Tuesday, June 22, 2021

935: Maths works....

Why does math works? At the core of this mystery lies an argument that mathemati­cians, physicists, philosophers and cognitive scientists have had for centuries: Is math an invented set of tools, as Einstein be­lieved?


 Or does it actually exist in some abstract realm, with hu­ mans merely discovering its truths? 


Many great mathemati­cians, including David Hilbert, Georg Cantor and the group known as Nicolas Bourbaki, have shared Einstein’s view, associated with a school of thought called Formalism. 


But other illustri­ous thinkers, among them Godfrey Harold Hardy, Roger Pen­rose and Kurt Gödel, have held the opposite view, Platonism. 


This debate about the nature of mathematics rages on today and seems to elude an answer.


I believe that by asking simply whether mathematics is invented or discovered, we ignore the possibility of a more intricate answer: both invention and dis­covery play a crucial role.


Although eliminating the dichotomy between invention and discovery does not fully explain "the un­reasonable effectiveness of mathematics" ,


 the title of a famous article by Eugene Wigner (1960), the problem is so pro­found that even a partial step toward solving it is progress. 


In the previous lecture, I referred to the passive side of mathematics when math calculations predict empirical observations


and the active side when pure mathematics accidentally happens to be very useful in describing some feature of nature.


A pattern emerges: humans invent mathematical concepts by way of abstracting elements from the world around them, 


shapes, lines, sets, groups, and so forth, either for some specific purpose or simply for fun. 

They then go on to discover the con­nections among those concepts. 


Because this process of inventing and discovering is man­made, unlike the kind of discovery to which the Platonists subscribe, our mathematics is ultimately based on our perceptions and the mental pictures we can conjure. 


For instance, we possess an innate talent, called subitizing, for in­stantly recognizing quantity, which undoubtedly led to the con­cept of number. 


We are very good at perceiving the edges of indi­vidual objects and at distinguishing between straight and curved lines and between different shapes, such as circles and ellipses,  


abilities that probably led to the development of arithmetic and geometry. 


So, too, the repeated human experience of cause and ef­fect at least partially contributed to the creation of logic and, with it, the notion that certain statements imply the validity of others. 


This is an interesting all be it a partial answer. Mathematics isn't THE universal language, describing reality, however, in certain areas, it is a highly effective one yet. 


There exists a whole host of phenomena for which no accurate mathematical predictions are possible, sometimes not even in principle. 


In economics, for example, many variables, the detailed psychology of the masses, to name one, do not easily lend themselves to quantitative analysis. 


The predictive value of any theory relies on the constancy of the underlying relations among variables. 


Other areas are, for instance, psychology sociology, literature or art. 


Mathematicians have developed statistics and probability to deal with such shortcomings, but mathematics itself is limited, as Austrian logician Gödel famously proved. 


Mathematical systems aren't universally applicable. Take for instance integers. Perfect for counting the number of raindrops, 1,2, 3, etc. 


But what to do with that system when the raindrop falls in the ocean and you still want to continue counting?


One thing is for sure, mathematics is probably the greatest example of our ability to recognize patterns and formulate the principles behind them.


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

[13:22] .: Beertje :. (beertje.beaumont): Thank you Herman

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

[13:23] herman Bergson: So, in general mathematics is the result of the interaction between the mind and empirical experiences caused by a real world

[13:23] Particle Physicist Bejiita (bejiita.imako): I guess thats a good explanation

[13:23] oola Neruda: Physicists have named some of their "found concepts" Truth and Beauty

[13:24] herman Bergson: It makes me think of the epistemology of Kant (ca.1730....)

[13:24] oola Neruda: and they have a reverentail attitude toward these mysteries of ath

[13:24] oola Neruda: math

[13:25] herman Bergson: Well...ti is our mind that appears the actual creator of maths

[13:26] oola Neruda: or call them "observed concepts"

[13:26] Particle Physicist Bejiita (bejiita.imako): like the relational concept of pi

[13:26] Particle Physicist Bejiita (bejiita.imako): circum/diameter

[13:26] herman Bergson: Like Kant said.....we never can know "das Ding an Sich", the object as such....we only have our sensory experiences and the categoris of the mind, causality, space , time, that enables us to know the external world

[13:27] herman Bergson: We only can know within the categories of space and time for instance....

[13:28] herman Bergson: they create the lasting object

[13:28] herman Bergson: Maybe you disagree and take a Platonist viewpoint?

