The Myth of Pattern
March 16, 2004
Einstein: "Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears it ticking, but he has no way of opening the case. If he is ingenious he may form some picture of the mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison."
This is a draft of an essay I've been formulating for years now. I’ve just finished reading several of Stephen Hawking’s books about physics, cosmology and the fate of the universe. I love reading his work because he isn’t lost in the scientific religion. He has a broad enough intellect to realize that science is simply a description of the world, and insofar as it corresponds with observation, it is extremely useful. He is the most eminent scientist I know who has admitted that there is no guarantee that we can apprehend the universe. Even so, “seeing the mind of God” is very dear to him and he proceeds on the premise that it might be possible, and if it isn’t, well, that’s very interesting to know, too.
The first issue is whether the universe is reducible to laws. This is so basic that it rarely is discussed or questioned. We are raised hearing about Newton’s Universal Law of Gravitation only to learn later that errors were found and Einstein came up with a better description. This made us wonder if Einstein’s General Relativity would someday be proved wrong. Well, it already has. At very high energies, we know it breaks down, so it’s at least incomplete. Now, the quest is on for a theory of Quantum Gravity which will resolve these issues. So, what does it mean to have Laws if they can change? The usual answer is that we just haven’t discovered the Real Laws yet. What’s seldom mentioned is the possibility that there aren’t any such laws. Many assume that the universe obeys laws, as if it is sentient, thinking about its next move. It’s a perfectly reasonable possibility that the universe simply is, and might be different everywhere. So the question should be can we find out if there are universal laws? Setting out with the assumption that there are universal laws is delivering the verdict in advance. Hawking admits that we can’t prove that universal laws exist but holds to the hope that they do. He quotes the famous scenario wherein a drunk, having lost his keys at night, looks for them under a lamp post. They might not be there, but it’s the only place he can look.
The second issue is whether the physical phenomena we see around us on Earth are the same throughout the universe. This assumption is fundamental to science and is fairly well supported by astrophysical observations, analysis of light spectra, etc. But we only have light from the visible universe, that part which is close enough for light to have traveled to us since the universe began (our light horizon). So, we can only speak about that for which we have data. This ratio of acquired data to the total amount of data in the universe is, of course, infinitesimal. Further, it appears that normal matter and energy account for less than a third of what is out there (or General Relativity is wrong), leading most scientists to postulate dark matter and dark energy to make up the difference. If these exist, then not only do we not have a full understanding of known particles, we haven't even identified what most of the universe is made of. Thus, we base our Laws of Nature on a vanishingly small sample. Hawking deals with this in his usual positivist philosophy, which I embrace, that it’s all we have, so we should make the best of it. Further, a theory is “correct” if it agrees with known data. Here is where I differ with the “mind of God” suggestion, that science is a discovery of how the universe operates, rather than an after-the-fact, approximate description of purely human origin.
As an example, Hawking himself has been credited with “discovering” Hawking radiation, the putative quantum emissions from black holes. I would instead call it a prediction, since Hawking radiation exists only in the mathematics and thought experiments of many of the world’s top physicists. Hawking radiation has never been detected and it is unclear if it will ever be detectable. This lack or testability is sometimes a death knell for a theory (as it once was for string theory), but Hawking’s reputation seems to have overcome the lack of testability. Moreover, Hawking describes ways in which black hole emissions might be detected and if they are detected, then I would concur that they had been discovered. This pattern of prediction and discovery has great precedent in the Standard Model, so Hawking is on firm ground. Here, it is just another example of people confusing scientific theories with reality. Maps are classic examples of this confusion. Maps represent land area in compact form by omitting details. We are so comfortable using them that some people think that the Mississippi river flows to the south1 and the north pole is at the top of the world.
For the moment, let’s sum this up as the following two postulates:
There is a concept lurking in this discussion that requires our attention: sameness. Physicists call two particles equivalent if they have the same quantum numbers of spin, charge, parity, etc. So, two particles are the “same” (except for location) if these values are the same within measurable accuracy. The Standard Model classifies particles and has reduced all known phenomena to 6 quarks (up, down, charm, strange, bottom and top), 6 leptons and some force-carrying particles. This is considered a huge accomplishment, since, theoretically, the entire universe (ignoring gravity) can be described by the interactions of this small number of particles. But are all up quarks the same? Our positivist approach says that if all our data says they are the same, then it is useful to consider them such. But now, we have completely left behind the notion that science explains the universe. It is only an approximate description within the limits of the data. Perhaps all up quarks are not the same, and perhaps, if we could zoom in on them like zooming in on the crowd at a football game, we might see that they are all individuals. We have no data to support this, but we know that data at these sizes is hard to come by and we can’t rule it out. Because viewing smaller sizes requires higher energies, there is a lower limit to what we can investigate called the Planck limit. It is humbling to think that there could be myriad layers of smaller and smaller forms that are intimately within us yet beyond observation. This is the opposite of the light horizon issue. Macroscopic objects such as snowflakes, as any school child knows, are never exactly the same, but we are in the habit of ignoring small differences to make the world more graspable. This is deadly serious for scientists, whose purpose is to construct a consistent theory of the universe. Indeed, this is what is causing the current crisis in physics, the fact that General Relativity and Quantum Mechanics can’t both be right at very high energies. We can’t ignore the small differences anymore, because at high energies, they’re not small! Smallness is relative.
