Re: JSH: Tag along society

jstevh@xxxxxxx wrote:
> I doubt many of you with much mathematical training get
> lost on how you can have non-trivial factors in rationals,
> and on why it doesn't make sense mathematically to say
> that there are more trivial than non-trivial factors in
> the set of rationals for any particular composite.

There are certain classical results. One would be to consider the
probability of a/b being a non-trivial rational factor, for all
fractions where a and b are between 1 and N. That is a well-defined
number. Then what happens to that formula when N goes to infinity is
calculated, and that is generally considered the answer.

Dealing with probability where countable infinities are involved is
tricky, and even those of us "with much mathematical training get
lost." I've done so twice in the past couple of weeks.

The remedy for this is to run the ideas by some other person, who can
more easily see what's going on without having concentrated on the
details. The "can't see the forest for the trees" thing, you know.

Another problem is that you haven't said what a non-trivial rational
factor should be, so some people are confused about what exactly you
mean. I'm planning a thread where I take a lot of the ideas and put
them in a formal mathematical setting.

> But you will tag along with what you see as the direction
> the group is going as I've seen over the years that math
> society is a conformist society.

Time for The Shovel.

> Like that story I keep mentioning of the math grad student
> from Cornell

Lagarias?

> who re-worked the simplified argument that
> forms the heart of a key paper now at the Annals of
> Mathematics.
>
> He offered to help me, possibly trusting in the Usenet
> crew here who argue with me all the time and dramatically
> claim I'm wrong, so I sent him a little math.

Is this still part of the story, or was the story just about a grad
student re-working an argument? And did your story occur while he was a
grad student, or some time after?

(The story about a bright grad student proving an unsolved problems,
thinking it was homework, is actually real and not an urban legend. G.
B. Dantzig was taking a class, and the professor had written up three
unsolved problems in statistics. Dantzig, arriving late, didn't
understand the context and figured that it was homework. A few weeks
later -- deadlines are a lot more lenient in grad school -- he turned
in some problems saying he'd gotten two but the third one was tricky.
The professor looked at his proofs of the two results, wrote up an
introduction, and submitted the paper.)

> It took him months to go over it, as he dragged his feet,
> in my opinion, but finally he'd covered it and seen that
> there weren't any errors, so he made up something and ran
> off.
>
> But what if? What if he'd jumped at the chance to be a
> revolutionary in the field?

This makes me think this second part occurred after he was in grad
school. A grad student, eager to make a mark on mathematical society,
would WANT to co-author a paper with revolutationary content in it,
especially if the mathematics was correct.

So I suspect he was working as a professor. If so, he also had teaching
and service, as well as HIS OWN research, taking up time, so it
shouldn't be surprising that he took so long. So, no, he wasn't
"dragging his feet."

> It might be over now and he could be set on the path to
> becoming one of the greatest mathematicians of his time
> versus being a story I tell to emphasize to you that you
> are part of a rigidly conformist group.
>
> So why wouldn't he seize such an opportunity?

That is a very good question. If he behaved in a rational manner, why
wouldn't he seize such an opportunity, especially if the mathematics
HAD been worked out? All he would have had to do was add an
introduction, add his name to the title page, and he'd have another
paper.

Maybe the mathematics was correct, but there was nothing beyond that.
If I had received the SF Theorem from anyone, I would have said, "Nice;
you can manipulate the symbols. So what's the point?" And I would have
added some information about what the sender should do at that point.

One thing is for sure: If it required more research on my part, I'd
probably put it aside instead of spending time on this new research
topic.

Did you tell him that this was an opportunity? Did you tell him what
grand plans you had in mind? Did you tell him exactly how to turn the
results into something meaningful? I suspect not. And results which
lead nowhere are not exactly the thing that ANYONE wants to spend their
time on.

> My take on it is that math students are taught to trust,

Which makes it completely obvious that you have no clue about
mathematical society. I took advanced courses in mathematics, covering
theoretical results and how to put together proofs. I went to grad
school. I worked on a couple of problems. (One went nowhere, so I
abandoned it after a year. I did the majority of the active work in the
other one.) I did not assume that the problem was unsolvable just
because none of the big names could do it. (I think this is what you
mean by "trust".) I worked on a thesis. The thesis was written so that
the committee passed me. Arizona State felt that my research was good
enough to continue, and they hired me as a Visiting Assistant
Professor.

In short, I have been a math student and been through the process. As
such, I know what happens. You are clueless to the truth.

