Alien Mathematics

[Sternwallow]

If you think mathematics would only be different in notation, try to unscramble an APL program. APL was the most mathematically-based language of its time. What, for instance would you make of "|/M" (modulus reduction of arbitrarily dimensioned structure M along its first coordinate).

Your ordinary alien has four fingers on one hand, six on another and three on the third. There are three hands on each of five arms so our creature uses a mixed-radix system which, good luck deciphering from their notation which is expressed in interfering wavefronts of infra-sonic sound impinging on plates with sand sprinkled on them. Lovely patterns, by the way. I can see them when I take off my tinfoil yarmulka.

Sternwallow wrote

If you think mathematics would only be different in notation, try to unscramble an APL program. APL was the most mathematically-based language of its time. What, for instance would you make of "|/M" (modulus reduction of arbitrarily dimensioned structure M along its first coordinate).

Your ordinary alien has four fingers on one hand, six on another and three on the third. There are three hands on each of five arms so our creature uses a mixed-radix system which, good luck deciphering from their notation which is expressed in interfering wavefronts of infra-sonic sound impinging on plates with sand sprinkled on them. Lovely patterns, by the way. I can see them when I take off my tinfoil yarmulka.

OK, Grump, but I still think they would have to understand physics, and mathematics is the language thereof, to get into space. "***" help us if they came pushing their own brand of "***", and anyone who did not accept "***" got a fnorking in the ombulous. :o

Tenspace wrote

Fingers?

How do we know they're not tentacles, or tractomorphic patches of luminescent white marshmallow skin?

Mmmm, exactly.

[Mog]

Sternwallow wrote

If you think mathematics would only be different in notation, try to unscramble an APL program. APL was the most mathematically-based language of its time. What, for instance would you make of "|/M" (modulus reduction of arbitrarily dimensioned structure M along its first coordinate).

Your ordinary alien has four fingers on one hand, six on another and three on the third. There are three hands on each of five arms so our creature uses a mixed-radix system which, good luck deciphering from their notation which is expressed in interfering wavefronts of infra-sonic sound impinging on plates with sand sprinkled on them. Lovely patterns, by the way. I can see them when I take off my tinfoil yarmulka.

I'm not sure it matters how complicated their bodies and senses are. The important thing is if they would come up with or at least recognize the binary number system. I think the occurrence of dualism in nature requires it.

[Philboid Studge]

John Gribbin theorizes that if there hadn't been a big fat meteorite 65 million years ago, then the Saurornithoides dinosaur would have evolved to be the intelligent life on Earth. It weighed about 50 kg, and had a brain-to-body wt ratio like modern baboons. It was also bipedal, and with four fingers on each hand (actually two fingers and two thumbs). Of course, it would have developed a base-eight arithmetic. And, had it followed an evolutionary path anything like hominids', its civilization would have developed space-flight 60 million years ago.

[Tenspace]

Is he the guy with the lizardman statue in his office?

[Sternwallow]

Mog wrote

I'm not sure it matters how complicated their bodies and senses are. The important thing is if they would come up with or at least recognize the binary number system. I think the occurrence of dualism in nature requires it.

I think that mathematics can take many forms both in notation and concept. Your aliens may have based all of their math on the "Yes, No, Maybe" of Fuzzy logic. And while we certainly can understand fuzzy logic concepts and operation, we might well not be able to recognize it under an alien representation system.

[anthonyjfuchs]

DJ KAPUT wrote

If we were to find life on another planet at least advanced as ourselves or more so...

Well, let's be perfectly honest: if there is any consciously self-aware life in the universe that is at least as advanced as ourselves, it will probably find us first. And it will probably consider us inferior lifeforms unworthy of its time and energy. Any species that believes in the kind of superstitious fairy tales to which humans cling doesn't rank very high on the universal intelligence scale.

As to their mathematics, even if it's nothing like our system, the nature of numbers indicates that, with a little work, we'll be able to translate seamlessly between the two systems.

