It's been mentioned a lot in sci-fi movies and TV, and I think in fact, that maths can be used as a universal language, that it's the one thing all intelligent specis would know. But after seeing the scene in Trek XI in the Vulcan education center I started to wonder if other races would teach mathematics similar to the way we would teach it? I mean an X and a Y to us could mean something totally different to other races. What about the other mathematical symbols that we have, would other races have these as well?
Mathematics as a universal language?
- Thread starter Crewman47
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That's not really what is meant by saying mathematics is a "universal language."
There are certain constants in the universe, such as the gravitational constant. Concepts such as prime numbers are also required for mathematics of any complexity. These things work no matter what kind of number system you're using.
Sure, they will use different symbols and might approach things differently, but if we were presented with some theorems and proofs from an alien math system, we should theoretically not have too much trouble deciphering it and relating it to our own mathematics. It should be far easier to do this than to, say, translate a linguistic message.
There are certain constants in the universe, such as the gravitational constant. Concepts such as prime numbers are also required for mathematics of any complexity. These things work no matter what kind of number system you're using.
Sure, they will use different symbols and might approach things differently, but if we were presented with some theorems and proofs from an alien math system, we should theoretically not have too much trouble deciphering it and relating it to our own mathematics. It should be far easier to do this than to, say, translate a linguistic message.
This thread title reminds me of that scene in Norton Juster's "The Phantom Tollbooth" where the Mathemagician of Digitopolis, who is enemies with King Azaz (the Unabridged) of Dictionopolis, once sent him a letter to try and clear the air, only for the letter to be flatly rejected as Azaz couldn't understand it. That letter consisted entirely of numbers arranged as if they were words, that made very little sense at all - but the Mathemagician argued contrarily, stating that a "3 is a 3" anywhere in the world. 
Hydrogen has one proton in its nucleus, no matter where you go.
They probably wouldn't use a base ten system. I tried thinking in another base (I think eight) once. It's difficult. It's true that it can't be overstated how important to our own cognitive faculties language, including numerical language, is--but the underlying math would remain the same, just as hydrogen is the same whether you call it hydrogen or glibnoop.
They probably wouldn't use a base ten system. I tried thinking in another base (I think eight) once. It's difficult. It's true that it can't be overstated how important to our own cognitive faculties language, including numerical language, is--but the underlying math would remain the same, just as hydrogen is the same whether you call it hydrogen or glibnoop.
It is definitely something that commands respect, no doubt about it.
Yes. Any sufficiently advanced and intelligent species out there would no doubt come to similar conclusions about the nature of the Universe as us, even though the names are different - for example, the base of their numerical system may be based on different numbers of digits on their upper limbs or something, just as our standard Base 10 system seemed to evolve from looking at the 5 digits on each of our hands and taking things from there. I'm racking my brains to see if there's a better explanation for the current theories in many forms of science, or if there's a better approach towards these theories - something that the aliens might have come up with but is beyond our way of thinking (just as some of our ways of thinking may be completely alien to them).
The trick is to see which aspects of our knowledge are things that the aliens can understand. Maybe they prefer to understand the musical compositions of JS Bach instead of the laws of calculus, for example.
Other bases really aren't so hard with practice... both binary and hexadecimal are used heavily in various computer-related things and you eventually get used to it. But as you say, the underlying math is all the same, just expressed differently.
^Sure. I reckon it's basically like learning grammatical rules. But it does take some practice. I know hexadecimal blows my mind. 
Yeah, once you get accustomed to translating decimal to binary, octal, hexadecimal, or even base64, it doesn't seem so bad. 
If we meet an advanced species somewhere Out There, both of us will have had to undertake some serious maths to get there. So Each side would first work out what symbols mean (1-10, +, -, etc) using simple demonstrations (10 strokes next to the number 10 and so on), and once the symbols were understood, it could probably progress fairly quickly from there, computers could translate fairly quickly.
It might only get confusing when we moved on to language, and there would be words with letters used in algebraic formulas. But that's another thread.
It might only get confusing when we moved on to language, and there would be words with letters used in algebraic formulas. But that's another thread.
