ET Math: How different could it be? - John Stillwell (SETI Talks)

SETI Talks archive: http://seti.org/talks

We like to think that intelligent aliens would have the same basic ideas about numbers and geometry as us, but, even if they do, they might express those ideas very differently. To illustrate what different forms a concept can take, I will show how differently the law ab=ba has been interpreted at different times in human mathematical culture. This seemingly basic law has several different origins -- in geometry, number theory, and set theory -- some of which seem alien even to experienced mathematicians.

Category:

Science & Technology

Tags:

• John Stillwell
• seti
• math
• Mathematics
• et
• Space
• carl sagan
• seti institute

[Zurround100]

The way we think about math changes even on Earth from culture to culture BUT actual math is the same EVERYWHERE in the ENTIRE UNIVERSE.

[AzraelAscoli]

@CentralConundrum Lol nice one...

Heh stop it with anal"yisis, even if it is functionnal against aliens. One thing those aliens do not have and will never have is Bourbaki. You could throw at them one of their tomes, theory of sets for example... Or make them read the article by Carleson-Benedicks called strange attractors and see if their head explode.

But I give it to you, Dunford-Schwartz is a good choice... infinite dimensional ergodic theory at its worse.

[AzraelAscoli]

@CentralConundrum Of course it is :P and by the way uniformity is also a transversal concept, equicontinuity much less.

Also, most of the time, when a proof is technical or boring what it really means is that the result associated to it is still not well understood: that there is still lots of margin for improvement. Or, that there is a much cleaner proof in a higher theoretical setting. But please do not get me started on this subject.

[AzraelAscoli]

@Icix1 I concure. The way the humanity discretize things is profoundly related to our senses and our physiology. It is related to the symmetries in our world, which is itself related to the great stability of our solar system. Breack the symmetries, instill a little bit more fluctuations and there is no reason why a civilization would find reals or hyper-reals a more adapted tool for their numbering. They would find out about integers, eventually, but it might be unatural for them.

[AzraelAscoli]

Not to say that this is obviously a talk for non mathematicians. It is quite incorrect to say that commutativity has many different origins. Commutativity is a concept that is transversal to many theories which has many different expressions some of which we probably do not even dream yet. In its own way, like duality and dimension it is a very abstract and universal concept. The theory of categories is one of the first steps we have made towards unifying these concepts.

[AzraelAscoli]

ET math will never be much different then ours for two very simple reasons: classification and invariance. More precisely, their applied mathematic, their engineering might be very different then ours but pure mathematics, i.e the reason why everything sticks together and is coherent as a whole is something totally independant of our normal perception. Take the simple example of the concept of duality: this is a tool transversal to all mathematics.

[sbergman27]

@0BSRV It's not about the math being different, but about how they might approach & think of it. For one thing, if they have 12 fingers they're likely to use a duodecimal system. If their place of origin is subject to very high gravitational fields then euclidean geometry might not have been their first. That last might seem contrived. But it convey's the idea that their textbooks may not be Sallas-Hille. Math has an infinite domain. Subjectively, we consider certain bits to be most significant.

[sbergman27]

@Gameboygenius Srinivasa Ramanujan

Wikipedia article at:

tinyurl . com / ttysh (remove spaces)

[Gameboygenius]

Could someone give me the correct spelling of the name of the mathematician mentioned at near the end, e.g. at 1:03:32?

[sbergman27]

@Icix1 Don't be so open-minded that your brain falls out. You're taking the "we know nothing!" idea a bit far. Any intelligence that *has* math is going to have to understand that some concepts are meaningful only in integer quantities. I could maybe buy that some intelligence might not understand non-integers. But integers are bedrock. That concept is literally built into the fabric of our Universe, from the level of the quantum up.