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From: JSH on 25 Jul 2010 00:11
On Jul 24, 8:00 pm, Joshua Cranmer <Pidgeo...(a)verizon.invalid> wrote:
> On 07/24/2010 08:24 PM, JSH wrote:
>
> > This thread though is about reasons for that "noise" and the question
> > of how much might that be about lack of education.  Or how much people
> > *think* it's about lack of education.
>
> > As a person with a degree in physics from Vanderbilt University, who
> > was a gifted child who read widely on a large number of mathematical
> > topics I'm actually at a very high level of math education by any
> > objective measure.
>
> I can tell you from my experience that saying you were a "gifted" child
> does not say anything, per se, about your math education. In particular:
>
> 1. If I interpret it to mean that you were labelled as such by the
> school system, and that no further action was taken, then it is has
> essentially no meaning. Education can be a touchy business, as most
> parents are adamant that their children are above average, objective
> results be damned.
>
> 2. If I interpret it to mean that you were enrolled into a Gifted and
> Talented program (as my school district called it, at least), it again
> means nothing. Math ability is not the sole determinant of this
> classification, so it can vary wildly: at an objective level, it means
> taking calculus anywhere from 8th grade to 12th grade, if at all.
>
> 3. Similarly, most schools are not well-equipped to handle the top
> echelon math students. Depending on your school district, calculus is
> either the end of the line, or perhaps you might get some multivariable
> calculus thrown in afterwords. Another alternative is taking actual math
> courses at a local university, but since you did not evidence of this,
> I'll assume it did not happen in your class.

I was part of Duke University's gifted and talented program called
T.I.P.

There I took accelerated math classes.

Regardless of that, however, on my own I taught myself calculus and
trigonometry, partly because I'd read that Einstein taught himself
calculus, when I was 12.

I also did extensive readings on my own, as gifted children do, though
I did find a lot of abstract algebra to be dry and boring.

But for a while I thought I'd be focused on the sciences, hence my
degree in physics later.

> 4. In addition, most "accelerated" math programs at the high school
> level focus on Calculus and related derivatives (multivar, linear
> algebra, differential equations). Your main area of "research" is more
> related to non-linear algebra or number theory, which is not typically
> taught in such cirricula.

It WAS taught at Duke University however, as part of their summer
program for gifted youth.

However, at that time I found it boring to the extreme, and didn't
pursue it much.

What I did complete there was a complete course work of geometry. In
six days.

The second time I went, I took a course in structured C--the time
period was the eighties--from an IBM researcher on loan from the
Research Triangle.

> 5. You mention getting a degree in physics. I'm not a physics major
> myself, but I believe most of the math involved is similarly
> calculus-track stuff, not number theory. About the only germane portion
> I can see being undertaken during such a degree is statistics, yet you
> seem to not understand statistical hypothesis testing correctly.

Yawn.

> While it may all be evidence that you understand some math at the
> appropriate level, it is not evidence that you understand the math that
> is germane to the topic at hand.

I've talked about these things before but that reality of my rather
extensive education, including some rather extraordinary aspects to
it, is something that people like you would rather not accept, so you
just ignore it.

You live in a reality you create and have no interest in what is true.

I was something of an extraordinary child, which to me as an adult is
just kind of like hearing about fun stories, but of course that is a
lot of why I'm immune to criticisms from people like you on some
Usenet newsgroup.

I long grew tired of people telling me how brilliant I was, before I
graduated high school.

I was a little celebrity in my little bowl of a small town Georgia
school. Already with college courses, before I was a senior in high
school.

Mindless mutterings from wannabe's on Usenet--as where else can they
go?--have no impact on me today.

I'm a product of the American educational system at its greatest
efforts.

The U.S. has invested quite a lot in me, since I was a child.


