Mathematics An Alien Language?

[Alex K]

If aliens had their own mathematics, wouldn't it be based on how many fingers/tentacles they have?

Ideally, they would use properties which do not depend on the choice of base of your numerical system. Just as an example: the Number 13 in decimal is a prime, as are the number D in hexadecimal, or the number 1101 in binary.

We can discover certain properties of pi which are independent of the base. No matter whether hexadecimal or decimal, pi has an infinitely long representation which does not repeat, for example. If there are features in the number pi which become particularly visible when using base 100 (a message from the centipede race), then we could in principle find them as well.

[Little lunch]

Yeah, thanks for those examples,Data, but aren't you needed on the bridge? ;-)

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That was a bit rough.
My brains only half yours, so take it easy on me. :-)

[Mudhammam]

A somewhat more plausible scenario to me would be the aliens didn't so much encode the mathematical message for purpose of information transfer, but rather adopted numerous repetitions of one specific construct out of many possible for efficiency and ease in designing and manufacturing our universe. This would be sort of like using a standardized screw in a machine even when slightly larger or smaller screw might have served each use in that machine better. The purpose isn't to communicate to observers of the engine. It is to ease the design and manufacturing of the engine, as well as later tinkering.

Awesome, let's throw fractals in the mix

I like the way you two are thinking!

[Alex K]

I like the way you two are thinking!

I'm a total sucker for that kind of stuff made into fiction!

[Smaug]

If aliens had their own mathematics, wouldn't it be based on how many fingers/tentacles they have?

I'd call the original idea science fiction because that's the genre it would be sold as if it was a book or movie.

The arythmetics are most likely to be based on this. Math in general becomes more complex and abstract throughout it's developement but historically it appears as a reflection of the most basic properties of physical space. These properties manifest themselves first and foremost as basic axioms and mathematical operations. For example Euclidean geometry and it's axioms and rules (parallel lines don't intersect, sum of angles in a triangle always equals to 180 dergees, the definition of Pi, vectors, dot product and general properties of measures etc.) basically reflect one of the most simple (in tems of locality and absense of curvatures and irregularities) ways of understanding of physical space.

[Surgenator]

If aliens had their own mathematics, wouldn't it be based on how many fingers/tentacles they have?

The human species have used base 60, and 20 in the past. Computers use base 8,16,32, or 64. Some electronics use base 14. So the number of fingers or tentacles doesn't necessarily lead to the base people use.

[I_am_not_mafia]

By the way, I'd say that the existance of numerical methods is one of the best examples of the limits not only of the means of computation but also of Math itself.

I'm remembering that one!

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If aliens had their own mathematics, wouldn't it be based on how many fingers/tentacles they have?

The human species have used base 60, and 20 in the past. Computers use base 8,16,32, or 64. Some electronics use base 14. So the number of fingers or tentacles doesn't necessarily lead to the base people use.

I find it surprising that the human species hasn't settled on base 11.

[Smaug]

The human species have used base 60, and 20 in the past. Computers use base 8,16,32, or 64. Some electronics use base 14. So the number of fingers or tentacles doesn't necessarily lead to the base people use.

Speaking of the original numeral systems, they were mostly based on fingers of course. The most common ones were with bases of 5 or 10. These systems were used practically world-wide. Good to know that these first systems lacked zero. Less common were those with bases of 20 and 25 (used by some Indian tribes as far as I remember). There also was a Chinese system based on counting each finger's phalanx bones and joints (thus each finger was equal to five).

The system with base 60 was in fact a unique one and originated in Sumer. Sumerians used both finger-based decimal system, base 12 system and this one. Base 60 system was initially used for astronomical purposes.

Among the uncommon historical systems it's good to note the aformentioned Sumerian base 12 system. 12 has more denominators than 10 which makes this system somewhat more attractive for the arythmetists. In 18-19 centuries there were discussions between some of the mathematicians who dealt in arithmetics and Number Theory that it would've been better to adopt this system as standard but it was historically and practically too late.

Speaking of all other systems mentioned (base 2, 16 etc.) they are historically secondary to common ones that has been just mentioned above. These systems may have had limited use in distant past but the main reason of their ascendance is the developement of digital computers.

[Alex K]

12 has more denominators than 10 which makes this system somewhat more attractive for the arythmetists.

Not only them...

https://www.youtube.com/watch?v=9_sMmuKPrnY