Reality and Proofs (was if vs. when vs. and: style question)

[Rusi]

On Monday, March 30, 2015 at 8:51:47 PM UTC+5:30, Marcin Borkowski wrote:
> Hello,
> 
> first of all: I stand in awe watching this discussion I've inadvertently
> started.

Yes the commission of elders is deliberating on the right scale and form
of punishment for this misdemeanor <wink>

> 
> On 2015-03-30, at 16:18, Stefan Monnier  wrote:
> 
> >>> Do you know any Mathematician that is paid by the hour? ;-)
> >> Or that is forced to use differential geometry to solve his problem,
> >> whatever it is, because the enterprises only has other specialists of
> >> differential geometry, and they are easy to find for hiring.
> >
> > Along the same lines, I don't know many programmers whose code is never
> > passed to a compiler/interpreter but is instead only read by other
> > human beings.
> 
> BTW: I think you nailed a serious problem with contemporary mathematics:
> that machine checking proofs isn't a routine part of the publishing
> process.  The number of erroneous papers in math journals is
> horrifying.  Substantial portion of my depatment's seminar is devoted to
> discussing errors in papers.  Once a colleague found a relatively simple
> /counterexample/ to a theorem which was a cornerstone of a whole theory
> (and a basis for several dozen other papers).

Thomas Kuhn points out that scientific paradigms not only shift slowly with
time, they may actually be incommensurable.
So Galileo was wrong and the pope/ecumenical council were right in punishing
Galileo for his ideas because the earth was *by definition* immovable.

IOW we have a different earth today than they had.

Likewise proofs/truth etc changed dramatically from Aristotle/Euclid to 
Galileo/Descartes/Newton and once again has seen vast changes post the computer 
era.

Some recent thoughts collected on that subject
http://blog.languager.org/2015/03/cs-history-0.html