How universal is math as we know it?

[nhnifong]

I think most of the supposedly universal mathematical ideas are in fact very arbitrarily framed and smothered in cultural accidents, linguistic quirks, and ulterior motives.

I've often had trouble with math, but only at the surface level so to speak. Usually the notation is confusing, even ambiguous (for example, angle brakets have different meanings depending on the field of study). The variables are almost always single letters, and one must be familiar with the history of a certain field in order to know what they refer to. Lexical scope is often not explicitly denoted with parentheses, but left to be inferred from context, such as in chained summation symbols.

But after I slog through the history and the cultural quirks, and the weird motives of the discoverers, it becomes clear that some concept was not new at all, and was in fact something I had been using in regular programming practice for years without knowing the name of. This frustrates me to no end every time it happens. Mathematics claims to be universal, when it is in fact just another natural human language, full of messy traditions and accidents just like english.

When will academia cast of this stupid pile of dogma and come up with something better? like Lisp?

[Nibb31]

Math is universal (although we discover new things every day, and some other civilization might not have discovered the same things). However, notations, numbering bases and conventions are deeply cultural, so we probably couldn't communicate with an alien species using only mathematics.

For example, we only use base-10 because we have 10 fingers. Some other culture might use base-12 (which has lots of advantages) or some other base. Their numbers might look like roman numerals or some other system, and their notation system might be totally different... However, just like any other language, you can only communicate when you have agreed on the communication protocol.

[Rune]

I think you answered yourself. Math concepts are universal. Math notation is very culturally-dependent. So you can use math to figure out the notation of any other math-using entity, which is what guys at SETI are excited about.

[allmappedout]

However, the one building block that you can start at is counting. One of anything is always one, and you can start from there. Indeed, Stargate SG-1 covered this when they used the Periodic table (another universal constant) to bring together 4 different languages. Of course, you eventually need the equivalent of a rosetta stone for more abstract things, but if you have one piece of commonality, you can begin to plot similar concepts between cultures and/or races.

[Sof]

Maths, people, Maths! There is more than one number so it has to be plural.

[lyndonguitar]

Math can be universal in the sense that it is a universal law, it is constant. if you have 6 objects, everyone will count it as 6 objects regardless of how and what they call that number. If you punch them three times, they will experience being punched the same number of times.

It may be possible to communicate to other species(or vice versa) by sending them a series patterning numbers, odd numbers, even, prime, exponential numbers, etc. through beeps (odd, even, numbers provide the smallest number of beeps required) and they could respond to it accordingly, despite the lack of "real" language.

send 2,4,6,8,10 beeps, and should they recognize the pattern(and they will if they are advanced enough to use radio), they might send back 12,14,16 beeps, 10,8,6,4,2 beeps, 1,3,5,7,9 beeps back,etc.

http://plus.maths.org/content/mathematics-aliens

[Nikolai]

Maths, people, Maths! There is more than one number so it has to be plural.

"Math" is not a noun that refers only to a collection of numbers. It's a discipline, short for "mathematics", and like "physics", "economics", "gymnastics", et cetera, tends to be treated as a singular noun in spite of the "s" at the end. (Besides, we don't tend to keep the "s" in the short form of a noun. We don't use "gyms" as a short form for "gymnastics"(*).

Which is grammatically correct: "Mathematics is my best subject", or "Mathematics are my best subject"? Or, if you prefer, "Maths is my best subject", or "Maths are my best subject"?

There's some debate on the subject, obviously, but there are things to be considered on both sides.

(*) Though, obviously, we do for "gymnasiums", where the noun itself is plural.

[Xeldrak]

Well, as you said yourself - mathematic concepts are universal, notation not so much

[K^2]

The framework of mathematics is universal. Particular algebras are not. Some people are convinced that 2+2=4 is a universal truth. It is not. It's a consequence of the way operations and relations are defined, and these are not universal. In fact, people study many different algebras. 2+2=1 is just as valid in Z₃ for example. What people normally understand as addition and multiplication is covered by algebraic rings and fields. Though, even with the relationship between the two operations locked, you still have quite a bit of freedom, such as with the Z₃ example. Individual operations are studied by group theory and there you have even more possibilities because you no longer have to worry about distributive properties.

[Scotius]

You had to do this, K^2. Didn't you? Remind us that people managed to prove that 2+2 not always equals 4. You couldn't leave us in sweet, sweet ignorance of this fact, and spare non-math oriented people headache? Damn you, math-geeks! *shakes fist at mathematicians in a fit of rage and frustration*

[Person012345]

I think most of the supposedly universal mathematical ideas are in fact very arbitrarily framed and smothered in cultural accidents, linguistic quirks, and ulterior motives.

I've often had trouble with math, but only at the surface level so to speak. Usually the notation is confusing, even ambiguous (for example, angle brakets have different meanings depending on the field of study). The variables are almost always single letters, and one must be familiar with the history of a certain field in order to know what they refer to. Lexical scope is often not explicitly denoted with parentheses, but left to be inferred from context, such as in chained summation symbols.

