Latest blog post: An unforseen hiatus. (2023-01-02)
I myself have never understood how math could help us in communications with aliens. I mean yes, it would allow us to learn some facts about them (for instance do they know math, or what counting system they're using) that could in turn offer some assistance in understanding them, but math is a contextual tool, not a language. X=18*299792458² makes sense only if you know that the first number is kilograms and the second number is the speed of light in meters per second. But how do you convey that information when all you have is some numbers and some operations on these numbers? you can't even give simple answers in math (like 0 is false and 1 is true), because you won't be able to receive and understand the question.
On the subject of math, It's a potentially useful tool for establishing contact, and with some physics you can communicate a few ideas in a way that (assuming your communication gets through) could provide information like distances (multiples of the nuclear distance of dihydrogen are in theory unambiguous). It's not a useful tool for general communication though. Much better to start the same way you would with a foreign human and no translation guides: just gesture at things and say what they're called, figure out a few basic words, then try to teach them the basics of grammar, and once you've got basic grammar and a basic vocabulary you can start using it to teach more.
An actual good starting point, for these people, might be a periodic table. It's pretty universally recognizable even if it's arranged differently, a high-end one has a decent selection of universal numbers, and it would allow Wikipedia-aided discussions of what chemicals various Earth substances contain.
Apropos of absolutely nothing, here's a potential headache that awaits any two alien civilizations that decide to join forces: how do you handle all the laws of reality that we at least chose to name after "the" discoverers? Aliens sure aren't going to be calling Ohm's law, Dzhanibekov effect, Leidenfrost effect and Coriolis forces by those names, but they sure will be calling them something.
I think I would listen to their names for the laws, and any stories they still remembered about why they had those names; and then tell them our names and the stories behind those. Most importantly I'd listen for any differences in emphasis. Consider for example the Peltier Effect, Seebeck Effect, and Thomson Effect. They're similar enough that they're often confused or just explained together; yet sometimes it's good to have the distinction. Alien versions of these effects would very likely have interesting shades of meaning, which would make it worth learning the aliens' own names.
For the most part though, I assume which names get used would be a matter of whose language you're speaking or who you're speaking to. Humans do tend to have instincts about what a thing is "really" called, which make it seem like more of a conundrum; but alien language intuitions might work much differently.
As for the credit for discovering -- for the most part, scientists recognize that there are more than one "real" discoverer of a thing. Names are attached because it makes them easy to refer to.
Establishing a shared vocabulary is largely about pointing at things and saying words. I think for the most part, math provides an extra thing to point at. And if you picture making contact as radio signals being sent over vast distances in space, it seems like the number of things available to point at is rather small. If the alien is already in the room with you, math is no longer the strongest candidate.
People like math for other reasons too, but anyone claiming math is universal hasn't been paying attention to recent developments. Classical logic isn't the only logic that works; "paraconsistent" logic is getting popular and actually allows contradictions, without losing power. Mathematics could be re-founded on topology, type theory, category theory, or even Chu spaces. Non-expert aliens might use group theory on a daily basis and not be particularly aware of numbers, let alone prime numbers.
You second paragraph... you are seriously misunderstanding the nature of mathematics.
"7" is always seven. Always. Not the representation, the written numeral, the actual number of things. You count them, there are seven. It is always a prime number - it is not divisible by any other integer, no matter the representation or base used.
Being unaware of numbers... that would require some kind of hive mind or something, where individuals have no meaning at all, and even then, it still really makes no sense, as you need actual counts for all kinds of things if you are actually going to build something that works.
Topology, type theory, category theory, etc... those are *additional* areas of math, not replacements for the basics.
Unrelated: PLEASE fix your website. The captcha picture is chopped on the left hand side, so I have to make multiple attempts until I can get all the pictures in the rightmost few columns.
When humans speak of founding mathematics on type theory, category theory etc., what we mean is considering that theory to be basic, and then building up the rest of mathematics from there. Typically Peano arithmetic would be the first thing to be built. The first time this happened historically was when Russel and Whitehead founded mathematics on set theory. (This foundation has more or less stuck; so in a technical sense set theory is more basic than numbers, and logic is more basic than set theory.)
Counting is basic to many *human* activities, and historically, numbers were the first big obsession of human mathematics (followed closely by geometry). I will admit, it seems to me counting would be pretty common among intelligent species. However, its familiarity and usefulness do not necessarily mean it would be universal. So I'll attempt in more detail to imagine why it might not occur to an intelligent species.
Counting and measurement are very top-down, control-oriented activities. If you want two things to be the same length, making a numerical measurement is actually a rather complicated way of doing it, which introduces error. Cutting them together or with a jig will do, and if you must measure, making a mark on a stick would work. Some of the earliest written numbers in human history were governments attempting to quantify farm productivity so that they could tax fairly. This was never really "fair" in the first place, since a variety of unquantified local conditions could affect what each farmer could afford to give up each year; the numbers were just appealing to human intuitions about fairness and serving as OK approximations.
