I hope this qualifies within the some room for nonsense rule. I am writing a story about aliens (related to the game mentioned in the other thread), and I wanted to give them an alien form of mathematics, which human researchers can barely understand or interpret.

Is this possible and plausible? I'll mention a few ideas I had (pseudo science is allowed, for the purpose of debunking), and hope someone might be kind enough to mention any that come to mind.

No Irrational Numbers:

Spoiler:

One idea I considered, was if the aliens lacked irrational numbers, and perhaps their number system revolved around PI. Of course, this implies that when dealing with whole numbers they'd get irrational numbers, doesn't it? The idea of something as horrifying to a mathematician as, "these people are beyond irrational numbers!" seems interesting to me, but perhaps it shouldn't be.

Exponential Numbers:

Spoiler:

"1" = 2. "2" = 2. "3" = 4. "4" = 8, etc. A system where each number is exponential could be interesting, and just about all calculations are done in curves and powers (if you're travelling the galaxy, no one said it was simple).

I'm naive as to how difficult it would be learn this system in an alien language. It will be tricky when you aren't sure what numbers J, Q, L and X represent, or even if they are numbers. After the way the math works is discovered, I imagine it won't be too hard to calculate the aliens' figures?

Psychic Images:

Spoiler:

What if, instead of seeing a symbol like 4, you just saw four objects? Or instead of seeing 2.5387777778, you just saw a partial-circle with that exact fraction? If it were possible for a star people to be able to just see the objects instead of representing them with numbers, this could be very difficult to interpret for Earth mathematicians. Of course, it's questionable whether this makes sense, and if the aliens can really tell the difference between 3.14159265359, and 3.14159265358.

Lovecraftian Mathematics:

Spoiler:

Just for fun, I'll mention this idea. Sometimes when you perform the math problem, it comes out exactly how you want it to. Other times, it doesn't, despite using the same formula. The only difference in whether it comes out right or not, whether the math succeeds or fails... is whether you think about it. It gets stranger, when you get to the geometry of non-Euclidean shapes.

I apologize if this thread is not suitable for this board.

There is already a number system with no irrationals. We usually denote it as Q, the set of rational numbers. I don't know what it would mean to have a number system that 1) is larger than the rationals and 2) contains no irrationals; what are the extra numbers, then? In any case, if you don't have irrationals, you definitely don't have pi.

You can have other number systems with all kinds of goofy properties though. In the p-adics, "integers" can be irrational, which is pretty trippy.

"Exponential numbers" is essentially writing in base 2, and would be fairly unsurprising to human scientists.

Psychic images sound cool. It would suggest that the aliens think and perceive in a totally different way than humans do, allowing them to make incredibly fine distinctions as easily as we read text.

No, even in theory, you cannot build a rocket more massive than the visible universe.

Really, any alien representation of math we know about will just take work to translate, but then can be dealt with. "They do arithmetic / counting / mechanics in a super weird way" wouldn't last.

Maybe one option would be to just make all of the relevant mathematics for what they are doing with interestellar travel so trivial to them that they don't know what steps they are following anymore. Like, I cannot explain to you how reading works. I just do it now. I would have a hard time teaching someone to read, other than, just be doing it. Or, when I was teaching Calc 2, I had a really hard time explaining fractions to my students. They were supposed to know! I was not supposed to have to teach this! I could draw the pizza pies on the blackboard and when that explanation didn't work for the kiddies, I just had to hang my head and send them elsewhere, I cannot explain 3rd grade math so well anymore.

Our scientists try to have a talk with the aliens, and they're a little frustrated... "We can try to get someone who specializes in early childhood education on the next ship... we just brought scientists the first time around, we were hoping... no no you're good people, you're cute."

LE4dGOLEM: What's a Doug? Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers. Or; Is that your eye butthairs?

If you want aliens who think in a fundamentally different way than we do, think about what the tortoise said to Achilles. The notion of direct inference is so fundamental to the way our minds work that it can't be explained without making use of the very concept you're trying to explain. "If you know A, and you know 'if A then B', then you know B" is exactly the type of if-then statement it's trying to explain.

You could suppose the aliens have other notions that are similarly fundamental to their thinking and cannot be explained. To us, a lot of their math would look like completely unjustified leaps of logic, but they're actually quite rigorous if only we could understand the alien concept. And every time we struggle through to an argument based on our own methods of logic it turns out the aliens were right all along, but got there much more easily thanks to the mysterious extra concept they have available to them.

