Thursday, May 6, 2021

922: Patterns in numbers......

 I try to imagine how the human brain moved from one stage to the next stage in learning arithmetics.


Remember the prehistoric homo sapiens. He carves notches in a stick every time a sheep enters the cave for the night.


The next day he uses the stick and his finger moves from notch to notch every time a sheep enters the cave. He is not yet counting.


Suppose he draws a short line in the sand and somewhat away from it another. He looks, then draws the two lines adjacent to each other.


Looks like the beginning of his tally stick. He does the same with four lines and he might begin to see a pattern.


He begins to give the notches and groups of notches names, so that he can talk about what he is doing: one and one adjacent to each other look like two.


This brings us to the more general questions. The basis of arithmetic is counting. But what do we actually know about counting? And on what rules is it based? 


The oldest transferred counting patterns in the world are the dash patterns of moon cycles from the Paleolithic, which we have seen in a previous lecture. 


But they made tally marks instead of counting. When moved people on from making tally marks to counting and then to search for patterns in numbers and shapes? 


All our knowledge about Babylonian arithmetic and geometry we get from four hundred clay tablets, of which the oldest dates back to 3000 BC. 


The first that stands out is that the Babylonians do not have a decimal system, which would be obvious when they counted with the fingers. 


Nor had the Babylonians a duodecimal system, which we encounter in many other places and which could also have been obvious 


on the basis of the number of phalanxes of the four long fingers (in total twelve), where the thumb is used as a pointer. 


The Babylonians, on the other hand, had a sexagesimal system, which means that they had 60 numbers where we have only 10. They had taken over this system from the Sumerians.


Why? I don't know. What we see is that all over the world homo sapiens began to count and began to discover patterns.


The system the Babylonians adopted satisfied their needs. We use base 10, the Babylonians base 60.


I am no mathematician, but it is said that you can calculate pretty easily in a sexagesimal system.


The fact is that we haven't forgotten the Babylonians as one of the first to introduce arithmetics in human culture.


We still think of them every day when we see that a circle is 6 x 60 = 360 degrees, or when we look at our watch and count the 60 minutes of an hour, easy to divide in halves or quarters.


Why are there 60 seconds in a minute? Go to the Babylonians and get your answer. And if you want more answers, google Babylonian mathematics. There is a lot to find.


What interests us here is the observation of the behavior of Homo Sapiens in relation to counting, his invention of counting and numbers and all kinds of patterns and principles in it and its consequences.


When you look at the list of Babylonian numbers, you may have noticed that one number is missing: the ZERO. They didn't have one.....


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

[13:21] Particle Physicist Bejiita (bejiita.imako): aaa so thats wHY A MINUTE HAVE 60 SECONDS!

[13:21] herman Bergson: Seems to be so yes....

[13:21] Particle Physicist Bejiita (bejiita.imako): wondered over that sometimes but never checked

[13:21] Particle Physicist Bejiita (bejiita.imako): i guesses it is just like that

[13:22] Particle Physicist Bejiita (bejiita.imako): but everything comes from something

[13:22] herman Bergson: Why this way of counting time stayed with us since the Babylonians I don't know

[13:22] Dien (djdien.bailey) is offline.

[13:22] herman Bergson: Maybe ut has to do with astronomy and astrology from that time

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

[13:23] Particle Physicist Bejiita (bejiita.imako): need to check this further

[13:23] herman Bergson: Astronomy works with orbs and circles....and in those days they used the sexagesimal dats back to the Babylonians

[13:24] herman Bergson: Astronomy has a long tradition/...

[13:24] CB Axel: But why would they use 60 as the basis of their mathematics.

[13:24] Particle Physicist Bejiita (bejiita.imako): seems a bit well uneven

[13:24] CB Axel: That seems like a large and cumbersome number.

[13:24] Particle Physicist Bejiita (bejiita.imako): a bit like (ugh) inches!

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

[13:25] herman Bergson: I only can have one answer...purely a pragmatic choice...

[13:25] theo Velde is online.

[13:25] herman Bergson: No no...the sexagesimal system seems to be, what I read about it, quite handy  and definitely not cumbersom

[13:26] herman Bergson: Recently I had a discussion with oola.....

[13:26] herman Bergson: about...

[13:26] herman Bergson: why using pictograms, Chinese characters, why the alphabet...?

[13:27] herman Bergson: I'd say...just coincidence and due to circumstances

[13:27] herman Bergson: Why pick the decimal system?

[13:27] CB Axel: Because we have 10 fingers.

[13:27] herman Bergson: Why pick the binary system....

[13:27] CB Axel: We don't have exactly 60 of anything.

[13:28] herman Bergson: simple....electricity can only be ON and OFF

[13:28] herman Bergson: Yes those ten fingers

[13:28] CB Axel: Right. That's makes sense. On. Off. A choice of 2.

[13:28] herman Bergson: But that also led to duodecimal systems

[13:28] CB Axel: 10 fingers. A choice of 10.

[13:28] herman Bergson: yes

[13:28] CB Axel: But 60?

[13:28] .: Beertje :. (beertje.beaumont): but what about a foot and an inch?

[13:29] CB Axel: What in nature occurs 60 times?

[13:29] herman Bergson: 5 times 12 (the phalanxes) is 60

[13:29] Particle Physicist Bejiita (bejiita.imako): indeed

[13:29] CB Axel: A foot started out as the length of someones foot.

[13:29] .: Beertje :. (beertje.beaumont): size 36 or size 46?

