> Mandelbrot just made up these arbitrary rules about this world that doesn’t exist, and that has no relevance to reality, but it turned out they created fascinating patterns.
Er, no, that's not at all what happened. Mandelbrot was trying to model real-world observations like the length of irregular coastlines varying based on the scale of the measuring unit, and the growth and decline of pond scum populations.
Also
> As any mathematician knows, you literally can have a set of mathematical equations in which three plus three equals two.
is quite wrong unless you're simply redefining the strings "three", "plus", "equals" and/or "two" to mean quite different things.
> Remember the person in school who always got the right answer? That person did it much more quickly that everybody else, and did it because he or she didn’t try to. That person didn’t learn how the problem was supposed to be done but, instead, just thought about the problem the right way.
That is quite confused and conflates several different things.
> The story goes that the great German mathematician Carl Friedrich Gauss was in school and his teacher was bored, so to keep the students preoccupied he instructed them to add up all the numbers between 1 and 100. The teacher expected the young people to take all day doing that. But the budding mathematician came back five minutes later with the correct answer: 5,050.
If this actually happened, I doubt that it took him as long as five minutes. And how does that square with "did it because he or she didn’t try to" ... surely Gauss tried to find a simpler way to calculate the sum. Also, Gauss had vastly more impressive achievements than this, although I suppose it depends on how young he was at the time.
> A great mathematician doesn’t solve a problem the long and boring way because he sees what the real pattern is behind the question, and applies that pattern to find the answer in a much better way.
Mediocre mathematicians do the same--I'm not even that, but I was on my high school math team and was routinely tasked with finding shortcuts to the answer. And great mathematicians spend their time creating (theorems, novel approaches, whole new fields of mathematics), not solving math problems (or calculating sums, which can barely be called math).
But yes, programming is great fun and much of that comes from the ability to make things happen in the real world--that's why I switched from my plan to be a math professor to becoming a programmer when I discovered programming while in high school many decades ago. And now I'm retired and still program both for the joy of it and the pragmatic results.
>is quite wrong unless you're simply redefining the strings "three", "plus", "equals" and/or "two" to mean quite different things.
Which are the different rules he talks about. Obviously he does not say that all rules have to apply t at the same time. What a silly thing to interpret into his words.
>That is quite confused and conflates several different things.
It isn't though? It is definitely an experience I had during my mathematics degree.
>If this actually happened, I doubt that it took him as long as five minutes. And how does that square with "did it because he or she didn’t try to" ... surely Gauss tried to find a simpler way to calculate the sum. Also, Gauss had vastly more impressive achievements than this, although I suppose it depends on how young he was at the time.
The point he is making is actually pretty clear. Namely, that there is a distinction between a good solution and a great solution. A good solution takes the hard way and does all the right things. A great solution completely understands the problem and gives a solution so clear that after that you do not even see the problem.
>Mediocre mathematicians do the same--I'm not even that, but I was on my high school math team and was routin
If you ever have done mathematics at a university level you will have encountered exactly what Torvalds describes. In your homework you make all the right arguments, and through many steps you work through a difficult proof. In the end it is correct.
When another student presents their argument or when you later go through some textbook, there is a deceptively simple transformation and suddenly the argument becomes a trivial case of a previous theorem. Suddenly the problem has disappeared all together.
What makes a great mathematician is no doubt that ability. In fact if you ask a mathematician what makes a great proof it will be exactly this, taking something which looks incredibly complicated and suddenly transforming it into something incredibly obvious.
Er, no, that's not at all what happened. Mandelbrot was trying to model real-world observations like the length of irregular coastlines varying based on the scale of the measuring unit, and the growth and decline of pond scum populations.
Also
> As any mathematician knows, you literally can have a set of mathematical equations in which three plus three equals two.
is quite wrong unless you're simply redefining the strings "three", "plus", "equals" and/or "two" to mean quite different things.
> Remember the person in school who always got the right answer? That person did it much more quickly that everybody else, and did it because he or she didn’t try to. That person didn’t learn how the problem was supposed to be done but, instead, just thought about the problem the right way.
That is quite confused and conflates several different things.
> The story goes that the great German mathematician Carl Friedrich Gauss was in school and his teacher was bored, so to keep the students preoccupied he instructed them to add up all the numbers between 1 and 100. The teacher expected the young people to take all day doing that. But the budding mathematician came back five minutes later with the correct answer: 5,050.
If this actually happened, I doubt that it took him as long as five minutes. And how does that square with "did it because he or she didn’t try to" ... surely Gauss tried to find a simpler way to calculate the sum. Also, Gauss had vastly more impressive achievements than this, although I suppose it depends on how young he was at the time.
> A great mathematician doesn’t solve a problem the long and boring way because he sees what the real pattern is behind the question, and applies that pattern to find the answer in a much better way.
Mediocre mathematicians do the same--I'm not even that, but I was on my high school math team and was routinely tasked with finding shortcuts to the answer. And great mathematicians spend their time creating (theorems, novel approaches, whole new fields of mathematics), not solving math problems (or calculating sums, which can barely be called math).
But yes, programming is great fun and much of that comes from the ability to make things happen in the real world--that's why I switched from my plan to be a math professor to becoming a programmer when I discovered programming while in high school many decades ago. And now I'm retired and still program both for the joy of it and the pragmatic results.