James Harris
From: Dark Horse on 26 Jul 2010 02:46
On Jul 25, 2:11 pm, JSH <jst...(a)gmail.com> wrote:
>
> I was part of Duke University's gifted and talented program called
> T.I.P.
>
> There I took accelerated math classes.
>
> Regardless of that, however, on my own I taught myself calculus and
> trigonometry, partly because I'd read that Einstein taught himself
> calculus, when I was 12.
>
> I also did extensive readings on my own, as gifted children do, though
> I did find a lot of abstract algebra to be dry and boring.
>
> But for a while I thought I'd be focused on the sciences, hence my
> degree in physics later.
>
> > 4. In addition, most "accelerated" math programs at the high school
> > level focus on Calculus and related derivatives (multivar, linear
> > algebra, differential equations). Your main area of "research" is more
> > related to non-linear algebra or number theory, which is not typically
> > taught in such cirricula.
>
> It WAS taught at Duke University however, as part of their summer
> program for gifted youth.
>
> However, at that time I found it boring to the extreme, and didn't
> pursue it much.
>
> What I did complete there was a complete course work of geometry.  In
> six days.
>
> The second time I went, I took a course in structured C--the time
> period was the eighties--from an IBM researcher on loan from the
> Research Triangle.
>
> > 5. You mention getting a degree in physics. I'm not a physics major
> > myself, but I believe most of the math involved is similarly
> > calculus-track stuff, not number theory. About the only germane portion
> > I can see being undertaken during such a degree is statistics, yet you
> > seem to not understand statistical hypothesis testing correctly.
>
> Yawn.
>
> > While it may all be evidence that you understand some math at the
> > appropriate level, it is not evidence that you understand the math that
> > is germane to the topic at hand.
>
> I've talked about these things before but that reality of my rather
> extensive education, including some rather extraordinary aspects to
> it, is something that people like you would rather not accept, so you
> just ignore it.
>
> You live in a reality you create and have no interest in what is true.
>
> I was something of an extraordinary child, which to me as an adult is
> just kind of like hearing about fun stories, but of course that is a
> lot of why I'm immune to criticisms from people like you on some
> Usenet newsgroup.
>
> I long grew tired of people telling me how brilliant I was, before I
> graduated high school.
>
> I was a little celebrity in my little bowl of a small town Georgia
> school.  Already with college courses, before I was a senior in high
> school.
>
> Mindless mutterings from wannabe's on Usenet--as where else can they
> go?--have no impact on me today.
>
> I'm a product of the American educational system at its greatest
> efforts.
>
> The U.S. has invested quite a lot in me, since I was a child.
>
> James Harris

This statement really gets to the core of your difficulties in maths.
Assuming your claims of going through talented student programs in
high school are correct (and I have no solid reason to doubt them),
then what you have is an advanced understanding of HIGH SCHOOL MATHS.

This is also clear to anyone who tries to look at your work - you do
lots of algebra and calculations but no real maths. By real maths I
mean deep, conceptual ideas about structural properties of (say) the
algebra you are working in.

You seem to just move algebra around and then claim some pattern in
the tea leaves that remain in the chaos of symbols. Now I know you
think you are motivated by some maths idea - something like "omg lets
introduce more parameters, then look they go away". But tellingly,
this is a very high school type of calculation technique, no genuine
maths here (ie some deep structural property at work).

Your most laughable effort recently has been this prime residue axiom
business. The whole point of studying the prime numbers and forming
conjectures like twin primes is to establish that they have no hidden
long term structure. Numerically people are confident of this, it is
very plausible and reasonable, but they cant PROVE it from existing
axioms. To do so would obviously demonstrate a fundamentally deep
property of the natural numbers.

Your solution to this, from which you derive the claim that you are
the greatest mathematician since Gauss, is to simply assume the answer
is true. You just say "forget trying to prove this - its an axiom!
LOL!!1".

So of course you will disregard what I am saying and carry on as you
are. But let it be known that your maths knowledge hasnt progressed
beyond a high school level. In the grand scheme of things, if
professional, research maths were like an athletics competition (ie
sprinting, distance running, long jump etc) then high school maths is
the equivalent of learning to crawl as a toddler. There is an immense
gulf between that and cutting edge maths, a gulf of abstraction,
technical expertise and rigorous thinking that you dont even know
exists.

As you wail away about how in 20 years the maths professors will be
sacked and interrogated by national security forces, imagine the view
from the other side of the gulf - from where the extremely intelligent
and well versed maths professors stand and can see your piteous claims
that are easily rejected. What a joke. You are certainly not a modern
incarnation of Gauss as you seem to imply.