[13:29] herman Bergson: hmmm...seems you don't ^_^

[13:30] herman Bergson: When we think of the universe we only can think in terms of space and time

[13:30] Particle Physicist Bejiita (bejiita.imako): well math is very special indeed

[13:30] Particle Physicist Bejiita (bejiita.imako): and indeed also it can not be applied to eevrything, chaos is one example cause there is no patterns

[13:30] herman Bergson: then we think of atoms, neutron, protons we only can thing of mass....which must be some substance with extension in space

[13:31] Particle Physicist Bejiita (bejiita.imako): one example, when u throw the dice in the plup-game its not truly random, a computer cant randomize cause it uses math

[13:31] Particle Physicist Bejiita (bejiita.imako): it can only simulate it good enough

[13:31] herman Bergson: true....

[13:31] Particle Physicist Bejiita (bejiita.imako): using an algorithm

[13:32] Particle Physicist Bejiita (bejiita.imako): for true randomization it would require filming truly random events like snowfall or lava lamps and use data from that film stream to create true randomization

[13:33] Particle Physicist Bejiita (bejiita.imako): thats the only way for a computer to create true randomness, using external truley random data

[13:34] herman Bergson: Interesting observation....

[13:34] .: Beertje :. (beertje.beaumont): wouldn't that be an algorithm too?

[13:34] Particle Physicist Bejiita (bejiita.imako): some crypto software generate their keys with lava lamps for ect

[13:34] Particle Physicist Bejiita (bejiita.imako): a computer films lots of them and makes crypto key

[13:35] Laz Dresler is online.

[13:35] herman Bergson: Beertje, that is according the principle that what data are used as input, such dat will appear as output

[13:35] Particle Physicist Bejiita (bejiita.imako): or as we commonly say

[13:35] herman Bergson: That is what an algorithm  can handle

[13:35] Particle Physicist Bejiita (bejiita.imako): shit in =  shit out

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

[13:36] herman Bergson: no no Bejiita....

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

[13:36] herman Bergson: the original phrase is garbage in, garbage out ^_^

[13:36] Particle Physicist Bejiita (bejiita.imako): yes i was referring to that but thats in Swedish

[13:37] herman Bergson: ^_^

[13:37] Particle Physicist Bejiita (bejiita.imako): skit in skit ut

[13:37] oola Neruda: smiles

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

[13:37] herman Bergson: Never to old to learn (Swedish:-)

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

[13:37] herman Bergson: But we can conlude a few things here

[13:37] CB Axel: In English it was originally GIGO.

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

[13:38] herman Bergson: At least mathematics is an impressive achievement of the brain of homo sapiens in recognizing pattern and the principles behind them

[13:38] herman Bergson: Ahh, CB, nice

[13:38] oola Neruda: fractles for example

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

[13:39] herman Bergson: A second thing is that the mathematical patterns and priciples aren't the complete tool for everything....

[13:39] herman Bergson: And what puzzles me already for a long time.....

[13:40] oola Neruda: depends upon what you are measuring

[13:40] herman Bergson: Astrophysics is an impressive theoretical science also build on mathematics....

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

[13:40] oola Neruda:  but does not need to be physical

[13:40] herman Bergson: the big bang is a mathematical extrapolation of mathematical data and observations.....

[13:41] herman Bergson: but it cant answer the where/when question....

[13:41] herman Bergson: ANd I wonder why they don't conclude that this is the result of how our brain computes?

[13:42] oola Neruda: scientists want evidence

[13:42] Particle Physicist Bejiita (bejiita.imako): our view of whats around us

[13:42] herman Bergson: we can only think in space and time....and Kant said that that are our computational tools to be able to have sensory experiences that make sense

[13:43] herman Bergson: Yes, evidence,  but it is created by our own mind to some extend....so, biased evidence

[13:43] oola Neruda: yup

[13:43] Particle Physicist Bejiita (bejiita.imako): aa i guess

[13:43] oola Neruda: theory

[13:44] oola Neruda: observation

[13:44] herman Bergson: I have no problem with that.....but science sometimes has problems with the observation that some things can not be knows by us due to how our brain computes and relates to the external reality

[13:45] CB Axel: Like trying to see in 4 dimensions.

[13:45] CB Axel: I try to imagine what the 4th dimension looks like, but I just can't.

[13:45] herman Bergson: With athematics we can  however create a useful model

[13:45] Particle Physicist Bejiita (bejiita.imako): ah

[13:45] herman Bergson: Indeed CB

[13:45] oola Neruda: and look at data very carefully...

