very opportunity for salvation and joy? Or have we not experienced the joy of completing the very task we dread? Is it not the non-doing that is the torture? Does it not damage our souls when we find excuse to argue and fight rather than find excuse not to? I know for darn sure the effects these things have on me. When I allow Ego to tear down the house to prove ItSelf justified, to defend the honor and reputation of ItSelf, or when I put off what I am duty bound to do, all of these actions suffer my soul much injury, whereas the opposite – sacrificing the self, obeying duties, etc have never ruffled a single feather in the wings of my soul. In fact, quite the contrary: I find that what the ego convinces me of is never the course of action that is in My best interest.

And doing what is in My best interest is what virtue is all about, for what is in My best interest, simply, is to Love – and there is but one and only one obstacle to Love, and that is Ego, for the Ego loves only ItSelf. Until this Selfish Love, which is the source of all evil, can be destroyed I cannot be saved. Thus I save myself by sacrificing myself. By giving (anything) away, I receive tenfold the joy in return. And by giving up the desire to be Right, I receive Peace and open myself to Wisdom.

These are the eternal words of Faith, and of Reason – further proof that Reason is not opposes to Faith. Marcus’ writings reflect the perfect harmony of a deep faith supported by strong powers of pure reason. There is one truth, after all. All paths lead home, even the wrong paths: the mistakes, errors… these in their folly reveal the truth of their negative. Thus the Truth is Everpresent.

From evil to our salvation

The brilliant irony of the human condition is that 1) we are NOT virtuous, and 2) we are fated to suffer “meddlesome fellows.”

It is an irony because it is only through 2) that we have the opportunity to reverse 1).

In all suffering is the opportunity to transcend to God. This is the “bravery paradox”. The courage only comes after we tremblingly walk through our fear. It is through the suffering of “meddlesome fellows,” in other words, that we transcend. This is the virtuous life.

politeness, fidelity, prudence, temperance, courage, justice, generosity, compassion, mercy, gratitude, humility, simplicity, tolerance, purity, gentleness, good faith, humor, and above all, love.

Our suffering of “meddlesome fellows” is but the precondition to our salvation.

This is another revelation in that what we prefer to see as the evils of life, are really the seeds of our salvation. Our vision spins us around a full 180 degrees and we see the world for the first time.

When this moment happens to us, this is called enlightenment.

Thank you, God, for these meddlesome fellows, for through them I have the opportunity to walk more closely with Jesus and experience the transcendent joy of Your love.

We realize that we were looking at things upside down and backwards; because we were looking from the inside out. But we cannot see the label from inside the bottle, so we missed it. The ego got the whole story wrong. It is only when we deny the ego’s vision of the world with us at the center of all desire do we find salvation, transcendence.

Now that we can see for the first time, we for the first time embrace all that life puts before us; for we see for the first time that all is blessing.

The Buddhists and Eastern Mystics, like Jesus, spoke in paradox, I believe, because many times these paradoxes echo this larger paradox… we see things reversed.

Paradoxes are a clue to our inside-out, twisted vision. Until we can see the perfectly straight lines of paradoxical truth, our vision remains warped. Paradox has the power to straighten our thinking. It seems a paradox that you have to act brave before you get to be courageous, but then again, nothing could ever make more sense!

Courage cannot grow within us if everything we do is easy.

Hunger and Desire

Plato thought of desire like a hunger, which is a suffering, based on a lack.

Only by eating can we destroy hunger. If only we weren’t such picky eaters, we would be so much the less consumed with hunger, for an abundance of (spiritual) food surrounds us at all times. Each and every day we get the opportunity to turn the other cheek. These moments are our chances to end our own suffering. This is a paradox, but it is the only thing that makes any sense! All you have to do is try it but once to be convinced. Giving is receiving. This is Karma, and it is not a fairy tale. It is the eternal truth of the soul.

