Pertti Lounesto's challenge: Invalidate my counterexamples
Pertti Lounesto
Here is my Christmas present for those who face a lonely Christmas,
without closeness of a family, and nothing significant to do:
Invalidate the counterexamples presented at my www-page with URL:
"http://www.hit.fi/~lounesto/counterexamples.htm".
In this www-page I give 30-40 counterexamples to proven theorems,
published in recent mathematical papers, whose authors are still
alive, so that they can participate in a debate about possible
correctness of my counterexamples to their purpoted "theorems".
The www-page was published half a year ago, and during this period
all my counterexamples have stood up against public scrutiny and
have not yet been invalidated.
Scientists generally accept that physical theories are falsifiable
whereas mathematical theorems hold for good. I have challenged this
traditional view of mathematics in my www-page on counterexamples.
In an ideal world, there are no counterexamples to math theorems.
However, we live in a real world, where theorems are written by
people, theorems are scrutinized by peers of the authors, theorems
are approved by reviewers, and are hold as true, maybe for an extended
periods, by the scientific community. If then a counterexample is
presented, we know, afterwards that the "theorem" did not hold. But
that is afterwisdom. How do we know of the present "theorems" that
they do not hold, especially if they are generally regarded as true?
An idealism is necessary: we need the concept of a theorem, a valid
statment which holds forever. I am taking a slightly more realistic
view: theorems remain theorems till the very moment that they are
falsified by counterexamples and rendered to purpoted "theorems".
In my www-page "http://www.hit.fi/~lounesto/counterexamples.htm"
I have falsified 30 published theorems of living mathematicians,
who can participate in a public debate about possible validity of
my counterexamples. In other words, I have rendered theorems to
"theorems", false statements with incorrect proofs. And here is
my challenge for serious members of the scientific community, and
a pastime for Christmas: try to invalidate my counterexamples.
--
Pertti Lounesto http://www.hit.fi/~lounesto
Ron Bloom
Pertti Lounesto (loun...@torstai.hit.fi) wrote:
: Here is my Christmas present for those who face a lonely Christmas,
: without closeness of a family, and nothing significant to do:
: Invalidate the counterexamples presented at my www-page with URL:
: "http://www.hit.fi/~lounesto/counterexamples.htm".
: In this www-page I give 30-40 counterexamples to proven theorems,
: published in recent mathematical papers, whose authors are still
: alive, so that they can participate in a debate about possible
: correctness of my counterexamples to their purpoted "theorems".
: The www-page was published half a year ago, and during this period
: all my counterexamples have stood up against public scrutiny and
: have not yet been invalidated.
I am curious. Have you published any of these results in
peer-reviewed literature? Most of your counterexamples are
way outside my field of competence, but I would be interested
to know, nevertheless, if you have been able, working backwards
from a counterexample, identify the logical error in the
proof(s) of the theorem which a particular counterexample
invalidates.
Pertti Lounesto
rbl...@netcom.com (Ron Bloom) writes:
> Pertti Lounesto (loun...@torstai.hit.fi) wrote:
>
> : Invalidate the counterexamples presented at my www-page with URL:
> : "http://www.hit.fi/~lounesto/counterexamples.htm".
>
> : In this www-page I give 30-40 counterexamples to proven theorems,
> : published in recent mathematical papers, whose authors are still
> : alive, so that they can participate in a debate about possible
> : correctness of my counterexamples to their purpoted "theorems".
> : The www-page was published half a year ago, and during this period
> : all my counterexamples have stood up against public scrutiny and
> : have not yet been invalidated.
>
>
> I am curious. Have you published any of these results in
> peer-reviewed literature?
No. The results have been published in a book, where I was the editor,
in a journal, where I am a member of the editorial board, and in two
conference proceedings. They have not appeared in a peer-reviewed
journal. Most probably peer-reviewed journals would have sent my
manuscript to be reviewed by somebody listed as a mistake-maker;
this would have easily resulted in fruitless debate of suitability
of my manusript for publication. The peers, so circumvented, can
defend their "theorems" now that I have published my list of
counterexamples.
> I would be interested to know if you have been able, working backwards
> from a counterexample, identify the logical error in the proof(s)
> of the theorem which a particular counterexample invalidates.
In some cases yes, but not always. Most often the case is that the
author has not considered some special case (e.g. a product is 0),
or is just guessing on the basis of what happens in low dimensions.
Ron Bloom
Pertti Lounesto (loun...@torstai.hit.fi) wrote:
: rbl...@netcom.com (Ron Bloom) writes:
: > Pertti Lounesto (loun...@torstai.hit.fi) wrote:
: >
: > : Invalidate the counterexamples presented at my www-page with URL:
: > : "http://www.hit.fi/~lounesto/counterexamples.htm".
: >
: > : In this www-page I give 30-40 counterexamples to proven theorems,
: > : published in recent mathematical papers, whose authors are still
: > : alive, so that they can participate in a debate about possible
: > : correctness of my counterexamples to their purpoted "theorems".
: > : The www-page was published half a year ago, and during this period
: > : all my counterexamples have stood up against public scrutiny and
: > : have not yet been invalidated.
: >
: >
: > I am curious. Have you published any of these results in
: > peer-reviewed literature?
: No. The results have been published in a book, where I was the editor,
: in a journal, where I am a member of the editorial board, and in two
: conference proceedings. They have not appeared in a peer-reviewed
: journal. Most probably peer-reviewed journals would have sent my
: manuscript to be reviewed by somebody listed as a mistake-maker;
: this would have easily resulted in fruitless debate of suitability
: of my manusript for publication. The peers, so circumvented, can
: defend their "theorems" now that I have published my list of
: counterexamples.
