Symmetry Is Hard Wired in our Brains

According to Wilczek, symmetry is "Change without change" - the most powerful single principle underlying the laws of both aesthetics and physics. In Wilczek's books, he provides simple examples and a few mind bending ones (such as the symmetry involved in the strong nuclear force - the rules governing quarks). For some reason, he neglects the most common example of symmetry that is always quite literally right in our face. This is the ability of our perceptual system to recognize "objects" in the world - "things" that seem to be the same no matter how they are oriented, how far away they are, or how they are illuminated. Sometimes we only need to hear or smell the "thing" to "see" it in our minds. Anyone who has attempted to "teach" a computer to do anything like this knows how incredible this ability is. And it's totally natural, totally automatic. What's more all "higher" animals (maybe all living things) seem to have some version this capability - at least when it comes to recognizing "objects" that are relevant to their survival. One capability that does see universal among all living things is the ability to detect change - relevant change or what a physicist would call "symmetry breaking".

The ability to handle "change without change" is therefore hard wired into our brains, making recognition of symmetry a fundamental principle of existence, not just "consciousness". Thinking like Wilczek, we see that the dog that "looks like" the "same" dog, even though I never see her in exactly the same way, is really the same dog. My dog has something like the same capability, being able to pick me out of a crowd at considerable distance.

Of course, Zen will quibble about how our brains chop reality up into "objects" that have somewhat arbitrary definitions and boundaries, but the truly remarkable fact is that our brains get it right 99.99% of the time and do so automatically and effortlessly. Fully one third of the cortex of the brain is devoted to the visual component of this capability, giving us a clue as to its importance.

Wylczek provides another way of thinking about this. Symmetry underlies our ability to compress information about the world. The ultimate example is how the Standard Model can be written on a single sheet of paper but sums up everything we know about the laws governing ordinary matter and energy. Along these lines, we can see language as a tool for compressing everything we can know (or at least say) about the world. Our taste for symmetry acts on this "compression algorithm", making things "feel" like they are the "same" even when they are obviously different. For example, the woman who says "all men are the same" has obviously saved herself a lot of work, compressing everything she knows about men into five words. It is her built-in preference for symmetry that allows her to be believing this or at least saying this.

More on compression here.

What is "Truth"?

Daniel Dennett likes to give Jaynes the benefit of the doubt: “There were a lot of really good ideas lurking among the completely wild junk.”

As Dennett hints (with typical subtly), there is a lot of "junk philosophy" around the subjects dear to Jaynes' heart. In this post, I'd like to extract one of Jayne's ideas and wipe a bit of "junk" off it to see where it gets me.

At the center of Jayne's theory is the "bicameral mind", which is firmly based on the idea that we have a "right brain" and a "left brain" with notably different capabilities, each capable of acting somewhat on their own. The "right brain" is good at seeing the "big picture" and sends its judgments to the left brain, where they are perceived as speech - sometimes the speech of the Gods. As things get historically more complicated, we evolve our present day "inner chatter", no longer attributed to the Gods (if we are sane), but now called "reason". Jaynes regards this as the emergence of consciousness itself, which is not what I want to take up in this post. What I like about Jaynes is that he sees language in a dynamic light, evolving and building up over time toward some critical point where the modern mind (along with "civilization") emerges.

There is no particular reason to locate these two faculties at some location in the brain and this is perhaps Jaynes main mistake - built in to his terminology. But we can understand his arguments very well without referring back to his neurological ideas. In fact, he rarely does so himself. You could go through his book and translate "Left Brain" as "Kidney" and "Right Brain" as "big toe" without impacting the meaning of what he's saying.

What we regard as "truth", at least in the Western traditions, is a linguistic concept. The "most" true statements are those of mathematics, which can be "proven". As Wittgenstein famously pointed out, such proofs are basically moves in a language game, where everyone agrees to the rules and agrees about what is "proven" in dialogue. As Hofstadter points out in Surfaces and Essences, the concept of language can be broadened to include the "models" of Physics - the underlying idea is metaphor and analogy.