[13:45] Particle Physicist Bejiita (bejiita.imako): we would just see strange blobs

[13:45] herman Bergson: What should it look like

[13:46] herman Bergson: Here in SL we have the X, Y and Z axes and time.....

[13:46] herman Bergson: But let's not begin to philosophize about time, please ^_^

[13:46] CB Axel: I was just watching a sci-fi show where people went missing and it was discovered that they had been sucked into another dimension.

[13:46] oola Neruda: i've had physicists try to explain alternate universes to me.... it is hare to follow and they step back to call it theory

[13:46] Particle Physicist Bejiita (bejiita.imako): a good way to visualize it is to think of a 2d character on a paper with a 3d object passing through, he would only see a slice of the object changing shape as it passes through

[13:47] CB Axel: Right. Like in Flatland.

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

[13:47] Particle Physicist Bejiita (bejiita.imako): thats what flatland is all about

[13:47] Particle Physicist Bejiita (bejiita.imako): to understand why we cant see 4d

[13:48] CB Axel: I understand why we can't see it, but I'd still like to. :)

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

[13:48] herman Bergson: isn't that some novel.....about flatland.....two dimensional beings?

[13:48] CB Axel: Yes.

[13:48] herman Bergson: I have read something like that long ago

[13:49] Particle Physicist Bejiita (bejiita.imako): yes but as i get it they then encounter a 3 dimensional object, and flatland was created with this very purpose as i understand

[13:49] Marlena Rickettsi (marlenalilly): And there is a painting by Dali, something of a four dimensional cross.

[13:49] herman Bergson: I remember it was fun to read....

[13:49] Particle Physicist Bejiita (bejiita.imako): i have not read/seen it though

[13:49] Particle Physicist Bejiita (bejiita.imako): aaa Dali is cool

[13:49] Particle Physicist Bejiita (bejiita.imako): and surrealism in general

[13:50] Particle Physicist Bejiita (bejiita.imako): mysterious anc cozy in a way i like

[13:50] herman Bergson: Do you know the book CB?

[13:50] Particle Physicist Bejiita (bejiita.imako): well its dream art

[13:50] Particle Physicist Bejiita (bejiita.imako): so

[13:50] CB Axel: Flatland? Yes. I've read most of it, but I can't seem to get through the whole thing.

[13:51] herman Bergson: Well...I guess thois was a somewhat tough philosophical session today .....

[13:51] Particle Physicist Bejiita (bejiita.imako): (checking up flatland)

[13:51] .: Beertje :. (beertje.beaumont): Flatland: A Romance of Many Dimensions is a satirical novella by the English schoolmaster Edwin Abbott Abbott, first published in 1884 by Seeley & Co

[13:51] herman Bergson: Ahhh....that's it!

[13:51] Particle Physicist Bejiita (bejiita.imako): ok 2d or 3dplupp today?

[13:51] Particle Physicist Bejiita (bejiita.imako):

[13:52] Particle Physicist Bejiita (bejiita.imako): we do the usual 3d version I think

[13:52] herman Bergson: Time to cool down, I think :-)

[13:52] herman Bergson: Next dimension is a pleasnat weekend, I'd say :-)

[13:52] Particle Physicist Bejiita (bejiita.imako): YAY! (yay!)

[13:52] .: Beertje :. (beertje.beaumont):

[13:53] Particle Physicist Bejiita (bejiita.imako): BEER BEER AND MORE BEER

[13:53] Particle Physicist Bejiita (bejiita.imako): yum!

[13:53] Particle Physicist Bejiita (bejiita.imako):

[13:53] bergfrau Apfelbaum: thank you! Herman and class:-)

[13:53] herman Bergson: Then, thank you all again......and see you again next Tuesday in good health, I wish ...

[13:53] CB Axel: Thank you, Herman and everyone.

[13:53] herman Bergson: Class dismissed.....

[13:53] Marlena Rickettsi (marlenalilly): thank you Professor.

