How different could alien mathematics be from ours?

The only thing that can change is the system of numeration

Please tell me you are just pretending to be retarded.

>But mathematics is not really a construction of ours.

It's a construction of our brain.

Look at all the difference between us and a monkey. We are basically the same except how our brain works. And yet, we are on the same planet and the product of co-evolution.

Now imagine a living being on another planet.

youtube.com/watch?v=Zh3Yz3PiXZw

Haven't observed this stuff ever outside of solar system.

I think atomic mass could be "different" because it's related to gravitational of the planet, wouldn't it be?

Or they would measure it's propagation somehow normal.

...

Very different is my guess. I find it highly unlikely that Aliens even have a similar conception of mathematics, the reason for that is that our mathematics enormously depends on our senses.
Geometry is the perfect reflection of that, if our main organs weren't eyes, then even the thought of geometry wouldn't make sense, you can't "hear, smell, or taste" a line, you can "feel and see" it.
So at least in a historical sense it is highly unlikely that aliens, who most likely have very different senses, would have developed something like our geometry.

It is the same with our modern approach to mathematics, set theory only makes sense if you have eyes, "inclusion" is something we can visually understand.

Imagine a highly intelligent bat, trying to develop mathematics. We need to think about how it would abstract the world it perceives with its senses, this is of course HIGHLY speculative.
Suppose most of the bat's understanding would come through echolocation, why would it develop something like geometry?
It really is hard to describe and just a wild guess, echolocation gives you the distance to a certain object, I find it likely that the bat would model that as some sort of polygonal line on spherical coordinates.
And from that the bat will develop new, wildly different abstractions, I doubt that at first the bat will eve have the concept of "counting".

>Its kernel would be the same
I highly doubt that.
For my argument see above.

>but the symbols would likely all be completely different
Remove the likely.

>In continuation of this, it would be good to create a system of mathematics with units derived from fundamental constants of the universe
That is just stupid.

I believe you are completely wrong, argument above.

...

If their brains have the same limitations as ours do (only being able to keep track of a limited number or objects, having to symbolically/semantically store information etc) their maths will probably contain similar hacks and tricks. After all if you were omniscient you wouldn't need math, it only comes in when you have to work with shit your brain cannot easily process automatically.

Totally this. Good post because you bring attention to the nature of perception in diversity of organic wildlife on the planet, and in theory, how they might evolve, and then theoretically develop mathematics.

Its fun to think about because yes bats, how would they do it, but also like a dolphin, whales, eagles, any animal, its interesting to think about

None of these animals can, or ever will, begin to produce mathematics in their own right. Not as they are now anyway.

I honestly believe the mathematics will likely have different notation and the preferred number base will be different. But you can't really write or build theories without having good eyes and visual recognition.

the idea of diversity in perceiving the physical within the animal kingdom represents instead a foundation in theoretical perception of an environment under particular conditions for a living being. This is why I specifically mentioned dolphins and whales.

Whales and dolphins communicate via sonar, like bats, except just in water. Therefore in theory one might consider developmental consciousness on a watery world with a theoretical amphibian extraterrestrial, and their system of mathematics

We have examples all around us, they are not evolved, its more like they provide theoretical insight to various environmental conditions, and interactions of development in a living being (which could be applied to other theoretical planets or species)

>Aliens probaly won`t have a sensory system to detect light being reflected from objects
t. brainlet

In these conversations I always wonder where you draw the line between aliens and animals

>>Aliens probaly won`t have a sensory system to detect light being reflected from objects
Why would they?
There are already mammals who use other things and have weakly developed eyesight.

Come on. No numbers? Quantity is fundamental part of experience. 4 wheels on a wagon. Soup recipe calls for 2 onions. Q'nar has 8 tentacles.
There's no way to be sapient without counting.

I think you are imagining aliens as "weird humans".
But it isn't even clear that they have even similar senses to us, why would they?

"Counting" makes no sense if you are relying purely on ear"sight", you can't really count sounds.

>"Counting" makes no sense if you are relying purely on ear"sight", you can't really count sounds.
You just say this because you can't conceive of a sonar animal having an accurate model of the world, but that's more a lack of imagination on your part I think.

good ol wildsperger

You have to be kidding.

They could be running on curvy fractals.
They could be disguised in 4th dimensional encryption.
They could have literaly 26 vowels and one consonant.
They could use a different number base for their 13 fingers.
They may even use innumerates for their odd tentacles.

