For example, a sapient doesn’t need integers to build a hearth with a cooking fire nor to make a stone-tipped spear. That is an example of science and technology without numbers.
I guess the question here is what we are calling ‘math’? Arithmetic perhaps obviously arises as something in a situation where things need to be counted or kept track of for practical purposes.
But a generalization from that to a formal system is an interesting question. The Greeks like Archimedes and Eristophanes started down that road. But if you follow it to its logical end, this leads to irrational numbers… powers and logarithms. And then to concepts like calculus and imaginary numbers…
True, but other species on Earth have been observed to use tools in some form. Of course this doesn’t imply that they developed them from any theoretical basis?
I guess you need math when you run out of fingers and toes. How useful is math for a species that can count on their individual cells?
Ha Ha! The genius amoba? Right out at the 20th standard distribution.. but not logically impossible.
You should write an SF story about that. The loneliness of being so far ahead of your kind! James Blish almost had something like that with his protos in ‘Surface Tension’…
Would the books be identical?
“Maxwell’s Equations” are actually Heaviside’s equations. The men were both geniuses, Maxwell for having the idea, Heaviside for actually understanding what Maxwell was writing about and formulating the equations we use. (And the notation is another rationalization). Without the Heaviside formulation and modern notation, the books would be quite different.
One of my universities, the math taught to 2nd year engineers was so badly taught, or so badly understood, that it could not be used to support the 3rd yr “Fields” course in the standard formulation. As a consequence of which, derivation of the fields equations was done by a rather different (and rather simpler) method than that used by ever other 4yr radio-comms engineering course on the planet
We’ve got standard approaches, zero chance that their books would be identical to ours.
One thing that always strikes me when I study the history of mathematics is how impenetrably different notation can be from one civilization to another. So I’d expect to see lots of differences among the books.
If we had a dozen examples of alien civilizations to work with, I suspect we would observe some commonalities. I would think that natural numbers and fractional numbers would precede integers and reals for example. That is not necessarily the case - @Chronus’s points are well taken - but I think it would be a reasonable working hypothesis. Similarly, the forces of natural selection are universal, but then so is path dependency. There might a single well-trodden path in mathematics (with yes, multiple variants) - or two, or some other number (possibly a non-integer real number for those accustomed to such thinking).
I’ve been wondering about the perception of time and how it is tied with processing speed. Fast moving residents of planets that average 50 degrees C would presumably have somewhat different chemical interests than our own. Same for slower residents of planets where liquid nitrogen is the norm. Here on earth mammals have constant lifespans if you measure it in heartbeats (well not really, the relationship is apparently inverse semilogarithmic so mutatis mutandis). There might be some universal cognition patterns if lifetime processing cycles in the ancestral environment are similar within an order of magnitude.
A team at MIT discussed the possibility of non-water liquid based life:
Ionic liquids have extremely low vapor pressure and do not evaporate; they can form and persist at higher temperatures and lower pressures than what liquid water can tolerate. The researchers note that ionic liquid can be a hospitable environment for some biomolecules, such as certain proteins that can remain stable in the fluid.
“We consider water to be required for life because that is what’s needed for Earth life. But if we look at a more general definition, we see that what we need is a liquid in which metabolism for life can take place,” says Rachana Agrawal, who led the study as a postdoc in MIT’s Department of Earth, Atmospheric and Planetary Sciences. “Now if we include ionic liquid as a possibility, this can dramatically increase the habitability zone for all rocky worlds."
Not officially. Any that hasn’t yet been created just has a placeholder name, that’s nothing more than a way to encode its number. When someone does create a new one, and that creation is recognized and accepted by the scientific community, then that creator gets to pick an official name (which is usually nowadays done to either honor a specific person, or a specific place).
Who’s this “we”? Indigo is only listed there because Newton thought that seven colors was mystically better than six. Almost nobody recognizes it.
But yes, of course, the division of the spectrum into colors is arbitrary.
I would not be at all surprised if most alien intelligences followed the path of natural numbers first, then generalizing to negatives and fractions (though those two could come in either order), then to reals, then complex (i.e., mostly the same path that we followed). We shouldn’t, a priori and without knowledge of any other sapiences, assume that our own path was an outlier. But there certainly could be some sapiences that followed a different path.
If I can question the premise a bit, there seems to be an assumption that books on math, physics, and chemistry in different earth cultures today – say, in China and France – are pretty much the same. Are they?
Maybe the answer for earth is yes. But even if so, in the solar system in a different galaxy, there could be – and I suspect are – big differences within that solar system. This would be especially likely if there are advanced civilization in different planets in that solar system, as could be true in ours just a few hundred years from now.
And even if everyone has books with pretty much the same content when at the same level of of development, if the other solar system was, say, a thousand years ahead of us, I’d think the books would be a lot different for that reason.
No. Like I mentioned, the periodic table in the Encyclopedia Brittanica would be unrecognizable to most Americans.
If I can question the premise a bit, there seems to be an assumption that books on math, physics, and chemistry in different earth cultures today – say, in China and France – are pretty much the same. Are they?
China and France today, sure. How about moderns and, say, classical Romans? I have heard (but don’t know for a fact) that they had no zero, and that Roman numerals only went up to a million. And that’s just math.
It might be instructive to find some isolated tribe in the Amazon, or on North Sentinel Island, and ask them what they know about math, physics and chemistry. I imagine it’s very different.
Here’s what I found and it looks like what I learned. What am I missing?