When we practice a virtue, it is like eating in that it destroys suffering. Jesus said to give everything away. Giving brings joy. Joy destroys suffering. Thus, giving is like the meal that destroys hunger. And it is like this with all the virtues. This is why the “acting” is transformative. The practice of acting virtuous is like eating in that it destroys our suffering. And yet, without those “meddlesome fellows” we would not be able to strengthen our virtue, and what is virtue worth, love worth, if it vanishes at the first sign of evil? We need a stronger virtue than that, and alas, the world gives us ample opportunities to practice and strengthen our love. What we have to realize is that this opportunity to practice is always with us; thus in each moment is food abundant enough that we might never be hungry.

Again, I think of Marcus Aurelius’ notes to himself: “since it has fallen to my share to understand the natural beauty of a good action and the deformity of an ill one… I cannot therefore hate or be angry with one of my own nature and family.

Jesus taught us what it means to love thy neighbor as thyself. This is not just the polite thing to do. It is our very salvation.

Reason, meet Faith… East, meet West… Love, meet Truth… Man, meet Jesus.

 

Sometimes when I am having trouble visualizing something, I find that it is the words themselves that fail me. Perhaps a word is too embedded in a concept that just doesn’t fit. This is especially true of words we use very frequently, but whose concepts are anything but well-understood. “Light”, “energy”, “force”, and “gravity” are good examples of this.

The greeks have different words for knowledge. There is propositional knowledge, or knowledge-that, and there is knowledge-how. Knowing-that is called  episteme and is what epistemology focues on. Knowing-how requires more theoretical knowledge than knowing-that.

For example, we “know that” light travels at a certain speed, has certain energies, etc. But to this very day, we have no explanation for how it does what it does. In other words, we have a lot of “know-that”, or epistemological, information about light. But we have very little “know-how” information about light.

We do not “know how” light works. We simply “know that” it does. We know that it does X, Y, and Z when A, B, and C are present. We have literally taken lightening out of the sky and made it to sing, yet we have no real theoretical knowledge of it all.

I find this amazing. After Feynman’s QED, and articles like this one, describing all the ways in which we have mastered the behavior of light – slowing it down, stopping it, turning it into matter and back – we still cannot explain how it does what it does.

I have written much more on this in my post on the sound of the color of the temperature of the universe,  and also this post, called the brink, but these are a work in progress and need refinement.

I am still trying to formulate a thought…

That words are maps, and are by necessity, limited. That is to say, there is more than that which mere words alone can say. The menu is not the meal. The Philosopher and the teacher of philosophy could not be more different.

Words are not the things in themselves. And this is what the mystics explore. Knowledge beyond epistemology. Tacit experience that words cannot touch. This is the difference between talking about God and experiencing God. Words can never replace the experience. Therefore, thought alone will never satisfy our desire. It is not in thinking, but in being that we find the peace we seek.

It is the path of the mystic, not the philosopher, that leads home.

 

I copied this out of a book I read the other day callled “The Happiness Hypothesis”.  The book takes ten good ideas passed down from the sages and examines them with all the modern scientific tools currently at our disposal. So while there is nothing “new” here, it is neat to watch it become a fixture of fact hanging on the wall of science.

The second biggest finding in happiness research, after the strong influence of genes upon a person’s average level of happiness, is that most environmental and demographic factors influence happiness very little. Try to imagine yourself changing places with either Bob or Mary. Bob is 35, single, white, attractive, and athletic. He earns $100,000 a year and lives in sunny southern California. He is highly intellectual and he spends his free time reading and going to museums. Mary and her husband live in Buffalo, NY where they earn a combined income of $42,000. Mary is 65 years old, black, overweight and plain in appearance. She is highly sociable and spends her free time mostly in activities related to her church. She is on dialysis for kidney problems.

Bob seems to have it all and few readers of this book would prefer Mary’s life to his. Yet if you had to bet on it, you should bet that Mary is happier than Bob.

What Mary has that Bob lacks are strong connections. A good marriage is one of the factors  most strongly and consistently associated with happiness. This benefit is due to the real and lasting effects of dependable companionship. Mary also has religion, and religious people are happier, on average, than non-religious people. This effect arises from the social ties of participation in a religious community, as well as feeling connected to something larger than oneself.

What Bob has going for him is a string of objective advantages in power, status, freedom, and health.  White Americans are freed from many of the hassels and indignities that affect black Americans, yet on average they are only very slightly on average any happier.