As I'm reading, I start to think "wow a good thread." Then I hit this brainlet trash.

are people ITT seriously saying that an alien civilization might not conceive of the natural numbers?
Depending on how far you stretch the definition of "usage" almost everything we call life has some innate knowledge of how the natural numbers behave.
Knowing the difference between one and many is extremel fundamental to any lifeform.

They are clearly not understanding the universality of core concepts like e, pi and natural numbers. Although our set theory would likely be different to theirs as would our base numbers, they would definitely understand basic geometry and many of the core concepts of mathematics.

Fun fact, echolocation is not just distance to object. First of all it is 2D. And secondly, it gives information about the shape and texture of objects. It is basically "seeing", but using sound waves instead of light.

youtube.com/watch?v=nUCwtLTUPQ4

>why would they?
because the senses we have(at least, the main ones that tell us about our surroundings) are the most sensible ones to have.
>ability to discern light in the small spectrum band that easily passes through our atmosphere(and water) but doesn't easily pass through solid objects like our flesh
>detection of vibration waves in the fluid medium that surrounds us
>detection of trace chemicals in the air, mainly focused around chemicals that are produced as byproducts of biological activity and/or chemicals that indicate a potential threat

>You just say this because you can't conceive of a sonar animal having an accurate model of the world
Of course I can't.
But I attempted in , to describe what such animal's mathematics might look like.

I am 100% serious.

>because the senses we have(at least, the main ones that tell us about our surroundings) are the most sensible ones to have.
I think that there is "some" truth to that, if you look at it from an evolutionary perspective, most animals have very similar senses.
But Imagine if this wouldn't be the earth, maybe a planet with a different atmosphere.

>>ability to discern light in the small spectrum band that easily passes through our atmosphere(and water) but doesn't easily pass through solid objects like our flesh
It isn't entire impossible to imagine a planet shrouded in permanent fog, which makes vision in our spectrum utterly useless.

>>detection of vibration waves in the fluid medium that surrounds us
There certainly is a case to be made for that, but we don't really understand much of our world through touching, that is very inefficient.

>>detection of trace chemicals in the air, mainly focused around chemicals that are produced as byproducts of biological activity and/or chemicals that indicate a potential threat
Again, our sense of smell is very underdeveloped, could you imagine our mathematics changing if our sense of smell was significantly more dominant?

>Fun fact, echolocation is not just distance to object. First of all it is 2D
I didn't mean to imply otherwise, I probably expressed myself very badly.
I have a picture in my head, which is very hard to explain in words.

>It is basically "seeing", but using sound waves instead of light.
I would really like to experience something like that, to make any kind of judgment about that.

>How different could alien mathematics be from ours?

Not very, the base of their number system will be different, and the symbols different, but the CORE will be identical. Mathematics will be how we communicate at first and it will NOT be difficult for us to quickly establish a shared understanding.

I don't think so, see

that rant is nonsense. Differences in senses would change the way they describe things, but the rules of geometry wouldn't change. An equilateral triangle has the same properties no matter what planet you're from or what crazy sensory organ you use to perceive it.

>>>detection of vibration waves in the fluid medium that surrounds us
>There certainly is a case to be made for that, but we don't really understand much of our world through touching, that is very inefficient.
I was describing hearing.

>but the rules of geometry wouldn't change
Why would a being with no eye sight develop geometry?

>An equilateral triangle has the same properties no matter what planet you're from or what crazy sensory organ you use to perceive it.
I don't think you actually understood what I said.

Mathematics is the abstraction of reality based on how we perceive reality, I think it is very unlikely that a drastic shift in perception wouldn't mean a drastic shift in mathematics.

I can get on board with notation that lets me draw dicks

This is the highest quality shitpost this board has seen in an age, well played my friend.

That doesn't really matter, hearing is not really a way in which we abstract reality.

Our perception of reality is based on our vision, even in very abstract mathematics, there is "visualization" going on.

>Why would a being with no eye sight develop geometry?
Because they live in an environment that has shape and structure in it and would necessarily have some ability to perceive it so that they could act upon it, without which there would be no impetus to develop intelligence.
>Mathematics is the abstraction of reality based on how we perceive reality, I think it is very unlikely that a drastic shift in perception wouldn't mean a drastic shift in mathematics.
You're just being pedantic then and not actually disagreeing with anyone. Everyone is saying "the way they describe things would change" but the rules and results and understanding of how the universe works would be the same.

