Wednesday, March 21, 2007

Perfect Symmetry or a Case of Mistaken Reality?

A long, long time ago, I was a college student. In 1976, I entered the University of Rochester extremely enthused about mathematics. I took two to three math classes in each term, and quickly moved into advanced subjects. Then during my second year, I discovered poetry, philosophy and politics. Mathematics instantly paled by comparison, and I shifted my course load (and extra-curricular activities) accordingly.

Imagine my surprise (and utter dismay) when, midway through my senior year, I got a call from the administrator at the math department. She told me in no uncertain terms that I would not be able to receive my degree in mathematics (hey, it was still my major!) unless I took one more course. And not just any course, of course. It would have to be a 300 or 400 level class. Oh, the agony! But I somehow muddled through and did in fact graduate in 1980 with a degree in mathematics with high distinction - I kid you not. There's no accounting for.....well concealed disengagement.

And off I went through a cascade of programming jobs, without a single conscious career choice, until I landed at Oracle Corporation and the rest, as they say, is my personal history.

Anyway....I mention all of that to show that I really did have a fascination with mathematics (more accurately, abstract thinking and symbolic logic), and that fascination survives to this day. It's certainly served me well in my chosen profession of programming. And lately, I have found my focus shifting from the abstract manipulations of formulas to the brain that performs these manipulations.

I am now sitting on a plane that maybe soon will take off and return me from San Diego to Chicago (the pilot just announced that a baggage handler banged his vehicle against a cargo door and bent some metal. They believe it is not structural and that they can fix it and we can be on our way. Sigh.....). While contemplating yet another seriously delayed arrival at O'Hare, an article in the NY Times Science section caught my eye. Titled "The Scientific Promise of Perfect Symmetry," the article describes the results of a collaboration among mathematicians: the full elaboration of the E8 Lie group. This elaboration involved the computation of some 200 billion numbers, resulting in an elegantly symmetrical form.

Yeah, right, whatever.

I am sure it is an accomplishment of the mind most remarkable, but what I found striking was the conjecture that this structure and the conclusions we (oh, you know, "we" as in those other humans who live in the world of string theory) can draw from it, may be helpful in understanding some fundamental characteristics of our world/universe.

And then I read the closing statement:

"It could well be E8 that determines the deep inner structure of the universe," Dr. Adams [professor of mathematics at the University of Maryland who led the project] said.

Several fibers of my being instantly rebelled. That statement, I believe, reflects a very deep arrogance and misunderstanding of our world. And I knew that you would want to know that I felt this way, and that you would now be on the edge of your seat, waiting for me to explain.


Here's my problem with such statements: mathematics, physics, etc. are incredibly powerful tools that help us figure out how to manipulate the world around us to meet our needs (make us more comfortable, make life more convenient, etc.).

But the theorems of mathematics and physics do not determine anything in the world outside of our heads. That world simply is.

Here's another way of considering my point: imagine for a moment that humans no longer existed in the world (given the proclivities of George Bush and his ilk, and the sadly weakened state of our democracy, this is not such a far-fetched idea). No more people. No more books, no more Internet. Got it?

OK, now ask yourself these questions:

* Would the deep inner structure of the universe still exist? I would say "yes". The universe, physical reality, would go on existing as it always has. It simply is.

* Would mathematics still exist? I would say "no." Mathematics has no existence outside of our brains. There are things in the world that seem to conform to various mathematical formulae, such as Fibonacci's sequence. But all that really confirms is that our brains, existing in the same physical world as flowers, planets and quarks, construct patterns along the same lines as other organic systems of the world.

* Would gravity still exist? I would say "no." Gravity is an explanation for why when we jump up into the air, we come back down to the ground. But there isn't really any such "thing" as gravity. It's an idea in our heads, and even if there is no brain to come up with the theory of gravity, when we jump up into the air, we will still come back down to the ground.

* Would the world go on, and likely in a much more sustainable and "natural" fashion? I would say "yes." Lately, in fact, I have found myself thinking: if insects disappear, the global ecology would be shot to hell. But if humans manage to snuff themselves (ourselves) out? I imagine there will be no great cataclysm.

I imagine you get the idea. And some of you are undoubtedly saying to yourself: "This is a ridiculous splitting of hairs." I beg to differ. I think that humans are all too enamored with themselves and have largely lost perspective on our place in the world.

We tend to lose sight that all of our scientific theories, our understanding of the molecular structure of the world, our explorations into the incredibly bizarre quantum mechanical structures are nothing more than mental constructs. They will never be anything more than mental constructs. How can they be anything but that? We look at the world around us, we take in that data, we identify patterns in that data, and draw conclusions about how the world works, in order to change the way we relate to that world. But the world simply is, simply "works," with or without us.

Having said that, I am not arguing that we ignore or reject these theories, nor that we should treat them on par with belief systems like "God created the heavens and the earth." Absolutely not. Scientific theories represent some of the greatest accomplishments of humanity. I, for one, have no interest in abandoning (all of) what we have learned and built. I like electricity. I like running water. I dearly love my low-flush toilet.

In contrast, organized religious belief systems, things we take on faith that are fundamentally irrational, are to my way of thinking inherently dangerous -- if they move from the personal, individual manifestation to the public sphere. I hope that someday we will consider them curious relics of a persistent but regrettable stage in our evolution towards truly civilized beings. [But I don't think we'll make it that far.]

The world exists, and we exist in it. We achieved self-awareness, and that great mystery allows us to utilize our brains in increasingly sophisticated ways to alter the world to suit our needs and desires.

And while I believe that the most arrogant statement a human being can say is "We are created in God's image," I would say that the declaration "It could well be E8 that determines the deep inner structure of the universe." does not trail all that far behind.


Unknown said...

Ahhhhhh... Now I see why you and I see eye to eye on many topics.. Philosophy is a wonderful thing. It allows each of us to stop thinking the way we have been told/trained and expand on our reality. It allows individuals to make decisions for themselves and decide on a personal level what they think is right or wrong. I think what amazes me the most about you is how you catch the subtle meanings in statements made in different mediums we have; tv, newspapers, magazines, etc. I hope the wait was not to long at the airport; hate the delays but thank god for reading material. Keep up the interesting blogging.

pathySR said...

It all come down to waves, man...

Unknown said...

I enjoyed reading this entry although I disagree with what you have said regarding the existence of gravity in the absence of man's perception of it.

As you rightly point out the established laws of Nature are used to determine regularities in Nature and not to impose our scientific structures on it. However, the regularity that we have labeled gravity would continue to exist outside of the existence of the label. You say there's no such 'thing' as gravity... I am saying there is a regularity of behaviour that exists. Just because we have lumped everything which makes up the regularity under one word doesn't render the underlying reality for the constituent parts as non existent. I feel you are being pedantic with semantics here.

The fact is, until some tangible proof comes along the philosophical "If a tree falls in a forest..." argument has no more validity than those who believe mathematics exists as part of the fabric of reality.

Put rhetorically isn't it interesting that you use logic (albeit via informal language) as a tool to make the point that logic doesn't actually exist in reality? Anyone for a dose of Russell's Paradox?