Jaynes, Hofstadter and others point out that language is a huge labyrinth of metaphor. We "bootstrap" our store of metaphors as children (Jaynes is particularly good at describing how this bootstrap process works) and we proceed to produce the vast store in our heads - tens of thousands of words. It is in this language that our "inner voice" speaks. If our inner voice proclaims something to be true, it does so according to the impenetrable rules of the language that has been programmed into our brains. In the vast majority of cases, the beleivability of that inner voice comes from uncounted assumptions and analogies buried in the language it speaks. For example, if my inner voice calls someone a "nigger" in my head, that one word carries centuries if history and thousands of voices. It will make no sense to me to say to the inner voice: No, that person is not a "nigger". In fact, given the language that is being spoken, such a question makes no sense.

If you think that "1" is a solution to "x squared minus one equals zero", you speak the language of mathematics. If it seems sensible to say "I think, therefore I am", you have learned to talk like Descartes. Like him, you will regard that statement as self-evidently true. Those who fail to see the statement as self-evident are used to speaking a different language in a whole different culture which, for example, may regard the "self" as an illusion. Such a statement would make no sense to Descartes. It's not a matter of "truth" outside of the rules of the "language game". Descartes spoke the language of the religion of his time, which regarded the soul as the "self" -- the "self evident" starting point for any discussion of what is "real".

Is there any other way we can reach the "truth"? Jaynes says there is: that "right brain" which sees the truth but speaks it to the "left brain". It's better to characterize this source of perception as some kind of holistic or aesthetic sense that goes beyond language and perhaps precedes language historically. It is an open question whether this "right brain" (or big toe) processing works according to analogy. I think it's better to say it works by hard wired recognition of symmetry, but that is another topic.

For example, this "right brain" truth pops up when we say a certain combination of notes "sounds right" or a scene is breathtakingly beautiful. It certainly shouts loudly at us when we judge another human being to be beautiful, honest or friendly.

This simple observation leads me to some wide-ranging conclusions.

• By definition, we cannot expect language to reach into non-linguistic "truth". Western philosophy, including that of Dennett, even when purged of "wild junk", has nothing to say about "truth" revealed by our innate mental capacity to judge certain experiences as special and valuable.
• Zen, emphasizes direct aesthetic perception and takes pains to isolate and ignore the "inner voice". There is no reason to prefer one path over the other. In fact, I'm perfectly happy to leave the whole idea of "truth" to the language experts and seek for other words that reflect the judgement of my "right brain". This consideration is a much needed justification for being open to Zen.
• Our "right brains" have a shared language, a culture and a history of their own, referred to as "art". I would also contend that they have a built-in "language" of their own - perhaps reaching back far into the past, perhaps part of the very definition of life itself. Even when the "art" in question is expressed in language (the novel for example), quality judgement are made by standards that are difficult to express in the language of logic, although critics struggle endlessly to do so.
• We need to distinguish between what is "real" and what is "true". Truth is the umpire's call in the language game. Reality is what remains after all alternatives are ruled out.

There is another road to "truth", described in our language as "Science". Advances in Scientific knowledge are made chiefly through language - vigorously expanding our vocabulary. There are maybe 180,000 words in the English language (give or take). Scientific journals add a few more with every published article. Moreover, Science is constantly adding new models of reality. The first of these was "Euclidean Space". More recently, Feynman Diagrams have added to our ability to "picture" and discuss quantum reactions. Many things are easily "said" with pictures but almost impossible to "say" with words. However, these pictures ("maps") obey the same principles as language as discussed by Hofstadter and Jaynes. All lovers of maps and models will agree that there is a strong element of aesthetic beauty in a good map. 

There is also a strong aesthetic motive in Science as a whole, most eloquently described in "The Beautiful Question" by Frank Wilczek. Wilczek makes a strong case that the universe really is governed by symmetric principles, which also appeal strongly to our sense of what "looks right" (this is a right-brain kind of "looking right"). In other words, our taste for symmetry is a reliable guide to what is real.

