Science is cool. In recent centuries, it’s become a profoundly transformative force in the world. Just think of all the electronic toys, space stations, skyscrapers, you name it. Naturally, math is a key part of this. It’s really hard–essentially impossible–to imagine physics without math. Not without justification is it called “the language of science.”
But sometimes, scientists and mathematicians get a little too cocky about the ontological status of their claims, confusing reality with our cognitive simulacra of reality, in other words, our knowledge of reality. Take a look at this article from New Science, “Mathematics: The only true universal language.” It claims:
If we ever establish contact with intelligent aliens living on a planet around a distant star, we would expect some problems communicating with them. . .However, the surest common culture would be mathematics.
Why? Because, the argument goes, the one and only thing we can be sure that we have in common with aliens, if they are out there at all, is that we’re real. Everything else about them may be a total mystery, but if they exist, and we exist, then both we and they are undeniably real. If math describes reality, as the article’s author suggests, then they would have to have the same math we do. They might know more or less math, but the nature of their math would be identical to ours. Probably with different symbols, but it would be the same underlying concepts. So we could at least count on that.
Is this right? No. Here’s why.
In presuming that we and the aliens share at least math, we’re making an unwarranted assumption that their minds are like ours in at least one other respect, besides the fact that they are real. The assumption is that they do the kind of symbolic reasoning that is the basis of our math. But why presume that? Abstract reasoning is supposedly the seat of our intelligence, the basis of logic, math, and language; but why insist it be the only possible one? Extrapolating that from a sample of one–us–hardly seems scientific. No trend there.
What if there is some cognitive activity or state that we can do, but they can’t? Or vice versa? Or both? Surely that’s a very real possibility. One species may insist the other isn’t truly intelligent, but on what grounds can either insist that? We have our kind of cognition, but how can we presume what aliens would have? It could be literally unimaginable.
It may be that there are real things that cannot be the object of our contemplation. A man named Gregory Chaitin may have successfully proved just that in the mathematical object known as Omega. This is a real number having complexity that goes beyond what any conceivable mathematical system–at least, math as we conceive it–can describe. Omega is a great example of visiting the edge of logos. Maybe the best example.
How can Omega exist if math was really the language of nature? How could some words of that language be beyond our ability to speak or write? And if there are things that are real that are beyond our comprehension, what’s to say that they are necessarily beyond the aliens’ ken as well? Maybe they have the right kind of mind for that domain of reality. Maybe they can get to Omega, even if we can’t, just as we have cognitive powers not found in cats. And conversely, maybe we can get to real things they can’t. What if they have language and consciousness–and are therefore able to communicate with us–but can’t conceive of natural numbers? How could their math be the same as ours without that? It would be naive to expect that their intelligence would map precisely to ours in every single respect. There’s no reason to think of cognition as an all-or-nothing phenomena; just think of how much mental phenomena we share, and don’t share with other animals. One might expect even bigger surprises with aliens that evolved elsewhere from a different tree of life.
The error is one of attribution: trying to make a metaphysical truth out of an epistemological one. Math may be the language of science, but science is a conception of reality. Science is what we know of reality, but it is not reality itself. So don’t confuse the menu with the food. Math is not the language of reality, so you can’t use it to pin down the aliens. It is the language of our scientific knowledge of reality.