Let’s return to our normal size scale and talk about sameness again. We often talk about the sun rising in the east and setting in the west, even though we know that the exact position is different every day. So, we say that on March 21 of each year, the sun is in the same position in the sky. Well, not exactly, since the earth precesses, the north pole won’t point at Polaris forever. Oh, and March 21 isn’t exact, since the year is 365.242 (give or take) days long, so we need a leap day every four years (and leap seconds once in awhile), except each century (and excepting that every 400 years). Whew, we’re wearing ourselves out trying to impose the pattern called the year on the motion of the earth and the sun. This is no problem as long as everyone knows that there really is no such thing as a year, that the earth and the sun don’t care a bit about our calendar and that nothing ever repeats exactly as the earth goes around the sun. (Hawking begins one of his chapters this way: "I was born....exactly 300 years after Galileo's death." Exactly? I wonder if he accounted for leap years. And leap seconds.)
The circle was once considered the perfect shape, so everyone tried to make sure that heavenly bodies went in circles around the earth, and, later, that the earth went in circles around the sun. The problem was that the earth didn’t care a bit about this argument and kept doing its thing. As better measurements were made, adjustments to this theory (the infamous epicycles2) were made to try to salvage it. Eventually, the theory became unwieldy and the paradigm shifted to a simpler, more elegant theory without all the fine-tuning of the epicycles. First came Newton’s Gravity, then Einstein’s General Relativity. These theories were more satisfying because they seemed more natural without all the baggage required by the previous theory and they agreed better with observation. Scientists and mathematicians frequently refer to elegance and simplicity when developing theories. I’m not sure why we feel one thing is more elegant than another, but we have no evidence the universe shares our taste. The actual Theory of Everything could be ugly by our standards or there might not be one. Some shudder at that prospect, but if our quest is understanding, wouldn’t this be just as beautiful a result, if it were true?
Now, let’s return to the two previous notions:
Both of these principles rely on the notion of sameness, that the number of possible configurations of matter and energy is limited and that events can be equivalent. We usually refer to sameness as pattern, which I define for our purposes here as a repeating form. Hydrogen atoms are usually considered a pattern, since their configuration of one proton and one electron is the same as every other hydrogen atom. We therefore treat them as interchangeable. We know, however, that hydrogen can absorb and emit light and bond with other atoms but we still call it a hydrogen atom through all these changing behaviors. What then, is the hydrogen atom? Isn’t it the same as the “year” we discussed earlier? Since it has so many forms and since it is vibrating and changing every instant, it seems that a “hydrogen atom” is just a convention, a term for an image in our minds that we all more or less agree on. And the real hydrogen atom “out there” is in a unique and perhaps unknowable state. Spectral analysis tells us that there are hydrogen atoms floating in intergalactic space right now, and there are some in the atmosphere on earth. But are they identical? Of course not. Any two hydrogen atoms that you could compare would differ in some way, at least in location. The same may be true of quarks and leptons. If we have lost the innocent notion that two things can be the same, then the larger idea of laws governing them must be abandoned, since we can’t even put things into categories or say that two systems are equivalent and thus should evolve in the same way. So, our first postulate is dead and, of course, the second becomes moot.
The tendency of all science is to generalize and ignore small discrepancies, forcing nature into compartments that suit our thinking. This is a very dangerous leaning and the scientific method has built-in safeguards against it. There is still a strong belief, though, that science can produce a consistent Theory of Everything. Many physicists, including Hawking, are well aware of the epistemological factors in such a quest and admit we don’t know if the universe is graspable. We must remain aware that generalizing is a convenience for us and has no bearing on the nature of reality. The notion of pattern rises to the level of myth because it is so widely accepted without proof, despite massive evidence against it. It differs from most traditional myths, however, because in our modern culture the word myth has the connotation of something that was once widely believed and has now been revealed to be false. Many people still feel, however, that the patterns we hold in our minds are actually "out there", that forms actually do repeat in nature. Most people think that seasons, mountains, bicycles and dogs actually exist as more than convenient categories. For example, we each know that we eat and eliminate several times a day, yet we still believe we have a static body. Over time, we are convinced by the incontrovertible evidence that we are changing and aging, but we can not be surprised. It is common knowledge that our bodies are different from moment to moment. Therefore, the only "body" we have is a mental construct we use, like an index card in a library's card catalog that refers to a book. Rather than seeing things directly, we see and have relationships with our thoughts that correspond to them most of the time. This relates to Plato's Cave Allegory; the cave is the mind and the shadows on the wall are our thoughts, but we can't turn around and see the true Forms. As long as we perceive reality with our brains, we are removed from it and live in an internally-projected simulation of it. Various mystical traditions address this issue and seek a more direct experience of reality. This is extremely interesting and profound, since their investigations hinge on another myth, that we are separate from the universe we are observing.
