8 ms·

Steven Strogatz on chaos theory, game theory, and why math isn’t boring

192 points by stpapa 10y ago

goldenkek 10y ago
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 needs two dimensions (or degrees of freedom.) Space for storage of the number. And time to increment the storage medium, again and again, at different points. You could use two dimensions of space instead, and you'd just draw two orthogonal lines..and say the area inside the rectangle is the product. So if counting is fundamentally related to the relationship between two dimensions, then so is addition since addition is repeated/recursive counting. And multiplication is repeated/recursive addition. Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe. Multiplication and addition are related in the way that f(x) and repeat(f(x), y) are related. They distribute over eachother and have certain properties. See: https://en.wikipedia.org/wiki/Ring_(mathematics) https://en.wikipedia.org/wiki/Ring_(mathematics) So..the primes, the chaotic relationship between the modularity of addition over multiplication and the modularity of multiplication over addition, is due to the relationship between our universe's dimensions. Want to study the universe at the most raw level? Mathematics. Want to study it a little higher? Physics. Want to study it at a higher level..maybe closer to the phaneron? Biology/neurochemistry. https://en.wikipedia.org/wiki/Phaneron https://en.wikipedia.org/wiki/Phaneron Want to study it at the thinking level? Zen buddhism. Choose your pick. The causal chain of human to universe doesn't discriminate. The whole chain could be the "real" reality. Pick your choice. It's all beautiful. It's all mystifying and enigmatic. Just do it.
- zeroer 10y ago
  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 https://arxiv.org/abs/0704.0646 But it's nonsense that the natural numbers require two dimensions. Time appears nowhere in the Zermelo–Fraenkel axioms: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
  - posterboy 10y ago
    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.
    - TeMPOraL 10y ago
      > 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.
      - posterboy 10y ago
        So, extending the analogy, we've as well been dividing the universe? If you go with quantum mechanics, you also have to consider the Entanglement that, if I understand correctly, posits non-locality, so your argument of spacial division is still nonsense to me. To be fair, quantum theory might as well be nonsense to me. I wouldn't know, it's over my head. But multiverse is stuff of sci-fi and theoretical physics. Theoretical physics is mostly maths, indeed. So I agree to a point, I just contest the schism that's between maths and physics, because it's not constructive.
      - posterboy 10y ago
        > Arguments from etymology are invalid, because words are not obliged to be backwards compatible. That's how you end up with loads of confusing homonyms, which the parent almost admited to. I mean, sure an etymologic argument can be insufficient or even wrong.
        TeMPOraL 10y ago
        My point is, words are only labels - pointers to concepts. You can't prove facts about objects from just their labels, nor do the labels have causal power over reality. Universe being derived from "uni" doesn't force the concept of universe to be a singleton. Proliferation of homonyms is another topic altogether; it is an issue, but it's about creating barriers to communication.
- armitron 10y ago
  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 mathematics together. Through mathematics we learn more about the limits of our own model building/cognition than any secrets of the universe.
  - posterboy 10y ago
    > [don't] talk about the "real" reality and mathematics together 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.
- posterboy 10y ago
  >Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe. But space and time are natural, ie. you mention a physical interpretation. And a paradox one at that, because you are explaining counting (numbers) by counting (dimensions). > Want to study the universe at the most raw level? I'd rather offer that mathematics is about formalization of what you know, while physics is about exploration of what you don't know. Maths is intrinsic, abstract and relies on intuition. Physics is extrinsic, concrete and relies on experimentation. These separations are arbitrary and not useful, if they don't serve a purpose. Why divide like that at all? If you talk hierarchy, I'd say logic is higher up there. To wrap it up, what's that got to do with bad teaching? I'd suppose that deductive reasoning cannot be taught, because it is learned before language is acquired, then used to acquire language. Maybe, memory can be trained, and curiosity can be stimulated, but school is hardly the right setting to inspire creativity, when most of the time there talking is forbidden. > Zen buddhism Sure, nihilism, or religion overall, is like an escape when you abandon all hope and try to recollect new hope. It is admitting you don't know anymore and going back to square one.
  - mathperson 10y ago
    if you think mathematics relies on intuition..you haven't done much mathematics unfortunately. the field is deeply paradoxical once you get into it deeply
- mannykannot 10y ago
  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.
  - posterboy 10y ago
    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.
    - justinpombrio 10y ago
      It's not very helpful to study the ideas that form in human brains, though, since so many of them are nonsense. It would largely be a study of misconceptions and biases. 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."
      - posterboy 10y ago
        It would well be notable which ideas are wrong, no? Sure I could've said, writing is physical. I just did, in another comment.
    - mannykannot 10y ago
      Does this get us into the question of whether anything mathematical exists before anyone (or anysomething) first thought of it, and exists even when no-one is currently thinking of it? If you answer yes, then mathematics has an existence independent of thought. If you answer no, then that conditional existence presumably extends to physics as well, especially if Max Tegmark is right about math being the reality of physics. In that case, then it seems to follow that the universe only exists when it is being thought about, a conclusion that appears to have a bootstrap problem... I think I can avoid the whole issue by observing that I can imagine things that do not physically exist, and they are not made to physically exist by dint of a conceptual representation of them physically existing in my brain.
- Ar-Curunir 10y ago
  This is pseudoscientific crap. Mathematics does not concern itself with physical reality.
  - goldenkek 10y ago