It's a universal language, but the encoding used by an alien race may still be very difficult to decipher, as people have said already.
An Alien race may not even use written forms composed of characters like ours; I tend to imagine what Dolphin maths would look like if they ever developed far enough to grasp such concepts. Imagine a writing system based on texture to alter reflected sound waves fully in three dimensions - better yet, imagine an equivalent system for senses we don't have that evolve in a completely alien atmosphere under an alien sun!
Now, worse yet, imagine how this alien race might communicate with others on its home planet: electromagnetic waves (radio, laser, x-rays, gamma rays), seismic waves, sound waves in a thicker atmosphere that go much further, neutrino communication, coherent electron or proton beams... the list isn't endless but is certainly very long, even counting just the physics we currently know!
Now, use one of those forms of encoding to encode the alien writing system.
We encode text in ASCII or unicode character, or worse yet, in to a bitmap image of a form that began as dried pigment on dead trees, especially if you're trying to send mathematical equations.
So what equivalents might there be for encoding dolphin sonar writing?
We compose these encoded characters in to computer 'files' (another invention based on stashing dead trees) and encode these files using non-trivial checksum algorithms and apply 'packets' from various digital networking or broadcast standards before we arbitrarily decide to module the frequency or amplitude of the radio waves and broadcast them at uselessly low power for interstellar reception.
To sum up - we may or may not be able to receive and decipher a signal from an alien race over interstellar distances.
If we receive it, we might recognise order.
Decoding it to anything meaningful would be another matter entirely.
If you can get over these hurdles, sure, you can talk maths. But these are fairly big hurdles!
An Alien race may not even use written forms composed of characters like ours; I tend to imagine what Dolphin maths would look like if they ever developed far enough to grasp such concepts. Imagine a writing system based on texture to alter reflected sound waves fully in three dimensions - better yet, imagine an equivalent system for senses we don't have that evolve in a completely alien atmosphere under an alien sun!
Now, worse yet, imagine how this alien race might communicate with others on its home planet: electromagnetic waves (radio, laser, x-rays, gamma rays), seismic waves, sound waves in a thicker atmosphere that go much further, neutrino communication, coherent electron or proton beams... the list isn't endless but is certainly very long, even counting just the physics we currently know!
Now, use one of those forms of encoding to encode the alien writing system.
We encode text in ASCII or unicode character, or worse yet, in to a bitmap image of a form that began as dried pigment on dead trees, especially if you're trying to send mathematical equations.
So what equivalents might there be for encoding dolphin sonar writing?
We compose these encoded characters in to computer 'files' (another invention based on stashing dead trees) and encode these files using non-trivial checksum algorithms and apply 'packets' from various digital networking or broadcast standards before we arbitrarily decide to module the frequency or amplitude of the radio waves and broadcast them at uselessly low power for interstellar reception.
To sum up - we may or may not be able to receive and decipher a signal from an alien race over interstellar distances.
If we receive it, we might recognise order.
Decoding it to anything meaningful would be another matter entirely.
If you can get over these hurdles, sure, you can talk maths. But these are fairly big hurdles!
Who would use neutrinos to communicate?
The only scenario I can think of where they would be both useful and remotely feasible to use would be if the intelligence using it lived inside a sun.
The only scenario I can think of where they would be both useful and remotely feasible to use would be if the intelligence using it lived inside a sun.
Who would use neutrinos to communicate?
One advantage of neutrinos for communication use is precisely that they're not affected as much by local conditions, so for sending information over interstellar distances may actually be more useful. Doing a quick Google reveals various papers and articles on their theorized use and possible advantages over communicating using EM.
Obviously it's not the symbols that are universal (in fact, they are not even universal on Earth, because half of the world uses different alphabets for starts), but the mathematical concept behind them.
Yeah, I found some after I wrote that. It does seem a bit pie-in-the-sky, but it's impossible. I retract my incredulity.Who would use neutrinos to communicate?
