November 14, 2010

Toward Order

Justin Katz

Further to this morning's post about cultural expectations for geniuses, I offer the suggestion that true revolutionaries aren't creating innovations, but discerning them in the patterns of the reality into which they've entered. Physicist Stephen Barr notes the corollary in science:

As we turn to the fundamental principles of physics, we discover that order does not really emerge from chaos, as we might naively assume; it always emerges from greater and more impressive order already present at a deeper level. It turns out that things are not more coarse or crude or unformed as one goes down into the foundations of the physical world but more subtle, sophisticated, and intricate the deeper one goes.

Barr uses the example of marbles in a box: When the box is tilted to one side, the marbles take a hexagonal pattern implied by their inherent shape. The order that we see in the packed marbles was, in a way of looking at it, part of the genius in the invention of the sphere. Such are the building blocks of all of reality.

Two responses are common from atheists or mere secularists to the species of notions of which Barr's is a member, that reality is, in fact, a divine thought: Either we happen to inhabit the one universe (of some unknowable number) in which these rules apply, thus de-necessitating God, or we happen to be privileging concepts of order and beauty that we prefer, given the universe that we inhabit. The first rejoinder doesn't actually address the argument; it merely pushes it to another level. After all, even if it took some number of universal false-starts to create our universe, the possibility of our universe must have existed within the initial concept of the multiverse.

To answer the second objection, I'll return to Barr:

Some might suspect that this beauty is in the eye of the beholder, or that scientists think their own theories beautiful simply out of vanity. But there is a remarkable fact that suggests otherwise. Again and again throughout history, what started as pure mathematics--ideas developed solely for the sake of their intrinsic interest and elegance--turned out later to be needed to express fundamental laws of physics.

For example, complex numbers were invented and the theory of them deeply investigated by the early nineteenth century, a mathematical development that seemed to have no relevance to physical reality. Only in the 1920s was it discovered that complex numbers were needed to write the equations of quantum mechanics. Or, in another instance, when the mathematician William Rowan Hamilton invented quaternions in the mid-nineteenth century, they were regarded as an ingenious but totally useless construct. Hamilton himself held this view. When asked by an aristocratic lady whether quaternions were useful for anything, Hamilton joked, "Aye, madam, quaternions are very useful--for solving problems involving quaternions." And yet, many decades later, quaternions were put to use to describe properties of subatomic particles such as the spin of electrons as well as the relation between neutrons and protons. Or again, Riemannian geometry was developed long before it was found to be needed for Einstein's theory of gravity. And a branch of mathematics called the theory of Lie groups was developed before it was found to describe the gauge symmetries of the fundamental forces.

This is where this afternoon's topic ties in with this morning's: Pure mathematics are logic crystallized, and sometimes that logic leads to peculiar and seemingly irrelevant rooms, but those who discover those rooms needn't be nonconformist radicals. What's required for effective exploration of reality, in any field, is not a bumbling and callous rebellion, but a respect for the universe and human society as we find them, and what's required for a lasting and profound change in the physical and social order is not wholesale rejection of standards, but long-seeing comprehension of the paths that they naturally take.

Comments, although monitored, are not necessarily representative of the views Anchor Rising's contributors or approved by them. We reserve the right to delete or modify comments for any reason.

Good post, that.

Posted by: BobN at November 14, 2010 8:56 PM

"with 5 percent of the world’s population, the United States imprisons 25 percent of all humans behind bars" Glenn Loury
From OldTimeLefty

Posted by: OldTimeLefty at November 14, 2010 9:37 PM

Because we have a working criminal ustice system unlike some large,populous countries which allow criminals to operate openly,being unable or unwilling to deal with them.
Of course there are those communist/socialist paradises that OTL is so enamored of which merely have "re education centers".

Posted by: joe bernstein at November 15, 2010 12:19 AM

Please don't speak for me or put words in my mouth and I won't do it to you.

Posted by: OldTimeLefty at November 15, 2010 11:20 AM

OTL-you've been peddling your line here long enough so that it's hardly putting words in your mouth-your whole attitude is positive toward socialist regimes.
I've never read one critical word from you about them.

Posted by: joe bernstein at November 15, 2010 2:10 PM

Thanks, joe,
I provided a statistic showing that the U.S. with 5% of the world's population holds 25% of its prisoners. You dragged in an unseemly comment. No rebuttal, no confirmation, just a nasty comment not even to the point. You can have the last word on this as I do not wish to pursue a fool's argument. No, I'm not calling you a fool. I am saying that your argument here is foolish.
Your pal

Posted by: OldTimeLefty at November 15, 2010 10:37 PM

Like your oft repeated "freely assert,freely deny"mantra?
Really,does the fact that we hold so many criminals in prison indicate a problem with our society or with the individuals?
In a free society,we have the choice to follow the laws or not and deal with the
consequences of the latter.
It's not like we have thousands of political prisoners.Think Cuba,Iran,Venezuela,Myanmar-not all "socialist"but certainly not free societies.
We won't even discuss China.

Posted by: joe bernstein at November 16, 2010 8:21 AM


In answer to your question - it indicates a problem with our society. Does this mean that there are no nasty people out there; no it does not. The problem is poverty and grossly inequitable income distribution. We, you and I, have been thru all this before. One more set of stats:

In 2003 4,834 out of every 100,000 black males were sentenced to prison compared to 681 per every 100,000 white males and 1,778 per 100,000 Hispanic males.

There are also those who will argue that so many of the poor in jail are evidence of a subtle class warfare. We can take that up in another post, but to get back to reaffirming my answer to your question, the problem is systemic.

Posted by: OldTimeLefty at November 16, 2010 10:26 PM
Post a comment

Remember personal info?

Important note: The text "http:" cannot appear anywhere in your comment.