Friday, May 7, 2021

923: From arithmetic to mathematics......

 The more you think about it the more fascinated it becomes. What has happened in prehistoric times to primate brains?


While the genetic difference between individual humans today is minuscule, about 0.1%, on average, study of the same aspects of the chimpanzee genome indicates a difference of about 1.2%. 


The bonobo which is the close cousin of chimpanzees, differs from humans to the same degree. 


The DNA difference with gorillas, another of the African apes, is about 1.6%. Most importantly, chimpanzees, bonobos, and humans all show this same amount of difference from gorillas. 


Humans, chimpanzees, and bonobos are more closely related to one another than either is to gorillas or any other primate. 


From the perspective of this powerful test of biological kinship, humans are not only related to the great apes. We are one. The human evolutionary tree is embedded within the great apes. 


What evolutionary changes happened to the brain, so that homo sapiens learned to count? He went from making tally marks on a stick or bone to giving the tally marks names. Somehow the concept of number emerged in his brain.


The Babylonians used 60 as base, not 10 like we do and we immediately think of our ten fingers.


Yet the use of base 60 is not arbitrary. We have two hands. On your left hand you step from one phalanx to another and count: 12.


When you have reached the last one you stretch one finger of your right hand. You repeat the procedure another 4 times and arrive at 60.


A pattern is a perceived regularity that contains an element of repetition that is not necessarily immutable 


but may be subject to exceptions and variation, was our definition in the first lecture of this project.


The Babylonians may have used the pattern in their hands to count and thence added quantification to reality.


That reality is quantifiable and that you can organize reality by adding, subtracting, multiplying and dividing, is one thing.


The brain of homo sapiens is curious. Philosophy begins with wondering about everything and in the same way homo sapiens began to wonder about numbers and counting. Are there patterns?


Arithmetic deals with addition, subtraction, multiplication, and division, but when you study  the relationships among numbers, shapes, and quantities,


you are wondering about underlying rules and principles. In other words we now talk about mathematics.


The Babylonians must have known underlying mathematical principles. This awareness started with them and certainly existed around 1800 BC. 


This is apparent from the fact that it has used Pythagoras's thesis 1200 years earlier than Pythagoras himself. 


The proof is the famous clay tablet "Plimpton 322", which you see behind me.


On that tablet there are lines with three numbers, which ultimately showed to be Pythagorean trifles according to the a2 + b2 = c2 principle.


In old Egypt occurred a similar development. The oldest papyri about arithmetic and mathematical subjects date from the Twelfth dynasty, 1990 to 1800 BC. They used a decimal system.


Thank you for your attention....



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

The Discussion

[13:16] .: Beertje :. (beertje.beaumont): Thank you Herman

[13:18] herman Bergson: It is amazing to see that 5000 years ago people have been smarter than me regarding mathematics.....

[13:18] .: Beertje :. (beertje.beaumont): :))

[13:18] herman Bergson: I must admit...that was easy, but yet

[13:18] Particle Physicist Bejiita (bejiita.imako):

[13:19] herman Bergson: The invention  of mathematics shows how intelligent people already were in those days....

[13:19] .: Beertje :. (beertje.beaumont): that was a huge step

[13:19] oola Neruda: in a way... the Roman numerals share some of that strategy... yet i think i prefer the Babyolonian

[13:19] herman Bergson: Yes it was Beertje

[13:20] herman Bergson: The Paleolithic homo sapiens learned to make tally marks.....the Babylonians learn how to count and developed mathematics

[13:20] herman Bergson: and not just simple maths....

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

[13:21] herman Bergson: Yhey knew how to calculate the circumference of a circle for instance

[13:22] herman Bergson: How they figured out the thesis of Pythagoras is a mystery. There are no tablets that explain their mathematical reasoning

[13:22] Particle Physicist Bejiita (bejiita.imako): indeed

[13:23] Particle Physicist Bejiita (bejiita.imako): how do you come up with these things in the first place

[13:23] herman Bergson: That is what I find so amazing Bejiita

[13:23] herman Bergson: Just imagine...

[13:23] herman Bergson: the tablet behind me....they first thought it was just bookkeeping data....

[13:24] Particle Physicist Bejiita (bejiita.imako): finding pi is one thing, someone came up with the idea to divide the circumference with the diameter

[13:24] Particle Physicist Bejiita (bejiita.imako): but discovering something like Pythagoras

[13:24] herman Bergson: Then in the 1940s mathematicians discovered that the numbers were Pythagorean triples

[13:24] Particle Physicist Bejiita (bejiita.imako): that i take all sides times 2 and then sqyare troot the result

[13:24] herman Bergson: Those number you can't find at random of by accident....

[13:25] Particle Physicist Bejiita (bejiita.imako): suare root

[13:25] Particle Physicist Bejiita (bejiita.imako): nope

[13:26] herman Bergson: Let me show you another picture

[13:27] herman Bergson: I guess that in those days people were puzzled by it and tried to discover the underlying principle

[13:28] herman Bergson: There is a pattern

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

[13:28] herman Bergson: When you divide side a in three equal parts, b will be 4 of these parts and c five

[13:29] herman Bergson: and whatever yo always will arrive at the same result

[13:30] herman Bergson: Just imagine that a 4000 years ago people already were pondering about those phenomenon

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

[13:30] herman Bergson: Today every child learns these mathematical principles in highschool (except me :-)

[13:31] herman Bergson: They figured it out..!

[13:31] oola Neruda: makes me think of the people building the pyramids

[13:31] herman Bergson: What did evolution to the brain?

