I love the question that's the title of this blog post. The question didn't come from me, but from David Wolpert. I learned about a paper he wrote when it was mentioned in a recent issue of New Scientist.
But there is a deeper question here: can we be sure that logic, even a reformed kind, is enough to understand the universe in all its fullness?
It is a question that David Wolpert at the Santa Fe Institute in New Mexico has been thinking about for decades. In a recent monograph, he spelled out his argument that it is more likely than not that there is some higher mode of logic that could be used to understand the universe, but that human minds wouldn't be able to grasp.
Just think of that humble linguistic device, the question. Wolpert says there are creatures -- things like a single-celled paramecium -- that couldn't conceive of the idea of a question. In fact, according to our standards of intelligence, every other species on Earth is limited in some regard in the way it understands the world around it.
Why should we be any different? "We are the paramecia," says Wolpert. "What is beyond us?"
Wolpert thinks there are ways we could potentially get at higher systems of thought that go beyond logic as we know it. Perhaps it will be a super Turing machine that can transcend the normal rules of computing or an intelligent form of extraterrestrial life that shares its wisdom with us.
Perhaps it will be something different altogether. And what will this new plane of understanding be like? "I can't conceive of it," says Wolpert. "But that's the whole point."
Wolpert's essay is 22 pages long, 30 including footnotes. I read it fairly quickly tonight. It deserves another reading. Maybe several readings. Parts are fairly dense, but most of the essay is understandable to anyone willing to make their way through some sophisticated thinking about the limits of human knowledge.
Here's a PDF file.
Download What can we know about that which we cannot even imagine?
lt's hard to disagree with Wolpert. Since every species on Earth is limited in its knowledge of what the world is all about, why would we humans be any different?
Here's a passage from the essay that I especially liked. Note: if you're a religious believer, or an admirer of mysticism, the same limitations of the human mind apply to you also. Meaning, even if you don't embrace logic or language as a guide to reality, you embrace some other human capacity, which leaves Wolpert's argument untouched.
To gain some insight into these questions, note that the highly limited form of all of human mathematics — sequences of finite strings of symbols — just happens to be exactly the structure that we humans use to converse with one another: the structure of human language. Indeed, starting back with Wittgenstein, it has become commonplace to identify mathematics as a special case of human language, casting its structure explicitly as grammar in the same sense as grammars arise in human conversation.
Note as well that it is a poetic cliche that libraries, and in particular mathematics libraries, are places where we converse (!) with past minds. The implication is that the contents of all the mathematics textbooks in those libraries is part of a conversation; i.e., an exercise in human language. Indeed, historically, mathematics textbooks and papers developed from written correspondence, i.e., from exercises in human language.
So, the form of human mathematics, and of our SAM more generally, just happens to exactly coincide with the form of inter-human communication. Some writers have pointed this out before, that human language’s design matches that of formal logic and Turing machine theory . They have taken this as a wonderful stroke of fortune, that we just so happen have a cognitive prosthesis — human language — that is capable of capturing formal logic. After all — they presume — this means we are capable of capturing all the laws of the physical universe.
A cynic might comment with heavy irony, “Gee, how lucky can you get? Humans have exactly the cognitive capabilities needed to capture all aspects of physical reality, and not a drop more!” This cynic might go on to wonder whether an ant, who is only capable of formulating the “rules of the universe” in terms of pheromone trails, would conclude that it is a great stroke of fortune that they happen to have the cognitive capability of doing precisely that; or whether a phototropic plant would conclude that it is a stroke of fortune that they happen to have the cognitive capability to track the sun, since that must mean that they can formulate the rules of the universe.
Sure, it’s possible that it is just a coincidence, that for some unknown reason the deepest nature of physical reality is expressible in terms of one of our cognitive prostheses. But it certainly seems as plausible that social computation is simply the most sophisticated cognitive prosthesis we have ever developed, and that even exploiting it to the hilt only allows us to capture a sliver of physical reality.
Yes, our science and mathematics — or more precisely, what they seem to be developing into — may be a complete description of what we understand physical reality to be. They might be developing into a complete description of what is experimentally accessible to us, even if only indirectly, both now and in the future [94, 95, 108, 109].
But in an exactly parallel manner, a putative ant- level theory of reality in terms of pheromone trails and environmental chemical signals could capture all that ants “understand physical reality to be”, of all that ants can “experimentally access”. And just as there is a huge expanse of physical reality lying beyond the charmed sliver that ants can conceive of, it may be that there is a huge expanse of physical reality beyond our ability to even conceive of.
After all, social computation — human language — was developed for communal sessions of shooting the shit around the campfire after a successful mastodon hunt (plus a few other purposes). There is no reason to believe that features well- suited for such exercises in nocturnal braggadocio can also be used to glean substantial insights into the shape of the hands of the Cosmic Baker, based solely on some crumbs we have discovered, scattered on their kitchen floor.