I'm going to try and imagine a few precision processes, replacing numbers with tight feedback and non-numerical mathematical concepts. Bear in mind we humans shouldn't expect to always be able to imagine alien solutions to problems, so "I can't imagine doing X without numbers" is far from proof that an alien society would use numbers. In theory, we already know that complex mechanisms can be designed and built without using numbers, since DNA doesn't code for numbers anywhere. Anyway I'll do my best to give a plausible example.
A computer screen produces various colors by coding for intensity of red, green and blue. We humans use numbers for these, but numbers bounded to some space, for example from 0 and 255. An alien society less familiar with numbers might simply use various binary codes from (say) 00000000 to 11111111, conceptualizing them as lying on a line without thinking of them as numerical. The codes might coincide with our binary counting codes, or might be grey codes or some other system. When designing displays with more color depth, they would choose a code with more elements, but might conceptualize it as having colors between the colors of the older display, rather than giving a numerical color depth.
A human chemical factory relies on many numerical measurements to work. But picture for example a chamber which must be heated to a precise temperature. Imagine for a moment that a thermometer readout is used to regulate a heating element. All the numbers on the thermometer seem quite superfluous; what matters is that one line representing the correct temperature. Perhaps mass-manufactured thermometers would have lines labeling various important transitions, such as freezing and boiling points of common materials, and things like body temperature. (A medical thermometer might label danger zones above and below body temperature.)
Experts in mathematics or physics might be aware that there's an abstract sense in which different parts of the temperature scale can be compared; IE, a standard amount of energy could heat a material by what we would call "one degree" whether it's currently cold or hot. But this is a very abstract fact, which only holds true once you correct for changes in specific heat at different temperatures.
Even those experts might not believe the "degrees" would continue being meaningful forever (IE, they can count but believe there's some highest number). There are, in fact, human mathematicians who don't believe in infinity, and much of math works just fine for them. Essentially unjustified logical axioms are needed to prove there are infinitely many numbers.
It seems like much works out fine if numbers are just an obscure topic for certain experts. Admittedly such aliens would seem a bit dim-witted around certain topics, like perhaps estimating how long something will take. But humans are by default fairly bad at recognizing Lie algebras or finite simple groups in daily activities, and aliens who are raised on those concepts (but not numbers) might think humans are pretty daft.
As for the website issues, you might want to complain directly to Disqus somehow, since the problem is kind of on their end.
There are some mathematical proofs that could assist, but if the subject you are attempting to communicate doesn't recognize it, you're out of luck. Some aliens, like humans, also probably flunked at math. It's utility is more in establishing you are dealing with something essentially able reason out problems intelligently. It's not going to get you to asking about the weather.
Actual communication in words between two languages will require establishing meaning both ways, and getting a grasp over just enough vocabulary to get the job done.
Math can allow you to break down anything else into logic. In WW2, math allowed the allies to decipher German codes. Computers do the same thing at extreme speeds. Your cyber life form was shown breaking down multiple languages. While not handy for a one to one scenario, it does have applications. One to one usually builds on simple commonalities , food , water, sleep etc.
Maybe you should learn a little science or read some of the better sf writers. Seriously. Math is fundamental to any rigorous, logical description of the physical world and to understanding exactly what people -or beings in this case - are trying to communicate. Oh, the savages can maybe chatter about simple scrap without it, but when the grownups have to have serious discussions about anything important maths will be at the center of it.
Where are you from? What are your nutritional requirements? What kind of tolerances do our machining and materials have to have for the spare parts you need? What kind of logics do you use to think? Those are just a few of the really crude-but-basic things serious communication with an alien species requires. Mathematics is foundational to all of them.
It is, perhaps, good that you are not telling a story about serious attempts at first contact and are doing a "spunky kids are better and smarter than the adults" one.
"Those are just a few of the really crude-but-basic things serious
communication with an alien species requires. Mathematics is
foundational to all of them."
Yes, but none of those are the first and most important things, and the only things there tangential to the first and most important things (calorie requirements, and such) will matter before a group like this could figure them out, anyway.
My my, so much salt.
Did I said that nobody needs math? I said that I don't understand how math is supposed to help us to start learning structure of an alien language. How would you say what's your name in math?
It is, perhaps, good that you are not telling a story about serious
attempts at first contact and are doing a "spunky kids are better and smarter than the adults" one.
On the contrary, I've been trying to show how moronic Dan is at every opportunity. Without going too far, since I still need an alive protagonist. and yes, spoilers - all the big important talks will be carried out by other characters, not these four.
Aliens might think in what we would find a very unfamiliar logic without being aware of it. They might use some other structure than numbers for much of their math-like activities. Existing human mathematics might not help bridge the gap. Understanding them might eventually involve doing math, but it may be a new branch of math - and all "math" really means in that more general sense is that a task is difficult and requires writing down symbols.
Starting point, maybe? Like, start from things that are universally obvious, like "one and one is two", and establish grammar from there?
That would probably be a useful technique if, like, a spaceship full of professional first-contacters was involved. For one guy alone among strangers, though, it's almost certainly not worth bothering with.