People are often surprised to learn that the old are happier than the young because the old have so many more health problems. But the adaptation principle applies here again. People adapt to most chronic health problems such as Mary’s. People who live in cold climates expect people who live in warm climates to be happier but they are wrong. People believe that attractive people are happier than unattractive people but they too are wrong.

 

Richard Feynman is a great popularizer of physics. He mastered the mathematics of light and wrote the QED, which is the most accurate and detailed description of the behavior of light, which is accessible to a lay audience. The following links are to a series of videos on You Tube. Similar to Six Easy Pieces, where Feynman brings hard to understand, mathematical and physical facts to a lay audience.

To one degree or another, Feynman is an embodiment of what this site is all about. He is Prometheus, has been to the brink and has brought fire back from the Gods.

Rules of Chess

Inertia and Epistemology

Jiggling Atoms

Fire

Rubber Bands

Electricity

Magnets and Why

The Mirror

The Train

Seeing Things

Ways of Thinking

In this last video, Feynman is talking about the limitations of language to “map” reality. This is true of all maps. Maps are by definition, limited. We have a word for space and a word for time, but these maps are limited. When this map begins to wear thin, we make a more useful, larger, map, called space-time. And this is how it is as we delve deeper and deeper into “reality”. Our maps wear thin and we find we need more precise, larger maps. As we try to “map” the atom, our map grows more and more unwieldy.. “and this difficulty, we are in.”

 

I can’t explain it any better than this

 

I have not read Douglas Hofstadter very thoroughly, but I have perused some of his work and I enjoy and recommend him. He whets the appetite for something more, which is a good thing. He stirs the passion of the subject…

What am I?

After reading large chunks of I am a Strange Loop, I found another book, The Concept of Mind which I have not yet read, but look forward to. The author, Gilbert Ryle is the father of the concept of a category mistake.

Ryle alleged that it was a mistake to treat the mind as an object made of an immaterial substance because predications of substance are not meaningful for a collection of dispositions and capacities.

This notion of a category mistake is an extremely important idea to digest, for it has the potential to solve so many so-called paradoxes in philosophy. It also serves as cure for some poorly-formed questions, such as “what is the meaning of life?” When we fail to recognize that this question makes the category mistake, we fall into a trap from which it is impossible to escape until the feedback loop is broken. Life cannot have meaning any more than red can have distance. MY life and YOUR life and the life a TURTLE may have meanings, but LIFE, an abstraction, cannot.

In other words, when we wrongly classify abstractions as objects, we make the “category mistake” and can fall prey to paradox. This is a common pitfall experienced by today’s young object-oriented computer programmers (like me) when first learning about classes and objects.

More on this in my post, Godel’s Incompleteness Theorem

 

In the preface of his book, Everything and More: A Compact History of Infinity, the late David Foster Wallace talks about the power of abstraction to suck you into an abyss of insanity. Mathematicians, who deal in pure abstraction, are more prone to insanity than poets and artists, he claims. Trying to define the mathematical properties of infinite sets is an extreme example and I have to wonder if some of the problems in this area of mathematics may arise from the category problem.

For example, Does it even make sense to consider “the set of all sets that do not contain themselves”, for example? I wonder sometimes. It certainly leads to paradoxes, and worse yet, it is this type of self-referential loop that is the source of Godel’s Incompleteness Theorem, which is a proof that mathematics is not free of contradiction (because there are truths that are not provable).

The following ideas need a lot of refinement, but here is my current thinking on this:

I think the failure has something to do with the characteristics of second-order logic but that is a guess. My very rudimentary understanding is that any “formal system” that is robust enough to make statements about itself (second-order logic?) fails David Hilbert’s Second Problem, which asks if mathematics, and logic, is free of contradiction.

Godel has proven that the answer to this question is in the negative.

But the source of the contradiction arises from a very specific case when a system of logic – be it mathematics or formal logic – is allowed to refer to, and operate on itself. Statements like, “I am lying” reveal the problem. If the statement is true then it is false. Only if the statement is false can it be true. And thus contradiction is inescapable, and unless you are quantum particle, this is just not allowed.