Have any of these mistakes been pointed out at open colloquia?
I remember in a graduate course on integration, I struggled and
struggled with some particular proof of the professor's. Finally,
it occurred to me: his proof was incorrect -- there was no way
in hell such and such an inequality was right. He wished some
inequality to go one way (at a crucial step) but it just
couldn't be forced to do that (except in error). I took the
page to his office and said: such and such inequality just
can't be. He said, "WHAT!?" .... "Let me see that...."
and then, ".... well I'll look at that."
The following Monday afternoon, he announced to the class,
"Mr. Bloom has pointed out that the proof of (___) I gave
on Friday was incorrect." He then gave a new proof, along
completely different lines. He later told me, I was the
only one who'd noticed the first proof was wrong.
My point: surely these counterexamples would be of
interest to the parties in question. Can't these matters
be argued in open colloquia and/or private correspondance?
ull...@math.okstate.edu
In article <rbloomEL...@netcom.com>,
rbl...@netcom.com (Ron Bloom) wrote:
>
[...]
>
> Have any of these mistakes been pointed out at open colloquia?
>
> I remember in a graduate course on integration, I struggled and
> struggled with some particular proof of the professor's. Finally,
> it occurred to me: his proof was incorrect -- there was no way
> in hell such and such an inequality was right. He wished some
> inequality to go one way (at a crucial step) but it just
> couldn't be forced to do that (except in error). I took the
> page to his office and said: such and such inequality just
> can't be. He said, "WHAT!?" .... "Let me see that...."
> and then, ".... well I'll look at that."
>
> The following Monday afternoon, he announced to the class,
> "Mr. Bloom has pointed out that the proof of (___) I gave
> on Friday was incorrect." He then gave a new proof, along
> completely different lines. He later told me, I was the
> only one who'd noticed the first proof was wrong.
>
> My point: surely these counterexamples would be of
> interest to the parties in question. Can't these matters
> be argued in open colloquia and/or private correspondance?
Of course not. Then it would turn out that half
of the errors were just quibbles about definitions - that
would make the whole thing look silly.
David C. Ullrich
-------------------==== Posted via Deja News ====-----------------------
http://www.dejanews.com/ Search, Read, Post to Usenet
Brian Hutchings
In a previous article, loun...@torstai.hit.fi (Pertti Lounesto) says:
have you done this in *any* case, *yet*, or
are you just a cyborgian dood?... it'd certainly make it harder
for the mystaquen entity to re-program, ha-ha.
>In some cases yes, but not always. Most often the case is that the
>author has not considered some special case (e.g. a product is 0),
>or is just guessing on the basis of what happens in low dimensions.
--
(Brian Hutchings, Living Space Programs, Santa Monica College)
Hemp for Haemorrhoids; Bogart that joint, my friend -- I beg you!
(ftp://soros.org/~emperor_herer/HighTimes/stonermanifestoes/)
KRamsay
Ron Bloom:
| I would be interested to know if you have been able, working backwards
|from a counterexample, identify the logical error in the proof(s) of the
|theorem which a particular counterexample invalidates.
In article <7lafdw4...@torstai.hit.fi>,
Pertti Lounesto <loun...@torstai.hit.fi> writes:
|In some cases yes, but not always. Most often the case is that the
|author has not considered some special case (e.g. a product is 0),
|or is just guessing on the basis of what happens in low dimensions.
I think it would help if you distinguished between serious mistakes
and less consequential mistakes.
You call these statements, to which you have found counterexamples,
"proven theorems". Most people I know call some statements expressed
in mathematical papers "theorems" and others merely "propositions",
"lemmas", "corollaries" or remarks, depending in part upon how major
the result is supposed to be.
I checked a few of the counterexamples. For example, I looked at Knus,
_Quadratic and Hermitian forms over Rings_. He defines Clifford
algebras over rings. On page 228, he writes "in general mu(x) lies
in C_0 not in R". Here R is the base ring, C is a Clifford algebra
over R, and C_0 is the "even" part. The function mu(x) is defined as
sigma(x)x where sigma is the anti-homomorphism of the Clifford algebra
which sends each vector v in a certain vector space (which generates
the Clifford algebra) to -v.
The remark on page 228 is a mistake. It is not a "theorem". It doesn't
have a "proof".
There is an obvious line of reasoning which Knus probably had in mind
to show mu(x) is in C_0: if we apply sigma to mu(x)=sigma(x)x, we get
sigma(x)sigma(sigma(x)) because sigma is an anti-homomorphism, and
since sigma is of order 2, we get that this equals mu(x). It is easy
to suppose that sigma is even on the even elements and odd on the odd
ones, since it sends vectors v to -v. But this forgets that reversing
the order of the multiplication involves another sign change: for
instance, sigma(v1v2)=(-v2)(-v1)=v2v1=-v1v2. So while the terms
appearing in mu(x) are special in a certain way, it's not the same as
being even. This is the kind of mistake Knus probably made.
In the first few examples I looked at, there is no easy way to tell
whether the mistakes are significant mistakes. Does it lead to further
errors later in the discussion? Would it require anything more than
removing the subscript 0 from C_0 to fix the mistake? In Knus, I
read further down the page. He has a short proof which appears to
assume that the values of mu(x) are in C_0. What about that claim, is
it mistaken? Or is it easy to prove a slightly different way?