Ditto. This looks just like the periodic table I’m familiar with as a former chemistry teacher. The groups were renumbered 1-18 several decades ago by IUPAC.
Here’s the standard IUPAC periodic table:
In addition to atomic number, it includes the standard atomic weight for each element as well (as a weighted average based on the isotopic ratio found on Earth.).
The periodic table in Britannica includes the same information, but you have to click on each element to see it.
Did you mean the 1911 version that was used to help kickstart wikipedia?
As far as color goes, there are species even on Earth that can see into the infrared or ultraviolet. And even among humans, men and women not only perceive color differently, we use a different color vocabulary.
So we can expect those alien books to differ significantly from ours on anything involving color, if for no other reason than things looking genuinely different to them. Just because sulfur “looks yellow” to us doesn’t mean it will to them.
For that matter, imagine if a species with a sense of smell as good as a dog’s wrote a chemical textbook. There’d be massive amounts of information on how chemicals and compounds smell that we don’t cover because we can’t begin to perceive them. A species with a sense we outright don’t have like electroreception would no doubt have major differences on how they describe things as well.
Also, such senses could easily shift the technological and scientific path of advancement they follow, leading to very different textbooks at different levels of knowledge. Who knows what theories a species that can detect electromagnetic fields directly would come up with to explain what they sense when they only have a Bronze Age understanding of the world?
Wiki has a nice article on different types of periodic tables:
Internet has a labor of love detailing some 1400 periodic tables:
Except for all the human societies that don’t use base 10. You gave an example of cultures that use base 12 counting a different part of the hand anatomy. They would say we use base 12 because we have 12 phalanges in our fingers. The Yuki used base 8, as you note, based on the spaces between their fingers.
Base 10 might be the most common number base used by humans, but it’s not the only one and thus not inevitable. If we encounter aliens with 8 finger-equivalents we might guess that base 8 is likely but we should be prepared for them to use a different number base.
Except… it may not be as arbitrary as it initially appears.
Human languages follow a pattern in regards to colors. Some languages have as few as three words for distinct colors, and those are for white, black, and red. Languages with four terms usually add green next but if not they add yellow. Fifth term is usually yellow, but if yellow was fourth then green is added, So languages with five color terms have black, white, red, green, and yellow. Blue is added next (languages without a separate term for blue tend to lump blue in with green - Japanese does this, with a separate term for “green” added only very recently. Brown is added after blue. Only after brown is added do you get the pink/purple/grey/orange/etc. So… maybe there’s something other than just arbitrary decisions going on?
But no, there are no isolated human tribes using ochre, teal, and taupe as primary colors.
But even if aliens perceive color differently it is possible we could still communicate. Parrots can be taught to identify colors with human language terms despite themselves seeing a far different and wider spectrum of color than we do. Parrots have not three but four types of cone cells and can see into the ultraviolet. On the other hand, we might struggle to use their color terms (if a parrot ever wanted train a human in that manner) because we simply can’t see what they see as they see it.
There’s a difference between folk taxonomy and scientific taxonomy. Plenty of cultures lump all flying things together, so bats and birds wind up in the same category. They lump all things that swim together so whales and fish are the same to them (in Medieval England beavers were considered fish for purposes of what was and wasn’t allowed on food-stricted “fast” days).
Science, however, divides creatures differently based on different criteria. That can lead to things like this video that explains how a contagious form of cancer, an STD of dogs, can itself be classified as a dog even though it’s, well, cancer and doesn’t look like a dog, act like a dog, has no limbs or sensory organs or… it’s weird, but there’s a certain logic there. It’s not arbitrary, it’s based on genes and descent. For that matter, the folk taxonomies aren’t arbitrary, either - they’re based on criteria, too, like “things that fly” or “things that live in the water” that are probably useful criteria to the people using them.
So… aliens may categorize things differently than us, but not arbitrarily. We should be able to learn their criteria and communicate, and vice versa.
That doesn’t mean communication would be easy - what if we meet aliens that can’t make sound and communicate by changing their skin colors and patterns? Which isn’t implausible, because that’s a trait of cuttlefish. A computer interface may be necessary to compensate for the fact one party can’t change their skin color and the other can’t produce sounds.
But no matter the folk taxonomies of hypothetical aliens, the periodic table isn’t arbitrary in the data it contains even if the way we arrange that information arguably is. Oxygen atoms have 8 protons. That’s universal. If the atom had 7 it would be nitrogen and if it had 9 it would be fluorine. The temperature of absolute zero is the same everywhere. There really are some constants in the universe, and that’s long been the argument that science is the basis for communication with aliens, starting with those constants.
Although when we communicate with “aliens” here on earth - that is, animals - we tend to start with food so maybe that assumption about science and communication is arbitrary. On the other hand, if we met an alien species in another star system we likely would have no idea what they eat and vice versa. Communicating with another species at our tech level is a different problem than training dogs. For that matter, when two human societies encounter each other we don’t start lobbing food treats at each other. It is necessary to use caution with analogies and metaphors.
I didn’t say or insinuate it was.
I don’t see how that negates what I said. I only said that I think it’s probable that alien math would have grown from a base organized around their biology. Regardless of what base early humans used for math, it was based on digits.
Years back, I read a SF story (by H Beam Piper, I think) in which the ruins of a long-dead civilization on Mars were discovered.
The “Rosetta Stone” was something like a periodic table.
Yes, assuming what we know about the universe is correct, the basic principles are going to be the same. Chemical reactions might be different depending on the environment, but the basic premises would be the same.