Re: From sign conventions to Galois Theory

From: Arturo Magidin (magidin_at_math.berkeley.edu)
Date: 02/23/05 

Date: Wed, 23 Feb 2005 21:14:07 +0000 (UTC)

In article <1109127347.389872.91240@g14g2000cwa.googlegroups.com>,
Nora Baron <norabaron@hotmail.com> wrote:
>Arturo Magidin wrote:
>> In article <1109113423.779445.180300@f14g2000cwb.googlegroups.com>,
>> Nora Baron <norabaron@hotmail.com> wrote:
>> >Arturo Magidin wrote:
>>
>> [.snip.]
>>
>> > The 'magical' part for him is the feeling that whatever he dreams
>> >up is basically correct, even though maybe wrong in detail - the
>> >idea that he has this special gift for seeing things that the rest
>> >of us pedestrian plodders with our limited imaginations - stunted
>> >by overexposure to modern math and abstraction - cannot.
>>
>> I agree with this, but then I would say that this is not really
>> relevant to the "cargo cult" analogy.
>>
>> My understanding is that when one talks about "cargo cult" in the
>> context like the one you used, what one usually refers to is the
>aping
>> of the form, coupled with a lack of understanding of the substance,
>in
>> the hopes of obtaining the same results.
>
> Of course I am no cargo cult expert -

Neither am I, of course. My exposure to cargo cult has been almost
exclusively by way of analogy (i.e., it being discussed because it is
being used in an analogy). The two places where I have seen it most
are (i) criticisms against the postmodernist deconstruction movement,
where the pomo practitioners are often compared to the cargo cultists;
and (ii) criticisms of policy in developing nations. For example, the
National University in Mexico decided to take a number of steps to
make itself a "world renowned world class university in all
areas". Since world renowned world class universities will only hire
people with terminal degrees into tenure track lines, UNAM enacted
rules saying that only those with terminal degrees could be hired to
tenured lines; since world renowned universities do not pay to send
their students to study abroad and come back, they abolished the
scholarship program; and a bunch of similar decisions, designed to
emulate the form of the universities it hopes to be compared to. The
result, of course, was that instead of raising the quality of the
faculty, they simply vastly enlarged the number of lecturers (as
opposed to tenure-line people), the quality of new people decreased
because they are not getting those trained in better places, etc. The
university is compared to the cargo cultists in engaging in an aping
of the form hoping to obtain the same results, without recognizing (or
understanding) that what they are aping are no the causes, but the
effects of what they attempt to achieve.

Mathematics language is replete with jargon because it needs to be
extremely precise; the jargon is a consequence of the mathematics and
logic, not a cause of it. James alternates between condemning the
jargon as impenetrable (which, in a sense, it is, but it is
nonetheless ->required<-), and attempting to ape it without
understanding that the jargon must be carefully defined prior to use
(witness the "properly units", "objects", "fraction-like" of recent
years, or going back even further his "rational and irrational part of
a number").

In that respect, "cargo cult" has extended a bit from its original
depiction of a religio-mystical phenomenon because it has been so
strongly used as analogy (it has, after all, been over 50 years since
the days of the original cargo cults, which flourished in the years
following World War II; though according to wikipedia, it started in
the XIX century):

http://en.wikipedia.org/wiki/Cargo_cult

   Cargo cult is a term for religious rituals where the believers
   imitate the practices of foreigners in hopes of receiving the
   wealth of the foreigners, all without actually understanding what
   they are doing.

    [...]

   Eventually, the Pacific cultists gave up. But, from time to time,
   the term "Cargo cult" is invoked as an English language idiom, to
   mean any group of people making obeisance to something that it is
   obvious they do not comprehend.

It is interesting to note (given some of the references James has made
to his religious upbringing) that the wikipedia article mentions some
connections between cargo cults and messianism.

   [.snip.]

> What Harris has in common with the cultists is (1) a belief that
>what he is doing is going to work and make him rich and famous,
>and (2) a failure to work hard to get what he wants.

I don't think the original cultists could be accused of not working
hard. They simply did not understand the meaning of what they were
aping, and so they failed to achieve the objectives they want. I agree
that James fails to work hard (and more importantly, to work
->smart<-) for what he wants, however.

