[FOM] pathology
Joe Shipman
joeshipman at aol.com
Fri Aug 21 20:48:05 EDT 2015
Bad typo--meant to say "provably" irrelevant not "probably irrelevant" below!
-- JS
Sent from my iPhone
> On Aug 21, 2015, at 8:27 PM, Joe Shipman <joeshipman at aol.com> wrote:
>
> I wonder about that. There are certainly strong mathematical criteria which can be used to identify "pathology" that is probably irrelevant to important questions (absoluteness results and so on).
>
> I don't find arguments about pathologies that require the axiom of choice to be interesting.
>
> One place where "a matter of taste" is worth debating is examples that are definable without Choice but whose very name indicates some kind of negative evaluation.
>
> I am thinking in particular of "Tarski monsters" in group theory. These are infinite groups all of whose proper subgroups are cyclic of prime order. Why are they called "monstrous"? Is that adjective because of something unsatisfactory about the proof they exist, or something unsatisfactory about the objects themselves?
>
> What other examples from "countable mathematics" are commonly regarded as "pathological"?
>
>
> Of course the "Monster" finite simple group is a much more special case, because as very well-known and important finite object it can't be regarded as illegitimate in any reasonable way, even though there is certainly dissatisfaction over our failure to understand it as well as we would like.
>
> -- JS
>
> Sent from my iPhone
>
>> On Aug 21, 2015, at 7:50 PM, Martin Davis <martin at eipye.com> wrote:
>>
>> Everywhere continuous nowhere differentiable functions were once regarded as pathological. At least since fractals have entered mathematical discourse, they are commonplace.
>>
>> I suspect that the concept of "pathological" is social rather than mathematical.
>>
>> Martin
>> _______________________________________________
>> FOM mailing list
>> FOM at cs.nyu.edu
>> http://www.cs.nyu.edu/mailman/listinfo/fom
-------------- next part --------------
An HTML attachment was scrubbed...
URL: </pipermail/fom/attachments/20150821/3882e471/attachment.html>
More information about the FOM
mailing list