It seems spooky to suggest that mathematical entities actually exist in and of themselves. But if math is only a product of the human imagination, how do we all end up agreeing on exactly the same math? Some might argue that mathematical entities are like chess pieces, elaborate fictions in a game invented by humans. But unlike chess, mathematics is indispensable to scientific theories describing our universe. And yet there are many mathematical concepts — from esoteric numerical systems to infinite-dimensional spaces — that we don’t currently find in the world around us. In what sense do they exist?
Many mathematicians, when pressed, admit to being Platonists. The great logician Kurt Gödel argued that mathematical concepts and ideas “form an objective reality of their own, which we cannot create or change, but only perceive and describe.” But if this is true, how do humans manage to access this hidden reality?
We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.
This may strike you as very unlikely. But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not. If such simulations are possible in theory, he reasons, then eventually humans will create them — presumably many of them. If this is so, in time there will be many more simulated worlds than nonsimulated ones. Statistically speaking, therefore, we are more likely to be living in a simulated world than the real one.
Frenkel says that there may actually be a way to empirically test this theory.
This brings to mind the Oxford quantum physicist Vlatko Vedral’s idea that the entire universe should be understood as information. Excerpt from an interview with him:
Quantum physicists think of the universe as being made up of particles and strings. Are you suggesting that information is superior to these physical properties?
It depends on what you ultimately aim to explain. In science, we start with a certain basic set of laws, like the ones described by particle physics. These laws rely on quantum mechanics and relativity and so on. We start from them and try to describe everything else – subatomic, atomic, larger objects and, ultimately, the universe. But the simple question raised at the end is: where do these laws come from?
In science, we’re criticised for being unable to go beyond these laws to explain their origins. It’s what philosophers call an infinite regression: you give me an explanation, but I can ask where that comes from. We never seem to be able to end the list of questions. I think information is the only concept capable of almost explaining itself, of closing this circle.
How are you not conflating information with a God or another deity?
The common answer is that there was some kind of original creator of this information. The trouble is that this answer doesn’t really solve anything because as a physicist I’d also like to understand this being itself. I’d like to explain the origin of God. And then you encounter the same infinite regression. For a scientist, “Why is there a universe? Well, because something even more complicated created it the way it is” isn’t an explanation. We want a better answer than that. You can argue that science will never get there, that it’s an open-ended enterprise. Maybe this is faith.
But we also have a set of beliefs in science. We believe in one method of understanding the ultimate, secure truth: the scientific method. We make a conjecture. We try to refute it as far as we can. Those conjectures that survive longest are those that currently define the laws of nature. We’re not dogmatic about it at all; if you have compelling evidence that something is wrong, we are very happy to upgrade ourselves to the new theory. Of course you can always challenge me and ask why I believe this is the only way to understand the world. The only answer is that it makes sense to me. I find it better than anything else.
Vedral is still, as he reveals, a materialist; he believes human beings are nothing more than collections of atoms. I wonder what, if anything, could falsify that belief.
Anyway, the YouTube video I’ve embedded above is a 2011 discussion from the World Science Festival among physicists who theorize that the entire universe may be a giant hologram. I was there for the talk. Very exciting stuff. I know all of this material in this post is only loosely related, but related it is. I find it fascinating that Frenkel is able to openly discuss the possibility of a design written into the laws of the universe without causing people to freak out about a Designer. If he were working in evolutionary biology, I bet he wouldn’t have nearly that freedom of thought and speculative discourse.
Vedral claims to be able to answer the question, Why is there something rather than nothing?, without the need for a source of the Information, or a Lawgiver (in the sense of physical and mathematical laws). I don’t have the training to critically examine his claim, but I hope some of you do, and will let us know what you think.