    Haters gonna hate ;-)
stpapa 10y ago
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.
- goldenkek 10y ago
  I agree. Most of mathematics is taught as calculations without motivation. If it was taught as the study of systems, and a toolbelt to understand the universe, more people would be passionate about it. All we can do is show the light to others.
  - cttet 10y ago
    Actually if you dig in the calculation techniques taught in primary school(Like multidigit addition/multiplication/ division), you would find some of them are actually quite clever ideas (O(log n) algorithms), but what almost all school do is to ask the student execute the algorithm like a computer, not how to come up with ideas like those...
  - chestervonwinch 10y ago
    > If it was taught as ... a toolbelt to understand the universe ... While true, I think that this is still a bit abstract. Rather than "a toolbelt to understand the universe", I would say "a toolbelt to formally characterize problems in order to analyze and solve them". Let me add in addition that in order to learn to use the fun tools in the toolbelt, one must first grasp the basic ones. This (in my limited experience teaching lower level math courses) is another obstacle in teaching math: (continuing with the tool analogy) it would be quite boring to spend 3 months studying screwdrivers, another 3 months on wrenches, etc. without applying these tools to any "fun" problems.
- GuiA 10y ago
  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 foundations strong enough to later support that kind of more abstract, artistic reasoning. This goes for other fields too. You have to practice your chords to play Bach, and learn your conjugations to write a novel.
ColinWright 10y ago
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 teaching? No money, no status, no respect, no flexibility, no control, crushing hours, crushing workload ... why would anyone do that?!? No wonder students are never exposed to the real beauty and elegance of mathematics.
- wodenokoto 10y ago
  By that logic no student is ever exposed to the real beauty and elegance of any subject.
  - TeMPOraL 10y ago
    You can be, just not in school - only at university level and above, when some time ago someone figured out a trick to combine research work with teaching responsibilities. This works well as long as there is no significant market demand for a given discipline.
  - dagw 10y ago
    If your degree/passion is for something like literature, history or music then teaching high school is, relatively speaking, one of the better jobs you can get where you can focus on your subject and use your degree. If someones degree/passion is in math, physics or programming then they simply have so many more options that the chances they end up in teaching is much lower.
- lordnacho 10y ago
  Because one way to appreciate beauty is to show others. One of my math teachers in school had no kids, lived frugally. He could have retired a long time before I ran into him. Instead, he gave me extra classes and put me on the math team. He spent lots of his own time to show me the interesting bits while also making sure I wouldn't get anything less than the top mark on the exams. You're right though. It's not enough to rely on passionate people, there's not enough of them. I mean I like math too, and I'm not gonna be a teacher. You can't even send your own kids to school on a teacher's salary.
j2kun 10y ago
Shameless promotion: I'm writing a book in which I introduce mathematics for programmers specifically. If you found yourself here you may be interested. https://jeremykun.com/2016/04/25/book-mailing-list https://jeremykun.com/2016/04/25/book-mailing-list
- akvar 10y ago
  I just wanted to say that I have really enjoyed Math ∩ Programming over the past year. Lot of interesting reading material for my commute. Keep up the good work! (Signed up for the mailing list. Good luck!)
- gravypod 10y ago
  I'd be willing to spend a good 40 bucks on something like this (that may not seem like a lot but 40$ to a college student is a lot). Something that has a twinkle of a promise in teaching a programmer math is something I need in my life. I just don't "get" what is being told to me when it's in the context of math-notation. As a result I do horrible in math classes in college. The only thing that was taught with a CS-Style notation was approximating using Newton's method. After I saw that it made sense, it was just a recursive method that zeroed in on that location. Very little aside from that in my calc 1 class made sense. Probably limits, but that's it really. It didn't click as well. I'd like to get to the point where I understand math concepts as well as I do most of the CS but I just think that's impossible at this point. It seems to be very "this is our garden, you stay in yours".
  - j2kun 10y ago
    In anticipating a book like this, would you ideally want to learn the math context and notation (provided one goal of the book is to teach that), or skip that entirely in favor of the underlying ideas (as in your example with Newton's Method). Also, would you be interested in being paid to read a chapter or two and provide feedback?
    - charlieflowers 10y ago
      Not the GP, but I'd want to learn both the ideas and the notation. That way, more math would become accessible to me. Just don't let the notation get in the way of reaching clarity on the ideas.
calhoun137 10y ago
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-Nonlinearity/dp/0738204536 https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications...
- yosyp 10y ago
  Used this book during an undergraduate introductory course. I am now revisiting some of the chapters again, this is a great book! I think those interested in "data science" should definitely be exposed to some of the concepts introduced in it.
- marai2 10y ago
  And I'd like to recommend Prof. Strogatz's book "The Joy of X" as a wonderful sampling of a number of basic math topics. It's very easily digestible. https://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/0544105850 https://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/0544...
- weerd 10y ago
  A great book! It's very readable and more of an applied math book written with engineers and scientists in mind. Starting out with the basics of state-space representations, it moves from 1D to 2D to 3D dynamics. The last section deals with the popular topics of chaos theory and fractals. But not from a simple pop-math perspective that you'll find in the math section of the book store. It's the real deal, except presented in a way that can be understood by non-mathematicians. Strogatz is also coauthor of the paper that introduced small world networks. I really admire him for being so brilliant and at the same time capable of getting these topics across to everybody. I also recommend his book Sync.