As far as I can see, you haven't given any information which would
help me figure out how serious a mistake it is. It is possible that
it causes him to make errors in deeper theorems elsewhere in the book.
As far as I can see, however, you haven't found any such complications.
So it is also possible that it is a minor problem, easily fixed. If
you care about being useful to the mathematical community, you will
make such a distinction at some point.
In another article:
|There are those who steal my idea, and implement the correction,
|whithout giving me the priority of presenting the counterexample.
It is nice to thank people for contributions to one's papers. Not all
forms of help actually require thanks, however. I have found typos in
people's papers; one doesn't expect to be thanked for finding a typo.
It's not "stealing" unless it is a signficantly more serious mistake
which you found, or the counterexample is interesting in some other
way.
I. Kaplansky once remarked that in published papers, there is a mistake
about every 10 pages, a mistake that a competent graduate student
could fix (more than just a typo). He also suggested that about every
100 pages there is a somewhat more serious mistake, one which requires
more serious work to fix. Other people have disagreed with his estimate
of how many mistakes there are, but we do know that there are mistakes.
Perhaps all it takes to find 30 mistakes is to read ~300 pages of
material on Clifford algebras carefully. I would like to think that
you would be interested in knowing whether any of them were major
errors, but I'm not so sure.
Proofreading is useful. There are limits to how important it is,
however. It is seldom worthwhile to take the time to write a perfect
book. It's not clear that we would be able to write perfect books.
Keith Ramsay In no way, shape or form did Kevin represent a viable
kra...@aol.com alternative to mental illness. --VALIS, Phillip Dick
Bill Dubuque
Pertti Lounesto <loun...@torstai.hit.fi> wrote to sci.math:
|
| Invalidate the counterexamples presented at my www-page with URL:
| "http://www.hit.fi/~lounesto/counterexamples.htm".
|
| In this www-page I give 30-40 counterexamples to proven theorems,
Ron Bloom <rbl...@netcom.com> replied:
: I would be interested to know if you have been able, working backwards
: from a counterexample, identify the logical error in the proof(s)
: of the theorem which a particular counterexample invalidates.
Pertti replied:
| In some cases yes, but not always. Most often the case is that the
| author has not considered some special case (e.g. a product is 0),
| or is just guessing on the basis of what happens in low dimensions.
There are plenty of analogous "extremal errors" in number theory
and algebra textbooks, especially having to do with whether 1 is
considered prime or not (and related instances such as whether
the entire ring is allowed as a prime ideal, or the one element
ring is allowed as an integral domain, etc). Even the well-known
classic time-tested textbook on number theory by Hardy and Wright
commits such errors: e.g. though they employ the modern definition
that 1 is not prime (p. 2), they later state the Lucas primality test
(the simple converse of Fermat's little Theorem FlT) in a form that
implies that one is prime (p. 72):
THEOREM 90. If a^(m-1) = 1 (mod m) and a^x != 1 (mod m)
for any divisor x of m-1 less than m-1, then m is prime.
If you flip through the pages of almost any number theory textbook
and check the case p=1 (or analogous extremal cases) you will almost
surely find errors like "Hardy's Theorem 90" (apologies to Hilbert!).
Analogous problems also occur for the "oddest" prime p=2, a situation
sometimes referred to as the "terrible 2s", or "the trouble with 2".
Perhaps in the old days p=1 was more properly the "oddest" prime!
This sloppy practice of stating "generic" results will probably
disappear in the future when automatic proof checkers are
routinely used to check math texts (especially considering that
the extremal cases usually have much simpler proofs than the
generic case). Landau's "Grundlagen" has already been checked in
the Automath system [1],[2],[3],[4]. It would be interesting to
do the same for Hardy and Wright.
Note also that threads on the topic of the primality of 1 often
appear both here on sci.math and also in the MAA math-history-list,
archived at http://forum.swarthmore.edu/epigone/math-history-list/
It would be interesting to consider the historical evolution of
this convention in all its equivalent forms, including the
ideal theoretic forms: 1 is disallowed as a prime for many more
reasons than unique factorization and it would be interesting to
study the historical interplay between these various motivations.
Based upon replies in earlier threads it would appear that currently
no such historical study exists. Perhaps fragments of such a
study are currently intermingled in other works. Anyone?
-Bill Dubuque
[1] van Benthem Jutting, L. S.
Checking Landau's "Grundlagen" in the Automath system [MR 58 #32124ab].
in [2]. CMP 1 429 425 03B35
[2] Selected papers on Automath. Edited by R. P. Nederpelt, J. H. Geuvers
and R. C. de Vrijer with the assistance of L. S. van Benthem Jutting and
D. T. van Daalen.
Studies in Logic and the Foundations of Mathematics, 133.
North-Holland Publishing Co., Amsterdam, 1994. xx+1024 pp.
ISBN: 0-444-89822-0 CMP 1 429 395 03B35 (03-06 03B40)
[3] de Bruijn, N. G. A survey of the project AUTOMATH.
To H. B. Curry: essays on combinatory logic, lambda calculus and formalism,
pp. 579--606, Academic Press, London-New York, 1980.
MR 81m:03017 (Reviewer: Frank Malloy Brown) 03B35 (03B40 68G15)
[4] van Benthem Jutting, L. S.
Checking Landau's Grundlagen in the AUTOMATH system.
Doctoral dissertation, Technische Hogeschool Eindhoven, Eindhoven, 1977.
