# Caveman Mathematicians



## RVM45 (Feb 20, 2008)

.....Does anyone think that it's remotely possible, that a band of hunter-gatherers who were really obsessive and persistant- over multiple generations- could develop a highly advanced and complicated mathmatics- passed down exclusively by word of mouth?

.....I mean, maybe sketching on the ground occasionally; to illustrate an idea- but with no written language- or paper/paper substitute good enough to pass diagrams onto the next generation either.

.....Might use the idea in a story sometime- but really, the idea just facinates me.

.....RVM45


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## Parson (Feb 20, 2008)

I want to say it would be possible, but I am tripping over "highly advanced and complicated mathematics." If that means what I understand mathematics to mean "addition, subtraction, multiplication, and division" then I would say yes. If you mean things like advanced algebra, plane geometry, trigonometry, etc. then I would say no. The concepts are too complex for more than 1 or 2 in a thousand to work with in their head. The odds of nomadic hunter gathers to have the contacts, to say nothing of the time, to pass on the knowledge to someone who understands it, is vanishingly small over the course of a couple of generations.


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## Overread (Feb 20, 2008)

I think Parson sums it up - the basics yes, they could be past along from generation to generation and also have a use in the lives of the caveman.
More complex mathematics is way to complex to convey by word of mouth only, and without writing it down many would not be able to work with it. Also, what use would it be to cavemen? Many advanced levels of maths link to architecture and design - things that hunter gatherers are not really focusing on in their daily lives


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## RVM45 (Feb 20, 2008)

.....Some races might be far more gifted at mathematical/abstract thought than humans.

.....The root question was: could people with primative technology; nonetheless have highly sophisticated inner thought lives?

.....The only other intellectual pursuit that might be open to them; would be to play chess; and carry hundreds of opening systems around in their heads.(or other games of strategy; where it's useful to carry around beaucoup "case law" in one's memories.)

.....People forced to live as primatives; might make a certain level of mathematical skill a necessary qualification to bear children- thus assuring that their brains didn't degenerate under their imposed rustification.

.....RVM45


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## Pyan (Feb 20, 2008)

Not quite the same, but the _flouwen_ in* Flight of the Dragonfly*, by Robert Forward, while being basically giant, coloured jellyfish, have developed extensive and advanced mathematical concepts, without the use of a written language.

Worth a read if you can find it.

*(Spoilers)*
Rocheworld


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## chrispenycate (Feb 20, 2008)

> If that means what I understand mathematics to mean "addition, subtraction, multiplication, and division"


 That, sir is arithmetic, a minor corner of number theory, itself not the largest subset of the universe of mathematics. It has gained precedence due to it's immediate practical use (already damning it in the eyes of a true mathematicin, for whom even relevance is a negative point) and is generally overlooked as even a twig by the pure, the unworldly, those who can apreciate the elegance of an indisputable truth.

The amount of verbal information that can be carried forward from generation to generation suggests mathematics would be entirely transmissible in this fashion, continuing unchanging until the next revelation occurs. However, mnemonics in these cases are generally aided by rhythm and rhyme, to which mathematics does not, unfortunately lend itself in English – indeed, most mathematicians would be incapable of translating their theorems into a language designed (well, evolved actually) for explaining practical matters.
If I were to say "Introducing imaginary numbers changes our number field from a scalar to a vector base, thus effectively adding a dimension." you would obviously understand, but memorising might be a little more complicated. If I rewrote the above as a limmerick, memorising would become considerably easier, but comprehension less so (it's all right, you can come out from under the table, I'm not going to do it).
We requir a language which is mathematecly precise, and the paradigms of polydimensional topology woud scan, and rhyme.
Unfortunately, in mathematics an important discovery can not merely change the vocabulary of the language (any discovery can do that) but the grammar – the discovery of infinite regress, leading to calculus, changes the grammar of all geometry beyond trigonometry, and the songs must follow…


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## Ragnar (Feb 21, 2008)

I can't help wondering why it would have to be developed by word of mouth. They may not have a written language or access to paper but you don't necessarily need either to make a lasting record. 

Ishango bone - Wikipedia, the free encyclopedia


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## Parson (Feb 21, 2008)

Chris,

I knew the distinction between Mathematics and Arithmetic, but few people use the distinction rigorously. Even my high school teachers would assign "arithmetic" homework, but called it "math." And as you said arithmetic is a subset (see mathematics term!  ) of mathematics. 

As for you limerick idea --- Well let's just say that if that idea were used my grades in plane geometry would certainly have been better. 

I'm trying to imagine such a Limerick, but since my imagination seems a little shaky this morning (trying to forgett the bawdy limericks that break me up with humor which is not considered appropriate for a parson) I'll have to settle for Ogden Nash.

It raineth on the Just
and on the Unjust.
But chiefly on the Just.
For the unjust
steals the just's umbrella.


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## chrispenycate (Feb 21, 2008)

Well, as an unfrocked mathematician myself, I will state that nothing prevents them from having poetic leanings (or in my case, Limmerickitus) James Clarke Maxwell, though a fizzycist rather than a true mathematician wrote verse; I cite his "Rigid body sings".