[13:31] Particle Physicist Bejiita (bejiita.imako): and today our GPS systems run on it!

[13:31] oola Neruda: and other architecture

[13:32] herman Bergson: Oh yes oola....lots off high quality maths in there

[13:32] Particle Physicist Bejiita (bejiita.imako): same old principle

[13:32] Particle Physicist Bejiita (bejiita.imako): the base formula for triangulation

[13:32] herman Bergson: How to calculate the measurements of a pyramid?

[13:33] oola Neruda: stone by stone

[13:33] herman Bergson: They figured it out with their brains

[13:33] herman Bergson: That is a good start oola ^_^

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

[13:33] oola Neruda: every stone had to be exactly right

[13:34] .: Beertje :. (beertje.beaumont): they developt to abstract thinking

[13:34] herman Bergson: google it....guess there will be info about this process

[13:34] herman Bergson: yes amazing....their brains were equal to our brains

[13:35] herman Bergson: Only the circumstances were different

[13:35] oola Neruda: imagine the limitation of the kine of tools they had...

[13:35] oola Neruda: whew

[13:35] herman Bergson: and then realize....these are just the first steps on the path of knowledge

[13:36] Particle Physicist Bejiita (bejiita.imako): indeed

[13:36] herman Bergson: indeed oola

[13:36] herman Bergson: They had no calculators or computers with 3D modeling

[13:37] oola Neruda: and leveling the stones... to exacting measurements... with low impact tools... no machines like we use

[13:38] oola Neruda: need geometry

[13:38] Particle Physicist Bejiita (bejiita.imako): exactly

[13:38] herman Bergson: not to speak of why they wanted to undertake such insane projects :-)

[13:38] Particle Physicist Bejiita (bejiita.imako): true

[13:38] herman Bergson: Also that relates to what is in the brain

[13:38] herman Bergson: What the brain is capable  of

[13:39] herman Bergson: Why stopped the evolution of the Bonobo brain and the chimp brain?

[13:40] herman Bergson: Why homo sapiens?

[13:40] .: Beertje :. (beertje.beaumont): why do we need such a brain?

[13:40] herman Bergson: Well...there is no why in is a non teleological process

[13:40] Particle Physicist Bejiita (bejiita.imako): indeed why are there no others like us

[13:41] Particle Physicist Bejiita (bejiita.imako): only we also have a real language, all other animals have one single sound

[13:41] Particle Physicist Bejiita (bejiita.imako): cats miau, dogs bark

[13:41] herman Bergson: We need a brain like all organisms to keep the system going and to survive, escape enemies, find food etc

[13:42] CB Axel: I think the thing that sets us apart from other animals is our need to explore new places.

[13:42] herman Bergson: My admiration for the people of a 4000 years ago is only growing.....

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

[13:43] herman Bergson: Yes CB....that curiosity......

[13:43] CB Axel: When we started moving away from equatorial Africa we needed to learn to build and navigate.

[13:43] CB Axel: We needed maths.

[13:43] herman Bergson: Not a single ape asks WHY......we do...every day

[13:44] CB Axel: Other apes may wonder why, but they can't communicate their questions to us.

[13:44] herman Bergson: you see the process here....

[13:44] CB Axel: Or to each other, it seems.

[13:44] herman Bergson: homo sapiens learned to count,,,then to wonder about number

[13:44] Particle Physicist Bejiita (bejiita.imako): apes can only say UUGH UUGH, also no langiage, just one single sound

[13:45] oola Neruda: I think the fact that we have thumbs... and not hoofs or paws is part of it

[13:45] herman Bergson: Yes.....they may understand causal relations

[13:45] .: Beertje :. (beertje.beaumont): no Bejiita they communicate with eachother

[13:45] CB Axel: Animals each have many sounds.

[13:45] Particle Physicist Bejiita (bejiita.imako): or just sounds same to us ?

[13:46] herman Bergson: You better read books of Frans de Waal Bejitta

[13:46] CB Axel: I always knew from their meows whether my cats wanted to be petted, or played with, or fed (usually fed).

[13:46] Particle Physicist Bejiita (bejiita.imako): because indeed they have to be able to communicate

[13:47] herman Bergson: He can tell you exactly how chimps can have complex conversations

[13:47] Particle Physicist Bejiita (bejiita.imako): well they can have a different tone to it i guess

[13:47] Particle Physicist Bejiita (bejiita.imako): and if u learn that

[13:47] Particle Physicist Bejiita (bejiita.imako): our office dog at work just barks as crazy when there is somneone at the door

[13:47] Particle Physicist Bejiita (bejiita.imako): lol

[13:47] Particle Physicist Bejiita (bejiita.imako): fun little fella

[13:47] herman Bergson: Saves you a bell

[13:48] Particle Physicist Bejiita (bejiita.imako): aaa even the alarm system have a chime

[13:48] Particle Physicist Bejiita (bejiita.imako): but

[13:48] Particle Physicist Bejiita (bejiita.imako): :9

[13:49] herman Bergson: Well, these are our first steps into a world full of patterns

[13:49] Particle Physicist Bejiita (bejiita.imako): there are many of them indeed

[13:49] herman Bergson: I hope you like the walk :-)

[13:49] .: Beertje :. (beertje.beaumont): yes

[13:49] CB Axel: It's interesting to think about.

[13:50] CB Axel: Thank you, Herman and class. :)

[13:50] herman Bergson: Thank you all gain for your participation.... 

[13:50] herman Bergson: Class dismissed....

[13:50] .: Beertje :. (beertje.beaumont): Thank you Herman

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