With a Dutch summary. Technische Hogeschool Eindhoven, Eindhoven, 1977.
v+121 pp. MR 58 #32124a (Reviewer: I. Kramosil) 68A40 (02-04 68A30)
Bill Dubuque
This is the crux of the matter. If Pertti's counterexamples occur
only in totally degenerate cases that would never be applied in
subsequent (non-degenerate) deductions then the errors have little
if any impact on any dependent results. For example, as I mentioned
in another post, there are often errors in number theory around the
"prime" p=1 (or the one element domain), but these are harmless because
they are rarely (if ever) used in any subsequent deductions (beware
the situation where the "trivial case" is the foundation of an
induction -- failure to do such results in well-known unfounded
inductions such as the "proof" that all horses have the same color).
Usually, the theory of trivial structures is trivial and is ignored.
However, this need not be the case if the "trivial structure"
is only one piece of a composite structure, e.g. if the trivial
structure is an empty structure that is a component of a many-sorted
structure. For example, see the URL below for an old thread I started
on "empty carriers" (carrier = underlying set = universe = sort)
http://x3.dejanews.com/dnquery.xp?QRY=dubuque%2Bempty%2Bcarrier&svcclass=dnold
Note: to see the entire thread, visit a match to the above query
then follow the "View Thread" link (the thread is large).
The usual equational logic has optimizations based on the fact that
one is working over a single-sorted structure; in the many-sorted
case these rules of deduction are no longer sound and require
modification (e.g. All x p(x) ==> Exist x p(x) fails).
Although the empty structure is usually of no interest in the case
of single sorted structures (so algebraic structures such as groups,
rings, etc are usually assumed nonempty), this is not the case for
many-sorted structures: if one has a structure built-up from more than
one set, then it is not necessarily trivial if some but not all of the
sets are empty. E.g. a group with operators (or R-module) with an empty
set of operators is just a group, which is most certainly not a structure
one wants to dismiss as trivial. The many-sorted case occurs quite
frequently in computer science, where such structures arise in the
algebraic approach to denotational semantics and indeed much of the
recent work in many-sorted logics has its motivation rooted there.
Moral: those who don't ignore trivial cases are doomed to become
computer scientists! :-)
-Bill Dubuque
P.S. Test: did you consider trivial cases of the the above moral?
Pertti Lounesto
On Dec 19, 1997 Pertti Lounesto (loun...@torstai.hit.fi) challenged:
: Invalidate the counterexamples presented at my www-page with URL:
: "http://www.hit.fi/~lounesto/counterexamples.htm".
:
: In this www-page I give 30-40 counterexamples to proven theorems,
: published in recent mathematical papers, whose authors are still
: alive, so that they can participate in a debate about possible
: correctness of my counterexamples to their purpoted "theorems".
: The www-page was published half a year ago, and during this period
: all my counterexamples have stood up against public scrutiny and
: have not yet been invalidated.
Today the Christmas holidays are over, but no-one has invalidated any
of the counterexanples on my www-page. Here is a summary of postings:
On Dec 20, 1997 rbl...@netcom.com (Ron Bloom) wrote:
> I am curious. Have you published any of these results in
> peer-reviewed literature?
On Dec 20, 1997 Pertti Lounesto responded:
: No. The results have been published in a book, where I was the editor,
: in a journal, where I am a member of the editorial board, and in two
: conference proceedings. They have not appeared in a peer-reviewed
: journal. Most probably peer-reviewed journals would have sent my
: manuscript to be reviewed by somebody listed as a mistake-maker;
: this would have easily resulted in fruitless debate of suitability
: of my manusript for publication. The peers, so circumvented, can
: defend their "theorems" now that I have published my list of
: counterexamples.
On Dec 22, 1997 Ron Bloom wrote:
> Have any of these mistakes been pointed out at open colloquia?
Yes and no. I have proposed giving talks about mistakes at meetings
of specialists. Part of my proposal were turned down. Part was
accepted, but those who made the particular mistakes did not arrive.
I have also tried to present my counterexamples at the end of some
talks, when questions about the talk were opened for discussion;
the charimen were not enthusiastic. More commonly, these matters
have been discussed privately during major meetings.
On Dec 22, 1997 Ron Bloom wrote:
> My point: surely these counterexamples would be of
> interest to the parties in question. Can't these matters
> be argued in open colloquia and/or private correspondance?
Private correspondence has been sent to all those who made the mistakes.
After a few years of privately informing about mistakes, I found myself
repeating clear explanations to those who did not believe they had made
a mistake. Then I changed my method: I sent out copies of the letters
written by me to members in this special field of mathematics. After
a few years, I found that some mistake-makers had just hardened their
activities: they did not respond to my mathematical arguments, but
instead tried to convince others that my behaviour is unorthodox.
Then I published my counterexamples in two papers. Those who had
argued for years that they did not make any mistakes admitted their
mistakes privately, but argued that their mistakes were not significant.
On Dec 27, 1997 kra...@aol.com (Keith Ramsay) wrote:
> I think it would help if you distinguished between serious mistakes
> and less consequential mistakes.
The less consequential mistakes are there to help reading my www-page,
especially at the beginning of the www-page. Distinguish? Indeed, that
would help some readers, if I would indicate the more serious mistakes.
However, I decided not to release this information for the following
reason: In many cases private debates had been going on for years,
before I published my papers/www-page. Some members of my scientific
community might think that I am in bad relations with those whom I
indicate as makers of serious mistakes. Since I am not aiming for bad
relations with them, I decided to withhold this information.
