It's a shame the title begins with 'Mathematica', makes one think the book is about the Wolfram software. That's the first thing I thought of when I saw the title. Hopefully Wolfram doesn't sue him for copyright violation or some such infringement.
Everyone is capable of, and can benefit from, mathematical thinking
271–280 of 419 posts
Re: Everyone is capable of, and can benefit from, mathematical thinking
#272Earlier quoted context omitted.
Since we are being pedantic, your statement may be true but it is unsupported by the data you presented. To make it simple, let's talk about the imaginary basketball league with four players, of unit less heights of 4, 4, 4, and 1. The average height is 3.25, yet 3/4 the players are taller than average. A paid promotion of International Median is not Average Association.
Most people have an above-average number of legs.
What's the average number of legs for humans ?
Re: Everyone is capable of, and can benefit from, mathematical thinking
#273Great to see so many reactions to my interview, thanks! I see that many people are confused by the interview's title, and also by my take that math talent isn't primarily a matter of genes. It may sound like naive egalitarianism, but it's not. It's a statement about the nature of math as a cognitive activity. For the sake of clarity, let me repost my reply to someone who had objected that my take was "clickbait". Thi…
> There are actual techniques that career mathematicians know about.
Your best example is the decimal system in contrast to roman numerals. I think that explains the point well. The zero is one of those tricks, and most people know it now, but that wasn't true until very recently.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#274Some very nice related works that dispel widespread math myths:
(1) What Is Mathematics, Really? Hersh, 1997. https://books.google.com/books/about/What_is_Mathematics_Rea...
(2) Where Mathematics Comes From. Lakoff and Nunez, 2000. https://en.wikipedia.org/wiki/Where_Mathematics_Comes_From
Re: Everyone is capable of, and can benefit from, mathematical thinking
#275It's a shame the title begins with 'Mathematica', makes one think the book is about the Wolfram software. That's the first thing I thought of when I saw the title. Hopefully Wolfram doesn't sue him for copyright violation or some such infringement.
I guess I assumed it was a reference to Alfred Whitehead's and Bertrand Russell's book Principia Mathematica, which predates Wolfram himself by several decades.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#276I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…
Would you say the book ventures more into the practical side of learning this stuff or is it closer to the tone of this article? I found this article hard to gain anything from. A lot of just motivational cliche statements and nothing really groundbreaking or mind altering. If the book is better at that, I'd love to read it. If it's stories and a lot of fluff, I'd rather skip. So I'm curious what you are getting from…
Agree. The article turned me off as well. No specific example, felt like an ad.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#277Great to see so many reactions to my interview, thanks! I see that many people are confused by the interview's title, and also by my take that math talent isn't primarily a matter of genes. It may sound like naive egalitarianism, but it's not. It's a statement about the nature of math as a cognitive activity. For the sake of clarity, let me repost my reply to someone who had objected that my take was "clickbait". Thi…
I think you've simply redefined genius. Many years ago I read an article on youth football, if I remember correctly, and in it there was a bit about the writers visit to the Ajax Youth Academy. In it he writes of a moment during practice when a plane flies over and all the 7(?) year olds on the pitch look up to see it except for one kid who keeps his eyes on the ball. That kid (of course) grows up to be a very good midfielder for Real (I'm forgetting the exact details, I think its Wesley Sniejder?). My point is: whatever that motive energy is that manifests as the single minded pre-occupation with math at an age when everybody else's attention is all over the place is that inherent thing that people call genius. I have read many of Thurston's non-mathematical writings about himself and in it this sort of singular pre-occupation is also clear -- which is why he developed his preternatural geometric vision.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#278"It's the economy stupid" is what I would say. Mental capacity is capacity. Most of us don't study math not because we don't want to but because we can't. I bet if you asked in a survey of people that if you were given a UBI that covered all your expenses and needs what would you do? It would be perfection of the self or art. Both of these are what is practicing and learning math.
Yeah, but we are all in software so for us economy is not a concern. All of us should learn maths.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#279I've been reading the author's book, Mathematica, and it's awesome. The title of this post doesn't do it justice. He shows that math skill is almost more like a sports talent than it is knowledge talent. He claims this based on the way people have to learn how to manipulate different math objects in their heads, whether treating them as rotated shapes, slot machines, or origami. It's like an imagination sport. Also,…
This sounds like a book I needed for one of my early comp sci classes in college. It was called something like Think Like a Programmer: An Introduction to Creative Problem Solving. Maybe it was this, maybe it was something like this.
I mean to say, just applied scientific thinking is important. Even if you never get into pure math or computer programming, applying concepts like "variables", "functions" or "proofs" is universally useful.
Re: Everyone is capable of, and can benefit from, mathematical thinking
#280I agree with the sentiment of this. I think our obsession with innate mathematical skill and genius is so detrimental to the growth mindset that you need to have in order to learn things. I've been working a lot on my math skills lately (as an adult). A mindset I've had in the past is that "if it's hard, then that means you've hit your ceiling and you're wasting your time." But really, the opposite is true. If it's e…
I am trying to stress pushing through these barriers with my kid right now. The second her brain encounters something beyond its current sphere she just shuts down.
I have heard it is the ego protecting itself by rejecting something outright rather than admitting you can't do it. It still happens to me all the time. My favorite technique was one I heard from a college professor. He starts reading while filling a notepad with sloppy notes, once a page is filled he just throws it away. He claimed it was the fastest way to "condition his brain to the problem space". More than the exercise I like the idea that your brain cannot even function in that space until it has been conditioned.