What for us is everyday and common is in fact the result of a learning process, which has taken millennia. Let's try a reconstruction.
Let us assume that every organism is an information processing mechanism: data in, response out.
Data in: pain --> process: danger --> data out ---> avoid. Data in: food --> process:growth --> data out: absorb. The battery of the engine: survival and reproduction.
This might somehow be the skeleton of evolution. Why matter has generated this mechanism isn't a meaningful question. It simply happened.
Let's skip a few billion years and arrive at the emergence of homo sapiens, with a brain that gives him self-awareness.
One of his first questions may have been the WHAT question. WHAT IS THIS? Being a social animal, his next step in relation to this question might be communication,
In telling your fellow man, what "this" is, you utter a sound. Thus you get the relation: empirical experience of an object <--> sound, equals object <---> (sound)symbol. He now can say: I KNOW what you mean by "BEAR".
From now on homo sapiens has learned to use symbols instead of pointing at objects to communicate about objects and thence he could draw his cave paintings.
Now he can say....let's go and find food and the members of his tribe come into action to perform a specific task.
In a previous lecture, I already suggested that after the WHAT question would have come the WHY question.
This goes on for millennia. Then the tribe settles somewhere and begins agriculture and cattle breeding.
If my neighbor has a lot of apples and I have some sheep, we could barter a sheep for some apples. This forces homo sapiens to come up with the next question: HOW MANY?
Around 7500 BC homo sapiens found a solution for his problem, You make a small clay token representing an apple and another on for sheep.
For every sheep, you put a token in a jar, like you do for every apple. Then, every time you want to barter apples for a sheep
you take the tokens from the jar and match each token with one apple or one sheep respectively. Homo sapiens taught himself to count.
The next step is, that you create a token that represents 10 apples. Thus the token, just one, doesn't visually match anymore with a single apple.
In other words, homo sapiens abstracted quantity from token and developed a concept of number. Now he can count by using numbers in his mind instead of using clay tokens.
Around 3100 BC these numbers in the mind of man were converted into written symbols as we have seen in Babylonia with its clay tablets.
Thus grew a relation between physical objects and the abstract entity of number, the concept of number or quantity. When A has 7 sheep and B has 10 sheep and you put them together, I predict that you will count 17 sheep after joining the two flocks.
This whole learning process, which took homo sapiens tenths of thousands of years, should eventually lead us to an answer to the question:
Why does mathematics work as a description of nature?
To be continued......
Thank you for your attention again.....
The Discussion
[13:15] Particle Physicist Bejiita (bejiita.imako): ㋡
[13:15] herman Bergson: I admit...it has been a warm and sunny day here...not the best weather for philosophy :-)
[13:15] Particle Physicist Bejiita (bejiita.imako): so he is the father of the horoscope then?
[13:16] Particle Physicist Bejiita (bejiita.imako): fun fact, when i read these they often sort of match
[13:16] herman Bergson: If you leave out Indian astrology, I guess so Bejiita.....
[13:16] Particle Physicist Bejiita (bejiita.imako): sometimes not at all but very often there is something there
[13:16] Particle Physicist Bejiita (bejiita.imako): a bit fun
[13:17] herman Bergson: But what is really means is that since Pythagoras the Greek saw mathematics probably also as something mystical
[13:17] CB Axel: If you read the horoscope for a different sign, though, can't you make that match up, too?
[13:17] herman Bergson: Let's not discuss the sense and nonsense of astrology here, please :-)
[13:18] CB Axel: :)
[13:18] Particle Physicist Bejiita (bejiita.imako): for ex if there is something going on at work ect i often have gotten matches for that day with "productive event filled day" and things like that
[13:18] Particle Physicist Bejiita (bejiita.imako): more then one time
[13:18] theo Velde is online.
[13:19] herman Bergson: No comment,, Bejiita ^_^
[13:19] Particle Physicist Bejiita (bejiita.imako): but thats in one of these, all papers for ex use different horoscopes
[13:19] Particle Physicist Bejiita (bejiita.imako): still a bit fun coincidence
[13:20] Particle Physicist Bejiita (bejiita.imako): in any case the discovery of all these connections like with math, and here we also can see how it is truly the language of the universe
[13:20] Particle Physicist Bejiita (bejiita.imako): as everything around us can be calculated
[13:21] herman Bergson: The main question here is ...how come that mathematics can be applied to real world things
[13:21] Particle Physicist Bejiita (bejiita.imako): well thats what is so amazing
[13:21] herman Bergson: Mathematics is a pure brain product
[13:21] Particle Physicist Bejiita (bejiita.imako): yes but still
[13:22] Particle Physicist Bejiita (bejiita.imako): it describes all these relation and it never lies (unless someone make a bad formula)¨
[13:22] herman Bergson: It doesn't seem to be deduced from empirical experiences
[13:22] Particle Physicist Bejiita (bejiita.imako): we can calculate and predict stuff of any kind
[13:22] herman Bergson: yes, Bejiita, and that is a very special feature of mathematics....