Indeed, not all the mistakes to which I give counterexamples are
formulated as theorems. In particular, Knus' mistake was not within
a theorem. But it was a mistake, as you point out. Knus was one
of the rare cases, who immediately admitted his mistake, and also
gave essentially the same reason for making his mistake as you give
above. So, I must congratulate Keith for his skills in evaluating
cognition of Knus.
The proof on page 228 is correct, alhough the last sentence would be
more unambiguous if formulated as "Since sigma(u)u is in C_0 for any
u in Gamma(q), sigma(u)u is an element in Center(C)\cup C_0 if (M,q)
is semiregular of odd rank".
On Dec 27, 1997 Keith Ramsay wrote:
> In another article Pertti Lounesto wrote:
> :There are those who steal my idea, and implement the correction,
> :whithout giving me the priority of presenting the counterexample.
>
> It is nice to thank people for contributions to one's papers. Not all
> forms of help actually require thanks, however. I have found typos in
> people's papers; one doesn't expect to be thanked for finding a typo.
> It's not "stealing" unless it is a signficantly more serious mistake
> which you found, or the counterexample is interesting in some other
> way.
>
> I. Kaplansky once remarked that in published papers, there is a mistake
> about every 10 pages, a mistake that a competent graduate student
> could fix (more than just a typo). He also suggested that about every
> 100 pages there is a somewhat more serious mistake, one which requires
> more serious work to fix. Other people have disagreed with his estimate
> of how many mistakes there are, but we do know that there are mistakes.
> Perhaps all it takes to find 30 mistakes is to read ~300 pages of
> material on Clifford algebras carefully. I would like to think that
> you would be interested in knowing whether any of them were major
> errors, but I'm not so sure.
>
> Proofreading is useful. There are limits to how important it is,
> however. It is seldom worthwhile to take the time to write a perfect
> book. It's not clear that we would be able to write perfect books.
I will refer to my article in R. Ablamowicz et al. (eds.): "Clifford
Algebras with Numeric and Symbolic Computations", Birkhauser, 1996
(rather than my www-page, which is only an abbreviation of the article).
The most significant counterexample (in the sense that there was a lot
of work to construct it, not in the sense that there was a severe
defence) is the one on pages 8-9: I knew that there was something
fishy in the argument, but found the counterexample only after several
months of concentrated work.
Discussion on pages 14-18 is also important: all the theory is mis-
guided; and not only in the particular book referred, but in all
books dealing with the matter.
The mistakes on pages 20-22 are most frequently repeated. Here I also
met the most severe defence of an error (finally admitted).
The mistakes on pages 22-26 were debated for the longest period
(almost 10 year). Both parties were wrong.
On Dec 29, 1997 Bill Dubuque <w...@nestle.ai.mit.edu> wrote:
> kra...@aol.com (KRamsay) writes:
> | I think it would help if you distinguished between serious
> | mistakes and less consequential mistakes. ...
>
> This is the crux of the matter. If Pertti's counterexamples occur
> only in totally degenerate cases that would never be applied in
> subsequent (non-degenerate) deductions then the errors have little
> if any impact on any dependent results.
This does not describe the actual situation in science making.
Only in one case does my observation invalidate a whole theory, as
presented in several books (the observations on pages 14-18).
In general, the counterexamples are to theorems recently presented,
still under public scrutiny for possible acceptance as true. So,
the "theorems" are in turmoil to be debated, with no important
deductions derived as yet. Mathematicians stop drawing conclusions
from "theorems" questioned by others. Fortunately, they get involved
in discussion about validity of their "theorems", before using them,
although they sometimes are too defensive.
Pertti Lounesto
On Dec 19, 1997 Pertti Lounesto (loun...@torstai.hit.fi) challenged:
: Invalidate the counterexamples presented at my www-page with URL:
: "http://www.hit.fi/~lounesto/counterexamples.htm".
:
: In this www-page I give 30-40 counterexamples to proven theorems,
: published in recent mathematical papers, whose authors are still
: alive, so that they can participate in a debate about possible
: correctness of my counterexamples to their purpoted "theorems".
: The www-page was published half a year ago, and during this period
: all my counterexamples have stood up against public scrutiny and
: have not yet been invalidated.
On Jan 6, 1998 Lounesto gave a summary of postings in this thread:
no one presented arguments to invalidate any of my counterexamples.
On Jan 16, 1998 d...@cwi.nl (Dik T. Winter) writes in another thread:
> Sigh, for some reason I am not surprised that someone does not
> acknowledge an error when you point to it. You have the knack
> of antagonizing people by using derogatory words when another
> choice of terminology would be better.
Winter brought this argument into another thread, out of context.
His intention was to defame me with extra-context arguments. Since
Winter's argument belongs in this thread, I hereby challenge Winter
to justify his argument of "antagonizing people by using derogatory
words" by pointing out even one such case in my www-page. If no
such point can be presented, I take it for granted that Winter is
not able to support his claim that "derogatory words" explain why
"someone did not acknowledge an error when I pointed to it".
--
Pertti Lounesto http://www.hit.fi/~lounesto/counterexamples.htm
Jan Stevens
In article <7lafcv31...@torstai.hit.fi>,
Pertti Lounesto <loun...@torstai.hit.fi> writes:
> On Jan 16, 1998 d...@cwi.nl (Dik T. Winter) writes in another thread:
>> Sigh, for some reason I am not surprised that someone does not
>> acknowledge an error when you point to it. You have the knack
>> of antagonizing people by using derogatory words when another
>> choice of terminology would be better.
