Saturday, May 1, 2021

921: And then we learned to count

 What has fascinated me from the moment I became a student of philosophy is mathematics. During high school I was a complete zero in mathematics. It seems I wasn't born for it.


But philosophy taught me what mathematics really is and how to understand and interpret it. It didn't make me a mathematician, but at least someone who understands what mathematics is.


Probably everybody will understand that mathematics must be a huge collection of regularities and principles.


This leads of course to the fascinating question: where do mathematics and the simpler branch of arithmetics come from.? 

The invention of numbers undoubtedly has an empirical basis. There must be a relationship with problems that occurred in the practice of everyday life. 


The people, for example, who owned those herds of sheep or goats had to be able to be sure that all the animals, with whom they had left in the morning to the meadow, returned to the cage in the evening.


Those who stored tools or weapons, or who had supervised the food stocks of the Community, had to be able 


to verify whether the number of foods or weapons or tools were still the same as when they left them in storage. 


And those who were enemies with their neighbors will have been worried when it came to an armed expedition, and have wanted to know if they could still have the same number of soldiers.


The people who lived from barter had also to be able to estimate which amount of food or other merchandise they had to exchange at what quantity..


But what to do when you can't count, when the concept of number has not yet emerged in your brain?


There still exist tribes in remote places that can not count. Their way of "counting" is: one, two,..... many.


How did the prehistoric man know, that the same number of sheep as yesterday enter his cave for the night?


He invented an ingenious solution. He sat at the entrance of his cave and every time a sheep entered the cave he scratched a marking in a bone or stick.


The next day his finger moved to the next marking on the bone, whenever a sheep entered the cave. 


In that way, he could check if he missed some sheep or if there was one more, a new lamb for instance.


Probably without knowing it consciously he used the principle of mutual relationship or the principle of proportionality.


the Ishango bone is a bone tool, dated to the Upper Paleolithic era, around 18,000 to 20,000 BC.  


It is a dark brown length of bone, the fibula of a baboon. It has a series of tally marks carved in three columns running the length of the tool.


I read an article, which explained that this was not just a simple tally stick but contains all kinds of possible mathematical interpretations.


How and when it happened that man moved from the tally stick to the abstract concept of number,


is as big a mystery as to how and when the humanoid primate moved from instinct-driven animal to self-conscious being.


Thank you for your attention again.....


MacMillan The Encyclopedia of Philosophy, 2nd edition
Routledge Encyclopedia of Philosophy, 1995
Rens Bod: "Een Wereld vol Patronen".  2019

The Discussion

[13:17] herman Bergson: A first step on the road of knowledge

[13:17] CB Axel: I suppose we started giving numbers names so we could stop carrying ape fibulas around.

[13:18] Particle Physicist Bejiita (bejiita.imako): we have an inbuilt sense for quantity and quantitative relations id say

[13:18] Particle Physicist Bejiita (bejiita.imako): but many animals have that too, u can learn a parrot to count for ex

[13:18] herman Bergson: It is not that simple Bejiita....

[13:19] CB Axel: Instead of pointing to the marks on a bone or stick we could tell someone we were bartering with that we'd trade them a certain number of sheep for whatever.

[13:19] Particle Physicist Bejiita (bejiita.imako): the really interesting thing is that mathematics is sort of the language of nature, it never lies, if u can calculate it its true

[13:19] herman Bergson: Some animals are able to discern quantities as long as the objects are less then 6

[13:19] Particle Physicist Bejiita (bejiita.imako): the higgs boson is the most striking example of this, it was just a calculation and then they ran the accelerator and BAM surely it was there! just as they had calculated 

[13:20] herman Bergson: Besides that we have no good eye for quantity....

[13:20] herman Bergson: A stack of plates....are those 12 plates, 15 plates?

[13:20] herman Bergson: We aren't able to see that

[13:20] herman Bergson: I read that our visual max is seeing 4 objects as a quantity

[13:21] Particle Physicist Bejiita (bejiita.imako): also computers rely 100% on math and since they can represent colors sound ect its also a proof that everythibng can be turned into and be described with a mathematical  expression

[13:21] Particle Physicist Bejiita (bejiita.imako): the very word computer mean literarily calculator or counter

[13:21] Particle Physicist Bejiita (bejiita.imako): and was used 10000s of years befor the machine was invented

[13:21] herman Bergson: But exactly THAT is the magic Bejiita.....from a philosophical point of view...

[13:21] Particle Physicist Bejiita (bejiita.imako): ah

[13:22] Particle Physicist Bejiita (bejiita.imako): its amazing stuff for sure

[13:22] herman Bergson: We can count objects if we have developed the abstract concept of number.....

[13:22] herman Bergson: But the next step is more exciting.....

[13:22] herman Bergson: By manipulating the numbers we can predict what will be the outcome...

[13:23] Particle Physicist Bejiita (bejiita.imako): yep

[13:23] herman Bergson: not only in the calculation but also what it will be in reality....thence we can build a bridge that will not collapse

[13:24] herman Bergson: We can calculate where the Mars lander will land....

[13:24] Particle Physicist Bejiita (bejiita.imako): aaaa

[13:24] Particle Physicist Bejiita (bejiita.imako): and then fly helicopter with it there

[13:24] herman Bergson: Phythagoras ascribed some mystic features to this observation

[13:25] herman Bergson: I myself still don't understand how the world can be mathimatical, while mathematics is a pure creation of our brain

[13:25] Particle Physicist Bejiita (bejiita.imako): but fact is its true

[13:26] Particle Physicist Bejiita (bejiita.imako): EVERYTHING can be described with math

[13:26] Particle Physicist Bejiita (bejiita.imako): so its the natures own language

[13:26] Particle Physicist Bejiita (bejiita.imako): universes own language

[13:26] herman Bergson: question about it.....but how must we understand the relation between reality and this brain product of ours?