Thus we learn that when a system of logic is allowed to refer to itself, contradiction creeps in. To me, that is all the Incompleteness Theorem reveals. It is not an indictment of mathematics and logic as much as it is of self-reflective systems (second order logic?).

I am straining to make this distinction in order to prevent the misuse of the idea because I read again and again of Godel being invoked as a way to discredit mathematics and logic.

But I find it too much to allow it to hold that mathematics is incomplete. Set theory may be incomplete, but lets not allow this to tarnish all of mathematics. This is why I bring up the category problem.

The incompleteness lives specifically in set theory, not Logic or Mathematics. It is this “second order” stuff that fails the test, because of the unavoidable consequences that arise when a system applies itself to itself, like a snake eating its own tail, or an MC Escher hand drawing itself. Paradox and contradiction arise when a certain kind of rule is broken, like the category rule.

Thesis

What we talk about when we talk about “the set of all sets that do not contain themselves” is non-sense (or at least redundant) because a set should never be able to contain itself. This is a gymnastics of words, misapplied. It is like saying the color red is ten miles long. It makes no sense. Neither does it make sense to discuss the set of all colors that have no length, or any other such nonsense.

Once this kind of idea – a set that contains itself – is allowed into formal logic, and ONLY when this is allowed, contradiction is a necessary result. For this reason alone, it should be clear that this should not be allowed.

But I am not mathematician or logician. Far from it. I would love for someone to correct my thinking on this. If nothing else, I would prefer if the Incompleteness Theorem could be more specific in identifying what it is that is incomplete. It seems to me that it is not “logic” that fails, but something else. Perhaps it is that “any logic (second order?) that attempts to apply itself to itself” fails.

At any rate, this failure is the same failure we see in metaphysical paradoxes, which usually seem to be victims of category mistakes. Can we really call a set that contains itself a “set”? Is it not some sort of meta-set, and thus separate from itself at that point? Suddenly we have jumped from logic to metaphysics!

These are the same kind of paradoxes that arise in fiction stories when a traveler goes back in time and runs into himself. How many of him are there? The logical conclusion is that there are infinite hims in time, or one for each nano second of his existence at least.

Well, if a set can contain itself, this begs the same question does it not? How many of this particular set is there to be contained? If there be but one set and that one set can contain itself, then why can’t it contain the set that contains itself as well?

See the problem here? It seems to me that we have made a mistake in our linguistics. The idea that a set can contain itself naturally leads to contradiction, therefore, like dividing by zero, it should not be allowed.

Problem solved.

OK, so someone help me out here! I am confident that I am wrong about all of this, having never studied “formal logic”. I am merely a meek man of common sense so I need someone to show me where I have gone off the rails.

One last note on this…

there can be no set that contains all sets, for the same reason there can be no greatest number. Show me the set that contains all sets and I will show you the set that contains THAT set. ad infinitum. QED.

 

What is the meaning of life?

You may have heard this question before. (Have you guessed the riddle yet? – Mad Hatter, Alice in Wonderland) Of course not. Because this question is actually logically invalid. See category mistake (the philosophical error of putting a thing into a class to which it does not belong). You programmers out there are nodding your heads in affirmation and need no further exposition on this topic. For the rest of us, a little more may be needed here…

Without getting tangled up in meta analysis and self referential loops and a discussion of the meaning of meaning, let me try to cut the infinite regression off at the knees and simply suggest that the question itself is flawed and perhaps can be improved with the following form:

What is the meaning of YOUR life? Better yet, is the question, “what is the meaning of YOU?”, or even, “what is the meaning of your life NOW?”

I believe that the error of the first question (see category mistake) is resolved in the second and improved further with these other forms. Once you realize that the concrete meaning in question cannot be ascribed to an abstraction, you are back on track to finding a specific answer. And specific is the key word here.

I have written more on this topic in my post, Strange Loops.

Endnote:

It is interesting to notice the difference of how a computer responds to invalid question and how a human responds. Because as humans we are less sensitive to errors in logic, we often respond to illogical proposistions – philosophical paradoxes, for example – as if they are either great mysteries worthy of pondering, or hold some clue to higher meaning when in fact in almost all cases they are merely products of poorly formed logical input. Instead of recognizing the poorly formed question for what it is, we go off on wild goose chases seeking impossible answers.