But after I slog through the history and the cultural quirks, and the weird motives of the discoverers, it becomes clear that some concept was not new at all, and was in fact something I had been using in regular programming practice for years without knowing the name of. This frustrates me to no end every time it happens. Mathematics claims to be universal, when it is in fact just another natural human language, full of messy traditions and accidents just like english.

When will academia cast of this stupid pile of dogma and come up with something better? like Lisp?

Mathematical notation is a "language" that is used to describe a universal concept.

[Xeldrak]

The framework of mathematics is universal. Particular algebras are not. Some people are convinced that 2+2=4 is a universal truth. It is not. It's a consequence of the way operations and relations are defined, and these are not universal. In fact, people study many different algebras. 2+2=1 is just as valid in Z₃ for example. What people normally understand as addition and multiplication is covered by algebraic rings and fields. Though, even with the relationship between the two operations locked, you still have quite a bit of freedom, such as with the Z₃ example. Individual operations are studied by group theory and there you have even more possibilities because you no longer have to worry about distributive properties.

Well, but this is allready notation and convention - the convention is, that if nothing else is said, we are doing stuff withing the Real Numbes (sorry, I don't know all the technical terms in english). Also, ist just convention, that the symbol "+" means the operation, we call addition

[hugix]

If we ever get the opportunity to communicate with another species I'd vote for using the golden ratio to make them notice our "smartness".

[allmappedout]

The framework of mathematics is universal. Particular algebras are not. Some people are convinced that 2+2=4 is a universal truth. It is not. It's a consequence of the way operations and relations are defined, and these are not universal. In fact, people study many different algebras. 2+2=1 is just as valid in Z₃ for example. What people normally understand as addition and multiplication is covered by algebraic rings and fields. Though, even with the relationship between the two operations locked, you still have quite a bit of freedom, such as with the Z₃ example. Individual operations are studied by group theory and there you have even more possibilities because you no longer have to worry about distributive properties.

I studied group theory primarily for my degree, I loved how elegant it was. However, I reckon were me to make contact with a new species, we'd probably count their 'fingers', and have a likely candidate for their base, if it wasn't 10 I doubt we'd start getting into simple groups and the first isomorphism theory from the off...

[allmappedout]

If we ever get the opportunity to communicate with another species I'd vote for using the golden ratio to make them notice our "smartness".

We could send them the continued fraction expansion: [1;1,1,1,1,1,1,1....] they probably wouldn't think of us as so smart if we just fired a ton of 1's at them though..

[The Jedi Master]

Math is universal. 1+1=2. Always. No exceptions.

[Xeldrak]

Math is universal. 1+1=2. Always. No exceptions.

Nope, in Z₂ it's 1+1=0

[Holo]

Nope, in Z₂ it's 1+1=0

It's a fair assumption that aliens will interpret maths we beam at them as referring to reality

[Yourself]

It's a fair assumption that aliens will interpret maths we beam at them as referring to reality

How exactly is it that the integers (or natural numbers) are more representative of reality than Z₂? For example, the statement 1 + 1 = 0 in Z₂ is the same as the statement "the sum of two odd integers is even". In some sense that statement also comes up in binary computer systems, since it resembles the XOR operator.

[patrickcanttype]

Some people are convinced that 2+2=4 is a universal truth. It is not. It's a consequence of the way operations and relations are defined, and these are not universal. In fact, people study many different algebras. 2+2=1 is just as valid in Z₃ for example.

I've always liked examples like this, and while it's an interesting way of thinking, I don't think it's applicable when talking about the universal-ness of math. Sure I can say that if it is 10 o'clock and we add 3 hours, it will be 1 o'clock. Thus 10+3=1. However, we know 10+3=13, and so calling it 1 is just a different way of measuring it. 10+3=1(+12) would be a better way of describing this measurement.

As numerous people have stated: Math is universal. F=ma will be applicable universally (although there may be exceptions due to forces/crazysciencethings we have not discovered) even if different notation is used.

[MatixCubix]

Well, the problem with comunication with other species is that we group things and we relate them with the world or whatever ,so for this to happen, this species have to have the same type of reasoning (percepcion) or a similar one so they can understand and see what we see . The representation is also a problem, the maths variate depending in what point you see them, I mean you can say 1 apple and 1 apple are 2 apples or 200 grams of apple and 200 grams of apple are 400 grams of apple or you can take that 1 apple are 2 apple and the first equation I done would result in 4 apples, the numbers are a representation so as the language , because you can also represent things differently in language.

[lyndonguitar]

In reality, Math is applicable universally, You don't need units, you certainly don't need notations, and you don't even need "numbers" so to say.

what you're trying to say has a point, that math isn't universal is just wrong. Math is universal, even if that the counting system might be different in other species it doesn't mean the math is very much different.

if you punch them three times, they will experience being punched the same number of times. If you punch them the same number of times again, they will experience the same number of punches, no more and no less

If you show them three objects and tell them to physically touch them all, If they understand it correctly they will touch only three objects, regardless of how many "units" they perceive three that is.