So, in Science all three roads to the truth come together. 

The Brain As an Amazing Symmetry Computer

I have a coffee cup in front of me (I usually do). If I rotate it or move or see it in different light it my brain automatically makes me experience it as the same cup. If you have ever tried to make a computer figure this out, you will see how astonishing this is. What's more, the cup will be seen as the same cup tomorrow and the same as the cup that I washed a week ago (or is it two weeks? The point is, that doesn't matter). This is symmetry under a transformation in time and space. It takes place so automatically that most of us will go through our entire lives without thinking of it at all.

There is another, related, trick that the brain does. It makes me "see" the cup as a form. A form is a bunch of "stuff" that is more or less arbitrarily treated as the "same thing". My dog is quite capable of seeing a flying tennis ball as a "thing" that can be snatched out of the air, but she seems to be uninterested in the "things" shown on our TV screen. This is just to point out that selection and recognition of "things" is a brain function and not "out there" in the real world.

Brains which make an isomorphic transformation (or I suppose a "reverse" transformation) are able to manipulate the "things" of the mind as if they are "things" of the real world. Brains are good at detecting relevant things and picking them out of the hurricane of sensation that presents itself to working memory in every second. You could say this allows working memory to "compress" the world into a very small set of "things". I don't expect the cup to turn into a cat, but I would quickly notice if it did. Otherwise, it can just sit on my desk and play a small part in what I perceive as my surroundings.

From Bacteria To Bach and Back (Dennett) provides a detailed exploration of how our minds come to recognize "things" and how the "thinginess" of the world arises from relevance rather than raw reality. An ant somehow recognizes certain things but presumably doesn't "know" it's doing it or even that it's an ant. "Consciousness" is not required to recognize "things". The brain has inherited this very ancient capability from the dawn of life and has had billions of years to perfect it. That's why it's so good at it. In Dennett's terminology, symmetry computations are a "competence" of brains: a competence without comprehension or, one might say, a pre-condition of comprehension. Dennet makes another subtle point: this competence doesn't depend on any kind of representation of the world in the ant's head or our head. In other words, we need not look for the set of neurons or synapses that "represent" my coffee cup in my brain. I picture the cup as a result of a result of a fantastically nested and fractal computation that the brain does "on the fly", a computation this is best described in Hofstader's"Surfaces and Essences"/ This computation relies mainly on analogy which is a special case of symmetry. This is why I refer to the brain as a "symmetry computer". It uses symmetry to "compress" all experience into "merely" a few billion connected neurons.

What is Symmetry

Here is a quick, painless introduction to the kind of symmetry that you probably learned in school. In that lesson, we learn that there are different kinds of symmetry:

• Rotational
• Translational
• Mirror

and so on. What this video (and your teacher) did not explain was what symmetry is in general. If you learned about symmetry in University Math, your idea was expanded a bit to come closer to what symmetry is in general. The first step is to think of symmetry as a set of transformations (rotate, move, flip) rather than a property of whatever it is that is being transformed.

And that's just the start. For example, in physics, you learned the Lorentz Transformation is a symmetry group in the "real world" that leaves the laws of physics unchanged. Newton's laws are not symmetric in this sense but with a bit of tweaking (Special Relativity) they can be fixed.

In physics, the Lorentz transformation (or transformations) are coordinate transformations between two coordinate frames that move at constant velocity relative to each other.

Frames of reference can be divided into two groups: inertial (relative motion with constant velocity) and non-inertial (accelerating in curved paths, rotational motion with constant angular velocity, etc.). The term "Lorentz transformations" only refers to transformations between inertial frames, usually in the context of special relativity.

Special relativity boils down to "fixing" the laws of physics so that they apply "locally" in non-inertial frames of reference.  I promise: no more about General Relativity.

