Summary April 4, 2019

BOXES

One fanciful vision of the (flat) Earth was that it was supported on the back of a turtle, which was, in turn, standing on another turtle and so on: Turtles all the way down.

Similarly, I find it useful to think of "boxes within boxes all the way down." Box 1 is the world we experience "in our head," which includes all experience and everything we know. In particular, it includes what we have been taught and what we have been taught to assume, which is, to a certain extent, "programmed". Box 1 is the "matrix" of individually shared reality. But, unlike the Matrix of Science Fiction fame, our matrix depends deeply on the "real world" outside and our senses within, as eloquently explained by Antonio Damasio.

Our evolutionary survival strategy involves survival as a member of a group, or "super person". Not only do we not "think for ourselves," we can't.

We experience ourselves as objects in the world (that's me) and assume that the world exists without us. It has been here long before we were born, will still be here long after and exposes only a tiny amount of itself to our investigation. This is "Box 2". Box 2 is contained in Box 1. Thinking in "box 2" terms, we recognize that other people exist and that they have an internal world - their "Box 1" which is, to us, Box 3. Of course, there are billions of Box 3's, including Box 3's that belonged to people long dead. We are in "Box 3" when we say things like "I know what he's thinking". Language uniquely provides access to Box 3, when we ask things like "What do you see" and expect an answer that makes sense. It can get pretty crazy. It makes sense to ask if Galileo correctly understood the discoveries and system of Kepler (he didn't). In a similar vein, we can ask of the Church threatened Galileo because of his beliefs or because he was, according to what was known at the time, wrong. All this depends on an acceptance of the fact that each of us lives in our personal "Box 1". This is an unavoidable consequence of our nature. It follows that persecuting an individual for his beliefs is misguided since nobody really "thinks for themselves."

When we are speaking of experience or "external reality," we need to be aware of which "box" we are speaking from. For example, statements about objective reality belong in Box 2 and should not contain "mind-like" concepts like the "laws" of physics. Laws of physics belong in Box 1. They are statements about our experience of the world.

I allow for "Box 0", which is the hypothetical and unobservable world - beyond the reach of our cleverest instruments, observation or reasoning. Like Box 1, Box 0 is relative. We are always biting chunks off Box 0, but we must admit that there are things we will never know about the Universe. At the very least, we must, as individuals, recognize that almost all of Box 0 is beyond what we will ever understand. I assume that "Box 0" exists even if there are no observers anywhere - the situation we assume at the time of the Big Bang and millions of years after that.

I regard all of mathematics as being in "Box 1" as something "mind like." This stands against the common intuition of physicists that the Universe is somehow fundamentally "mathematical" and that we are "discovering" mathematical laws that exist apart from our minds. This assumption is certainly worth challenging, but it's good to make it explicit. Similarly, any statement that includes an "observer" or an "apparatus" is a statement in Box 1, not Box 0.  As far as I know, such "mind like" concepts can be removed from relativity and quantum mechanics without losing anything but hooks for idle philosophers to make their speculations sound "scientific."

"Theory of Boxes" takes a dim view of theories that attempt to explain either of these questions:

• Why is there anything?
• Why does it feel like something to exist (Chambers "hard question")

I am greatly aided in this skepticism by knowing that not all perfectly sensible questions have answers.  While it has not been proven that either of the above questions is formally undecidable, I think it's reasonable to think of them in this way until some future genius settles the matter. For now, at least, I proceed on the assumption that we have something called "experience" and that it is an experience of something other than ourselves. Not much of a stretch I think.

THE INTERFACE

In effect, what we call "mind" is an interface between the "real world" and "Box 1". You could say it's responsible for creating the whole stack of boxes. It is worth asking how it does this, which boils down to curiosity about neuroscience - the brain. More subtly, it involves asking about the nature of the universe we inhabit and what it takes to survive in it.

In this area of concern, we also consider how the interface is "programmed" by language and other cultural factors. Analogy plays a key role here, as outlined in "Surfaces and Essences". A key concept in that books is "isomorphism" - the idea that some analogies are better than others. In fact, the best ones allow us to learn about one system from the properties of another. For example, we assume that objects in the universe behave as if they "obey" laws of gravity (mind-like ideas). Thus, we can predict how objects will behave (say the date of an eclipse) by working out the math in the model. On a broader scale, we can ask which of our ideas genuinely underpin reality itself, the subject of "A Beautiful Question".

Evolution has gifted humans with an obsession with "figuring out what's really going on". Many of our guesses are wide of the mark and wind up as "mythology". Some are impressively robust and useful - they are called "Science". So far, we can't be sure how closely our ideas mirror the "real world", but we can help ourselves by keeping in mind the difference between our ideas (mind-like) and the actual reality we attempt to approach.

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".