192 points by stpapa 10y ago

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 needs two dimensions (or degrees of freedom.) Space for storage of the number. And time to increment the storage medium, again and again, at different points. You could use two dimensions of space instead, and you'd just draw two orthogonal lines..and say the area inside the rectangle is the product. So if counting is fundamentally related to the relationship between two dimensions, then so is addition since addition is repeated/recursive counting. And multiplication is repeated/recursive addition. Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe. Multiplication and addition are related in the way that f(x) and repeat(f(x), y) are related. They distribute over eachother and have certain properties. See: https://en.wikipedia.org/wiki/Ring_(mathematics) https://en.wikipedia.org/wiki/Ring_(mathematics) So..the primes, the chaotic relationship between the modularity of addition over multiplication and the modularity of multiplication over addition, is due to the relationship between our universe's dimensions. Want to study the universe at the most raw level? Mathematics. Want to study it a little higher? Physics. Want to study it at a higher level..maybe closer to the phaneron? Biology/neurochemistry. https://en.wikipedia.org/wiki/Phaneron https://en.wikipedia.org/wiki/Phaneron Want to study it at the thinking level? Zen buddhism. Choose your pick. The causal chain of human to universe doesn't discriminate. The whole chain could be the "real" reality. Pick your choice. It's all beautiful. It's all mystifying and enigmatic. Just do it.

