Saturday, June 07, 2003
Easily stumping mathematicians
One of the more profound errors of Western civilization has been a continual collapse to dogma, and current dogma claims that mathematicians as a group represent a blessed society which is extraordinarily intelligent and not prone to error.
That may sound weirdly phrased but when you think about it carefully as I've had reason to do, it is the best explanation for the current situation I'm facing, where I can stump mathematicians—no matter how supposedly brilliant or "genius", anywhere in the world—with a rather simple thing.
Now I'll give this simple thing in just a bit but I want those of you who aren't part of math society to watch carefully what happens next. If mathematicians were what I'm sure many of you think they are, then what I'm about to do would be news. But in reality they are NOT a blessed society, and in general they are not much more intelligent than average—by my standards.
However, they live and breathe in a special status based on your BELIEF of their blessed state of supposedly superior knowledge and ability, and make the lives of people like me miserable when we make important discoveries, but refuse to play by their rules.
So then to stump your local mathematican, simply ask them to prove that given,
abc=5
where 'a', 'b', and 'c' are certain special numbers called algebraic integers, that no 'a' and 'b' exists such that neither a=1, b=1, nor ab=1, which is what most of them BELIEVE though in fact their belief is false.
It's actually rather easy to prove that their belief is false, but I proved it, wrote a paper, and now math society appears to be doing its best to ignore me!
The question is not trivial because though they can't prove it, mathematicians teach the belief as fact. It's basically just a mistake within "core" mathematics.
I've been puzzling about the behavior of mathematicians as I'd think that when I pointed out their mistake they'd work to fix it. After all, a mistake is a mistake no matter how blessedly brilliant other people think you are.
I had a bit of a realization when I came across the following tonite on the web.
From "When is a proof?" http://www.maa.org/devlin/devlin_06_03.html, excerpt is first paragraph and beginning of second.
So for those of you who believe in mathematical certainty the argument is that what mathematicians really talk about when they say "proof" is something that convinces *them* and not necessarily something that is unequivocably the truth.
That math society aspect is what has given me problems as I have certain rather dramatic math finds, which mathematicians have the easy claim for ignoring by simply claiming that they don't understand me.
If you're curious about what those finds are simply go to
http://groups.msn.com/AmateurMath
where you'll also see a paper that gives you the route to solving the little conundrum I presented. It also highlights an error that mathematicians teach to their trusting students, which they should no longer teach now that I've pointed the error out.
Understand that the work at my site is irrefutable, and actually represents what that author above calls that "right wing" definition of a proof.
My work is irrefutable. But I'm not part of the math community.
However, the math community has a certain position based on general belief that mathematicians represent a blessed group—blessed with superior mental faculties and knowledge.
So what happens when an irrefutable proof from outside the community i.e. an irresistable force meets that community's recalcitrance?
We'll see if the truth wins sooner or later against the mathematical community.
But what will happen is that the truth will win as the truth, you see, is an irresistable force and an immovable object.
Though I'm sure there are mathematicians who are wishing it were more movable and "left wing" because I'm the discoverer.
Oh yeah, don't mathematicians say the damndest things?
That may sound weirdly phrased but when you think about it carefully as I've had reason to do, it is the best explanation for the current situation I'm facing, where I can stump mathematicians—no matter how supposedly brilliant or "genius", anywhere in the world—with a rather simple thing.
Now I'll give this simple thing in just a bit but I want those of you who aren't part of math society to watch carefully what happens next. If mathematicians were what I'm sure many of you think they are, then what I'm about to do would be news. But in reality they are NOT a blessed society, and in general they are not much more intelligent than average—by my standards.
However, they live and breathe in a special status based on your BELIEF of their blessed state of supposedly superior knowledge and ability, and make the lives of people like me miserable when we make important discoveries, but refuse to play by their rules.
So then to stump your local mathematican, simply ask them to prove that given,
abc=5
where 'a', 'b', and 'c' are certain special numbers called algebraic integers, that no 'a' and 'b' exists such that neither a=1, b=1, nor ab=1, which is what most of them BELIEVE though in fact their belief is false.
It's actually rather easy to prove that their belief is false, but I proved it, wrote a paper, and now math society appears to be doing its best to ignore me!
The question is not trivial because though they can't prove it, mathematicians teach the belief as fact. It's basically just a mistake within "core" mathematics.
I've been puzzling about the behavior of mathematicians as I'd think that when I pointed out their mistake they'd work to fix it. After all, a mistake is a mistake no matter how blessedly brilliant other people think you are.
I had a bit of a realization when I came across the following tonite on the web.
What is a proof? The question has two answers. The right wing ("right-or-wrong", "rule-of-law") definition is that a proof is a logically correct argument that establishes the truth of a given statement. The left wing answer (fuzzy, democratic, and human centered) is that a proof is an argument that convinces a typical mathematician of the truth of a given statement.
While valid in an idealistic sense, the right wing definition of a proof has the problem that, except for trivial examples, it is not clear that anyone has ever seen such a thing.
From "When is a proof?" http://www.maa.org/devlin/devlin_06_03.html, excerpt is first paragraph and beginning of second.
So for those of you who believe in mathematical certainty the argument is that what mathematicians really talk about when they say "proof" is something that convinces *them* and not necessarily something that is unequivocably the truth.
That math society aspect is what has given me problems as I have certain rather dramatic math finds, which mathematicians have the easy claim for ignoring by simply claiming that they don't understand me.
If you're curious about what those finds are simply go to
http://groups.msn.com/AmateurMath
where you'll also see a paper that gives you the route to solving the little conundrum I presented. It also highlights an error that mathematicians teach to their trusting students, which they should no longer teach now that I've pointed the error out.
Understand that the work at my site is irrefutable, and actually represents what that author above calls that "right wing" definition of a proof.
My work is irrefutable. But I'm not part of the math community.
However, the math community has a certain position based on general belief that mathematicians represent a blessed group—blessed with superior mental faculties and knowledge.
So what happens when an irrefutable proof from outside the community i.e. an irresistable force meets that community's recalcitrance?
We'll see if the truth wins sooner or later against the mathematical community.
But what will happen is that the truth will win as the truth, you see, is an irresistable force and an immovable object.
Though I'm sure there are mathematicians who are wishing it were more movable and "left wing" because I'm the discoverer.
Oh yeah, don't mathematicians say the damndest things?
# posted by James Harris @ 23:50 