[13:23] Particle Physicist Bejiita (bejiita.imako): and everything can be represented in math, color sound ect which is what makes computers possible as they describe entire virtual worlds using only that
[13:23] Particle Physicist Bejiita (bejiita.imako): this place, my game projects ect., its all done with 100% math
[13:23] herman Bergson: indeed.... and we have a strong inclination to quantify everything
[13:23] Particle Physicist Bejiita (bejiita.imako): and 2 values
[13:23] Particle Physicist Bejiita (bejiita.imako): 1 and 0
[13:24] Particle Physicist Bejiita (bejiita.imako): amazing that its possible
[13:24] herman Bergson: to me it is still an unanswered question
[13:26] Particle Physicist Bejiita (bejiita.imako): another fascinating thing is they used purely math to predict the higgs boson and its properties 40 years before the LHC was built, Then comes LHC, ZAAAAM! and sure it was there witl ALL the parameters as predicted
[13:27] Particle Physicist Bejiita (bejiita.imako): thats quite cool!
[13:27] herman Bergson: Since nonof you comes forward with an answer, I make it your homework to find the answer :-)
[13:27] Particle Physicist Bejiita (bejiita.imako): well i have to dig deeper WHY this is the case
[13:28] Particle Physicist Bejiita (bejiita.imako): but that can be quite fun
[13:28] herman Bergson: One google search can be "Why does mathematics work?"
[13:28] Particle Physicist Bejiita (bejiita.imako): yes
[13:29] CB Axel: Did we discover math or did we make it up to explain things.
[13:29] CB Axel: ?
[[13:29] Particle Physicist Bejiita (bejiita.imako): good suggestion
[[13:29] Particle Physicist Bejiita (bejiita.imako): is math man made or just laying out here waiting to be discovered
[13:29] Particle Physicist Bejiita (bejiita.imako): head spins when going into these things
[13:30] Particle Physicist Bejiita (bejiita.imako): into the deep
[13:30] herman Bergson: I think that THAT is a hot discussion among mathematicians
[13:30] Particle Physicist Bejiita (bejiita.imako): ah
[13:30] herman Bergson: Is reality in itself mathematical?
[13:30] Particle Physicist Bejiita (bejiita.imako): well indeed
[13:31] herman Bergson: Is mathematics empirically or brainily based?
[13:31] Particle Physicist Bejiita (bejiita.imako): i mean it seems so since everything there is can be described 100% using it
[13:31] Particle Physicist Bejiita (bejiita.imako): the relations are there
[13:31] herman Bergson: No Bejiita that isn't true.....
[13:31] CB Axel: Is there a god or is there just a master mathematical equation? :)
[13:32] Particle Physicist Bejiita (bejiita.imako): from pi to fractals
[13:32] herman Bergson: what can not be described 100% is described by using statistics
[13:32] Particle Physicist Bejiita (bejiita.imako): haha
[13:32] Particle Physicist Bejiita (bejiita.imako): there are lies, damn lies and statistics!
[13:32] Particle Physicist Bejiita (bejiita.imako): looool
[13:32] herman Bergson: you can't quantify human emotions for instance
[13:32] Particle Physicist Bejiita (bejiita.imako): a classic
[13:32] herman Bergson: Indeed Bejiita
[13:32] Particle Physicist Bejiita (bejiita.imako): well THAT u can not indeed
[13:33] Particle Physicist Bejiita (bejiita.imako): but also we cant read others minds and thus directly measure them
[13:34] herman Bergson: You can statistically predict the possible occurrence of an emotion with a probability of 80%
[13:34] Particle Physicist Bejiita (bejiita.imako): u can say using a programming analogy that emotions are only accessible in the local scope
[13:34] herman Bergson: but you can't predict the emotion of person A
[13:34] Particle Physicist Bejiita (bejiita.imako): = to yourself
[13:34] Particle Physicist Bejiita (bejiita.imako): only u can feel them
[13:35] Particle Physicist Bejiita (bejiita.imako): no
[13:35] Particle Physicist Bejiita (bejiita.imako): and indeed i cant predict mine either
[13:35] Particle Physicist Bejiita (bejiita.imako): its all depending on whats happening right now
[13:35] Particle Physicist Bejiita (bejiita.imako): and indeed u can not predict the future
[13:36] herman Bergson: Well, I'd say...have some fun with the query on "Why does mathematics work".....plenty of hits in Google....lots to study there :-)
[13:36] Particle Physicist Bejiita (bejiita.imako): ah
[13:37] Particle Physicist Bejiita (bejiita.imako): now lets dwell into some randomly chaotic dice throwing pluppgames
[13:37] herman Bergson: Time to put our brains to rest, I'd say....
[13:37] herman Bergson: unless you still have an urgent question or remark :-))
[13:37] Particle Physicist Bejiita (bejiita.imako): however not truly random (computers cant be truly chaotic but good enough for dice games)
[13:37] herman Bergson: Ok.....Class dismissed .....
[13:38] bergfrau Apfelbaum: thank you Herman and class
[13:38] CB Axel: Thank you, Herman and class.
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