How universal is math as we know it?

[TheCardinal]

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.

No, i meant it exactly like that. Of course you are right but when you only consider volume, the result is different even though the endvolume is the same.

[Kerbface]

No, i meant it exactly like that. Of course you are right but when you only consider volume, the result is different even though the endvolume is the same.

Yeah, so if you're looking at it purely mathematically, 1 + 2 is the same as 2 + 1. It's only when you use those numbers as adjectives for different things that you get a different result, and that result is different only in nature, not number.

[Inspector Gadget]

I like how this thread turned from "How universal as math as we know it?" to "How can we communicate with alien species using math?"

[ialdabaoth]

Of course, all of this depends on having a brain that comprehends the concept of "discreteness", which may not be necessary. It might be possible to construct valid mathematical systems that operate entirely on principles of continuum, with no capacity for "counting".

[Natsarugiy]

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

Never. Mostly because those teaching all of the concepts use notation they are familiar with already, which is the old and traditional notation. Sure, when a new language is adopted by the majority of the population, then mathematical notation will sure make some changes to adapt to the new language, but older concepts will probably maintain the older notation (which is why so many Greek characters are still used in modern math).

Low level math will probably always be taught in a form that closely resembles the popular language being used, since the children being taught this math will also have just been taught the language, and it is easier to just reuse notation they are already familiar with than to overwhelm them with new notation. But higher levels of math will continue to use older notation because there is no reason to change it. Sure, it's difficult for people who aren't very interested in familiarizing themselves with math (that high school mindset that I'll never use this stuff outside of class) and the varying levels of notation will obviously cause these people many problems when they attempt to quickly learn the higher level math.

That being said, the concept of math being "universal" is a completely separate idea that has nothing to do with notation. It's the basics that allow us to form scientific "laws." If I were to show you a variety of right triangles, you'd begin to notice patterns between the triangles. That even though the sides may be different lengths, there are still relationships that exist, otherwise the shape wouldn't look like a right triangle anymore. Concepts like these are what make math "universal." No matter what language you speak. The image of the right triangle stays the same. And given enough time, two completely different languages will be able to convey the same idea to each other.

As a simpler example: any civilization in the history of our planet has been able to recognize 10 fingers. It doesn't matter what language you speak, or what language you use. 10 fingers is 10 fingers.

So how is this universal? Well these mathematical concepts can be used as a base for higher ideas. I can describe the electromagnetic force with a mathematical model. Then I can use that model to describe other physics. Therefore, physics is just applied math. I can then make physical models that describe how particles interact. So chemistry is just applied physics. And chemical models can then be made to describe how organisms act. So biology is just applied chemistry. And so on. All science can exist because of these most basic and universal mathematical models. This is why math is considered to be universal.

Interesting bonus thought: Some claim that math is just applied philosophy.

Edited May 24, 2013 by Natsarugiy

[Holo]

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?

Mediocrity Principle . Xenology is only possible if you assume that life in the universe willl be similar to us.

[Mihara]

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.

Many people in this thread have already mentioned that notation is culturally dependent while mathematical concepts are not, however... Mathematical concepts are also a little more culturally dependent than is normally believed. See constructivist mathematics for an example of a disagreement over some seriously fundamental mathematical concepts.

[Stochasty]

Mediocrity Principle . Xenology is only possible if you assume that life in the universe willl be similar to us.

Not true at all; it's just a bit more speculative if you don't make that assumption. As someone who makes his living toying around with quantum gravity ideas, there's quite a lot of "just a bit more speculative" I'm willing to tolerate in the name of SCIENCE!