The question of the meaning of life can only be answered by life itself, so before we go chasing this particular windmill, we might do better to ask ourselves what the meaning is of our particular lives. And yet this will not get us very much farther, for what is “my life”? What is the past? What is the future? I think best of all is to ask, what is the meaning of this moment, for me? Right now, “my life” means reflecting on my life. Yesterday my life meant finding the perfect balance to the furniture in my living room. Who knows what my life will mean tomorrow? Hopefully in a few hours the meaning of my life will be bagels, eggs and orange juice.

 

What is it?

It is the single most beautiful equation in all of mathematics.

e^{i \pi} +1 = 0.\,\!

As this blogger points out:

It relates five of the Most Important Numbers in the World (0, 1, e, i, and \pi) using three of the Most Important Operations in the World (addition, multiplication, and exponentiation) and nothing else.

According to Gauss, if the truth of this equation is not immediately apparent to you, now having been shown it, you will never be a first-rate mathematician.

So that settles that.

Here’s what it means:

 

What is it?

You may know of this by it’s common name, “fuzzy” logic. I prefer the term “fractal”, because it gets to the heart of the matter. We don’t have fuzzy dimensions, but we do have fractal dimensions. Fractal dimensions are “fractional” dimensions like 1.2 and 2.3. Likewise with “fuzzy” logic. As opposed to the binary logic of 0 and 1, fractal or “fuzzy” logic allows for a range of values between 0 and 1. You won’t hear anyone talk about fractal logic, though. I use the term here merely for visualization purposes. (When I am trying to understand something, I often find it helpful to rename the ideas, change the metaphor, redraw the picture for myself).

So what it is good for? What can we use this funny logic for? That’s simple. We all know that there are degrees of truth. The world ain’t black and white, you know. Take a glass of water, for example. Is it empty or full? Binary logic cannot answer this, but according to fractal logic, the “truth value” of the emptiness or fullness of the glass is easily calculated, sort of like a percentage.

Binary logic deals with true and false values while fractal logic tries to address “degrees” of truth in values such as hot-cold, where you have a continuum of values between extremes.

Here is a logic tutorial I found interesting:

http://logictutorial.com/

I need more example to flush this out. How is fuzzy logic NOT just statistics (percentages)?

 

Our understanding of multiplication changed over time:

  • With integers (3 × 4), multiplication is repeated addition
  • With real numbers (3.12 x sqrt(2)), multiplication is scaling
  • With negative numbers (-2.3 * 4.3), multiplication is flipping and scaling
  • With complex numbers (3 * 3i), multiplication is rotating and scaling

We’re evolving towards a general notion of “applying” one number to another, and the properties we apply (repeated counting, scaling, flipping or rotating) can vary. Integration is another step along this path.

credit above goes to Better Explained

I need some more examples on this topic and to flush out the ideas above (scaling, flipping, rotating)

 

The following excerpts are taken from the book, “A Short History of Nearly Everything”. These are truly awesome statements.

 

The Measure of Things

Astronomers these days can do the most amazing things. If someone struck a match on the Moon, they could spot the flare.

With their radio telescopes they can capture wisps of radiation so preposterously faint that the TOTAL amount of energy collected from outside the solar system by all of them together since collecting began in 1951 is “less than the energy of a single snowflake striking the ground,” in the words of Carl Sagan.

Weighing the Earth

Henry Cavendish is often credited with being the first person to use Newton’s law of gravitation to calculate the mass of the earth, but he did so with a machine developed by a man named John Michell, who died before he could use it.

Delicacy was the key word. Not a whisper of disturbance could be allowed into the room containing the apparatus, so Cavendish took up a position in an adjoining room and made his observations with a telescope aimed through a peephole. The work was incredibly exacting and involved seventeen delicate, interconnected measurements, which together took nearly a year to complete…

Today, scientists have at their disposal machines so precise they can detect the weight of a single bacterium and so sensitive that readings be disturbed by someone yawning seventy-five feet away, but they have not significantly improved on Cavendish’s measurements of 1979.