And you know - I am sure Gauss would be the first to laugh at you (via
time travel or something) if you presented your rubbish to him.

> I'm a product of the American educational system at its greatest
> efforts.

No - those people who spend years toiling and learning in grad schools
and doing research to obtain PhDs take this place.

DH.
From: JSH on 26 Jul 2010 21:14
On Jul 25, 11:46 pm, Dark Horse <dark.horse....(a)gmail.com> wrote:
> On Jul 25, 2:11 pm, JSH <jst...(a)gmail.com> wrote:
>
>
>
>
>
>
>
> > I was part of Duke University's gifted and talented program called
> > T.I.P.
>
> > There I took accelerated math classes.
>
> > Regardless of that, however, on my own I taught myself calculus and
> > trigonometry, partly because I'd read that Einstein taught himself
> > calculus, when I was 12.
>
> > I also did extensive readings on my own, as gifted children do, though
> > I did find a lot of abstract algebra to be dry and boring.
>
> > But for a while I thought I'd be focused on the sciences, hence my
> > degree in physics later.
>
> > > 4. In addition, most "accelerated" math programs at the high school
> > > level focus on Calculus and related derivatives (multivar, linear
> > > algebra, differential equations). Your main area of "research" is more
> > > related to non-linear algebra or number theory, which is not typically
> > > taught in such cirricula.
>
> > It WAS taught at Duke University however, as part of their summer
> > program for gifted youth.
>
> > However, at that time I found it boring to the extreme, and didn't
> > pursue it much.
>
> > What I did complete there was a complete course work of geometry.  In
> > six days.
>
> > The second time I went, I took a course in structured C--the time
> > period was the eighties--from an IBM researcher on loan from the
> > Research Triangle.
>
> > > 5. You mention getting a degree in physics. I'm not a physics major
> > > myself, but I believe most of the math involved is similarly
> > > calculus-track stuff, not number theory. About the only germane portion
> > > I can see being undertaken during such a degree is statistics, yet you
> > > seem to not understand statistical hypothesis testing correctly.
>
> > Yawn.
>
> > > While it may all be evidence that you understand some math at the
> > > appropriate level, it is not evidence that you understand the math that
> > > is germane to the topic at hand.
>
> > I've talked about these things before but that reality of my rather
> > extensive education, including some rather extraordinary aspects to
> > it, is something that people like you would rather not accept, so you
> > just ignore it.
>
> > You live in a reality you create and have no interest in what is true.
>
> > I was something of an extraordinary child, which to me as an adult is
> > just kind of like hearing about fun stories, but of course that is a
> > lot of why I'm immune to criticisms from people like you on some
> > Usenet newsgroup.
>
> > I long grew tired of people telling me how brilliant I was, before I
> > graduated high school.
>
> > I was a little celebrity in my little bowl of a small town Georgia
> > school.  Already with college courses, before I was a senior in high
> > school.
>
> > Mindless mutterings from wannabe's on Usenet--as where else can they
> > go?--have no impact on me today.
>
> > I'm a product of the American educational system at its greatest
> > efforts.
>
> > The U.S. has invested quite a lot in me, since I was a child.
>
> > James Harris
>
> This statement really gets to the core of your difficulties in maths.
> Assuming your claims of going through talented student programs in
> high school are correct (and I have no solid reason to doubt them),
> then what you have is an advanced understanding of HIGH SCHOOL MATHS.

Um, guess you glossed over the part about going to Duke University for
their T.I.P. program where they had coursework far beyond.

But admittedly I found abstract algebra boring, so didn't do much
there.

Duke University DOES have rather advanced mathematics, however, and
put a lot available for its gifted students. I just didn't find much
of it interesting at the time.

> This is also clear to anyone who tries to look at your work - you do
> lots of algebra and calculations but no real maths. By real maths I
> mean deep, conceptual ideas about structural properties of (say) the
> algebra you are working in.

I try to keep it simple.

Besides, I think modern math people gild the lily as the saying goes
to give themselves busy work, and make it look more complicated than
it is.