[13:53] Particle Physicist Bejiita (bejiita.imako):

[13:53] .: Beertje :. (beertje.beaumont): Thank you Herman

[13:54] herman Bergson: You all survived....good ^_^

[13:54] .: Beertje :. (beertje.beaumont): i need vacation:)

[13:54] CB Axel: Me,  too. :)

[13:54] Particle Physicist Bejiita (bejiita.imako): aaa soon time

[13:54] Particle Physicist Bejiita (bejiita.imako): july for me

[13:54] Particle Physicist Bejiita (bejiita.imako): as usual

[13:55] herman Bergson: Yes....vacation is closing in on us :-)

[13:55] .: Beertje :. (beertje.beaumont): going tomorrow;)

[13:55] .: Beertje :. (beertje.beaumont): yay

[13:55] Particle Physicist Bejiita (bejiita.imako): nice

[13:55] Particle Physicist Bejiita (bejiita.imako):

[13:55] bergfrau Apfelbaum: your vacation starts tomorrow, yes?

[13:55] bergfrau Apfelbaum: ahjaa

[13:55] bergfrau Apfelbaum: yay

[13:55] .: Beertje :. (beertje.beaumont): yes

[13:55] CB Axel: Are you going somewhere nice?

[13:55] .: Beertje :. (beertje.beaumont): yes yes:)


Thursday, June 17, 2021

934: Mathematics....

 "When Rebecca Goldin, a professor of mathematical sciences at George Mason, spoke to a recent class of incoming freshmen at George Mason University, 


she relayed a disheartening statistic: According to a recent study, 36 percent of college students don’t significantly improve in critical thinking 


during their four-year tenure. “These students had trouble distinguishing fact from opinion, and cause from correlation,”  (QuantaMagazine, Ariel Bleicher September 2017)


When looking closer at the data, she concluded that the reason for this was, that this third of the students didn't take science classes.


As Galileo already said: mathematics is the language of nature. So we have to conclude that this third of students studied "sciences", that don't use mathematics. I'll get back to this later.


Let's try to figure out what mathematics is. Mathematics has been called the language of the universe. Scientists and engineers often speak of the elegance of mathematics 


when describing physical reality, citing examples such as π, E=mc2, and even something as simple as using abstract integers to count real-world objects. 


Yet while these examples demonstrate how useful math can be for us, does it mean that the physical world naturally follows the rules of mathematics as its "mother tongue," 


and that this mathematics has its own existence that is out there waiting to be discovered? 


This point of view on the nature of the relationship between mathematics and the physical world is called Platonism, but not everyone agrees with it.


Einstein, a mathematical non-Platonist, was one scientist who marveled at the power of mathematics. He asked, "How can it be that mathematics, 


being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?"


This leads to the question: Is mathematics discovered or invented?


Mathematics has two sides:  it has an active and a passive side. An example of the active side is, 


that mathematical calculations showed that Higgs particles had to exist. That was long before these particles ever were observed.


An example of the passive side of mathematics:  French mathematician Évariste Galois, for example, developed group theory in the early 1800s for the sole purpose of determining the solvability of polynomial equations. 


What he did I have no idea except that I understand that it was a purely theoretical and mathematical problem. However, in 20th­ century phys­ics, this rather abstract field of group theory 


turned out to be the most fruitful way of categorizing elementary particles, the building blocks of matter. 


In the 1960s physicists Murray Gell­-Mann and Yuval Ne’eman made use of it and won a Nobel Prize in 1969. 


So far, so good. We still haven't an answer. We'll need an extra lecture to complete the story....


To be continued....


Thank you for your attention...



The Discussion

[13:24] Particle Physicist Bejiita (bejiita.imako): YAY! (yay!)

[13:25] herman Bergson: At least we have the question...is mathematics discovered or invented?

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

[13:25] oola Neruda: a lot of the guys working on the earlier accelerators wore their badges that tell how much radiation they were getting.... on their pants zipper.... thinking in terms of children they might have

[13:26] CB Axel: Maybe mathematics was discovered but we've invented new ways to use it. :)

[13:26] herman Bergson: Or we love to play with mathematical concepts

[13:27] Particle Physicist Bejiita (bejiita.imako): we created the symbols bit the relation Pi for ex we did not create, The relation of circumference and diameter is not our creation

[13:27] Particle Physicist Bejiita (bejiita.imako): it is  just there

[13:27] Particle Physicist Bejiita (bejiita.imako): by nature

[13:27] Particle Physicist Bejiita (bejiita.imako): we just found a way to visualize it

[13:27] herman Bergson: Makes me think of this.....the circle....is it discovered or invented?

[13:27] Particle Physicist Bejiita (bejiita.imako): another example

[13:27] Particle Physicist Bejiita (bejiita.imako): you can find fractal patterns in seashells and leaves

[13:28] herman Bergson: Well...when you look at the moon...what do you see....a specific shape....

