It happens again and again that, when there are many possible descriptions of a physical situation—all making equivalent predictions, yet all wildly different in premise—one will turn out to be preferable, because it extends to an underlying reality, seeming to account for more of the universe at once. And yet this new description might, in turn, have multiple formulations—and one of those alternatives may apply even more broadly. It’s as though physicists are playing a modified telephone game in which, with each whisper, the message is translated into a different language. The languages describe different scales or domains of the same reality but aren’t always related etymologically. In this modified game, the objective isn’t—or isn’t only—to seek a bedrock equation governing reality’s smallest bits. The existence of this branching, interconnected web of mathematical languages, each with its own associated picture of the world, is what needs to be understood.
Now, is that because Wittgenstein helps us understand reality as it is? Or is that because we understand reality as it is through the ideas, now, of Wittgenstein? Did he, in other words, discover something true about reality? Or do we interpret reality because of the influence of his ideas on our discourse? And even if one answer "extends to a deeper or more general description of reality," does that mean that answer is right? When I studied the New Testament under a member of the Jesus Seminar (ask your grandpa, punk!), he taught us the probabilities (not mathematical!) of statements in the Gospels being the authentic words of Jesus of Nazareth, and how the Seminar decided which words were invented, which were distorted, and which were closest to the original speaker. And it was all, of course, a matter of interpretation and argument. Where is the hard reality? Somewhere in between, just as the nature of God and God's revelation is known, not in the words of Scripture, but in the interpretations of Scripture, and the interpretations of those interpretations, and the interpretations of the interpretations of the interpretations. It's turtles all the way down!, although in this case the description applies to the Midrash of the Hebrew Scriptures, not to the failure of "religion" to be a "hard science."
It’s for this reason that Paul Dirac, a British pioneer of quantum theory, stressed the importance of reformulating existing theories: it’s by finding new ways of describing known phenomena that you can escape the trap of provisional or limited belief. This was the trick that led Dirac to predict antimatter, in 1928. “It is not always so that theories which are equivalent are equally good,” he said, five decades later, “because one of them may be more suitable than the other for future developments.”
Or, as the E&R church put it long ago:
Grant that thy Church may be delivered from traditions which have lost their life, from usage which has lost its spirit, from institutions which no longer give life and power to their generation; that the Church may ever shine as a light in the world and be as a city set on a hill.
HEAR OUR PRAYER, O LORD.
Which sentiment is the illegitimate rewriting of rules to suit changed circumstances, and which is the legitimate alteration of understanding to fit new insights and discoveries? This, for example, is something I've always understood about philosophy and theology; that is, that you can't discard the ideas you don't like and simply replace them with those that you do, or ignore new ideas because they challenge your preferred notions:
Take general relativity. Physicists know that Einstein’s theory is incomplete. Yet it is a spectacular artifice, with a spare, taut mathematical structure. Fiddle with the equations even a little and you lose all of its beauty and simplicity. It turns out that, if you want to discover a deeper way of explaining the universe, you can’t take the equations of the existing description and subtly deform them. Instead, you must make a jump to a totally different, equally perfect mathematical structure. What’s the point, theorists wonder, of the perfection found at every level, if it’s bound to be superseded?That last, of course, is the question of philosophers and theologians for millennia. In theology it's the source of humility (one; theology itself should be founded on the humility of the servant, but that's a theological issue, too). And this is where it really seems religious (although this thinking may simply be founded in Aristotle's conviction that all things have a telos; but then were does that telos come from?):
It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation. But what might such an explanation look like? One common conception of physics is that its laws are like a machine that humans are building in order to predict what will happen in the future. The “theory of everything” is like the ultimate prediction machine—a single equation from which everything follows. But this outlook ignores the existence of the many different machines, built in all manner of ingenious ways, that give us equivalent predictions.Oddly, this language sounds extremely religious to me, too; but maybe that's because I know the work of the Christian mystics, and am inclined to hear echoes of the Cloud of Unknowing (which I understand not as beyond knowledge, but as actually shedding knowledge in order to...well, know):
So is the question "God"? Or "42"? The question to which the universe is the answer is not really a religious question, since religion is not really concerned with "why" on that scale, or more accurately, in that language game. And which language game is physics going to play now? Because this is all getting very Godelian, too.....
Arkani-Hamed now sees the ultimate goal of physics as figuring out the mathematical question from which all the answers flow. “The ascension to the tenth level of intellectual heaven,” he told me, “would be if we find the question to which the universe is the answer, and the nature of that question in and of itself explains why it was possible to describe it in so many different ways.” It’s as though physics has been turned inside out. It now appears that the answers already surround us. It’s the question we don’t know.