From: michaelg@Xenon.Stanford.EDU (Michael Greenwald)
Subject: Re: Fermat's flunkeys (was Re: A Real Challenge)
Organization: CS Department, Stanford University, California, USA
Date: 10 Apr 92 19:51:26 GMT

Chris, I think you're overreacting, (a little unfairly, at that), and
missing my point.  It's possible that this is because my post was
unclear, and if so, I apologize. 

I think it's worth continuing, because I'd like to make my real point
clearer.  (Along the way I add a couple of digressions, I hope no one
minds.)

Just to set the context: I wasn't "gloating over your error".  I was
correcting a mistake and speaking to the issue of the reliability of
information posted on the net.

In this post, though, I do have Yet Another Agenda.  I'm trying to
point out ways where you misinterpreted things as (personal?) attacks,
and where you respond in a way that might escalate into flame-bait,
rather than an argument.  Yes, this is pompous and self-glorifying of
me (I mean, who am I to judge your rhetorical skills/style?).  I was
of two minds about actually sending this, but I am going to because
(a) I hope it isn't done in an offensive style, and (b) I think other
people are going to post, and it's easier to steer a
conversation/argument back on track at the beginning, before the train
of thought gets derailed too wildly.

cjdcosta@eos.ncsu.edu (CHRISTOPHER J DCOSTA) writes:

>michaelg@Xenon.Stanford.EDU (Michael Greenwald) claims:

>>I'm not trying to argue about what's ok and what's not ok on this
>>newsgroup, I just don't want to let a potential misconception about
>>Fermat's Last Theorem stand.  

Chris, note the above.  I wasn't bashing you, or arguing that it
wasn't ok for you to post your question.  I was correcting a
potentionally confusing issue -- precisely because I was surprised to
find that knowledge of FLT was not as commonplace as I thought.
"Surprised", not angry, upset, proud because
I-know-something-you-don't.  I was also frustrated that it persisted
after several specific references (including mine) to a number theory
texts had been posted.  "Frustrated" not angry, distressed, vengeful,
moved to tears or oratory.

The particular article I was responding to had you saying that of all
the responses only one had said that FLT had been proven for n=3, and
that you had a response saying it had been solved for all n <
some-large-n, *except* for n=3.

My response seems like a reasonable thing to post to the net, in order
to clear up this misconception. FLT has been proven for n=3, and for
all n smaller than some number (currently in the six figures), and
rising.  Several references had been posted, I repeated mine.  I
inserted a second point, which I believed to be more important than
FLT.  I inserted it >before< my response to the FLT posting, because I
thought it was more important.  I don't think it came across well in
my short statement.  I'll explain it in more detail later in this
post, because doing so now would confuse the rest of the argument.
(I'm including it as originally written, with underlines added for
emphasis, though)

>>			The thing that is frustrating about this
>>thread, is that the so-called "Fermat's Last Theorem" (it ain't a
>>theorem. Yet) isn't hard to look up (it is one of the more famous
>>mathematical conjectures and makes its way into many available
>>reference books).  It is frustrating that easily verifiable mistaken
                                            ^^^^^^^^^^^^^^^^^    
>>assertions are posted (I'm not talking about "cjdcosta" who, I
>>believe, simply asked about it) -- it leads one to question how much
                                                     ^^^^^^^^ ^^^^^^^^
>>care is being taken before some people post other, less easily
  ^^^^                ^^^^^^                         ^^^^^^^^^^^
>>verifiable, assertions.
  ^^^^^^^^^^
>>
>>In any case, at >least< 3 people have posted that the n=3 case has
>>been proven.  It is in almost >any< number theory text.  I previously
>>posted a reference to Hardy & Wright, 4th edition, Section 13.4,
>>Theorem 227.
>[deleted]

>I do not, for a second, accept the argument that Fermat's theorem is
>something as commonplace as the wind, as some have made it out to be.

I did not say that it was as "commonplace as the wind".  I said it was
easy to look up.  There's a difference.  I stand by the claim that I
actually made: it is easy to look up.

There's a strawman argument being proposed here; it's not the point.
I agree with you.  Evidence on the net is clear: many people are not
familiar with FLT.  "That's reality.  Accept it"  I may want to change
reality, but it would be ridiculous for me not to accept current
reality.  It's also unreasonable for you to assume that I don't.  We
clearly agree on this, but it is not relevant to the main point.

>It's an even bet that many netters here haven't heard of it. 

I have no bone to pick with netters who haven't heard of it.  I was
surprised (and a little disappointed, but they probably know tons of
things I didn't pick up in >my< education) that so few had, but I
don't argue with this at all.  I was referring to people who post
about it - by definition they've heard of it.

>								  What I
>suspect is that it has recently been introduced into the undergraduate
>math curriculum of some Universities, which is why so many prunes around
>here are so keen to show off their newly acquired knowledge.