> Certainly
>he *thinks* he works hard now, but huge amounts of his time are
>spent not in working but in fantasizing about success and wishful
>thinking - he has no idea how hard real math is, how much you
>have to know, how deep the concentration must be, how narrow the
>path. His ideas are like duckweed on a pond, compared to the
>depths that one must go to now to contribute to modern math. He
>doesn't know this. I think the cultists, too, thought that their
>little models were pretty much the same as real airplanes - just
>lacking size and some kind of magic that would make them fly.
>They had no idea of a real airplane's complexity.

As I understand it, the cultists didn't make mock ups of the planes:
they made mock ups of the control towers and the landing strips, and
aped the daily routines of the airmen that were stationed there; they
viewed the actions on the ground as rituals that produced the
airplanes.

But that is neither here nor there. (-:

    [.snip.]

    [.re Alexander Abian.]

>> Alexander Abian used to have this quote at the end of all his posts:
>>
>> IF IT EXISTS IT IS MASS
>> TIME IS MASS. ABIAN MASS-TIME EQUIVALENCE FORMULA T=(10^18)Log(1-m/Mo)
>> SECONDS. ALTERING EARTH'S ORBIT AND TILT - STOPPING GLOBAL DISASTERS
>> AND EPIDEMICS. ALTERING THE SOLAR SYSTEM. REORBITING VENUS INTO A
>> NEAR EARTH-LIKE ORBIT TO CREATE A BORN AGAIN EARTH
>>
>
> Whoa. I would say he was definitely in the deep end of the
>pool there. Harris may have some ways to go after all.

A bit, yes.

>> When asked about actually making his ideas work, he would often reply
>> with a quote from Einstein ("IMAGINATION IS BETTER THAN KNOWLEDGE"),
>> preceded with one of his own making (" IMAGINATION IS THE ESSENCE THE
>> REST ARE DETAILS "). His role was coming with the ideas...
>>
>> I must be showing my net.age. His is the name that pops into my head
>> when I discuss that sort of attitude...
>>
>
> The name sounds familiar (of course it sounds a little too much
>like 'A. Adrian Albert', the famed 'A-Cubed" of the University of
>Chicago). Did Abian ever do creditable work at some time in
>the past?

Yes, Abian was a mainstream mathematician and member of the AMS for
many years. Mathscinet has 250 hits for him. The Berkeley library has
three books by him: a 1965 book on set theory and transfinite
arithmetic; a 1971 book on linear associative algebras; and a 1976
book on boolean algebras.

   [.snip.]

> I would not be surprised if the 'advanced placement' classes that
>he might have taken in high school, or the honors classes, tried
>to teach calculus at the epsilon-delta level - and might not
>have succeeded, at least not with Harris.

I would be completely surprised. His description of the classes he
took were that he took college level classes one term before
graduating. That sounds like he went to a regular calculus class being
taught at the university.

> I still maintain that
>his problem is with teaching that he hasn't actually experienced,
>at the graduate level

I agree; but I would go beyond that and even mention upper division
level.

>- Galois theory, for example - he claimed as
>recently as yesterday that he had disproved basic stuff that
>undermined Wiles' proof of the Taniyama conjecture - stuff that
>he thinks has been taught without question to grad students for
>the last 150 years.

That's my point: "taught without question to grad students" betrays a
complete ignorance of how math is learned and taught beyond the
calculus level.

Of course, note that he has become ever less explicit and precise
about just what it is he thinks is wrong with Wiles's proof of the
semi-stable case of the T-S-W conjecture (now a theorem)...

   [.snip.]

> I was thinking earlier today - Harris of course thinks I am a
>total liar and hypocrite bent on suppressing his genius - and
>what does he think now of Arturo Magidin?

I confess to feeling some mild curiosity on the point; feel free to
ask him. Or wait until May before asking... I certainly will not put
the question forth myself, though.

   [...]

> Then there is SWJPAM fiasco. Harris believes that getting
>something published confers magic as well. Once it gets into
>print, it has been Certified as True, for All Time.

(hence my suggestion that you wait until May)

   [...] 

-- 
======================================================================
"It's not denial. I'm just very selective about
 what I accept as reality."
    --- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu