I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes “999999”, so that I could recite it out loud, come to those six 9s, and then impishly say, “and so on!”
So, years ago in college in Linear Algebra our professor said to us to study about idempotent matrices. So I checked out that wiki page and saw the example for 2x2 matrix, that are composed by the numbers 3, -6, 1 and -2. And I was like wait a second, 3×-2=-6 there’s no way they are not relationship there, so I started trying other numbers, and found and proved (using induction) that any n, -n(n-1), 1, -(n-1) is an idempotent matrix. At the test there were no questions about that, and I was short of 0.5 poits to pass the class without having to present a final exam and I told my professor that I spent a lot of time learning that and that even discovered something and proved he pass me the chart and asked me to proved it, after that he gave the missing points. Was really good.
I mean, mathematics are an invention. A useful one, sure, but the whole thing is just made up by people playing around with numbers and going “what if we had a new, different kind of numbers…”
This reminds me of a friend who said “I like to think of dividing by zero as giving zero instead of infinity, because it means you can keep doing math on it” and I just thought that was so pure.
Shit like this makes me realise why people become mathematicians. You just play around with numbers and find funny facts about them.
—Douglas Hofstadter
That would be an amazing party trick.
Actually come to think of it, even more amazing in the age of smart phones, when it’s possible to easily verify to numbers you’re reciting.
Well said.
Thanks!
You’re welcome.
Haha
Haha.
So, years ago in college in Linear Algebra our professor said to us to study about idempotent matrices. So I checked out that wiki page and saw the example for 2x2 matrix, that are composed by the numbers 3, -6, 1 and -2. And I was like wait a second, 3×-2=-6 there’s no way they are not relationship there, so I started trying other numbers, and found and proved (using induction) that any n, -n(n-1), 1, -(n-1) is an idempotent matrix. At the test there were no questions about that, and I was short of 0.5 poits to pass the class without having to present a final exam and I told my professor that I spent a lot of time learning that and that even discovered something and proved he pass me the chart and asked me to proved it, after that he gave the missing points. Was really good.
You need to put the name inside the brackets and the link inside the parentheses.
Thanks
Then you try to figure out why they do be like that
I mean, mathematics are an invention. A useful one, sure, but the whole thing is just made up by people playing around with numbers and going “what if we had a new, different kind of numbers…”
if we play around with it and find out we can better describe how reality works it is not strictly made up
some of it anyway and maybe all with a better understanding
That’s when it stops being maths and becomes science
sure but if the discovery was done in pure math and only later was the relevance found?
This reminds me of a friend who said “I like to think of dividing by zero as giving zero instead of infinity, because it means you can keep doing math on it” and I just thought that was so pure.
there are number systems that work differently