Lorentz transformations are a special case of Gauge Symmetry, which is a concept used in the "Core Theory" of Quantum Mechanics and gets us finally to the point where we are talking about "real" symmetry in the "real" world. You need it to understand quarks for example.

This can all get pretty abstract and make your head hurt if you follow it all the way to Quantum Mechanics. It's best to stand back and ask what symmetry is. Wilczek describes it briefly as "change without change".  Or perhaps we could say you can change one thing that doesn't matter and everything that does matter is still the same.

In this blog we will be interested in a few kids of symmetry that aren't covered in school and are perhaps just a bit more general than even Gauge Symmetry. These involve transformations between domains I, M and R and within those domains or within sub-domains. For example the relationship between two ideas that are "like" each other (within the M-domain) is seen as a symmetry transformation. Some transformations are "better" than others and the criterion is symmetry. Does the transformation leave the idea the "same" in important aspects. This is similar to Hofstadter's idea of the "Essence" that is preserved in a "good" analogy.

Human beings seem to love all kinds of symmetry for good reason - they help economize on "representation" of "things" in the brain. Wylczek draws an interesting parallel with data compression. The Core Theory of Quantum Mechanics, which more or less represents everything we know about the physical world, can be written down in a few dozen strange looking characters, yet everything in human experience is a special case of it. Wylcze's treatment of this issue inspires this whole blog since he wrote a whole book about it: "A Beautiful Question" which basically points out the astonishing symmetry between our ideas (especially the Core Theory) and the real world. The equations of the Core Theory are incredibly symmetric and the real world seems to "like" symmetry a lot too. The "Beautiful Question" is a response to this situation. You are left with astonishment and wonder: a question rather than a "theory".

The Domains of I, M and R

Quick and dirty definitions, to be clarified as we go along:

• R Refers to the "real world". Accepted wisdom is that we have no direct access to R.  It turns out that we actually do have quite a good access to the R domain - the M/R interface, also known as "Science". For the individual, the I domain is tiny compared to the vastness of both M and R. However, with effort and training, it is possible for the individual to open a tiny peephole into R - at least so far as to put to rest the notion that R does not exist at all - that it's all an illusion.
• M Refers to "meme space" or the entire set of ideas, actual and possible. For example, all of Science exists in M, existing uncomfortably with all religions, past present and future. It is everything we know or could know or think we know, possibly including all those things that may be conceivable by some alien intelligence or even "God". M happily accommodates all the wrong ideas and the opposite of every idea.
• I Refers to memes that can be called to working memory. These may be thought of as a subset of M but it's more fruitful to regard the I/M interface as closely analogous to the M/R interface. "Calling up" memes to working memory involves a meme translation. We say we "get" the idea if our translation from a meme m from M to I leaves m unchanged in some way. Or we could say that m will translate to an isomorphic version of m no matter who calls it to working memory. This is a kind of symmetry, which the theory is all about. 

I call the theory that links all this together IMR Symmetry or IMR for short. At bottom, IMR is an extended analogy, asking us to visualize three worlds and ask questions about the interfaces between them. Much of the work consists of cleaning up or ideas about what these three worlds consist of and how we imagine that they communicate.  Advanced warning: many of these ideas will seem counter intuitive unless you "do your homework" and check the references liberally referenced in the text.

• The idea of "self" and "consciousness" are disassembled and put back together into something very different from the common understanding of these ideas.
• The "modern" concept of the "mind" as being an epiphenomenon of something going on in the neurons of our brains is also tossed aside.
• Many of the big philosophical questions, such as "Idealism vs. Realism" are implicitly solved by a new picture of what the mind is and what reality is. This will annoy professional philosophers. Physicists have more to say about this issue, resulting from actually examining the world rather than just thinking about it.
• IMR brings aesthetics, art and science under the same umbrella. This rows against the current fashion of considering such things as fundamentally incompatible ways of experiencing the world. For example, we can find "truth" and "beauty" in all three worlds using very similar criteria.
• My view of the self and consciousness is deeply informed by Zen. By this I don't mean that Zen is "right" but only that Zen is free from many of the misconceptions and fuzzy language that underpins the way most of us talk about the issues under discussion here. Readers not familiar with Zen (or its cousin "mindfulness") may find it worthwhile to take a detour to "wake up" to what they are actually experiencing day to day (the I world).

