Sunday, December 24, 2006
JSH: Dumb as rocks
So the weird reality at the heart of the debates that have gone on for years is that I say that functions like sqrt() return more than one value while posters maintain that it has one solution—because it is defined to have one.
So I say, sqrt(4) is 2 or -2, and they claim it's just 2.
I say, look (-2)(-2) = 4, and they claim, so what, mathematicians DEFINED sqrt(4) to be 2, so who cares if (-2)(-2) = 4?
It may seem trivial, but by getting away with that dumb argument, posters can with that single small logical error keep going with bigger and bigger errors that grow from it, which is why these arguments don't get resolved.
So I say they are dumb as rocks because I'd think most of you can comprehend that people can DEFINE something to be true, even with the best of intentions, and it just fall apart as a concept with more advanced knowledge.
And while to many of you it may see this trivial thing which you think you always handle—mentally shifting as needed if you need sqrt(4) to be -2—it turns out that it breaks a lot of mathematics to make even one, small, seemingly trivial, logical mistake.
No matter how much you hate it, sqrt(4) has TWO SOLUTIONS.
And if you can get away with saying it only has one, you break mathematical reasoning at a low enough level that it's pointless to explain and explain and explain and mathematical proofs just bounce off of you as you are a rock, at such a basic level of denial about mathematics that more advanced concepts are totally beyond you.
So the debates continue because posters hold on to the most obvious error, refusing to accept that sqrt() has TWO SOLUTIONS, and that has implications over much of number theory.
Hard to believe but that is how mathematics escapes people who don't understand it is about perfection.
Even seemingly trivial mistakes can break huge swathes of mathematics.
In contrast in your daily lives little errors are just a fact of life.
So you carry over your mundane existence to an area where the tiniest of mental mistakes break so much, and then can't accept that it's happening because your mind keeps telling you that it is too small of a thing.
But in mathematics there is no such thing as too small of an error.
So I say, sqrt(4) is 2 or -2, and they claim it's just 2.
I say, look (-2)(-2) = 4, and they claim, so what, mathematicians DEFINED sqrt(4) to be 2, so who cares if (-2)(-2) = 4?
It may seem trivial, but by getting away with that dumb argument, posters can with that single small logical error keep going with bigger and bigger errors that grow from it, which is why these arguments don't get resolved.
So I say they are dumb as rocks because I'd think most of you can comprehend that people can DEFINE something to be true, even with the best of intentions, and it just fall apart as a concept with more advanced knowledge.
And while to many of you it may see this trivial thing which you think you always handle—mentally shifting as needed if you need sqrt(4) to be -2—it turns out that it breaks a lot of mathematics to make even one, small, seemingly trivial, logical mistake.
No matter how much you hate it, sqrt(4) has TWO SOLUTIONS.
And if you can get away with saying it only has one, you break mathematical reasoning at a low enough level that it's pointless to explain and explain and explain and mathematical proofs just bounce off of you as you are a rock, at such a basic level of denial about mathematics that more advanced concepts are totally beyond you.
So the debates continue because posters hold on to the most obvious error, refusing to accept that sqrt() has TWO SOLUTIONS, and that has implications over much of number theory.
Hard to believe but that is how mathematics escapes people who don't understand it is about perfection.
Even seemingly trivial mistakes can break huge swathes of mathematics.
In contrast in your daily lives little errors are just a fact of life.
So you carry over your mundane existence to an area where the tiniest of mental mistakes break so much, and then can't accept that it's happening because your mind keeps telling you that it is too small of a thing.
But in mathematics there is no such thing as too small of an error.
# posted by James Harris @ 16:27 
