"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.....