In line with Frank Wylczek, I take symmetry to be the key to usefully describing the "machinery" in all three domains -- an important criterion for what "works" and what doesn't "work":

• In the I domain, symmetry saves a lot of work by allowing us to work with "chunks" of ideas that don't change when we make "irrelevant" transformations. For example, we have an idea of our house which is the same house from any angle and over a long period of time.
• In the M domain, symmetric ideas have special appeal. For example, we like ideas that apply everywhere and at all times, like Newton's laws of motion. This illustrates the fact that an idea (meme) may be a "good" one (persistent) if it is symmetric but not strictly "right" in that it doesn't always map perfectly to the corresponding phenomena in the R world. "Good" ideas tend to spawn fruitful analogies - that is, they retain many of their essential features when they undergo the "like" transformation.
• Wylczek goes to great lengths to point out that there is enormous real symmetry in the R domain ("real world). In fact, he proceeds by assuming this symmetry then going out to find out if experiments agree with what such symmetry concepts (M world) will predict. A Scientific theory is valid if and only if predictions of the theory is isomorphic with results conducted in the "Real" world.

Dennett helps to free ourselves from thinking that someone must "have" ideas (M domain). As Plato suspected, the world of ideals has a life and existence of its own. We can thank Wylczek for drawing a clear line from Pythagoras to the Standard Model of Physics, illustrating the persistent idea that the world of memes (especially mathematics) is somehow real. For example, the number 321,534,332 has definite real properties even if nobody has ever thought of that particular number.  

Many authors have concentrated on the concept of "working memory" or "attention" as a surrogate for what we call "consciousness". However, when we read about this idea, the impression is created that the contents of "working memory" are somehow conjured up from what is sitting around in the brain (or possibly on the "live" channel to the outside world - the sensations). Here, we take a somewhat more dynamic and open-ended view. For example, 321,534,332 can be conjured up in the brain of the reader as a "chunk" to be divided by two, squared or verified as non-prime. This illustrates that the "chunks" of working memory (consciousness) are constructed on the fly. The brain helps with this process by providing all kinds of tools (What Dennett would call installed subroutines) but it is not correct to say that the mind is entirely an "epiphenomenon" arising in a few billion neurons. If it is an epiphenomenon at all, it arises from M and R through to a process in the brain.

It is worthwhile to come up with a temporary vision of what the M domain looks like. It's vast. it includes:

• Every book ever written or could be written in any language past present or possible.
• Every word in every language, along with their definitions
• All of Science, including all possible Science and all incorrect theory
• All of Religion
• Every possible sensation
• Every possible inference from sensation or theory (the result of any possible experiment)

As the name suggests, I'm temporarily trusting M to be the world of "memes", but I will have a lot to say about memes. They are not created equal. In a way, they fight for survival. In the language of IMR Symmetry, what they "fight for" is the ability to survive through time and through translation (installation) in many different brains (I-worlds). This is a form of symmetry - a form underlies "evolution" in the M-domain, just as Dawkins suspected in 1979 when he coined the term. Hopefully, our discussion of the M-domain will prove to be a contribution to the field of memetics - an attempt to nail down the "meme" concept with some semblance of rigour. 