(-: (in case a closing smiley isn't sufficient, since I'm treading on
dangerous ground)

Whoa!  I know that hole!  I won't step in it!  as in:

"You're jealous that you couldn't get into Mensa" 
  "I >could< have gotten into Mensa, I had ..." 
"Why do you feel the need to show off your dubious intellectual `credentials'?"
  ...
"When did you stop lying about when you stopped beating your wife?"
  ...
:-)

Or, we could imagine a complete diversion at this point, if I were to
point out that "prunes" is usually (but not always) used to refer to
elderly curmudgeons, which conflicts with your characterization of
recent introduction into the undergraduate curriculum.  Anyway... :-)

[further evidence that FLT isn't as commonplace as the wind accepted,
and deleted]

>Another report I stand by is when I spoke about some
>mathematicians reasoning about why Fermat's theorem was, (at that time)
>unsolvable. 

I have no argument about this (although perhaps you mean
"undecidable"?); I will point out that (a) I think (but am not
certain) that very few serious mathematicians are attempting to show
it is undecidable, and few believe it is (I base this on the fact that
no references to undecidability of FLT appear in survey articles that
I know about), and (b) as you are probably aware, undecidability of
either case of FLT does not imply the undecidability of FLT for a
fixed exponent.  I can certainly believe that there >are<
mathematicians who believe it is undecidable, although there is
circumstancial evidence that is decidable.

>	I *can* dig this out, if necessary, but really don't have the
>time to..(And please, I don't want any dweebs asking me to produce facts and
>figures. I *know* what I read, and don't really care what you think.)

A note on the positive side: I'm not arguing with your forceful
statement here, since you explain the reason for your emphatic remark
in the next paragraph.  On the other hand, there's a certain
escalation of tone, don't you think?  Of course you care what we
think, else you wouldn't have posted.  Luckily this isn't an emotional
topic, because that's a spark that could ignite a .... well, you know.

>The reason for this outburst? that it's nauseous how some people fail to 
>take a posting in the spirit for which it was intended. My objective in making 
>the posting was to stimulate a discussion on other similar 'unsolvable' 
>math puzzles. I even prefaced the article with the words:
>"To the best of my knowledge.."

I'm sorry you viewed my post as an attack.  I similarly prefaced my
post with a statement describing my intent (not to bury you, but to
inform the listeners following the thread).  Since you seem to have
made the same mistake you accuse others of (missing a preface, and
mistaking the "spirit of the post"), I'd think you'd use a little
more charity towards misinterpreters.

In any case, I simply wanted to correct a "potential misconception"
[my words] so that thousands of net readers (who had not heard of FLT)
wouldn't think that FLT had been unsolved for n=3.

>WHAT do you think that was *for* ?? Aesthetic purposes??? I *wanted* to get
>some feedback from this group! 

And you did, which as far as I can tell were mainly references to
texts or to FAQ lists on sci.math.

>			I *did* have some shadowy suspicion that F.T.
>may*had* been solved and I had been unaware of it. Under the circumstances,
>my article was at the worst, outdated. Results like Fermat's have remained
>unsolved *FOR DECADES* (or is it centuries?) and only a hopeless nerd would
>resort to checking the library out every little while to see if it'd been
>solved as yet.. especially if you're not into math!! 

To keep it clear: neither the first nor second case of FLT have been
solved in general.  The n=3 case has been solved since before the
American Revolution.  That's all we were talking about.  

Also, if the general case had been solved, you probably wouldn't have
needed to check the library, since even unsuccessful (but "close")
attempts have made it to newspapers around the country.  First page,
even.  You'd hear about it.

>							A far better source
>would be a friend, or as the case may be, a newsgroup.  Replies like those
>from Derek Bell, or Roger Lustig for instance were very much in order, and
>in fact, most welcome. They correct me, I accept the error, and
>that's that.

Uh, my first post was simply a pointer to Hardy & Wright's number
theory text, section 13.4.  My post that you are complaining about was
posted only after subsequent posts by you and others.  I became
frustrated that the references clearly hadn't been checked up or
looked at.  As I said above, I had no quarrel with your original post.
I had no quarrel with the later posts, either, just frustration that
>given references< people continued to post assertions or speculations
that they could have verified.

[A digression, if no one minds, which has nothing to do with any of
the larger issues in this message:]

Also, a friend is a fine source, but the newsgroup is not
>necessarily< so.  It depends on your view of society's role in burden
sharing.  If you believe in the concept of insurance for distributing
the cost over society as a whole, (which previous posts about
education for the gifted tend to belie), then this is no problem.

However, if you believe that an individual shouldn't share the burden
of other people's troubles (welfare, national health insurance, etc.)
then, when the readership of a group gets large, posting a broadcast
for information that is available "cheaply" implies that the sum total
of effort expended by the readers of this newsgroup is less valuable
than the corresponding time spent by you.  (i.e. if 50 people read
this and respond in 1/20th the time it would take you, there's still a
greater cost to society).  So in some sense, in this case you would
not be respecting the value of other peoples time.