In another response, the poster and I talk about how when we managed to
find the ideas that make the proofs work for our theses, how the
advisor played little role in guiding. The 5/14 result which I got
published was a joint work with my advisor. The 3/8 result was one
where we worked on an initial idea, but then I came up with the idea of
a recursive construction, which makes the proof work. THIS WAS A
SURPRISE TO MY ADVISOR.

My advisor suggested that I prove when equality occurs in "our
theorem". He intended me to do this for "Theorem A," but I did it for
"Theorem B". I've written up this "equality condition" and submitted it
as a paper.

He was my advisor, not my mommy.

Trust is not rampant in mathematics. I was told that "planarity can be
tested for in linear time." If I don't believe it, I can search for the
paper where it's proven, read it for myself, go through the proof, and
see that all the steps are valid, and that the result really follows.

This is what I mean when I say, "Mathematics cannot be hidden."

> and they are taught that they build on the greats who came
> *before* them, who are believed absolutely.

Again, this is not 100% true. Sure, people nowadays use the same terms
as before, and use previous results, but belief is not necessary; once
again, the importance of mathematics is that of PROOF, which explains
WHY a result is true. If there is no error in the proof, then the
result MUST be true, regardless of who said it. (You said this before,
remember? "After you've proved something, there is no argument about
it", or something like that?)

> They follow their professors.

But not like lemmings.

> They follow their textbooks.

I hardly used any of my textbooks in actual reasearch. Why? Because the
results I was working on weren't known at that point; it wouldn't be
research otherwise. The textbooks only talk about terminology,
notation, and what ideas have been tried BEFORE. Anyone who reads these
books knows they are not the say-all and be-all of that part of
mathematics, only a place to start exploration from.

> They follow.

There have to be deciding factors in what works and what doesn't work;
if there weren't, then your paper would not have been withdrawn. If
there weren't standards, then every paper that arrives at a journal
would have to be published.

So, yes, if you want to play against Kasparov, you have to learn how to
play chess. But that's simply a given.

> They do not lead.

They do if they make a breakthrough. But the breakthrough won't happen
in grad school. Grad school is a very tough test to see if you've got
what it takes to do research and find these new results.

> They are even taught who can make a major mathematical
> discovery.

Not who "can make" a major discovery, but who "tends to" make a major
discovery. The majority of mathematics results over the past few
centuries have been proved by grad students or young faculty. (Results
tend to drop off after the age of 30 or so.)

Do you expect a 5-year old to be able to play professional golf? No,
certainly not. Tiger Woods was good at a young age, though. And his
story is the exception to the rule, not what usually happens.

No major crime has been solved by a psychic; no psychic has provided
enough hard evidence to lead police to a certain place; it's only been
afterwards that what they said was found to connect with what happened.

Professional results come from mainly professionals.

There are exceptions, but that's what they are: Exceptions.

> No fantasy there, no "Good Will Hunting" they're taught,

"Good Will Hunting" was made for entertainment purposes, not
educational purposes.

> as, you know, math professors teach that math professors
> make the major mathematical discoveries, right?

Again, this has been responded to better in other places.

> So it's like, you look at the person, and forget history.

Why stop there? Why not forget arithmetic as well? That's what some of
your results suggest we do. Why not pull out our hair, climb into
trees, and live there?

> People like me are high-strung, can be loud, or quiet,

Usually loud, though.

> but often are loud, challenging, and willing to push other
> people on what they know, or think they know.

I was going to add the "think they know", because in your case, with
Surrogate Factoring, what you think you know doesn't match up with any
useful aspects of the problems.

Do you really think you are the first person in history ever to think
about surrogate factoring? Do you really think you're the only person
who has taken the work this far? Do you really think that someone
working on surrogate factoring wouldn't have tried what you've already
tried, and in fact, may have found reasons why it doesn't work?

I may be wrong, but the odds are in my favor. It would be the sort of
thing I'd be willing to bet one year of my salary against one year of
your salary for, if I was a gambling person.

> I fit the profile of a major discoverer.

But you haven't found a way to express it properly. This is why you
need to take some math courses where you look at proofs, and a number
theory class, in the very least.

> I know I can make major discoveries,

I'm not saying you can't; I'm just saying that once you make the
discovery, you don't know how to express it. Or you may have discovered
something other than what you think you have.

> and I don't care what rules other people toss up about
> who can or cannot or that many of you believe that only
> established mathematicians who have gone through a
> particular training can make.

Here we go again.

You COULD walk into a fire station in Atlanta and say you're a
firefighter. That would be fun, sliding down the pole, driving the
truck, breaking down doors with axes, rescuing people, and being a
hero, wouldn't it?

But if you're caught in a bad situation -- if you can't drag someone's
body out of the house, or if you get trapped when the ceiling collapses
-- that's when everything turns bad. And at that point, you should
realize that firefighting training really does have a purpose.