In Surfaces and Essences, Hofstadter and Sander make a heroic attempt to show the key role of analogy in structuring human thought - in other words, a key role in the structure of M. They show how analogy plays a fundamental role in human language but also more complex structures of ideas, such as Scientific Theory. Our commentary on M will always keep this insight in mind: "Surfaces" provides powerful insight into the kinds of transformation that memes (ideas) can undergo through the process of analogy. Sometimes when we say A is like B, we are saying that A and B are isomorphic - for all intents and purposes, the same thing. This is another way of saying that the analogy transformation from A to B is symmetric. Other analogies are not so "powerful", extracting only a few properties common to A and B. In fact, we can put A and B in the same "category bag" arbitrarily without them sharing any properties at all. "Surfaces" is well worth reading as a brave attempt to map M. Is there more to say about M? I would say, yes. "Surfaces" is about one kind of transformation we can make on a meme. We are left asking about where memes come from in the first place and whether there are other kinds of transformation - especially transformations that claim to be strong mapping to R or "ideas" that can pop up in working memory (I).

As a career systems analyst, I have been particularly interested in the problems we face when mapping "real world" problems into the M-domain of the computer. We need to build a "model" of the real world situation in order to "computerize" decisions that ultimately have effect in R. One key insight in the last 50 years of the discipline is that our models should be, as far as possible, isomorphic with the entities we think exist in R. Strictly speaking, we have a conceptual model m in M that is usually thought of as "being" real. We need a machine version m*of m that is as isomorphic as possible (symmetric) to m. To do this, our model has entities corresponding to "real" things like "persons", properties of persons and transactions between persons. In the early days of computing, our models consisted of thinly disguised pictures of machine operations like "decisions", "calculations" and free-floating "data" such as integers and text. Today, all this is summarized by the Universal Modeling Language (UML). UML itself is a giant meme, which, when installed in the brains of human analysts, allows them to construct conceptual models in M that can be isomorphically mapped to real models in physical machines operating in R. Such models can turn out to have real impact on real people and other objects in R, such as the ability to drive cars in the real world or land real robots on the real planet Mars.

As a computer geek, I think of I-domain as a "virtual machine" simulating in M in the R-world "hardware" of the brain. "Chunks" of M (memes) are called into working memory either directly out of the brain (buffer to M) or "calculated" by programs installed in the brain from M. We can think of the dynamic aspect of I (he flow of consciousness) as a continual calculation - producing on set of "chunks"after another at a rate of a few cycles per second  For those of us who inhabit the "google sphere", we are familiar with the fact that we can "think" about "chunks" that can be instantly called up from the entire universe of human knowledge. In a profound sense, we swim in a world of information that is not somehow encoded in our heads. What I "know" and what "we" know is becoming more and more difficult to sort out. In fact, my model has no place for what "I" know - only what "I" am able to bring to mind at any particular moment. "I" am a virtual machine running in R, simulating M. I don't think of M as static either. Millions of people are churning away in M to bring new ideas to the surface. As Dennett has shown, ideas can float to the surface and acquire a life of their own even if nobody "has" the idea. Ultimately, the "affordances" of R (what is possible) strongly effect what "bubbles up" in M, so ultimately R has a strong influence on what happens in M. In particular, the process of evolution is a result of R "thinking" or conducting a program of R&D without anyone "having" the ideas behind life itself - ideas we find in "M". I and M also have their "affordances". Wittgenstein said that what cannot be said must be passed over in silence (commenting on what can arise in the language domain - part of M). We know that the brain cannot deal with more than a limited number (less than 10) of "chunks" at any one time.

In subsequent postings, I will flesh out the ideas of the I, M and R domains along with the idea that we best understand the relationship between these worlds in terms of symmetry. The analogy is with the success that such projects have had in reconciling the part of M called "Science" with experiments that confirm that our "Scientific" ideas map very well to the real world. The flagship example of this mapping is the Standard Theory of Quantum Mechanics, which so far maps to the real world to a precision of 12 decimal places or more. The success of this model has come in large part from the concept that the most useful ideas ("laws" in M) are the ones that are symmetric in some sense because it turns out that reality itself (R) is governed by symmetric principles. I claim that the most useful "chunks" to hold in memory are those that are in some sense "symmetric" and that the most useful ideas in "M" also have this property.