How else do you justify those Ph.D programs?

> You seem to just move algebra around and then claim some pattern in
> the tea leaves that remain in the chaos of symbols. Now I know you
> think you are motivated by some maths idea - something like "omg lets
> introduce more parameters, then look they go away". But tellingly,
> this is a very high school type of calculation technique, no genuine
> maths here (ie some deep structural property at work).

Well, with k^m = q mod N, I DID use a technique which introduces m
unknown variables I call the a's, where the algebra dynamically sets m-
c of them, which means, if c=4--it's the count of factors of some
number q^2 mod N--you can find the discrete log, i.e. get m, for an m
of arbitrary size, by using only 4 factors.

Turns out that algebra is rather trivial.

So you could find m^100000000000000 with 4 factors, by the theory. (I
just sat and typed a 1 followed by a lot of 0's without counting as
"arbitrary size" is less impressive.)

My take on the situation is that modern math people PURSUE abstruse
and complicated ideas not because that's what works best for
mathematics itself, but because that's what works for justifying long
degree programs.

Make it complicated--make more money.

> Your most laughable effort recently has been this prime residue axiom
> business. The whole point of studying the prime numbers and forming
> conjectures like twin primes is to establish that they have no hidden
> long term structure. Numerically people are confident of this, it is
> very plausible and reasonable, but they cant PROVE it from existing
> axioms. To do so would obviously demonstrate a fundamentally deep
> property of the natural numbers.

Oh, you mean how I *explain* twin primes and other prime gaps simply
with an idea that removes the need for, gasp, more research!!!

More money, more money, more money.

Again, extra complexity can be linked to a need for some math people
to make more money.

If they ignore the simple idea which explains best.

Humanity quit simply evolved a math system that abhors simple solution
by having career math people who need busy work to get paid, pay their
mortgages, and well, to eat!

> Your solution to this, from which you derive the claim that you are
> the greatest mathematician since Gauss, is to simply assume the answer
> is true. You just say "forget trying to prove this - its an axiom!
> LOL!!1".

I'm not a mathematician. So how can I claim to be the greatest since
anyone?

What I DO note are that a lot of these errors and over complexity
arguments came in after Gauss died.

With the rise of "pure math" math practitioners could divorce their
work from reality which we see today allows them also to continue in
error against mathematical proof.

Without the real world to hold them back, they can make things up, and
just use community to live, breathe, and promote error.

Error is now the greatest reality of the modern mathematical world--in
"pure math" areas of number theory.

But prove the error and what can they do as a group--ignore you.
Without real world application, there is no way to show that the math
they are doing does not work in a way that stops them from just saying
you're wrong, or more simply, ignoring you.

> So of course you will disregard what I am saying and carry on as you
> are. But let it be known that your maths knowledge hasnt progressed
> beyond a high school level. In the grand scheme of things, if
> professional, research maths were like an athletics competition (ie
> sprinting, distance running, long jump etc) then high school maths is
> the equivalent of learning to crawl as a toddler. There is an immense
> gulf between that and cutting edge maths, a gulf of abstraction,
> technical expertise and rigorous thinking that you dont even know
> exists.

Yawn.

> As you wail away about how in 20 years the maths professors will be
> sacked and interrogated by national security forces, imagine the view
> from the other side of the gulf - from where the extremely intelligent
> and well versed maths professors stand and can see your piteous claims
> that are easily rejected. What a joke. You are certainly not a modern
> incarnation of Gauss as you seem to imply.

Hey, my research on k^m = q mod N if potent probably won't take 20
years to be known, and I'm trying to run away from it myself, but if
it's NOT that important, then the 20 years thing is more about the
errors.

My research simplifies vast stretches of number theory.

You may think you insult it by calling it high school level, but
consider some kid who learns it while she or he is in high school,
learns all the convoluted stuff you say is much greater and after an
intense learning experience of maybe a decade, comes out on the other
side--and can do it all more simply with my math.

Think she'll thank you then? For wasting her life?

> And you know - I am sure Gauss would be the first to laugh at you (via
> time travel or something) if you presented your rubbish to him.

Gauss could, I'm sure, be extremely mean.