May I suggest you read Stories of Your Life, a short story by Ted Chiang? It's a first contact story, and this is one of the elements discussed in it. Not exactly the same, but definitely a similar vibe.

Mighty Jalapeno: "See, Zohar agrees, and he's nice to people." SecondTalon: "Still better looking than Jesus."

Giant Calculator The computers the aliens use aren't used quite the same way. They compute about half of the problems the ship faces--the rest being calculated mentally by the engineers. The engineers need to manually input a lot of the answers, because the machines can't work them out as quickly.

There are some mathematical problems a human does seem better able to solve than a computer, so a technologically enhanced alien may be better still when dealing with incredibly complex ideas. In submarines for example many calculations are still done by hand. If much of the information was missing from the computers, and locked deep in the brain of some alien, it may be impossible to understand what's going on.

Does this seem a reasonable idea?

arbiteroftruth wrote:

Spoiler:

If you want aliens who think in a fundamentally different way than we do, think about what the tortoise said to Achilles. The notion of direct inference is so fundamental to the way our minds work that it can't be explained without making use of the very concept you're trying to explain. "If you know A, and you know 'if A then B', then you know B" is exactly the type of if-then statement it's trying to explain.

You could suppose the aliens have other notions that are similarly fundamental to their thinking and cannot be explained. To us, a lot of their math would look like completely unjustified leaps of logic, but they're actually quite rigorous if only we could understand the alien concept. And every time we struggle through to an argument based on our own methods of logic it turns out the aliens were right all along, but got there much more easily thanks to the mysterious extra concept they have available to them.

Spoiler:

Oh, I like this idea! It would be confusing enough with symbols that represent complex formulas that don't seem to be described. But it'd be stranger still if, "Hey! This doesn't add up!" "That's because you haven't multiplied it by the speed of light." "But it doesn't say to do that." "Does it need to? We're dealing with hyper-speed travel, of course you need to add the speed of light when considering drag forces, as that's the maximum velocity a physical object outside the stasis field can apply. You'll also need to add the Yelk equation." "What is the Yelk equation?" "My friend! If you can remember how to calculate the speed of light, then you remember the Yelk equation!"

When dealing with aliens who basically have a perfect ability to remember mathematical formula, and perhaps a programming that causes them to associate certain formulas with certain tasks and problems, you could shorthand a whole lot of stuff.

The only problem is that computers generally can't short-hand things, can they? They can't make logical leaps as humans can? Generally, you'd expect to be able to look at the computer's code and calculations in depth, and find out everything it does to come to a conclusion. Unless the computer is so advanced no one can work out how to get such a debugging window.

Meteoric wrote:

Spoiler:

There is already a number system with no irrationals. We usually denote it as Q, the set of rational numbers. I don't know what it would mean to have a number system that 1) is larger than the rationals and 2) contains no irrationals; what are the extra numbers, then? In any case, if you don't have irrationals, you definitely don't have pi.

You can have other number systems with all kinds of goofy properties though. In the p-adics, "integers" can be irrational, which is pretty trippy.

"Exponential numbers" is essentially writing in base 2, and would be fairly unsurprising to human scientists.

Psychic images sound cool. It would suggest that the aliens think and perceive in a totally different way than humans do, allowing them to make incredibly fine distinctions as easily as we read text.

Hmm, this gives me an idea.

Irrational Math A system where every number is irrational and calculated to the millionth or even the quadrillionth digit could be very interesting. The computer mightn't like it if you miss out on digits, due to the extreme accuracy necessary for hyper-speed travel. This also makes me wonder if it would be possible to use an irrational base (calculated to the quadrillionth digit making it accurate enough).

The question then being how the computer stores these numbers, as if they're just on the keyboard... you can just type out 2 + 2 without worrying about the quadrillion digits of the irrational. The aliens surely can't be expected to type out a quadrillion digits or the like, unless they do it mentally and their brains just work that precisely and quickly with the computers.

With this system, it'd surely take researchers a long time to use the computer, as PI has only been calculated to the trillionth digit, and this computer requires you to calculate for every number, all of which are irrational.

And thanks, I hoped someone might find that last idea interesting. It may be the one I go with, as the other ideas have questionable aspects.

doogly wrote:

Spoiler:

Really, any alien representation of math we know about will just take work to translate, but then can be dealt with. "They do arithmetic / counting / mechanics in a super weird way" wouldn't last.