zeroer 10y ago
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 https://arxiv.org/abs/0704.0646 But it's nonsense that the natural numbers require two dimensions. Time appears nowhere in the Zermelo–Fraenkel axioms: https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory
- posterboy 10y ago
  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.
  - TeMPOraL 10y ago
    > 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.
    - posterboy 10y ago
      So, extending the analogy, we've as well been dividing the universe? If you go with quantum mechanics, you also have to consider the Entanglement that, if I understand correctly, posits non-locality, so your argument of spacial division is still nonsense to me. To be fair, quantum theory might as well be nonsense to me. I wouldn't know, it's over my head. But multiverse is stuff of sci-fi and theoretical physics. Theoretical physics is mostly maths, indeed. So I agree to a point, I just contest the schism that's between maths and physics, because it's not constructive.
    - posterboy 10y ago
      > Arguments from etymology are invalid, because words are not obliged to be backwards compatible. That's how you end up with loads of confusing homonyms, which the parent almost admited to. I mean, sure an etymologic argument can be insufficient or even wrong.
      - TeMPOraL 10y ago
        My point is, words are only labels - pointers to concepts. You can't prove facts about objects from just their labels, nor do the labels have causal power over reality. Universe being derived from "uni" doesn't force the concept of universe to be a singleton. Proliferation of homonyms is another topic altogether; it is an issue, but it's about creating barriers to communication.
armitron 10y ago
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 mathematics together. Through mathematics we learn more about the limits of our own model building/cognition than any secrets of the universe.
- posterboy 10y ago
  > [don't] talk about the "real" reality and mathematics together 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.
posterboy 10y ago
>Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe. But space and time are natural, ie. you mention a physical interpretation. And a paradox one at that, because you are explaining counting (numbers) by counting (dimensions). > Want to study the universe at the most raw level? I'd rather offer that mathematics is about formalization of what you know, while physics is about exploration of what you don't know. Maths is intrinsic, abstract and relies on intuition. Physics is extrinsic, concrete and relies on experimentation. These separations are arbitrary and not useful, if they don't serve a purpose. Why divide like that at all? If you talk hierarchy, I'd say logic is higher up there. To wrap it up, what's that got to do with bad teaching? I'd suppose that deductive reasoning cannot be taught, because it is learned before language is acquired, then used to acquire language. Maybe, memory can be trained, and curiosity can be stimulated, but school is hardly the right setting to inspire creativity, when most of the time there talking is forbidden. > Zen buddhism Sure, nihilism, or religion overall, is like an escape when you abandon all hope and try to recollect new hope. It is admitting you don't know anymore and going back to square one.
- mathperson 10y ago
  if you think mathematics relies on intuition..you haven't done much mathematics unfortunately. the field is deeply paradoxical once you get into it deeply
mannykannot 10y ago
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.
- posterboy 10y ago
  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.
  - justinpombrio 10y ago
    It's not very helpful to study the ideas that form in human brains, though, since so many of them are nonsense. It would largely be a study of misconceptions and biases. 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."
    - posterboy 10y ago
      It would well be notable which ideas are wrong, no? Sure I could've said, writing is physical. I just did, in another comment.
  - mannykannot 10y ago
    Does this get us into the question of whether anything mathematical exists before anyone (or anysomething) first thought of it, and exists even when no-one is currently thinking of it? If you answer yes, then mathematics has an existence independent of thought. If you answer no, then that conditional existence presumably extends to physics as well, especially if Max Tegmark is right about math being the reality of physics. In that case, then it seems to follow that the universe only exists when it is being thought about, a conclusion that appears to have a bootstrap problem... I think I can avoid the whole issue by observing that I can imagine things that do not physically exist, and they are not made to physically exist by dint of a conceptual representation of them physically existing in my brain.
Ar-Curunir 10y ago
This is pseudoscientific crap. Mathematics does not concern itself with physical reality.
- goldenkek 10y ago
  Haters gonna hate ;-)

stpapa 10y ago

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.

goldenkek 10y ago
I agree. Most of mathematics is taught as calculations without motivation. If it was taught as the study of systems, and a toolbelt to understand the universe, more people would be passionate about it. All we can do is show the light to others.
- cttet 10y ago
  Actually if you dig in the calculation techniques taught in primary school(Like multidigit addition/multiplication/ division), you would find some of them are actually quite clever ideas (O(log n) algorithms), but what almost all school do is to ask the student execute the algorithm like a computer, not how to come up with ideas like those...
- chestervonwinch 10y ago
  > If it was taught as ... a toolbelt to understand the universe ... While true, I think that this is still a bit abstract. Rather than "a toolbelt to understand the universe", I would say "a toolbelt to formally characterize problems in order to analyze and solve them". Let me add in addition that in order to learn to use the fun tools in the toolbelt, one must first grasp the basic ones. This (in my limited experience teaching lower level math courses) is another obstacle in teaching math: (continuing with the tool analogy) it would be quite boring to spend 3 months studying screwdrivers, another 3 months on wrenches, etc. without applying these tools to any "fun" problems.
GuiA 10y ago
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 foundations strong enough to later support that kind of more abstract, artistic reasoning. This goes for other fields too. You have to practice your chords to play Bach, and learn your conjugations to write a novel.