He'd be more interested in beating people I'd think.

Sir Isaac Newton could be very mean as well.

Those kind of people tended to have very mean nasty sides, which
history doesn't like to report as much.

So if I'm right, and Gauss could be beamed forward in time, and he was
among modern "mathematicians", he'd probably have you beaten, as in
physically beaten.

> > I'm a product of the American educational system at its greatest
> > efforts.
>
> No - those people who spend years toiling and learning in grad schools
> and doing research to obtain PhDs take this place.

Um, I had a scholarship to Vanderbilt University where I got my degree
in physics, having already received college coursework from Duke
University, plus special classes as a "gifted child", so the United
States of America *has* invested quite a lot in me, and if you think
it did that without effort then say that to all the kids who don't get
such support--even when they deserve it--all over the world.

Wrapped up in me are the efforts of a nation which spent quite a bit
of money alone besides everything else, on my education at some of the
finest educational institutions in the world.

To you Duke University and Vanderbilt University may not amount to
much, but you're just some Usenet poster anyway, and people like you
will SAY ANYTHING.


James Harris
From: Joshua Cranmer on 26 Jul 2010 22:37
On 07/26/2010 09:14 PM, JSH wrote:
> Oh, you mean how I *explain* twin primes and other prime gaps simply
> with an idea that removes the need for, gasp, more research!!!

What you have clearly missed is the entire core rationale of why people
are not accepting your result. Your entire result is based on a
vaguely-worded assertion (your so called prime residue axiom) which is
given without proof or even evidence.

To put in clear layman's term, you argument boils down to "If we assume
that primes have no structural patterns, then there are an infinitude of
twin primes. And the primes sure don't look like they have structural
patterns to me." The premise and conclusion are both believed to be true
by many, but there is no formal proof of this, by which I mean that the
very definitions of prime numbers, etc., preclude an errant structural
pattern from arising.

> Those kind of people tended to have very mean nasty sides, which
> history doesn't like to report as much.

Much in the vein of xkcd (<http://xkcd.com/285/>), I would like to say:
[citation needed].

>> No - those people who spend years toiling and learning in grad schools
>> and doing research to obtain PhDs take this place.
>
> Um, I had a scholarship to Vanderbilt University where I got my degree
> in physics, having already received college coursework from Duke
> University, plus special classes as a "gifted child", so the United
> States of America *has* invested quite a lot in me, and if you think
> it did that without effort then say that to all the kids who don't get
> such support--even when they deserve it--all over the world.

I am assuming that by "degree" you mean a "bachelor" degree, not a PhD.
And, if you want to be pedantic, Vanderbilt is a *private* institution,
so it is not as much supported by the government as a public state
school. Although, even then, a large portion of the money is likely
coming from at least a subset of the student body (out-of-state students
subsidize a fair amount of in-state students) as well as the
university's endowment funds, funded mostly by alumni and the financial
market at large.

Actually, I suppose the most investment you'll get by the government is
to have gone to an underperforming school (I do believe D.C. gets
shovelfuls of cash without much bang for the buck, as does NY, it
appears), then go to a community college for two years and then get
enrolled, with a full-ride financial aid scholarship, at a state
institution for 5 years or so for undergraduate degree (who's on the
4-year plan these days? :-P), another 2 years (or longer, as it may be)
for a masters (with financial aid or research stipend, etc.), and then a
PhD for however long it takes. Bonus points for being held back a few
years or being enrolled in kindergarten or prekindergarten. And also
after/before-school child care, since technically that is also
expenditure by the school system.

> Wrapped up in me are the efforts of a nation which spent quite a bit
> of money alone besides everything else, on my education at some of the
> finest educational institutions in the world.

Much of the United States' school system below the collegiate level is
pretty shitty, if you look at international test results. I do believe
the last test showed our students on par with Kenya's students. I come
from a relatively well-performing school district, and I would not call
the schools I went to "some of the finest educational institutions in
the world." Given what I've heard of the Georgian school system, nor
would I classify those schools at that high a level. Even if they have a
gifted program.

--
Beware of bugs in the above code; I have only proved it correct, not
tried it. -- Donald E. Knuth
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