Maybe one option would be to just make all of the relevant mathematics for what they are doing with interestellar travel so trivial to them that they don't know what steps they are following anymore. Like, I cannot explain to you how reading works. I just do it now. I would have a hard time teaching someone to read, other than, just be doing it. Or, when I was teaching Calc 2, I had a really hard time explaining fractions to my students. They were supposed to know! I was not supposed to have to teach this! I could draw the pizza pies on the blackboard and when that explanation didn't work for the kiddies, I just had to hang my head and send them elsewhere, I cannot explain 3rd grade math so well anymore.

Our scientists try to have a talk with the aliens, and they're a little frustrated... "We can try to get someone who specializes in early childhood education on the next ship... we just brought scientists the first time around, we were hoping... no no you're good people, you're cute."

Spoiler:

Yeah, that's what makes this challenging to try and present a bizarre form of mathematics. It may be impossible, or may just be impossible for humans.

Like a kid with a calculator who has forgotten how to calculate by hand. I like that idea. And... wow, the kids just didn't know fractions? Talk about a school system failure (no offence to you). I'm totally stealing that line, just so you know.

I like the idea of aliens with calculators who don't understand it. You just need to make sure the scientists can't take apart the calculator so as to understand it. Maybe the calculator is attached to a large brain, or maybe it's some kind of Tesla-looking electric calculator that gets results through voltage and energy (where it's just going to take a long time to safely test the voltage, amps, and resistance involved, and reverse-engineer how the aliens use these to math).

Zohar wrote:May I suggest you read Stories of Your Life, a short story by Ted Chiang? It's a first contact story, and this is one of the elements discussed in it. Not exactly the same, but definitely a similar vibe.

I will look that one up. Thank you Zohar, it may well give me some ideas on how to handle this. How would you rate its presentation for alien math (or whatever the subject was)?

Yes, I was just about to mention Story of Your Life. That's the one "Arrival" (the recent movie) is based off of. I'm not sure if I would say the story is necessarily better than the movie or vice-versa; they're different approaches to similar subject matter. But the movie definitely doesn't bother with the nifty mathy bits.

I wonder how far you could get disregarding precision? Like, an alien species who regards it as not merely eccentric, but unthinkably insane to start rattling off the digits of pi even past ten decimal places. One that makes do with 22/7 the majority of the time, and regards resorting to 355/113 as downright transgressive? After all, how many cases are there that you actually need particular precision with pi?

Also along those lines, I might envision a species who regards it as anathema to write "3.14159..." and insists that the series representation is the only reasonable thing to use.

Another thing that comes to mind is Sawyer's Calculating God, which posits a species that can intuitively perceive numbers as high as 46 (or something) in the same way humans can perceive groups of five or six objects without actually having to mentally enumerate them. Said species, however, actually has no representation for numbers larger than 46.

What if the universe they come from (or the bit of ours, because of *mumble mumble cough*) had a pi that was 22/7? Or 3. Or 4. They'd never have to have to deal with irrationals. (Yeah, we got to do something even more skewy to rid ourselves of root(2), etc, as well.. Or else they "refuse to deal with them in normal circumstances" like we avoid dealing with negative, or even imaginary, roots.)

But we're talking weirdness beyond mere "taking a different perspective on life" a la the Jatravartid delay in developing the wheel, in favour of the under-arm deodorant. Probably have to bring their own bubble-universes with them to stop their structures/molecules/atoms/nucleons/etc not being quite right.

I'm not sure we won't just be encountering aliens with different ideas of number base (or place-variable-bases, perhaps, with triangular numbers being useful, even a Sierpinskiesque manner of holding increasing values without running out of names) and some weird tricks we haven't thought of while they've ignored some of the ones we take for granted (like finding a different form of trigonometry that still gives the same answers when properly applied).

Although, thinking about it only as I write, there's always a chance that they have adopted a set-theory style of notation (in different symbolics) from the assumed similar origins of numbers to ours of "packaging up" tokens into administrative enclosures, then going a different way from us.

Jorpho wrote:Also along those lines, I might envision a species who regards it as anathema to write "3.14159..." and insists that the series representation is the only reasonable thing to use.

That species is human mathematicians.

LE4dGOLEM: What's a Doug? Noc: A larval Doogly. They grow the tail and stinger upon reaching adulthood.

Keep waggling your butt brows Brothers. Or; Is that your eye butthairs?

As a suggestion for a premise, how about aliens with brains that function in some part like quantum computers so they percieve numbers as superpositions.