If you kill 10 aliens, 10 aliens will die. If they send 5 aliens to our planet, with no intention of combining/dying/mutating/replication in weird way. they still will arrive with 5 aliens.

Here's an example.

We count 0,1,2,3,5,6,7,8,9, then a new add number to the left, which is then next unused digit of the rightmost number pattern, then the rightmost will start at zero again, up to nine.

Lets say they count very different, WAY different. They have two fingers, let's assume they count only two variables. They start with the unit called "A", then "B". then after it the third number they call it A-B because they only have two fingers to represent such values. they divided A-B the basic unit with the sub-units A, B and A-B (0.334,0.667, 1)

the second unit can be then called C, then D, then C-D. then E, F. E-F.

It is very, very different, very alien indeed. Humans may feel comfortable with numbers ending in 0 values like 1000, 2000, 43000, always counting near that value, but you'd be surprised they are comfortable with A-B, C-D, E-F, G-H. which is 3,6,9,12 in our representations.

However this doesn't change the fact that math is universal. You kick them 16 times. they represent it as "G-HC" which is 12 + 4, "That human kicked me G-HC times!" we say its sixteen they say its G-HC, regardless it has the same value.

They contact to you through beeps. one for each of their basic unit in increasing form. they used A-B, then C-D E-F, then G-H I-J K-L. for them, it represented 3, then 3,6 then 3,6,9. but since one unit for them is 3 already. they only beep once every unit.

So we interpret the beep as 1 beep, then 2 beeps, then 3 beeps. ofcourse we recognize the pattern. so we send 4,5,6 beeps. if we send 4,2,8,3 beeps, then there's no pattern at all, so it is wrong and it is not considered "math"

They will then receive it as 12,15,18. There is a difference in number, but regardless we can show that we understand them, by understanding the pattern. and therefore it is proven that math is universal.

Edited May 21, 2013 by lyndonguitar

[Stochasty]

Well, the problem with comunication with other species is that we group things and we relate them with the world or whatever.

They will then receive it as 12,15,18.

The two of you are on the right track here, but you don't take things nearly far enough. Math is universal, but a specific representation of math depends both on choice of axiom and choice of notation. A large part of the reason that math developed as it did for humans is because most of the resources we use and things we interact with come in discrete packages: 1 apple, 17 blood thirsty wolves, etc. Even for things that don't come in discrete packages, we try our best to discretize them when thinking about them: 5 miles, 2 and a half hours, etc. (Even fractions are just a way of discretizing quantities that don't consist of whole numbers.) This is why our system of math is based on counting - it's how we interact with the world, so it makes sense to us and is useful.

Imagine an alien species with an entirely different way of perceiving and interacting with the world. Perhaps they live in a fluid environment (a water world, say, or maybe as plasma-based entities inside a star) and the resources they use come not as discrete packages but as densities (say, density of dissolved minerals, etc.) Their primary sense then might be something akin to scent, rather than vision, and they'd view the world in terms of gradients rather than discrete quantities. What use to them would counting be? Rather, they might base their maths on a basic set of ordered relations (greater than, less than) instead of number, addition, and subtraction. Calculus (integrals, derivatives) might come as naturally to them as Algebra does to us. Topology and differential geometry (using density isosurfaces to define open sets and generate geometric structure) might come more naturally than Euclidean geometry. Sure, eventually, when their math became sophisticated enough, they'd work their way back around to Algebra, but there's no reason to expect them to see it as fundamental.

Given this, suppose such a creature were to become sufficiently technologically sophisticated to communicate with us. How would we go about recognizing their maths? We try to base a dictionary on their symbols for 1, 2, etc. only to find out that, when they bother to count at all (not often), they do it in base e! And that's just one possible example, based upon a series of speculations I find potentially plausible. If I can imagine it, then I'm sure nature can come up with something even weirder that I am incapable of imagining.

Math might be universal, but that's no reason to assume that we can use it to establish come ground for communication. Sure, sophonts which evolved in similar conditions to us probably think a lot like we do, but that's a rather limiting assumption, don't you think?

Edited May 21, 2013 by Stochasty

[TheCardinal]

A mathematic teacher told me once ( a long time ago) that in some cases 2 + 1 isn't the same as 1 + 2. I couldn't believe it then but i do now. It all depends on the definition of rules, f.e 7 + 1 isn't the same as 1 + 7 when making lemonade with water and syrup.

[Kerbface]

A mathematic teacher told me once ( a long time ago) that in some cases 2 + 1 isn't the same as 1 + 2. I couldn't believe it then but i do now. It all depends on the definition of rules, f.e 7 + 1 isn't the same as 1 + 7 when making lemonade with water and syrup.

Are you sure you don't mean "2a + 1b is not the same as 2b + 1a"? Because that's how I'm reading the lemonade with water and syrup argument, water and syrup being a and b. 1 + 2 (by itself with no other variables) is the same as 2 + 1.