I think SETI’s bet is a good one regarding mathematics. I suppose its entirely possible that there could be a sentient being with such a drastically different way of conceptualizing its existence that it doesn’t have any concept of math that’s analogous to ours – but in that case it seems impossible that we could communicate with them, and indeed unlikely that we would even recognize each other’s sentience.

Also one of the most divisive – a lot of people hate it, I suppose because they can’t get over the inherent silliness of the dialogue. But too bad for them, because it is indeed awesome.

It’s not about addition and subtraction or imaginary numbers or anything. That comes later.

The point lies in a simple concept: the idea of one.

That is the only thing that we can reasonably expect to have in common with another sentient life form, since that is essentially our definition of sentience: the ability to recognize one’s self as separate from one’s environment. From that recognition springs the actual conceptualization of separate objects, and thus it forms the basis of all consciousness and communication.

Once you have “one” you realize you have two and three and four as well – but we use arbitrary symbols for those, so we can’t use them as a basis of communication. However, establishing a symbology for 1 and not-1 (or zero) seems like something that can be done across language barriers – thus the choice of binary code for this communication.

Once you have “one” any advanced species is likely to arrive at all the same mathematical concepts we have (after all, we had most of the core ones figured out long before we even conceived of radio waves or any other form of long-distance communication) – and yes that includes imaginary numbers, or a different mechanism for representing what they represent. They may seem rather strange because they occupy a weird spot that is sort of shoe-horned into our symbology – indeed it is possible that another species would have developed a system in which they are more intuitive – but they are not arbitrary: they represent an inevitable consequence of numbers – inevitable all the way back to that initial idea of “one”

There is another TNG in which Picard taps out prime numbers on a keypad to ensure his unseen captors know he is intelligent and not simply an animal of some sort. That is a very significant idea: prime numbers are something that would be impossible to not notice once you start multiplying and dividing, so regardless of what names you give to all these things, someone counting out “1, 3, 5, 7, 11” would be a recognizable pattern.

Math is a funny thing, because it is both arbitrary and not arbitrary. Many of the “rules” are indeed invented by people – but they are not invented just for fun, they are invented to create a consistent system for describing patterns. One great quote about math: “the fun thing about your creations is that they talk back”. And that’s just the point: the moment you have the idea of “one”, it begins talking back to you, and demanding a more complex language for the dialogue – so before long you have prime numbers and imaginary numbers and limits and set theory and all that other fun stuff.

Seedless or regular?

And yeah, “Who Watches” is better, and in fact one of the best – no argument there.