Whenever I look closely enough, I see that what I think in my mind is only an approximation of an infinitely-varying, always-different universe that is patternless. It is alarming for physicists to think that we might as well be amnesiacs, since our memories (past data) will have no exact bearing on future events. Hawking investigates to what extent we can predict events given the Uncertainty Principle and the loss of information in black holes. Here we posit another factor, the possibility that nothing ever really repeats at all. The good news is that for most human purposes, approximate descriptions work very well. For the lofty purpose of trying to understand the full behavior of the universe they fail. This certainly doesn’t mean we should cease trying, because the refinement of approximate theories is valuable by itself. Hawking does a great job of dissecting this issue and proposes that, if we live in a universe characterized by what he calls a no boundary condition, it should be possible to form a consistent explanation of the universe without appealing to outside agencies such as God. This leaves us in the hopeful position of eventually finding a Theory of Everything, but Hawking wisely reminds us that such a theory will only consistently describe how the universe works, not why it bothered to exist in the first place. If, however, the universe turns out to have a different geometry, then Hawking acknowledges it is likely that no such theory will be found.
The
human brain has evolved to allow us to navigate and survive in an unpredictable
environment. Rather than being a pattern-identifying device, however, it
is a pattern generator. It tells us a white lie about reality: that
if something happened one way one time, it might happen that way again.
This is close enough to the truth to help in hunting animals and raising crops,
but it is still a lie. This is easy to see, for example, when we see faces
in clouds. The brain's face-recognition cells are initially fooled and
other senses recognize the error. No one would put clouds and faces in the
same category, but part of the brain does just that. This is why we have
to be extremely careful when we do science. Our brains can perceive
patterns that are not there, and the error is not always as obvious as seeing
faces in clouds. Sometimes, we aren't aware of what our brains are doing.
There are numerous optical illusions that illustrate this. Certain gases
and light outside the visible spectrum don't register in our senses at all.
In other words, we can't trust our brains and we must check what they tell us.
Imagine looking at a cloud and really thinking it is someone's face. This
happens all the time in science. The ether
and the cosmological
constant are two examples of human ideas that may or may not correspond with
reality, but which have been thought to be part of nature at one time or
another. Our thoughts, including our awareness of patterns, can be
perceptual illusions.
The brain's job is to reduce reality to something manageable, and to reduce the number of responses we make to it. It does this by selectively ignoring data that don't fit its invented schemes. If a scheme is close enough to reality, it will result in improved survival. We have taken the success of our thought patterns to indicate their veracity. This is fallacious in the realm of formulating a theory of how the universe works. We are easily hypnotized by our brains since they have a near monopoly on our personal realities. Like Gödel's Incompleteness Theorem in mathematics, though, our own capacity for thought can lead us to an understanding of the brain's limitations. Many common sense notions have fallen in the last century as we investigate high energies and extremely small sizes in physics: time has been found to be relative, the universe has an infinite number of histories (as Hawking puts it, 'we live in the most probable of all possible worlds'), we can't know the exact physical location and momentum of a particle at the same time, etc. Pattern is another cherished idea that must be seen for what it is, a convenience and a contrivance having no existence outside our minds.
The important point, then, is an epistemological one. We must always remember that we live our lives in a neural matrix constrained by our genetics. We see a tiny sliver of the electromagnetic spectrum, we sense a thin range of sounds, pressures, tastes, etc. We extend our senses with instruments but will always be short on information. Further, we form this paucity of data into a mental construct that is many times removed from the universe we are studying. Instead of connecting us to the outside world, then, our senses are walls which remove us from it. In the movie trilogy, The Matrix, humans were confined in a neural construct created by machines. This is actually the case, except we make our own illusion, and the illusion is not enforced. We are free to keep in mind that we live in a mental construct and that the universe “out there” is rich in mystery and variety beyond our comprehension.
1Water flows downward, towards the center of the earth's mass, regardless of its path along other axes. While its overall path is south, the Mississippi river meanders in many places, following the topology of the land, and flows east, north, west and every direction in between. The Nile's path is predominantly north, but it is always flowing downward.
2Aristotle, Ptolemy and even Copernicus thought circles were perfect and used epicycles to patch up their theories. Later, they were proved wrong when it was "discovered" that the planets move in ellipses. My assertion is that they don't move in perfect ellipses or any other mathematical construct exactly. This is, in fact, well known to keepers of atomic clocks who are regularly taking into account the earth's deceleration due to tidal effects, etc.