The Rise of Life – the Big Birth

Whatever prompted life to begin, it happened just once. That is the most extraordinary fact in biology, perhaps the most extraordinary fact we know. Everything that has ever lived, plant or animal, dates its beginnings from the same primordial twitch. At some point in an unimaginably distant past some little bag of chemicals fidgeted to life. It absorbed some nutrients, gently pushed, had a brief existence. This much my have happened before, perhaps many times. But this ancestral packet did something additional and extraordinary: it cleaved itself and produced an heir. A tiny bundle of genetic material passed from one living entity to another, and has never stopped moving since. It was the moment of creation for us all. Biologists sometimes call it the Big Birth.

“Wherever you go in the world, whatever animal, plant, bug, or blob you look at, if it is alive, it will us the same dictionary and know the same code. All life is one,” says Matt Ridley. We are all the result of a single genetic trick handed down from generation to generation nearly four billion years, to such an extent that you can take a fragment of human genetic instruction, patch it into a faulty yeast cell, and the yeast cell will put it to work as if it were its own. In a very real sense, it is its own.

- “Humans are here today because our particular line never fractured – never once at any of the billion points that could have erased us from history.”

Small World

Bacteria may not build cities or have interesting social lives, but they will be here when the Sun explodes. This is their planet, and we are on it only because they allow us to be.

Bacteria, never forget, got along for billions of years without us. We couldn’t survive a day without them. they process our wastes and make them usable again; without their diligent munching nothing would rot. They purify our water and keep our soils productive. Bacteria synthesize vitamins in our gut, convert the things we eat into useful sugars and polysaccharides, and go to war on alien microbes that slip down our gullet.

We depend totally on bacteria to pluck nitrogen from the air and convert it into useful nucleotides and amino acids for us. It is a prodigious and gratifying feat. As Margulis and Sagan note, to do the same thing industrially (as when making fertilizers) manufacturers must heat the source material to 500 degrees centigrade and squeeze them to three hundred times normal pressures. Bacteria do it all the time without fuss, and thank goodness, for no larger organism could survive without the nitrogen the pass on. Above all, microbes continue to provide us with the air we breathe and to keep the atmosphere stable. Microbes, including the modern versions of cyanobacteria, supply the greater part of the planet’s breathable oxygen. Algae and other tiny organisms bubbling away in the sea blow out about 150 billion kilos of the stuff every year.

And they are amazingly prolific. The more frantic of them can yield a new generation in less than ten minutes; Clostridium perfringens, the disagreeable little organism that causes gangrene, can reproduce in nine minutes. At such a rate, a single bacterium could theoretically produce more offspring in two days than there are protons in the universe.

… Bacteria share information. Any bacterium can take pieces of genetic coding from any other. Essentially, as Margulis and Sagan put it, all bacteria swim in a single gene pool. Any adaptive change that occurs in one area of the bacterial universe can spread to any other. [...it's important to remember that one bacteria is as different from its neighbors as animals are from plants]. It’s rather as if a human could go to an insect to get the necessary genetic coding to sprout wings or walk on ceilings. It means that from a genetic point of view bacteria have become a single superorganism – tiny, dispersed, but invincible.

They will live and thrive on almost anything you spill, dribble, or shake loose. Just give them a little moisture – as when you run a damp cloth over a counter and they will bloom as if created from nothing. They will eat wood, the glue in wallpaper, the metals in hardened paint. Scientists in Australia found microbes … that live in – indeed, could not live without – concentrations of sulfuric acid strong enough to dissolve metal. A species called Micrococcus radiophilus was found living happily in the waste tanks of nuclear reactors, gorging itself on plutonium and whatever else was there.

…Some of them seem to be practically indestructible. Deinococcus radiodurans is, according to the Economist, “almost immune to radioactivity.” Blast its DNA with radiation, and the pieces immediately reform “like the scuttling limbs of an undead creature from a horror movie.”

…Slime molds are, make no mistake, among the most interesting  organisms in nature. When times are good, they exist as one-celled individuals, much like amoebas. But when conditions grow tough, they crawl to a central gathering place and beceome, almost miraculously, a slug. The slug is not a thing of beauty and it doesn’t go terribly far – usually just from the bottom of a pile of leaf litter to the top, where it is in a slightly more exposed position – but for millions of years this may have been the niftiest trick in the universe.