Wrong. If we meet a technological species they
will have a solid understanding of binary mathematics and we can use that to communicate.

It make NO DIFFERENCE how a bat creature models the physical world... we will just do a transformation from their model to a common Cartesian model.

We did not make mathematics we discovered mathematics... mathematics CORE is just a set of core rules that we observed the universe follows.

It makes ZERO difference if you are a bat, ant, or dolphin. The basic core of math is same for EVERYONE!

Their axioms might be a different but the results will be the same.

A Binary computer is a binary computer, the core operations are the same for everyone in the universe. They might have a freaky operation
(a strange binary function (we use AND, OR, NOT, etc.), but it can be decomposed into the one we know.

>Because they live in an environment that has shape and structure in it and would necessarily have some ability to perceive it so that they could act upon it, without which there would be no impetus to develop intelligence.
How does that lead to geometry?

That is a very specific thing you know, and humans have already found multiple ways in which geometry can be replaced or further abstracted.

>You're just being pedantic then and not actually disagreeing with anyone.
I don't think so.

>the rules and results and understanding of how the universe works would be the same.
I don't say that.

>they
>will have a solid understanding of binary mathematics and we can use that to communicate.
Why?
That is absurd ans stupid.
Why is it binary, when it could be a billion other things.

>mathematics CORE is just a set of core rules that we observed the universe follows.
Why? You just state this again and again. WHY?

>They might have a freaky operation (a strange binary function (we use AND, OR, NOT, etc.)
There are EXACTLY 16 binary operations with two operands, there are no "freaky" operations.
But this is irrelevant, why would they use "binary" computers anyway, there are a billion different ways to do things.

>Why? You just state this again and again. WHY?
>1+1=2 is an arbitrary social construct

+1=2 is an arbitrary social construct
Yes, of course it is, how could you believe otherwise?

Even ignoring the symbols, I don't see why addition has to be the central part of mathematics, geometry works without that...

You are just saying things, not making arguments for them.

so if an alien takes a thing, and takes another thing, it'll have a number of things that isn't two because it's an alien

>Why is it binary,

Binary is the root of all mathematics.
If we meet a technological alien race they WILL have a solid understanding of binary mathematics.

I don't actually believe you can be this retarded...

No, that is plain stupid.
Binary has VERY little to do with mathematics.

Explain to me why the idea of "binary" should exist in an alien.

They will also understand things like prime numbers and real numbers and sine functions ETC.
There is nothing HUMAN about these things, they just are
They WILL have the same constants:
1, 0, e, pi, i
The universe has these constants man did not make them up, they just ARE.

>Binary has VERY little to do with mathematics.
I shouldn't have said that, I mean it plays a VERY minor role.
Excuse me.

>They will also understand things like prime numbers and real numbers and sine functions ETC.
Why?

>There is nothing HUMAN about these things, they just are
You say that, but I see no reason why it would be true.

>They WILL have the same constants:
Explain to me why they will have numbers in the first place.

>The universe has these constants man did not make them up, they just ARE.
Yes. But certainly they are independent of the mathematics one uses.

Wait... I am assuming you are speaking of a technological alien species...

If not, then sure they can have a weird fucked up system of 1 + 1 =2 when temp above 30 but otherwise is 17.
Any bat-shit weird ideas they use to explain the universe.
Aztecs believed that the gods needed blood sacrifice for a good crop...
100 human heart + 27 severed penis = 2000 Avacodoes
Fucked up math but it worked for them

>I am assuming you are speaking of a technological alien species...
Yes.

But I am not saying that their system will be "what we use, but with some fucked up arbitrary shit".
I am saying that their mathematics will have NOTHING to do with ours, not because they are any less "intuitive" then ours, but because the have senses completely different to ours and thus have a radical difference in "intuition".

Have a look at the geometry of the ancient Greeks, you didn't need the idea of "number" at all for that.
I am arguing that the idea of "number" is not a necessary part of an aliens mathematics.

Imagine a being with just a sense of hearing, can there be "one discrete sound"?
No, such a thing doesn't happen in nature a being like that might not even conceive of the idea "number".

(Keep in mind that, you are heavily biased here, your vision and sense of touch has already predisposed you to the idea of number, it might be literally impossible to imagine what a being with just hearing might "be" like)

>They could have literaly 26 vowels and one consonant.
Numerous examples show that they at least have consonants L and M.

