Re: Delusions and occasional bleak truth

Venkat Reddy wrote:
Today's Calvin & Hobbes comic has this final statement from Calvin:
"Isn't it sad how people grip on their lives is so precarious that
they'll embrace any preposterous delusion rather than face an
occasioanl truth". Though Calvin was wrong in the context of the
comic, this seems to be true with us to some extent.

I would say any branch of mathematics (topology etc) which desires to
model physical continuum and depends on the notion of "open and closed
intervals of continuum" needs clean up. Because by allowing those open
and close notions, we are modeling only descretum by assuming that it
is possible to strip off zero extent boundaries from their regions.

I'm going to go more with Angus than your detractors. However, personally, it had never occurred to me that someone might think that the convenient abstraction called topology, and the physics of reality, were anything close to be exactly the same. Rather, it is that the language of topology provides an extremely effective method for getting at some of the truth about reality.

While the mathematics will probably need to be completely reinvented one day, I don't think that now is the time. I think the time will come when we come against discrepancies between our mathematical models and reality that have pragmatic consequences. The nature of these pragmatic discrepancies will be what will clue us in to finding what to replace it with. I don't wish to invalidate your philosophical musings in the mean time, but I think that you should be equally willing not to invalidate those who don't wish to follow the same path at this time.

Why we can't strip off boundaries? because you can't subtract dogs
from kilometers. Regions are of one dimension higher than their
boundaries.

While I must admit that I don't quite get what you are saying here, nevertheless I do admit that boundaries can definitely be a tremendous practical difficulty. For example, I know people who are trying to model fluids going around porous cell membranes, and modeling what exactly is the boundary/membrane is really very difficult. Similarly, I once had an inquiry from a biologist who needed an effective way to compute the surface area of a coffee bean (apparently the surface contained some useful chemical, which incidentally is also responsible for upsetting some peoples' stomachs - so remove this substance and more people can enjoy coffee). He showed me shapes of various beans, and the best I could offer was that he consult with a computer graphics expert who might be able to triangulate the surface. But it is really like computing the perimeter of England - it depends so much on how detailed your calculation is, and potentially the perimeter could be like the famous snowflake curve, and of infinite length.

Stephen
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