[a different tim]

There are SF short stories about this kind of thing (the best of which is probably Greg Egan's "Luminous" - he's sound on the whole religion question as well and I strongly recommend him to those of you who like me are are SF geeks readers). I think that, as there's a lot of maths we don't know, there's likely to be a lot of maths that any putative alien would know, but we don't. Like, an intelligent gas cloud or something might have an incredibly advanced understanding of, say, set theory, but arithmetic might be this arcane and little understood discipline (assuming that we developed arithmetic from counting solid objects). So they may not have a system of numbers as such.

It's also possible (I think) that a mathematics inconsistent with ours might exist - that seems to be an implication of Godel if I understand him correctly.

Philboid Studge wrote

John Gribbin theorizes that if there hadn't been a big fat meteorite 65 million years ago, then the Saurornithoides dinosaur would have evolved to be the intelligent life on Earth. It weighed about 50 kg, and had a brain-to-body wt ratio like modern baboons. It was also bipedal, and with four fingers on each hand (actually two fingers and two thumbs). Of course, it would have developed a base-eight arithmetic. And, had it followed an evolutionary path anything like hominids', its civilization would have developed space-flight 60 million years ago.

Now THAT explains where the cocksuckers went! How do we know they really didn't? Have you found proof in the geologic column?!? [/Salty]

[Sternwallow]

logarithm wrote

Now THAT explains where the cocksuckers went! How do we know they really didn't? Have you found proof in the geologic column?!? [/Salty]

Yeah, maybe they are the guys who really ran those defunct underground nuclear reactors that were found in Africa and labeled "Natural". Maybe they got to be as intelligent as we are, started a war they couldn't finish somewhere northeast of the Nile and killed themselves off with preemptive nukes.

Oz wrote

I imagine the biggest difference would be the base of their number system - ours is base ten, but how many fingers do these aliens have?

In Childhood's End, the aliens based their math on 12. I didn't know if it was because they had 12 fingers but it got me thinking. Is there a better number for man to base their arithmetic on? Hell, is any number better than another? Well after a few minutes of pondering (yes, only minutes), I came upon what I think would be the perfect number: 8

With 10, you can only break it down to 5 and when you multiply 10x10=100, 100 can be divided to 50 then 25 and that's the end of it. But with 8, you can break it down all the way to 1. And 8x8=64. 64 breaks to 32, then 16, then 8 all the way back to 1. I think an alien race, if it was more intelligent than us, would have picked this up and gone with it instead of just looking at their hands.

[Sternwallow]

ArchyDeluxe wrote

In Childhood's End, the aliens based their math on 12. I didn't know if it was because they had 12 fingers but it got me thinking. Is there a better number for man to base their arithmetic on? Hell, is any number better than another? Well after a few minutes of pondering (yes, only minutes), I came upon what I think would be the perfect number: 8

With 10, you can only break it down to 5 and when you multiply 10x10=100, 100 can be divided to 50 then 25 and that's the end of it. But with 8, you can break it down all the way to 1. And 8x8=64. 64 breaks to 32, then 16, then 8 all the way back to 1. I think an alien race, if it was more intelligent than us, would have picked this up and gone with it instead of just looking at their hands.

An alien race did choose a different base number than 10, they picked 16. 16^2=256 which is a very convenient value for representing character sets, angles (instead of degrees) and lots of other small sets of things. 16^4=65536 which can easily represent many of the values we use daily (especially when it is configured as -32768 to 32767). 16 has the same break-down properties you mentioned for base 8. The aliens I'm referring to are terrestrial computer geeks. They find their extra six digits in letters. 10 is called "Alpha", 11 is called "Bravo", 12 is called "Charlie", 13 is called "Delta", 14 is called "Echo", and 15 is called "Foxtrot". These are the phonetic letters used by the military.
"0123456789ABCDEF" works just fine for math and it has the advantage of being easily represented inside the computer in 4 bits.
Want to know the binary version of "1947C"? "0001 1001 0100 0111 1100". In decimal, of course, it is
"(16*(16*(16*(16*1)+9)+4)+7)+12" or "103548"