>
> Winter brought this argument into another thread, out of context.
> His intention was to defame me with extra-context arguments. Since
> Winter's argument belongs in this thread, I hereby challenge Winter
> to justify his argument of "antagonizing people by using derogatory
> words" by pointing out even one such case in my www-page. If no
> such point can be presented, I take it for granted that Winter is
> not able to support his claim that "derogatory words" explain why
> "someone did not acknowledge an error when I pointed to it".
>
Pertti should read what he writes, and also read and try to understand
what Dik writes. I can see no intention whatsoever on Dik's side to
defame someone, but only someone being paranoid.
For some reason I am not surprised if Dik does not take up the challenge.
groetjes,
Jan
--
email: ste...@math.chalmers.se
Matematiska Institutionen
Chalmers Tekniska H"ogskola
SE 412 96 G"oteborg
Sweden
Pertti Lounesto
ste...@math.chalmers.se (Jan Stevens) writes:
: Pertti Lounesto <loun...@torstai.hit.fi> writes:
:
: > On Jan 16, 1998 d...@cwi.nl (Dik T. Winter) writes in another thread:
: >> Sigh, for some reason I am not surprised that someone does not
: >> acknowledge an error when you point to it. You have the knack
: >> of antagonizing people by using derogatory words when another
: >> choice of terminology would be better.
: >
: > Winter brought this argument into another thread, out of context.
: > His intention was to defame me with extra-context arguments. Since
: > Winter's argument belongs in this thread, I hereby challenge Winter
: > to justify his argument of "antagonizing people by using derogatory
: > words" by pointing out even one such case in my www-page. If no
: > such point can be presented, I take it for granted that Winter is
: > not able to support his claim that "derogatory words" explain why
: > "someone did not acknowledge an error when I pointed to it".
:
: Pertti should read what he writes, and also read and try to understand
: what Dik writes. I can see no intention whatsoever on Dik's side to
: defame someone, but only someone being paranoid. For some reason I
: am not surprised if Dik does not take up the challenge.
Jan Stevens did not invalidate any of the counterexamples presented
in my www-page http://www.hit.fi/~lounesto/counterexamples.htm. Jan
Stevens did not indicate any place in my www-page where "derogatory
words" explain why "someone did not acknowledge an error when I
pointed to it".
--
Pertti Lounesto http://www.math.hut.fi/~lounesto
Pertti Lounesto
Winter's posting of Jan 16, referred to "errors", which were not
previously discussed int this thread. The posting belonged to
another thread, dealing with the 30 errors of proven theorems
published in recent mathematical literature, discussed in my
the following response:
On Jan 20 ste...@math.chalmers.se (Jan Stevens) writes:
: On Jan 19 Pertti Lounesto <loun...@torstai.hit.fi> writes:
:
:> On Jan 16, 1998 d...@cwi.nl (Dik T. Winter) writes in another thread:
:>> Sigh, for some reason I am not surprised that someone does not
:>> acknowledge an error when you point to it. You have the knack
:>> of antagonizing people by using derogatory words when another
:>> choice of terminology would be better.
:>
:> Winter brought this argument into another thread, out of context.
:> His intention was to defame me with extra-context arguments. Since
:> Winter's argument belongs in this thread, I hereby challenge Winter
:> to justify his argument of "antagonizing people by using derogatory
:> words" by pointing out even one such case in my www-page. If no
:> such point can be presented, I take it for granted that Winter is
:> not able to support his claim that "derogatory words" explain why
:> "someone did not acknowledge an error when I pointed to it".
:
: Pertti should read what he writes, and also read and try to understand
: what Dik writes. I can see no intention whatsoever on Dik's side to
: defame someone, but only someone being paranoid. For some reason I
: am not surprised if Dik does not take up the challenge.
How does Jan Stevens know the intensions of Dik T. Winter?
Why doesn't Winter announce that his intention was not to defame
Lounesto, if indeed that was not his intention? Does Stevens'
word "paranoid" describe Winter's intentions when he wrote that
"another choice of terminology would be better". Why doesn't
Stevens point out in his follow-up any "derogatory words" (in my
www-page), which explain why "someone did not acknowledge an
error when I pointed to it"?
--
Pertti Lounesto http://www.math.hut.fi/~lounesto/counterexamples.htm
Dik T. Winter
In article <7lafcv31...@torstai.hit.fi> Pertti Lounesto <loun...@torstai.hit.fi> writes:
> On Jan 16, 1998 d...@cwi.nl (Dik T. Winter) writes in another thread:
> > Sigh, for some reason I am not surprised that someone does not
> > acknowledge an error when you point to it. You have the knack
> > of antagonizing people by using derogatory words when another
> > choice of terminology would be better.
>
> Winter brought this argument into another thread, out of context.
> His intention was to defame me with extra-context arguments.
In which way did I try to defame you? Where is the defamation?
> Since
> Winter's argument belongs in this thread, I hereby challenge Winter
> to justify his argument of "antagonizing people by using derogatory
> words" by pointing out even one such case in my www-page.
There are two probabilities. Either you wrote to the authors in person
about their errors, in that case your web page does not show the words
you used in your communication and are irrelevant in this context. Or
you published your page (and your articles) without notifying the authors
that something like that was about to happen. The latter is in itself
already extremely rude.
--
dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
Pertti Lounesto
On Dec 19, 1997 Pertti Lounesto (loun...@torstai.hit.fi) challenged:
: Invalidate the counterexamples presented at my www-page with URL:
: "http://www.hit.fi/~lounesto/counterexamples.htm".
