A Little More Everything

A few weeks ago I wrote a post suggesting that the mathematical concept of zero may interfere with our understanding of the physical world around us.  Because of zero, maybe we believe that there's a smallest thing--that there's a floor, a hard limit on the low end of sizes, distances, and quantities--when in fact, that may not be true.  Every point of matter--every atom--may contain infinite regress within it.  Or... the concepts of "large" or "small" or "inward" and "outward" may simply not be well-founded.

Just after writing that post, I caught Radiolab's "The Trouble with Everything."  In the second half of the episode, Radiolab co-host Robert Krulwich argues with Columbia physicist Brian Greene.  Now that physics suggests that there may be infinite possible universes (there's no reason to think that the big bang happened only once, in one location, i.e., our universe), Krulwich argues, the dream that Physics can lead humankind to an understanding of everything is out the window.  In other universes, the underlying physical laws of our universe may not apply.  More importantly, we have no way of ever observing or gathering data about these other universes, so we can never know.

Greene sticks to his equations, though, and claims that Physics is the logical pursuit that leads us to understandings like gravity, the solar system, the universe, the big bang, and now the multi-verse.  It's only because of "the equations" that we're able to know these things at all, and so it's only logical to continue to believe that by following "the equations" we will continue to be able to know more and more and, eventually, know everything.  Greene and Krulwich debate the merits of this Greene's Enlightenment-era confidence--ultimately debating whether Physics is really a logical inductive pursuit or a nearly religious process of deduction.  While neither persuades the other, I think that Greene makes a couple of interesting concessions:

1. "I do have a deep faith that the universe ["call it the multiverse," he later says, "or whatever word you want to use"] is coherent." 
2. And somewhat cartoonishly: "It may be the case that when we talk to those aliens that we encounter one day and they say, 'all right, show us what you got,' and we bring out our equations, they kind of laugh at us and say 'oh, you guys are still stuck on math?'  Yeah, 10,000 years ago we were doing math, too, but here's the real way of describing it."

I think most people live fairly comfortably with the idea that language is an arbitrary system of signs--that there's no inevitable reason why the word "tree" is assigned to large-ish rooted vegetation, and that there's no inevitable reason why we have words for the things we have words for, and not for other things.  Ultimately, we're immersed in our language systems, and much of our ability not only to communicate but to think and perceive in the world is based on that language.  Maybe there are things we can't say.  Maybe there are things we can't see, really, or understand, because we don't have the language system for those things.  I think most people can handle this idea.

But the idea that math may be an arbitrary human system is different.  Most people, I think, believe that math is woven into the "fiber of existence" or something like that, and that Physicists are discovering math rather than applying it.  Greene's second comment suggests the more likely truth, that math is a human system, like language.  Because calculations work in practical ways, we rarely consider that its human origins may place limits on the system.  Georg Cantor approached understandings of how the idea of infinity at all points stressed the numerical system near to breaking--perhaps beyond breaking: the idea certainly broke Cantor's mind.  And Greene, in his cartoonish way, is getting at that point.  Math is a very powerful human tool, but faced with the possibility of other universes in which the basic laws we know may not apply, we have to admit that math may in fact be just as contingent as language.  Math may not be the measuring stick for the universe, the key to unlocking everything.

And the first item--Greene's "faith" in "coherence"--seems very close to an admission that his discipline really has no ground to stand on outside of the ground it creates for itself.  It's an admission, basically, that Physics is deductive: that the idea of organizing principles precedes inductive observation, and that therefore the scientific method, useful as it is, does not mark a pathway toward transcendent knowledge.  That's fine.  No big deal.  Since Heisenberg, most disciplines have accepted the limitations of their methodologies.  The idea of "knowing everything" has come to seem like a relic of the "Age of Enlightenment."  It's strange, in 2013, to hear a thinker as advanced as Brian Greene admit to "faith" while insisting on the impenetrability of logic.

Every discovery leads to another question.  Every infinity, outward or inward, is subject to the child's play of "infinity plus one."  Can we know more?  Of course.  Can we know everything?  To me, the evidence suggests that obviously we can't.  But... I'm not Brian Greene.