1. Gin a body meet a body
Flyin' through the air.
Gin a body hit a body,
Will it fly? And where?
Ilka impact has its measure,
Ne'er a ane hae I,
Yet a' the lads they measure me,
Or, at least, they try.

2. Gin a body meet a body
Altogether free,
How they travel afterwards
We do not always see.
Ilka problem has its method
By analytics high;
For me, I ken na ane o' them,
But what the waur am I?

Wouldn't Physics and mathematics be easier to remember if they were presented like this (starts scribbling notes for the "second law of thermodynamics rag" – no, Flanders and Swann did that one, didn't they?


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## Lith (Feb 22, 2008)

Charles Dodgson also did double duty as a poet/writer and a mathematician. But I still don't have a clue what those two limericks mean...



> .....Does anyone think that it's remotely possible, that a band of hunter-gatherers who were really obsessive and persistant- over multiple generations- could develop a highly advanced and complicated mathmatics- passed down exclusively by word of mouth?


It's as you said, _remotely_ possible. They'd have to have a _reason_ to indulge all that math, and what use is it, when it has no relevance to their life? Possibly if it was semi-religious in nature, it would be valuable, but otherwise? I doubt it. There is a language out there that has no numbers higher than 4- anything over that is simply "a lot". The tribe that speaks it has apparently never needed more. 

That said, _if_ there was any form of mathematics among them, it would probably be geometry. And what would they use it for? Calculating fortunes? Staring at the stars and figuring out the whole concept of time? Would they even know what a straight line was for? A pure circle?

Questions to think about...


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## Parson (Feb 22, 2008)

chrispenycate said:


> Well, as an unfrocked mathematician myself, I will state that nothing prevents them from having poetic leanings (or in my case, Limmerickitus) James Clarke Maxwell, though a fizzycist rather than a true mathematician wrote verse; I cite his "Rigid body sings".
> 
> 
> 
> ...



Chris,

Are these limericks some sort of Scots? or Irish? The contractions are very obtuse (another mathematical term!) to me. Ilka = I like a? or is it a technical name for a problem? I haven't a clue as to "ane." Methinks that the limericks have to do with the laws of inertia, but I might be off on a tangent (another mathematical term!)


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## chrispenycate (Feb 22, 2008)

James Clarke Maxwell was a Scott, and the entire piece is a take off of a Burns piece, and yes, it is the law of conservation of momentum.

I fear they are not limericks, those are my personal perversion, and would presumably be done with an Irish accent. "ane" is, I believe "one", "ilka" each or every

Mind you "Heat won't pass from a colder to a hotter
You can try it if you like but you'd far better notta"  (or you can't win, you can't even break even, and you can't quit the game) are mnemonically better than their mathematical equivalents.


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## Parson (Feb 22, 2008)

Thanks! The "near limericks" make sense now.


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## Montero (Feb 22, 2008)

I think that if there were an advanced form of thinking that was passed on orally, other than religion, it would more likely to be some form of philosophy.

Read an autobiography the other month (forgotten man's name already) - by someone who grew up in Wales before WW2.  He gave an account of riding in the cab of the lorry with his father and uncle, both of whom were illiterate.  They were discussing, in great detail, the sermon they'd heard on Sunday, and comparing it with other sermons and other preachers.  They had excellent memories of all the sermons and were making sophisticated points about style, delivery and content.  This was a regular pass time for the pair of them.


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## manephelien (Feb 22, 2008)

I highly doubt the people who built Stonehenge as a way to determine the exact time of summer solstice were literate, but I could be wrong.


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## Montero (Feb 22, 2008)

Thought just occurred to me.  We have no records of writing from the caveman period, though there are some very good cave paintings of hunting.
So, things involving building, astronomy etc could have been portrayed pictorially.  May just be the records that were used in the period haven't survived.  It is possible that there were records put on skins, to roll up and take with you to the buildings site.  Just not provable.



> I highly doubt the people who built Stonehenge as a way to determine the exact time of summer solstice were literate, but I could be wrong.



Medieval master builders of cathedrals probably couldn't read and write to any level we'd refer to as literate, possibly little more than a signature, but they would have been trained in the tools of their trade.  Compasses, set squares, plumb lines etc.  A lot easier than to learn and hand on a visible skill than a wholly invisible one like mathematics.  I can just picture Medieval builders better than those of Stonehenge having seen various illustrations, documentaries and reconstructions.


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## Xelebes (Feb 25, 2008)

Accountants use ancient mathematics - simple addition and multiplication with no negatives and no zeros.  In this way of mathematics, you can easily do math without using numbers.  All you have to do is credit something.

I have an apple.  He has an orange.  I trade the apple for the orange, so I'm down an apple and he is down an orange.  If we do this over and over again, how much apples will I need to have exchanged with him to have the oranges I have now?  What if I could only get fewer oranges for every apple that I gave?


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