:
: In this www-page I give 30-40 counterexamples to proven theorems,
: published in recent mathematical papers, whose authors are still
: alive, so that they can participate in a debate about possible
: correctness of my counterexamples to their purpoted "theorems".
: The www-page was published half a year ago, and during this period
: all my counterexamples have stood up against public scrutiny and
: have not yet been invalidated.
This week one month has passed without anybody being able to
invalidate any of my counterexamples. Here is an updated summary:
On Dec 20, 1997 rbl...@netcom.com (Ron Bloom) wrote:
> I am curious. Have you published any of these results in
> peer-reviewed literature?
On Dec 20, 1997 Pertti Lounesto responded:
: No. The results have been published in a book, where I was the editor,
: in a journal, where I am a member of the editorial board, and in two
: conference proceedings. They have not appeared in a peer-reviewed
: journal. Most probably peer-reviewed journals would have sent my
: manuscript to be reviewed by somebody listed as a mistake-maker;
: this would have easily resulted in fruitless debate of suitability
: of my manusript for publication. The peers, so circumvented, can
: defend their "theorems" now that I have published my list of
: counterexamples.
I could also reply: Yes. The results have appeared in a peer-reviewed
journal, Advances in Applied Clifford Algebras 6 (1996), 69-104.
The international advisory board of this journal has 9 members,
8 members plus me. Of the 8 members 5 have been listed as mistake-
makers (plus myself of all 9).
On Dec 22, 1997 Ron Bloom wrote:
> Have any of these mistakes been pointed out at open colloquia?
On Jan 6, 1998 Pertti Lounesto responded:
: Yes and no. I have proposed giving talks about mistakes at meetings
: of specialists. Part of my proposal were turned down. Part was
: accepted, but those who made the particular mistakes did not arrive.
: I have also tried to present my counterexamples at the end of some
: talks, when questions about the talk were opened for discussion;
: the charimen were not enthusiastic. More commonly, these matters
: have been discussed privately during major meetings.
On Dec 22, 1997 Ron Bloom wrote:
> My point: surely these counterexamples would be of
> interest to the parties in question. Can't these matters
> be argued in open colloquia and/or private correspondance?
On Jan 6, 1998 Pertti Lounesto responded:
: Private correspondence has been sent to all those who made the mistakes.
: After a few years of privately informing about mistakes, I found myself
: repeating clear explanations to those who did not believe they had made
: a mistake. Then I changed my method: I sent out copies of the letters
: written by me to members in this special field of mathematics. After
: a few years, I found that some mistake-makers had just hardened their
: activities: they did not respond to my mathematical arguments, but
: instead tried to convince others that my behaviour is unorthodox.
: Then I published my counterexamples in two papers. Those who had
: argued for years that they did not make any mistakes admitted their
: mistakes privately, but argued that their mistakes were not significant.
On Dec 27, 1997 kra...@aol.com (Keith Ramsay) wrote:
> I think it would help if you distinguished between serious mistakes
> and less consequential mistakes.
On Jan 6, 1998 Pertti Lounesto responded:
: The less consequential mistakes are there to help reading my www-page,
: especially at the beginning of the www-page. Distinguish? Indeed, that
: would help some readers, if I would indicate the more serious mistakes.
: However, I decided not to release this information for the following
: reason: In many cases private debates had been going on for years,
: before I published my papers/www-page. Some members of my scientific
: community might think that I am in bad relations with those whom I
: indicate as makers of serious mistakes. Since I am not aiming for bad
: relations with them, I decided to withhold this information.
On Dec 27, 1997 Keith Ramsay wrote:
> In another article Pertti Lounesto wrote:
> :There are those who steal my idea, and implement the correction,
> :whithout giving me the priority of presenting the counterexample.
>
> It is nice to thank people for contributions to one's papers. Not all
> forms of help actually require thanks, however. I have found typos in
> people's papers; one doesn't expect to be thanked for finding a typo.
> It's not "stealing" unless it is a signficantly more serious mistake
> which you found, or the counterexample is interesting in some other
> way.
I am not discussing about typos. I discuss about misconceptions,
and justify my findings by explicit mistakes which actually
incarnated in some publications, not just hypothetical errors,
which might occur. To fix manners of speaking, let me fix
my criterion of significance of an error:
Criterion of Lounesto: An error in a mathematical paper is the more
significant, the more time and correspondence the author needs to
understand that he is mistaken, and to rectify his error.
An average time for errors listed in my www-page was:
3 months to convince the author that there was actually a mistake.
1 more month to find out a correct version of the theorem.
On Dec 29, 1997 Bill Dubuque <w...@nestle.ai.mit.edu> wrote:
> kra...@aol.com (KRamsay) writes:
> | I think it would help if you distinguished between serious
> | mistakes and less consequential mistakes. ...
>
> This is the crux of the matter. If Pertti's counterexamples occur
> only in totally degenerate cases that would never be applied in
> subsequent (non-degenerate) deductions then the errors have little
> if any impact on any dependent results.
On Jan 6, 1998 Pertti Lounesto responded:
: This does not describe the actual situation in science making.
: Only in one case does my observation invalidate a whole theory, as
: presented in several books (the observations on pages 14-18).
: In general, the counterexamples are to theorems recently presented,
: still under public scrutiny for possible acceptance as true. So,
: the "theorems" are in turmoil to be debated, with no important
: deductions derived as yet. Mathematicians stop drawing conclusions
: from "theorems" questioned by others. Fortunately, they get involved
: in discussion about validity of their "theorems", before using them,
: although they sometimes are too defensive.