And it doesn’t stop there. Having hauled itself up to a more favorable locale, the slime mold transforms itself yet again, taking on the form of a plant. By some curious orderly process the cells reconfigure, like the members of a tiny marching band, to make a stalk atop of which forms a bulb known as a fruiting body. Inside the fruiting body are millions of spores, that, at the appropriate moment, are released to the wind to blow away and become single-celled organisms that can start the process again.

Life Goes on

It is almost impossible for us whose time on Earth is limited to a breezy few decades to appreciate how remote in time from us the Cambrian outburst was. If you could fly backwards into the past at the rate of one year per second, it would take you about half an hour to reach the time of Christ, and a little over three weeks to get back to the beginnings of human life. But it would take you twenty years to reach the dawn of the Cambrian period. It was, in other words, an extremely long time ago, and the world was a very different place.

 

Good-Bye To All That

So why, out of all the thousands of impacts Earth has endured, was the KT event so singularly devastating? Well, first it was positively enormous. It struck with the force of 100 million megatons. Such an outburst is not easily imagined, but as James Lawrence Powell has pointed out, if you exploded one Hiroshima-sized bomb for every person alive on earth today you would still be about a billion bombs short of the size of the KT impact.

 

 

 

Everyone knows Albert Einstein’s famous equation, but do you know why he was awarded the Nobel Prize? It was not for Relativity, but for giving birth to the Quantum Universe, which is in direct conflict with the Relative Universe!

Thanks to QED we know that all known physical phenomena in the universe from the Big Bang to present can be described by the interaction of photons and electrons. Or, put another way, light transforming back and forth between its two known forms of matter and energy.

This view of material phenomena helps with the explanation of why rods shorten in the direction of motion. It was not Einstein who discovered this. Neither was it Einstein who discovered that the speed of light was constant. Maxwell discovered the speed of light. Michelson and Morley did an experiment that showed the speed of light was constant to all frames of reference. Fitzgerald tried to explain this with the idea that rods in motion shorten. But no one accepted this. It was Lorentz, the undisputed master of Maxwell’s equations of electromagnetism who explained how rods shorten. And unlike Fitzgerald, he did so CONVINCINGLY.

It was Lorentz, who understood the properties of the electron better than anyone, who explained the mechanics of how electrons would contract in the direction of motion, and that since electrons were the emitters of photons, or light, this contraction affected the observed speed of light such that the contraction exactly compensates for the motion. Although Fitzgerald posited that rods would shorten, it was Lorentz that showed HOW this happens.

Poincare, one of the world’s greatest mathematicians understood the logical implication of this: namely, that time itself had to stretch and contract. He even stated as much (the term, “relativity” in Einstein’s theory is understood as “Poincare’s relativity”) and commented that the laws of physics needed to change. It was inevitable. Logic dictated that it be so. But so far, there were only hints of what this change would look like. But a visionary patent clerk was piecing the images together.

Einstein was the first one who really took all of this in and put it together in a cohesive formulation, expanding these ideas to the level of fundamental principles from which all descriptions  of the universe must be derived from. It was in THIS where his genius on this issued lay. He had the vision to literally re-write physics.

In his attempts to draw it all out, he got help from another great mathematician of the ages. Minkowski, who had formulated a mathematics of higher dimensions showed Einstein how to draw his picture, this new concept of space-time. With this tool, the new picture could be completed, and it was Einstein that finished it. He took Maxwell, Michelson, Lorentz, Poincare, and Minkowski and added them all up. The unification of space and time and the removal of the concept of absolute rest in the universe was the result.

Einstein’s genius was not merely in discovering, but his ability to synthesize, visualize and draw logical conclusions. Much of his “work” was pure thought.

Here is a very, very good video of some of this.

And yet, for this “Theory of Relativity,” he did not win any prizes. It was for something much larger that he won the Nobel. And it is this thing, which is currently at war with the “Theory of Relativity”

Quantum phyics

more to come on this…

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