Well, you've been caught in an emergency. You can't justify your
results, and you have no experience in doing anything like that, other
than let loose The Hammer, or stick your fingers in your ears and sing
loud.

Real researchers don't do that.

> You go through mind control training.

"Mind control training" is the same as "indoctrination", or "learning
to fit in with society." It's just a word, with a negative connotation,
which just means modifying your behavior so that you can get along in a
new situation.

And if people are getting ready to do research, to go after the
unknown, mind control is the LAST thing that you want to do to them.

> The way you're taught mathematics allows you to be easily
> controlled by your society, so that even mathematical
> proof itself is not enough to move many of you, as seen by
> that math grad student, still a grad student, at Cornell.

I guess it wasn't Laragias, then. (I only got down here.)

But if the grad student is behaving rationally, he has some other, more
promising, more immediate result in the works.

If someone came to your door and offered you $1000, would you refuse
the money, run down the street, and buy a lottery ticket? No. You'd go
with the more sure thing. And that's what I suspect he's doing;
continuing the research that he's spent a lot of time on, and is more
familiar with.

> Even now that mind control will tell you that there's no
> way this will go the way it must go, as society will
> probably finally figure out some of what's going on,
> and ostracize many in your society.

Actually, they would charge after the government, because the
government has been doing "mind control" for more nefarious reasons,
for a longer time.

> The teaching techniques that many of you go through
> will be abolished, and math students will be pushed to
> be more creative, more open to new ideas, and less
> trusting that there is an absolute canon of mathematics
> that is absolutely perfect, never to be challenged.

That's what grad school is like. You obviously haven't been there, so
how can you know what it's like? This is only fiction.

> But many of you will wait, holding on, believing

Belief represents the ceasation of thought. It is the very opposite of
the ideas behind mathematical research.

> when there is no reason to believe it that I'm not one
> of the biggest figues to emerge in mathematics in its
> history, but instead am just some nut mouthing off on
> Usenet.

I'm going to call your bluff.

Prove that you're not a nut.

Post NOTHING about society, just post about the mathematics, and
explain to us, like 5-year olds, how exactly your method factors
integers. Show that it ALWAYS works. When we raise topical questions,
answer them, again without ranting and raving about conspiracies, or
going off on other tangents (a sure sign that someone IS a nut).

Your very behavior, that of being a nut, suggests that you are one.

If you are the Euler of the moment, speak like the Euler of the moment.

If you can, of course.

If you can't talk rationally about Surrogate Factoring here, what makes
you qualified to determine who can, in your Google group?

> And for that you will find that you will probably end
> up out of mathematics because it will no longer be the
> field for which you were trained.

Again, do it if it's necessary. However, I think this is a hollow
threat.

> You were trained to follow.

Who were we trained to follow? MATHEMATICIANS! Which directly
contradicts what you say next:

> I say, mathematicians are to be leaders.

Well, at least those of them who aren't followers, anyway.

--- Christopher Heckman

.

Relevant Pages

  • Re: SF: Areas of confusion, infinity
    ... >> clearly that from the theorem only, but math people are pushing me ... > rationals will produce non-trivial factorisations of M, ... the mathematics does not distinguish between trivial and non-trivial ... The surrogate factoring theorem does in fact connect two infinite sets. ...
    (sci.crypt)
  • JSH: The lying charge
    ... I now routinely talk about "math people" lying, ... revolutionary mathematics. ... Some of you may say that all factors in the set of rationals are ... And they don't believe in mathematical proof. ...
    (sci.crypt)
  • Re: Surrogate Factoring Theorem
    ... Absent a reason, the mathematics will act without prejudice, and simply ... Now the "Nora Baron" poster routinely makes statements without proof, ... Those four possibilities each have an *infinite* number of rationals ... But with "pure math" results, people would just join in with the lies ...
    (sci.crypt)
  • Re: why lorentz transformation?
    ... If he didn't think that it was mathematics, ... Deal with the math or shut the fuck up. ... >| new coordinates xi, eta, zeta, tau, and no symbol is used to denote ... notation became important for you later in your posting. ...
    (sci.physics.relativity)
  • =?UTF-8?B?2YHYsdmI2LQg2YXYrNmF2YjYudmHINqp2KfZhdmEINqp2KrYp9io2YfYp9uMINix24zYpw==?= =?UTF-8
    ... Probability Theory The Logic of Science, ... Copyright © 1989 by Addison-Wesley Publishing ... Elliptic Curves Number Theory and Cryptography Discrete Mathematics ...
    (sci.math.num-analysis)