Bill Dubuque gives another criterion for significance of errors in
mathematical publications:
Criterion of Dubuque: The error is more significant if it is more
often applied in subsequent (non-degenerate) deductions, and
the more impact there is on subsequent results.
In anonther related thread, started by Dubuque in Dec 29, 1997, Subject:
"sloppy proofs everywhere: extremal errors; 1 is prime? [was: Pertti L]"
Dubuque discusses "extremal errors" in number theory and algebra
textbooks, especially having to do with whether 1 is considered prime
or not. Dubuque gives several examples, significant according to his
criteria. Dubuque's examples are not significant according to my
criterion, and my findings are not significant according to Dubuque's
criterion. The errors are of different type.
Dubuque's errors occur when definitions are changed. A most significant
occurrence, in the sense of both criteria, happens when two groups of
mathematicians, with different backgrounds, begin to work together.
Although the common body of knowledge does not grow, several individuals
experience cognitive growth when they rectify their misconceptions
(which might later result in growth of the common body of knowledge).
Lounesto's errors occur when the common body of knowledge grows: when
scientists move to new frontiers to be explored, where cognitive
charts are still inaccurate. Errors are corrected in the public
scrutiny of scientific papers.
The rest of this postings deals with fallacies of Dik T. Winter.
In another thread, Dik T. Winter referred to mathematical "errors",
although there was no prior mentioning of any "errors" in that thread.
Winter explained that people do not "acknowledge an error" because I
use "antagonistic" and "derogatory" words. By referring to "errors"
Winter indicated to my www-page falsifying proven theorems published in
recent mathematical literature. Winter's appeals to fallacies, since
0. he attacked on the person and not on the argument (at that thread)
1. there are no "derogatory" words in my www-page
2. all relevant errors have been "ackowledged"
3. the "errors" are actually misconceptions
Here is "relevant" quotation of 1 of 4 Winter's postings of Jan 16:
> Sigh, for some reason I am not surprised that someone does not
> acknowledge an error when you point to it. You have the knack
> of antagonizing people by using derogatory words when another
> choice of terminology would be better.
Winter's behaviour is not interesting as such; but it does reflect,
how people tend to explain new phenomena, which they encounter,
by their earlier limited experiences. The mathematical errors, or
misconceptions, listed in my www-page, have been "acknowledged",
unlike Winter assumed, although often after long disputes, lasting
several months or even years. The reason for a delay needed by a
mathematician to ackowledge his misconception is not "antagonizing"
or "derogatory" words from my part, as Winter incorrectly assumed,
but the simple fact that learning new things takes time, even for
creative mathematicians. Winter's explanation reflects his own
experiences, not my actual case, exhibited in my www-page. To
Winter's dismay: the wordings in my www-page are direct copies of
my private letters to the mathematicians whose mistakes I corrected.
On Jan 22, 1998 Dik T. Winter wrote in this thread:
>: Pertti Lounesto wrote:
>: Since Winter's argument belongs in this thread, I hereby challenge
>: Winter to justify his argument of "antagonizing people by using
>: derogatory words" by pointing out even one such case in my www-page.
>
> There are two probabilities. Either you wrote to the authors in person
> about their errors, in that case your web page does not show the words
> you used in your communication and are irrelevant in this context. Or
> you published your page (and your articles) without notifying the authors
> that something like that was about to happen. The latter is in itself
> already extremely rude.
Gedanken experiment: If Copernicus had been obliged to notify first
Ptolemy, would the Sun still go around the Earth? It is common
practice, in science, to critisize scientific findings in the same
forum as the authors, without any prior notification. This is what
some authors prefer, since they want to avoid all speculations of
conspiracies: private settling of discrepancies. Winter has build
up the following logical construction with three "logical" steps:
1. Lounesto's private letters are "irrelevant in this context".
2. Publishing "without notifying the authors" is "extremely rude".
3. By 1. we cannot take into account Lounesto's private letters
"notifying the authors", so by 2. Lounesto is extremely rude.
Winter's artificial construction would not deserve any attention,
if it were not caused by a common misconception among novices in
science making: scientific disputes are results of "derogatory"
words. The comment mentioned earlier might help Winter to rectify
his misconception:
On Jan 23, 1998, Pertti Lounesto wrote in this posting:
> The results have appeared in a peer-reviewed journal, Advances in
> Applied Clifford Algebras 6 (1996), 69-104. The international
> advisory board of this journal has 9 members, 8 members plus me.
> Of the 8 members 5 have been listed as mistakemakers.
In addition, the editor of the journal is listed as a mistakemaker.
So, there is a published record that Winter's criterion is fulfilled,
although not for the reason that Winter stipulated; I informed the
authors, since I was driven by curiosity on mathematics and cognition:
I wanted to know the nature of misconceptions of the authors.
Since I have some experience in pointing out errors in theorems
published by my renowned peers, I would like to share them with
novices like Dik T. Winter:
How to write a letter pointing out mathematical errors of a peer:
1. Use the peer's terminology, notations and concepts.
2. Make sure your interpretation is the one intended by the peer.
3. Give a detailed counterexample to the incorrect "theorem".
4. Do not send out the first letter before you make sure that your
counterexample falsifies all interpretations of the "theorem".
5. Do not try to fix the "theorem" by giving your version of the
intended theorem: the peer might have intended something else.
6. Do not use fallacious arguments, even if provoked.