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

[13:28] CB Axel: Does a perfect circle occur anywhere in nature?

[13:28] .: Beertje :. (beertje.beaumont): the earth itself is a specific shape

[13:28] herman Bergson: We copy the shape and start playing with it....

[13:28] CB Axel: Planets aren't perfectly spherical.

[13:28] Particle Physicist Bejiita (bejiita.imako): a perfect sphere occurs if u pour water in 0 gravity

[13:29] herman Bergson: Yes but they didn't know that in Ancient times, Beertje

[13:29] herman Bergson: Aren't they CB?

[13:30] herman Bergson: all pictures show planets as  nice balls

[13:30] CB Axel: The Earth bulges.

[13:30] herman Bergson: ahhh...

[13:30] CB Axel: Don't the others bulge in the middle, too?

[13:30] herman Bergson: I really don't know

[13:30] CB Axel: I don't either. :(

[13:31] CB Axel: Gravity does affect things, though. Like soap bubbles.

[13:31] CB Axel: In zero gravity are soup bubbles perfectly round?

[13:32] Particle Physicist Bejiita (bejiita.imako): i think so cause there is no force in either direction

[13:32] Particle Physicist Bejiita (bejiita.imako): they should be a perfect sphere

[13:32] herman Bergson: Like I discussed before...we see single objects and learn to count, arithmetics, we see shapes and learn to measure, geometry....

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

[13:33] herman Bergson: I get the feeling that mathematics has something to do with an exchange between mind and matter, observations and thinking

[13:33] oola Neruda: with partiicals. the orbits decay

[13:34] Particle Physicist Bejiita (bejiita.imako): that sounds probable Herman

[13:34] oola Neruda: math

[13:34] herman Bergson: invented or discovered....? And what about the Platonist view?

[13:35] herman Bergson: Mathematical concepts independently existing in nature?

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

[13:35] herman Bergson: We just need to discover them...

[13:36] oola Neruda: observe

[13:36] oola Neruda: from theory

[13:36] herman Bergson: But didn't we first observe fractal like shapes in nature and then tried to describe them with the language of mathematics, Bejiita?

[13:36] Particle Physicist Bejiita (bejiita.imako): https://www.diygenius.com/fractals-in-nature/

[13:37] Particle Physicist Bejiita (bejiita.imako): that i have no idea of actually, i just know they are repeating patterns described with iterations

[13:37] herman Bergson: When we see a pattern we can try to cast it into some mathematical formula or calculation

[13:37] Particle Physicist Bejiita (bejiita.imako): first time i heard of fractals was actually when i programmed  my Casio calculator in elementary school to draw them

[13:38] Particle Physicist Bejiita (bejiita.imako): but i had no idea of what iterations or any of the code i put in did i just wrote it from a book

[13:38] Particle Physicist Bejiita (bejiita.imako): later i learned more about them

[13:39] herman Bergson: iterations is a pure mathematical matter....you don't need nature to learn about the maths of iteration

[13:39] herman Bergson: Yet is seems to describe fractals quite nicely

[13:39] Particle Physicist Bejiita (bejiita.imako): https://www.diygenius.com/fractals-in-nature/

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

[13:40] Particle Physicist Bejiita (bejiita.imako): some nice examples

[13:40] herman Bergson: yes amazing stuff

[13:40] Particle Physicist Bejiita (bejiita.imako): in any case they are beautiful

[13:40] Particle Physicist Bejiita (bejiita.imako): and really cool

[13:41] CB Axel: Songwriter Jonathan Coulton wrote a song about fractals called The Mandelbrot Set. :)

[13:41] herman Bergson: Well...maths is still a mystery.....next lecture we'll try to find out how the relation discovered - invented works out

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

[13:42] herman Bergson: Fractals are worth a song indeed :-)

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

[13:43] herman Bergson: Ok....next Thursday we'll have an answer of what to think about mathematics in relation to science and nature

[13:43] herman Bergson: For now...put your brain particles to rest unless you still have a question

[13:43] Guestboook van tipjar stand: CB Axel donated L$100. Thank you very much, it is much appreciated!

[13:43] herman Bergson: Thank you for your attention again....

[13:44] .: Beertje :. (beertje.beaumont): Thank you Herman

[13:44] herman Bergson: Class dismissed.....


Sunday, June 13, 2021

933: A reconstruction.....

 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.....


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

The Discussion

[13:15] Particle Physicist Bejiita (bejiita.imako):

[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.