[13:29] herman Bergson: so you can count to 50 on your fingers....wich are 5 per hand

[13:29] Particle Physicist Bejiita (bejiita.imako): indeed foot is a such arbirtary measure

[13:30] CB Axel: But we don't have 5 hands. That seems more like a coincidence than anything.

[13:30] Particle Physicist Bejiita (bejiita.imako): same inch is the lengh of someones arbitrary thumb

[13:30] Particle Physicist Bejiita (bejiita.imako): just some average definition

[13:30] .: Beertje :. (beertje.beaumont): and an el is about 69 cm

[13:30] CB Axel: Right, Bejiita. And a yard was from nose to outstretched finger tips.

[13:30] herman Bergson: There is a ton of info on Babylonian mathematics on internet....You can have fun with it searching for answers

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

[13:31] Particle Physicist Bejiita (bejiita.imako): same with Fahrenheit,

[13:31] Particle Physicist Bejiita (bejiita.imako): i cant tell if something is hot or cold on that like i can easily with the C scale

[13:31] herman Bergson: I began reading about it, but is endless :-)

[13:31] .: Beertje :. (beertje.beaumont): and Kelvin?

[13:31] CB Axel: Farhenheit was a mistake.

[13:32] herman Bergson: Sometimes man chose the wrong pattern indeed CB :-)

[13:32] Particle Physicist Bejiita (bejiita.imako): water freexe at 32 , boils at 212 and 108 degrees between

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

[13:32] CB Axel: Farhenheit (the man) got the boiling point of water wrong.

[13:32] Particle Physicist Bejiita (bejiita.imako): 180

[13:33] herman Bergson: Interesting to look into that :-)))

[13:33] herman Bergson: The Origin of Fahrenheit

[13:33] Particle Physicist Bejiita (bejiita.imako): as i get it 0 on farhrenheit was where concentrated brine freeze or something

[13:33] Particle Physicist Bejiita (bejiita.imako): and used that as measure

[13:33] Particle Physicist Bejiita (bejiita.imako): for some reason

[13:34] herman Bergson: As you see...the introduction of numbers and counting has become a source of fun :-)

[13:34] Particle Physicist Bejiita (bejiita.imako): kelvin is logical when working with low temperature things like the LHC magnet system

[13:34] CB Axel: If you find headaches fun, Herman. LOL

[13:34] Particle Physicist Bejiita (bejiita.imako): same base as C

[13:35] Particle Physicist Bejiita (bejiita.imako): hahahah

[13:35] herman Bergson: lol

[13:35] Particle Physicist Bejiita (bejiita.imako): indeed u can have loads of fun with math and stuff

[13:35] herman Bergson: I know where to stop, CB :-)

[13:35] Particle Physicist Bejiita (bejiita.imako): aaa COME ON NOW HERMAN!

[13:35] Particle Physicist Bejiita (bejiita.imako): lol

[13:35] herman Bergson: I still regret thata I had such a bad maths education


[13:36] Particle Physicist Bejiita (bejiita.imako): but more advanced it gets

[13:36] Particle Physicist Bejiita (bejiita.imako): the more fun and exciting it also gets

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

[13:37] CB Axel: I'm hungry, so 1 pear and 2 apples sound good to me right now.

[13:37] herman Bergson: yes ...2 pears and 4 apples I guess :-)

[13:37] Particle Physicist Bejiita (bejiita.imako): mmmm its tasty

[13:37] Particle Physicist Bejiita (bejiita.imako): and i eat mandarines now

[13:37] CB Axel: With some Stilton cheese and port wine!

[13:37] Particle Physicist Bejiita (bejiita.imako): aaaa yum

[13:37] Particle Physicist Bejiita (bejiita.imako): cheese bricks

[13:38] herman Bergson: Ok...I understand....let's take a break till Thursday and enjoy the cheese , port and mandarins in the meantime :-)

[13:38] CB Axel: :)

[13:38] Particle Physicist Bejiita (bejiita.imako): in the right quantities( A LOT)

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

[13:39] herman Bergson: You don't need to count them :-)

[13:39] Particle Physicist Bejiita (bejiita.imako): no just MUNCH

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

[13:39] oola Neruda: I wonder if 60 is a result of dividing a circle over and over until it gets "clogged" and hard to keep dividing it?

[13:39] herman Bergson: Thank you all again :-)

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

[13:39] CB Axel: That could be, oola. :)

[13:39] Particle Physicist Bejiita (bejiita.imako): why is a circle 360 degrees?

[13:39] herman Bergson: We'll discuss that after class oola ^_^

[13:40] herman Bergson: Class dismissed

[13:40] oola Neruda: smiles

[13:40] Particle Physicist Bejiita (bejiita.imako): also based on 60?

[13:40] .: Beertje :. (beertje.beaumont): Thank you Herman

[13:40] CB Axel: Because of those damned Babylonians, Bejiita.

[13:40] Particle Physicist Bejiita (bejiita.imako): 6x6 = 36 so

[13:40] CB Axel: Thank you, Herman.

[13:40] herman Bergson: 360 /2 = 180/2 =90/2 = 45

[13:40] Particle Physicist Bejiita (bejiita.imako): ah

[13:41] herman Bergson: but then?

[13:41] CB Axel: I'm going to get something  to eat. I'll see you all Thursday. :)

[13:41] Particle Physicist Bejiita (bejiita.imako): there is another unit with 400 degrees

[13:41] herman Bergson: Enjoy CB :-))

[13:41] .: Beertje :. (beertje.beaumont): Cheddar cheese CB?

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