ColinWright 10y ago

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 teaching? No money, no status, no respect, no flexibility, no control, crushing hours, crushing workload ... why would anyone do that?!? No wonder students are never exposed to the real beauty and elegance of mathematics.

wodenokoto 10y ago
By that logic no student is ever exposed to the real beauty and elegance of any subject.
- TeMPOraL 10y ago
  You can be, just not in school - only at university level and above, when some time ago someone figured out a trick to combine research work with teaching responsibilities. This works well as long as there is no significant market demand for a given discipline.
- dagw 10y ago
  If your degree/passion is for something like literature, history or music then teaching high school is, relatively speaking, one of the better jobs you can get where you can focus on your subject and use your degree. If someones degree/passion is in math, physics or programming then they simply have so many more options that the chances they end up in teaching is much lower.
lordnacho 10y ago
Because one way to appreciate beauty is to show others. One of my math teachers in school had no kids, lived frugally. He could have retired a long time before I ran into him. Instead, he gave me extra classes and put me on the math team. He spent lots of his own time to show me the interesting bits while also making sure I wouldn't get anything less than the top mark on the exams. You're right though. It's not enough to rely on passionate people, there's not enough of them. I mean I like math too, and I'm not gonna be a teacher. You can't even send your own kids to school on a teacher's salary.

j2kun 10y ago

Shameless promotion: I'm writing a book in which I introduce mathematics for programmers specifically. If you found yourself here you may be interested. https://jeremykun.com/2016/04/25/book-mailing-list https://jeremykun.com/2016/04/25/book-mailing-list

akvar 10y ago
I just wanted to say that I have really enjoyed Math ∩ Programming over the past year. Lot of interesting reading material for my commute. Keep up the good work! (Signed up for the mailing list. Good luck!)
gravypod 10y ago
I'd be willing to spend a good 40 bucks on something like this (that may not seem like a lot but 40$ to a college student is a lot). Something that has a twinkle of a promise in teaching a programmer math is something I need in my life. I just don't "get" what is being told to me when it's in the context of math-notation. As a result I do horrible in math classes in college. The only thing that was taught with a CS-Style notation was approximating using Newton's method. After I saw that it made sense, it was just a recursive method that zeroed in on that location. Very little aside from that in my calc 1 class made sense. Probably limits, but that's it really. It didn't click as well. I'd like to get to the point where I understand math concepts as well as I do most of the CS but I just think that's impossible at this point. It seems to be very "this is our garden, you stay in yours".
- j2kun 10y ago
  In anticipating a book like this, would you ideally want to learn the math context and notation (provided one goal of the book is to teach that), or skip that entirely in favor of the underlying ideas (as in your example with Newton's Method). Also, would you be interested in being paid to read a chapter or two and provide feedback?
  - charlieflowers 10y ago
    Not the GP, but I'd want to learn both the ideas and the notation. That way, more math would become accessible to me. Just don't let the notation get in the way of reaching clarity on the ideas.

calhoun137 10y ago

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-Nonlinearity/dp/0738204536 https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications...

yosyp 10y ago
Used this book during an undergraduate introductory course. I am now revisiting some of the chapters again, this is a great book! I think those interested in "data science" should definitely be exposed to some of the concepts introduced in it.
marai2 10y ago
And I'd like to recommend Prof. Strogatz's book "The Joy of X" as a wonderful sampling of a number of basic math topics. It's very easily digestible. https://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/0544105850 https://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/0544...
weerd 10y ago
A great book! It's very readable and more of an applied math book written with engineers and scientists in mind. Starting out with the basics of state-space representations, it moves from 1D to 2D to 3D dynamics. The last section deals with the popular topics of chaos theory and fractals. But not from a simple pop-math perspective that you'll find in the math section of the book store. It's the real deal, except presented in a way that can be understood by non-mathematicians. Strogatz is also coauthor of the paper that introduced small world networks. I really admire him for being so brilliant and at the same time capable of getting these topics across to everybody. I also recommend his book Sync.