If a planet has light constantly on the surface THERE WILL BE VISION.

>but because the have senses completely different to ours and thus have a radical difference in "intuition".

But that is just complete irrelevant to mathematics.
We did not make up pi because we view the earth a special way, nor did we make up prime numbers because we see the universe a special way. Mathematics is universal. Sure that might have a strange coordinate system (we usually have Cartesian, cylindrical and spherical), but no matter what their system is we can transform it to one we are familiar with.

You think we made mathematics but there you are wrong, we discovered mathematics.

We could be water breathing ants and still
1 + 1 = 2
the most common constants are i, 1, 0, pi, e

You are correct that you can do a lot a math without numbers but we already have a good understanding of Geometry (Euclidean and non-Euclidean).

Mathematics is the LEAST difference between any two technological species.

>If a planet has light constantly on the surface THERE WILL BE VISION.
Suppose that is correct, why is their sense of vision the same as ours?
We already have animals with weakly developed vision who rely on echolocation, or who have more then two eyes.

It might be infrared vision or ultraviolet though depending on the type of star they have. What about life on a planet like Europa where survival on the surface is impossible but in the deep dark ocean it could be viable?

>But that is just complete irrelevant to mathematics.
No, I don't think you understand mathematics and its History.

>We did not make up pi because we view the earth a special way, nor did we make up prime numbers because we see the universe a special way.
That is "correct", although irrelevant.

>Sure that might have a strange coordinate system (we usually have Cartesian, cylindrical and spherical), but no matter what their system is we can transform it to one we are familiar with.
Why should they even use numbers?
I already asked you this question.

>We could be water breathing ants and still
>1 + 1 = 2
>the most common constants are i, 1, 0, pi, e
You said that two times already, I gave you an example of a species which might have no concepts of NUMBER.
Why do you think they could even understand the concept of "adding".

>You are correct that you can do a lot a math without numbers
Exactly and why would a species have the concept of number?

>Mathematics is the LEAST difference between any two technological species.
Can you PLEASE do anything else but "state the opposite" case, there wasn't a single argument in your post.

Concerning: Natural numbers and counting:
I think it is doubtable that a species who can build big, different houses, manage complex transport systems, automate calculations, exploring space around their planet etc. would not have at least developed a system of counting (i.e. natural numbers).

>Why should they even use numbers?
Natural numbers are among the simplest possible notion that can be expressed in most if not all foundational systems. As an example, they are literally the simplest possible recursive structure, or constructed type. Even a mathematics based on geometry will get you to natural numbers and its properties really fucking quick.

We have studied and made up quite a few different fundamental ways of doing mathematics, and they ALL feature natural numbers as a mathematical structure in the system that immediately presents itself. That's not because we are looking so hard for numbers everywhere; it's because natural numbers are in fact a very basic mathematical construction, and you WILL find it without looking for it wherever in math-land you are currently exploring. Which means any alien system will inevitably have them.

Now set theory, for example, is something I can easily see being absent entirely in an alien system of mathematics. It plays a prominent role in our most common systems of mathematics, but it is much less prominent in others, and could easily be considered an irrelevant piece of arcana to other cultures. But not numbers, they are too fundamental and omnipresent.

Those evolve because they live or hunt in environments where light is scarce or at least inconsistent. Bats need to be able to hunt even when it's a new moon and pitch black out, and making their eyes bigger to collect more light doesn't really work because they're tiny and need to stay tiny to fly nimbly through trees and catch bugs.
Further, counting has nothing to do with vision, it has to do with there being discrete objects. And unless it's the fucking changeling world from star trek where everything is a blob and just a divisible part of everything else, any alien species will have the understanding that there is a thing and another thing and that makes two things and so on.

On a liquid planet?

are you suggesting the actual changeling world where there aren't discrete countable organisms?
Because while I imagine it's not outside the realm of possibility of an entire biosphere joining in effective symbiosis, I can't imagine intelligence enough to count rising from a single organism system where there is no need for even something like survival instincts. It'd basically be like a giant slime mold covering the whole plant and absorbing energy from wherever, evenly distributing it.. To no end. Which makes me think that eventually by chance some parts of it would mutate to gain advantage over the other parts to get more of the available resources, leading to defenses against whatever those parts do arising in other parts under the selection pressure, and eventually the whole thing falls apart in to a bunch of discrete, countable animals producing and consuming.