It happens I believe in insurance as cost-sharing, so I don't mind
responding to (and am not offended by) "broadcast" requests.  On the
other hand, just as I believe in trying to minimize the cost to
society of health insurance, by using it mainly for catastrophic care
and paying for what I can afford, I'd like to think that people aren't
"corrupted" by the easy availability of net resouces/health insurance.

I'm just pointing out that (a) not everyone believes that you should
use the net as a resource (except as a last resort), and that (b) it
might be logically inconsistent to both "ask the net" and to believe
that things like welfare are immoral.  But that's a different topic,
and not entirely serious...

Actually, belief in special-ed for the gifted and sending "broadcast"
requests to the whole mailing list aren't necessarily logically
incompatible beliefs: You can argue that special ed for the gifted
clearly costs society more (whenever there are extra categories of
students, there's an incremental cost because you can no longer treat
them as interchangeable, identical commodities.)  Perhaps you can
argue that spending extra time responding to broadcast requests with
the "extra" knowledge you might have gleaned by virtue of a gifted ed
program is a return on the investment in the cost of gifted ed.... But
I have digressed >>way<< too far....

>But to dub the posting as "misinformation" and an "easily verifiable
>assertion".. 

I don't believe that I used the word "misinformation", but "potential
misconception".  That's not a nitpick.  The former would imply some
(deliberate?) action on your part, the latter was in the minds of the
many readers of this thread.  Changing my word(s) to beligerent one(s)
and responding to them is not a reasonable way to argue.

The phrase "easily verifiable [mistaken] assertion" was used (if you
will recall the precise argument I was making - please reread my post,
since you seem to have completely missed my point) >in contrast to<
"less easily verifiable" assertions.  My point was, to repeat, that if
something as easily verifiable as FLT for n=3 could be posted without
verification, then we should conclude that most of the information
(which is far less verifiable) that comes over the net is, sadly, hard
to believe.  This is frustrating.  

>	WHAT'S GOING ON? Are you going to get NUKED if I say that a vague
>result hadn't been proved, when in  fact it has??

I hate to get pedantic, but how is FLT for n=3 >vague< in any way?  

I didn't get upset, or respond as if I was going to get NUKED, I just
tried to correct the mistake.

The reasons to respond to this were two:

First, to correct the mistake, in and of itself.

Second, to point out that the trend reduces the value of the net >as a
whole<.  It devalues the information you receive.  The net >is< a
resource, but when a list is large it is a resource of last-resort.
Hence FAQ lists.

>					 Is this subject of such
>*critical importance* anyway? In fact, I think that this result, being true,
>will now become a lot less interesting to most mathematicians & enthusiasts .
>And if you expect postings to be Gospel - Truth, then it's YOU who are
>the fool. ROM is NOT some kind of SPEAKER's FORUM where you're invited to
>hold forth on topics of technical expertise!! It's a forum for *CONVERSATION*,
>a two - way street, where besides speaking, you also listen and (hopefully)
>learn!

My complaint about the style here is it seems to me that you are
assuming answers to your questions (some rhetorical), and are being
angered or annoyed by the responses.  Which are in your head!  You've
allowed this to escalate by anticipating pessimal responses to your
sallies.  Why not assume optimal responses?  Imagine the most
excusable response I could give -- perhaps that's the interpretation
you should place on my post.  

Lest you take that too far -- I'm only talking about for purposes of
emotional level.  There >are< often fundamental disagreements about
>content<.  Not all conflicts can be resolved.  However, why make it
worse by assuming the worst?  Keep it calm, and you can get your point
across more clearly >and hear what the other person is saying<.

If the network equivalent of a rape is happening, then intervention
rather than politeness is in order.  But frankly, I haven't seen many
cases that justified net.unprovoked.anger.

>Get a LIFE, people! Find some better way to distinguish yourself than gloating
>about other people's errors! (if you can, that is.) No wonder so many people
>think of mensans as a bunch of pompous stuffed - shirts. *YOU'RE* the
>cause!!

Well, actually, I'm a pompous stuffed-shirt NON-Mensan who thinks that
you should count to 10 before escalating from "Get a LIFE" to "if you
can,..".  "pompous stuffed-shirt" is reasonable, because, after all, I
was correcting a post.  I'll accept "pompous" - although I am sad that
I came across that way (and regretting that I >know< I'm coming across
that way in this post, too).  I'm just trying to increase the signal
to noise ratio.

>Sheesh!!

>(Sorry Michael, I didn't intend for you to take all the flak.)

It's OK.  As long as you don't mind my using your post as an example
of "How Not To Avoid An Argument".