[13:27] Particle Physicist Bejiita (bejiita.imako): well i guess math and numbers is our interpretation of it, an interpretation that works 100%

[13:28] herman Bergson: there must be some relation between the fact that we can count objects

[13:28] Particle Physicist Bejiita (bejiita.imako): we created the system but its based on everything around us and how it relates

[13:28] Particle Physicist Bejiita (bejiita.imako): all things

[13:29] herman Bergson: But when Pythagoras says a2 + b2 - c2.....there is no empirical base for that

[13:30] herman Bergson: But when you draw a triangle with a 90 degree fits

[13:30] Particle Physicist Bejiita (bejiita.imako): aaa yes

[13:30] Particle Physicist Bejiita (bejiita.imako): but how did he discover that?

[13:30] herman Bergson: The Babylonians already had discover it....

[13:31] oola Neruda: many things require an object or whatever that can be quantified... and a predictable possible answer... the numbers do not work in a vacuums

[13:31] herman Bergson: me..^_^

[13:31] Particle Physicist Bejiita (bejiita.imako): same with pi, although thats a bit simpler, someone divided diameter with circumference and voilla

[13:31] Particle Physicist Bejiita (bejiita.imako): then we created supercomputers to get as many decimals as possible for no real meaning

[13:31] oola Neruda: data

[13:31] Particle Physicist Bejiita (bejiita.imako): other then it's a cult number

[13:32] herman Bergson: I think numbers work in a vaccum without any object related to them oola....

[13:32] herman Bergson: a lot of theoretical mathematics  is like that

[13:32] Particle Physicist Bejiita (bejiita.imako): ah

[13:32] oola Neruda: yes... but that is not the entire process...

[13:32] oola Neruda: a goal... something to be measured or discussed etc

[13:32] Particle Physicist Bejiita (bejiita.imako): like how they decided there MUST be a higgs field!

[13:33] Particle Physicist Bejiita (bejiita.imako): and then they proved it

[13:33] herman Bergson: The question could it related to an empirical process?

[13:33] theo Velde is online.

[13:33] Particle Physicist Bejiita (bejiita.imako): but was just theory first

[13:33] oola Neruda: well said

[13:33] oola Neruda: emperical process

[13:33] Particle Physicist Bejiita (bejiita.imako): aaaa yes

[13:33] herman Bergson: I still haven't figure out an answer.....

[13:34] Particle Physicist Bejiita (bejiita.imako): connected to an object or not 1+1 is always 2

[13:34] Particle Physicist Bejiita (bejiita.imako): except in politics lol

[13:34] herman Bergson: based on the principles of arithmetic yes

[13:35] herman Bergson: You con't need objects for the calculation

[13:35] oola Neruda: think quantum theory.... and its relationship to math

[13:35] oola Neruda: something to put data to

[13:36] oola Neruda: you need to be able to measure or imagine

[13:36] herman Bergson: what I find fascinating is that tenth of thousands of years ago man began to use his brain in a mathematical way

[13:36] herman Bergson: we can register it, but I see no way to explain it

[13:37] Particle Physicist Bejiita (bejiita.imako): aaa indeed its amazing stuff

[13:37] herman Bergson: So...maybe this something interesting for you to ponder about during this weekend ^_^

[13:37] Particle Physicist Bejiita (bejiita.imako): easy to explain one way but almost impossible another

[13:37] Particle Physicist Bejiita (bejiita.imako): almost like magic

[13:37] oola Neruda: early math was very functional... useful... needed

[13:38] oola Neruda: like the sheep that needed to be counted

[13:38] oola Neruda: NEEDED

[13:38] herman Bergson: In the early stage of mankind they weren't counted....

[13:39] Particle Physicist Bejiita (bejiita.imako): wel its what enables me to turn a CAD drawing into JD coasters using a machine

[13:39] Particle Physicist Bejiita (bejiita.imako):

[13:39] Particle Physicist Bejiita (bejiita.imako): hehe

[13:39] herman Bergson: they were compared with the carves in a stick

[13:39] oola Neruda: by name...

[13:39] Particle Physicist Bejiita (bejiita.imako): that one needs improovement though

[13:39] oola Neruda: no... but kept track of

[13:39] Particle Physicist Bejiita (bejiita.imako):

[13:39] herman Bergson: yes

[13:40] herman Bergson: Next time we may pay attention to what part our fingers played in this whole process ^_^

[13:41] herman Bergson: For now I think we are done counting :-)

[13:41] CB Axel: Very interesting.

[13:41] herman Bergson: Unless you still have that final question or remark

[13:41] CB Axel: Thank you, Herman.

[13:41] Particle Physicist Bejiita (bejiita.imako): we are down for counting!

[13:41] Particle Physicist Bejiita (bejiita.imako): lol

[13:41] Particle Physicist Bejiita (bejiita.imako): so lets count some plupps!

[13:41] herman Bergson: Count me out Bejiita ^_^

[13:41] Particle Physicist Bejiita (bejiita.imako): as a final

[13:41] Particle Physicist Bejiita (bejiita.imako):

[13:41] bergfrau Apfelbaum: interesting! thank you Herman and class

[13:41] herman Bergson: Thank you all again for your participation.....:-)

[13:42] herman Bergson: Class dismissed......

[[13:42] Particle Physicist Bejiita (bejiita.imako): u are coming!

[13:42] Particle Physicist Bejiita (bejiita.imako): lol

[13:42] herman Bergson: lol

[13:42] herman Bergson: can count on me Bejiita ^_^

[13:42] .: Beertje :. (beertje.beaumont): Thank you Herman

[13:42] Particle Physicist Bejiita (bejiita.imako): YAY! (yay!)

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