>no need for survival
It's all in the distribution, like genes on our planet.
Even humans aren't as discrete as we pretend to be.

>cutting off part of a quote when anyone can see what I actually said right there
Survival instincts are the basic defense against predation and method of procuring resources when they aren't abundant in your surroundings, and the beginning of a complex nervous system and brain. A single planetary slime mold organism thing wouldn't need them.

Do dolphins count?

maybe not, consider a sentient slime mould

what makes you think dolphins can't count?

I know they can count when they interact with their human handlers.. but do they do it naturally? Has any evidence been presented of dolphins counting in the wild?

No, look into swarm intelligence

Maybe there are a lot of other universal 'constants' that we haven't yet discovered, that are described in alien mathematics and the alien mathematics are entirelly centered around those unkwon constants.

So you are assuming we already know everything, wich is not the case imo. Alien math will probably very different

holy fucking cringe

>Aliens arrive using mega-EM Drives
>Alien math didn't say it couldn't work, so it quantumally decided that it could work
>Humans point out that it can't work because of X, Aliens now stranded.
You dicks.

Surely they understand that fish are discrete things and there are quantities of them. I don't know if they ever count them or why they would, maybe to try and divide them fairly? But I have no idea if dolphin society is advanced enough to have such ideas of fair play.
There'd be no reason for any intelligence let alone sentience to arise in a system of total symbiosis where everything constitutes one giant multicellular organism. That'd be like if your kidneys evolved brains to compete to suck up more poison.

There's still competition.

if things are competing with each other they can't be said to be one thing and would thus be discrete and quantifiable and any intelligent form of this life that arose would be able to distinguish them from one another and count them.

No, that's not true at all. I said earlier, it's like genes in humans. Competition for distribution.

>all those absolute brainlets ITT who can't even into the concept of math and evolution
Christ

>>In continuation of this, it would be good to create a system of mathematics with units derived from fundamental constants of the universe
WHAT THE FUCK ARE PLANCK UNITS
JESUS CHRIST

>Why would they?

Same reason almost all complex life on Earth does, retard.

It's hard to imagine living in this universe and never analyzing things like spheres, circles, and exponential growth enough to come up with pi and e. They will at least have those concepts, even if they're not really in use. They might have many more constants that we do not.

I'm thinking the symbols, bases, and several of the specifics will change. What won't change are things like physical, calculable properties of the world around them. That leads me to bet that there would be a pretty good way to translate between the two.

>Basic Geometry
>Yfw they "See" the world from a fourth dimensional extrapolation.

Aliens might use a different number-base and they will certainly use different notation.
But we are both trying to describe the same universe, so there will be a lot of overlap.
You wouldn't expect them to believe addition is non-commutative; i.e. 3+4 is not equal to 4+3. That doesn't reflect reality. (I'm talking real numbers, in case anyone wants to bring up mathematical "objects" which don't commute.)

I cannot imagine anyone building a technological civilization without the concepts of prime numbers, conic sections, pi, e, and the basic arithmetic operations.
They might know things we don't. If we'd met aliens in 1950, fractals and the Mandelbrot set would have been novelty to us. Or they might not have a proof of the 4-color theorem or Fermat's Last Problem. What they know and what we know won't be identical. But mathematicians of both species would agree on much and be able to work from there.

In my opinion it seems that most arguments here have different assumptions on what kind of aliens we are talking about, as in what level of social/technological development they would have.

There's only one mathematics, all that could be different is the extent to which they've discovered it and the superficial representations they make of it.

well there's not much point in talking about the mathematics of aliens that haven't developed a rigorous discipline of mathematics at least equivalent in reliability to our own. Because if we're talking about primitive aliens who just do whatever the fuck then who knows. Their idea of math could be anything.

Exactly.
If they built some kind of society then it's likely so form of exchange developed, so basic arithmetic would be fundimental.
If they build structures then calculations for area would also be fundimental.

The calculations they use would have to work universally too, so they would likely be equivalent to ours but in a different form, either simplified or more complex.
One question would be if they have same basic value for pi, or do they derive pi in the calculation from a more basic value. But in the end if they want to calculate the circumference of a round thing they're going to need to find pi in there somewhere.

Idk why no one has just told you that mathematical concepts exist outside of human cognition. As another user said 1+1=2 if you are a human or an ant, any advanced alien species would have a number system because without one they cant be advanced.