21–30 of 66 posts
Proffesor Strogatz wrote a book called Ninlinear Dynamics and Chaos which is the best intro book on non linear diff eq I have ever come across. I highly recomenend it: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications...
So here's the dilemma. People who see the beauty and elegance of mathematics are always going to go into something that exercises that, and will never go into teaching. Why would anyone who is seriously good at lots of math go into teaching? Especially in the USA, UK, or other countries where teaching has such a low status. In many cases teachers are genuinely despised. Why would anyone good at math ever go into teac…
Mathematics is the study of objective truth in a universe that has certain rules. How could knowing the universe in all its glory be boring? Wish they taught this rather than calculation at school. It's very uninspiring to not realize this and do math. In fact, natural numbers are the basis for almost all of mathematics. And natural numbers are a manifestation of counting. Information theoretically, to count, one nee…
If there exists an absolute reality it only make sense to be non-objective [nirguna brahman in advaita] nothingness, in contrast to objective nothingness which conceptually is nihilism. Mathematics can be used to study the universe at the objective level but do not make the mistake of treating numbers as ineffable, existing in some platonic realm outside of space/time/causation or talk about the "real" reality and ma…
That stopped me just at the right moment, but then you went and still did it:
> Through mathematics we learn more about the limits of our own model building/cognition than any secrets of the universe.
This is illogic, assuming we are part of the universe. Ignoring that last part, as you wanted, I get the reference. It comes down to saying, through learning about models we learn more about models. I agree if the stress is on learning, because to learn is part of the root of the word mathematics.
The real kicker nowadays is learning about learning, the mind, neurology, etc. directly.
Mathematics is the study of objective truth in a universe that has certain rules. How could knowing the universe in all its glory be boring? Wish they taught this rather than calculation at school. It's very uninspiring to not realize this and do math. In fact, natural numbers are the basis for almost all of mathematics. And natural numbers are a manifestation of counting. Information theoretically, to count, one nee…
I first came across an alternative view in Godel, Escher, Bach, where Hofstadter was writing about Euclid's parallel postulate and the development of non-euclidean geometry. The latter could have been accepted sooner, he suggests, if people were not hung up on the idea that geometry was about physical space, rather than a derivation from axioms. Ironically, it turned out later that physical space is not euclidean.
Earlier quoted context omitted.
Yea, mathematics is more fundamental than physics, in the sense that it would be possible for different universes to exist with different physics, but it's not clear at all that universes could exist with different mathematics. What would that even mean? You may like Max Tegmark's idea that the universe is math: https://arxiv.org/abs/0704.0646 But it's nonsense that the natural numbers require two dimensions. Time ap…
Do you know what the uni~ i universe means? It means only (one-ly). How could there be multiple? That's just non-sense. The parent implied counting, not the natural numbers, need two dimensions. But even in Set Theory you need at least one level deep nested sets to build the natural numbers. Qunatification is the (a?) difference between zero and higher order logic, I suppose.
As for your second paragraph, I really don't have any idea what you two are on about.
Earlier quoted context omitted.
Do you know what the uni~ i universe means? It means only (one-ly). How could there be multiple? That's just non-sense. The parent implied counting, not the natural numbers, need two dimensions. But even in Set Theory you need at least one level deep nested sets to build the natural numbers. Qunatification is the (a?) difference between zero and higher order logic, I suppose.
> Do you know what the uni~ i universe means? It means only (one-ly). How could there be multiple? That's just non-sense. Do you know what "atom" in "atom" means? "Indivisible". But somehow we've been dividing them for power for quite some time. Arguments from etymology are invalid, because words are not obliged to be backwards compatible.
The reason I posted this article was that this is the second mathematician I've come across in two days to talk about the elegance and beauty of mathematics. I wish I had seen some of this beauty from a younger age. It goes to show how much the right teacher, especially early on, can have a profound impact on your life.
Thx for posting this excellent article.
The reason I posted this article was that this is the second mathematician I've come across in two days to talk about the elegance and beauty of mathematics. I wish I had seen some of this beauty from a younger age. It goes to show how much the right teacher, especially early on, can have a profound impact on your life.
I feel the same way as you. But I don't know that my younger self had the maturity to see the deeper beauty. It was only starting college that I had the necessary complexity of thought (combined with wonderful professors). It takes a while to develop a taste refined enough to perceive these things. In the meantime, rote memorizing your multiplication tables and polynomial expansions might be a necessary evil to have…
I disagree on both ideological and technical terms. Won't students lose the "flow" as soon as they start memorizing? It seems like an anti-intellectual activity to memorize data or particular steps (e.g. (a+b)^2 = a^2 + 2ab + b^2). I think the further we stay from memorization the better the learner's experience will be.
Now for the technical objection. You said some degree of memorization might be a "necessary" evil, but I have a counter example: me. I've been doing math for the past 15+ years, but to this day I never learned the multiplication table. People are often surprised when I need 78 and I have to do 74 and add the result twice. "I thought you were a math person, and you don't know the multiplication table?" some will say... and I'm, like, yeah.
Earlier quoted context omitted.
I first came across an alternative view in Godel, Escher, Bach, where Hofstadter was writing about Euclid's parallel postulate and the development of non-euclidean geometry. The latter could have been accepted sooner, he suggests, if people were not hung up on the idea that geometry was about physical space, rather than a derivation from axioms. Ironically, it turned out later that physical space is not euclidean.
I believe our ideas are formed in our brain, that is part of the physical word. So I think the schism you presented would be void.
I think you could just as well have said "I believe our ideas are often formed on paper, when we write therm down. And that writing is part of the physical world. So I think the schism you presented would be void."
The reason I posted this article was that this is the second mathematician I've come across in two days to talk about the elegance and beauty of mathematics. I wish I had seen some of this beauty from a younger age. It goes to show how much the right teacher, especially early on, can have a profound impact on your life.