One advantage of neutrinos for communication use is precisely that they're not affected as much by local conditions, so for sending information over interstellar distances may actually be more useful. Doing a quick Google reveals various papers and articles on their theorized use and possible advantages over communicating using EM.
Really, it doesn't sound all that impossible for a species to develop maths without the concept of integers. Any species corporeally even roughly similar to us (i.e. bodies and limbs) would probably start out thinking in integers, but there could be other kinds of intellects. And if they based maths on the observable nature of the universe, they might come to the conclusion that the only numbers that exist for real are zero and one. Nothing in nature exists in greater numbers than one; at most there can be a group of more or less similar things, a group of unique ones, never two or three of the same. 2, 3 and so forth would be considered "imaginary numbers" of sorts, thereby altering the basic language even if not content of maths, perhaps so far as to make deciphering human maths near-impossible.
Also, many of our ideas of geometry might be completely missed by folks living in a 3D rather than 2D environment (i.e. floating). They'd get there like we might get to tesseracts, but again the language would be formulated quite differently when it evolved from a different starting point.
Timo Saloniemi
Also, many of our ideas of geometry might be completely missed by folks living in a 3D rather than 2D environment (i.e. floating). They'd get there like we might get to tesseracts, but again the language would be formulated quite differently when it evolved from a different starting point.
Timo Saloniemi
FYI our geometry is not limited to 2 or even 3 dimensions.
In practice, it is.
That is, our geometry does acknowledge the existence of an infinite number of dimensions, but our environment features just two dimensions of significance - the ones pertaining to the horizontal plane, be they axes in a carthesian coordinate system, or an axis and an angle, or whatnot. We perceive the universe through those, often projecting it on a piece of flat paper; adding a third dimension is something of a mental exercise.
I don't mean to imply that creatures living in a fully 3D environment would have an easier time perceiving dimensions beyond the third. I just mean they would organize their concepts of geometry differently to start with.
Timo Saloniemi
That is, our geometry does acknowledge the existence of an infinite number of dimensions, but our environment features just two dimensions of significance - the ones pertaining to the horizontal plane, be they axes in a carthesian coordinate system, or an axis and an angle, or whatnot. We perceive the universe through those, often projecting it on a piece of flat paper; adding a third dimension is something of a mental exercise.
I don't mean to imply that creatures living in a fully 3D environment would have an easier time perceiving dimensions beyond the third. I just mean they would organize their concepts of geometry differently to start with.
Timo Saloniemi
I'm confused. I live in a three-dimensional environment.
I completely disagree. The main reason why plane geometry is far more prevalent is because it's much easier to calculate (it's literally 2/3's the work). It's a inarguable fact of our 4D space-time universe. There is no possible way you can calculate the volume of an object with less work than finding the area of a face of that object. 2D by its nature is also easier to depict using traditional materials. A square can be copied onto a piece of paper, a globe (no matter how hard Mercator tried) cannot.
Now, you don't have to use a Cartesian X/Y/Z system, but that isn't the only system we've figured out either. It's just, again, the easiest. I could think of 1-2 other ways of describing coordinates, but all those involve calculating arcs. Is it possible that there's aliens that reason that way? Sure. However, just because we don't default to such thinking it doesn't mean we can't.
Personally, I tend to think 3D and 2D equally well, though there's more applications for the latter. However, that's a skill that was acquired with a lot of time spent manipulating 3D models with Autodesk StudioMax, before my head started doing it by itself. There's research suggesting that, with the right kind of simulator, people can be taught to comprehend and easily manipulate objects (tesseract, hyperpyramid) in 4 dimensions in less than an hour. It makes one wonder where exactly the limits of the mind really are.
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Only for those who didn't take much math beyond high school.
I find it amazing how little people know about math (specially geometry/topology) beyond Euclid. Just because your experiences with math are limited, don't go projecting that limitation on the rest of mankind.
Of course one would hope that if we find someone out there to talk to that they are also not so limited... but then again, that is why we have measures for a species' mathematical prowess.
For example, π shows up everywhere in math, but it's value is still being worked out. One way to see how advanced a species might be is to see how far they have calculated π compared to where we currently are.
