What is a Proof, Really?

[ original thread ]

On Sat, Nov 29, 2014 at 11:12 AM, Joe Niederberger wrote:
<< SNIP >>

> Finally, I'm happy to accept your chess problem as mathematical. Frankly, I
> don't know what a survey on that question, given to working mathematicians,
> would turn up. And, any mathematically acceptable way of arguing it would
> have to be logical in my opinion. (If you have an illogical approach that
> is also mathematical I'd be fascinated to hear about it.)
>
> Cheers,
> Joe N
>


I think we mostly agree. Criteria apply.

A proof is not a recipe nor even algorithm.

An algorithm tends to have proofs in the background, to back it up as it were, e.g. we make use of V + F = E + 2 in some step in a computer program, e.g. we get E from V + F - 2, but then why is it safe to get E in this way?

In the background: Euler's Theorem for Polyhedrons and the many proofs thereof, my favorite probably the one by G. K. C. Von Staudt:

http://www.ics.uci.edu/~eppstein/junkyard/euler/interdig.html

[ however this is not my favorite forumulation of it; that would be in Peter Cromwell's Polyhedra, cite http://www.liv.ac.uk/~spmr02/book/ ]

The other thing I'd say is: lets not go overboard in assuming some finite roster of individuals tagged as "mathematician" truly owns or controls or governs the discipline and shared heritage we loosely call mathematics ("loosely" because anything tighter would be clearly too tight and therefore outright wrong).

Innovations come in from left field all the time e.g. most naturally from closely neighboring disciplines, and those self-identifying as official spokespersons for mathematics, i.e. mathematicians, must scramble to keep their background cosmetically acceptable i.e. the pros keep it looking professional, add the right panache (sometimes a little lipstick on the pig is all one needs).

Kirby

Global Data Revisited

So where's the math in all this?

We clearly need better and more reliable global data.

However I'm skeptical that partitioning the world up into a jigsaw puzzle and collating by "nation" is an at all useful way to be measuring humanity's progress or lack of same.

The UN has to do it that way, for political reasons, but supranationals like Google (or some hypothetical Global Data Corporation) would not need to present and/or visualize global data in those obsolete terms.

More context:
Reply to Israeli Knight (math-teach, Nov 25 2014)
The Mapparium (Feb 09 2005)
FAQ:  What is Global Data?
Checking Global Data

Dear White People (movie review)

I'd deliberately avoided reading any reviews so wasn't sure what to expect.  I drove to within a half mile of Cinema 21 and loped a lot of the way, not wanting to miss even previews.  I got there on time.

The film is set in a somewhat timeless world called "college", not the real world at all.  Obama and current events get cursory mention, but Sam (a girl) is using a 1950s style Bell & Howell looking movie camera that helps catapult us back to some other time.  The college president is straight out of MAD.

The most disturbed individual is the shy-teased guy with the Afro, way out of style.  He's the first to break glass and turn the scene violent.  He destroys property, expensive stuff.  Then he sexually assaults another guy.

Everyone else is relatively mature and touchy issues of racism and classism are dealt with without violence.  College is a cerebral place and these kids are a brainy bunch, especially Choco or whatever she goes by, the ghetto girl from Chicago.

The anti-racists get to be segregationists as Black Pride is just another form of professional elitism and deserves its own circle in the Venn Diagram of "things to be".  The college administration had been trying to randomize "blackness" out of existence but disrupting memes-with-inertia is even harder than disrupting genes, as to accomplish the latter you just need condoms, as these students appear to comprehend.

My university had houses for social clubs like this one and we were expected to intelligently work through differences.  A Third World Center and a Womens Center helped add balance, plus the particular house I lived in junior and senior years, 2 Dickinson Street, was about balancing some of the more conservative houses.  Ours was in favor of boycott, disinvestment and sanctions (BDS) against apartheid in South Africa for example.  My roommate for a time was editor of the Daily Princetonian.

The college portrayed in this movie seems a lot less in touch with the real world than Princeton, and more stuck in a time warp, but that's fiction for ya.

Gender Again

 
:: gender tweets ::

For further reading:
Gender Wars

Wanderers 2014.11.13

:: steve holden ::

Steve delivered a well-received and attended presentation on The Impostor Syndrome, perhaps a syndrome he made up, but then I haven't Googled it yet.

He was using the Wanderers format to best advantage: prototyping a talk he might give someday, and getting behind the scenes, before you go on stage feedback. He took notes as feedback was freely offered.

This being an early morning crowd, buzzed on coffee, we chimed in with a lot of witticisms.  I liked Steve's "I was gonna write my paper on the Stockholm Syndrome but I think I'd rather stay with my new friends."

Dave DiNucci of NASA background was present and avidly following the comet landing story.  We were in the suspenseful moments before knowing for sure whether the landing module had actually managed to arrive at its surface destination.

Steve naturally traced the syndrome back to childhood first experiences, and recommended what we might do in adulthood to counter some of the more hampering habits of mind.

Steve's track record rivals Terry's in some ways, of being able to deliver public events.  That's apples and oranges really as the lecture circuit and conference venues are different sides of the business.  Just saying:  both have been highly successful, and those are only tips of the iceberg in both cases.

Steve was also a chairman of the Python Software Foundation and continues to teach classes as well as mentor newer teachers in many IT-related topics.

However, as I discovered at Princeton and many other places since, one will continue to be astounded by neighbors and random strangers with skills one doesn't have, like at a circus.

Sometimes the Impostor Syndrome might mean feeling less good at being human than say some role model or super type, some example.

Anyway looking up to others is healthy.  I'm not one to say "putting so-and-so on a pedestal" is always a bad idea.  I've got people on pedestals everywhere I look; kinda "sepulchral" as Ed Applewhite might have said.

The Mountain

Common Core Mathematics as Poverty Line

I sound naively "born yesterday" in this outburst on math-teach (Math Forum) against Common Core Mathematics, whereas those following the action more closely could have told me years ago:  the standard advocates teaching base 10 operations, but stays silent on teaching what "base 10" actually means.

What people maybe don't understand about Common Core Mathematics is it deliberately sets a very low bar and schools are encouraged to rise above it.

To actually cover no more mathematics than is contained in that standard is to be mathematically disabled and in dire need of remedial practice, but then what curriculum worth its salt would only cover Common Core Mathematics?

In some earlier posts, I appeared to understand that, saying I could embrace Common Core Mathematics Standards only to exceed them.  That's what I'm saying here too.

In contrast, this "US Coalition" believes the Common Core should be "world class".

By my reasoning, no it should merely set a very low barrier to entry and be used as a criterion in that way.

Common Core Mathematics is "gruel thin" but not "non-nutritious".

Common Core Mathematics defines the mental "poverty line" we all strive to stay above.

No one wants to really be as mathematically unsophisticated as a hypothetical Common Core Mathematics person would be.

Meatup

Remembering Dora Farms

The curtain opened on the Attack Iraq scenario with what was billed as an heroic bid to end the war before it started.  If only the head of state, and former ally, could be murdered in his bed using high altitude precision guided bombs, steerable even through cloud cover, we could call it a day.   Worth a try, right?

The new bunker busters had been ordered up in a hurry and having stealth bombers drop some was the Beltway Goon wet dream du jour.  A pretext for pre-emption was all the Neocons needed.  Since the War on Terror had been personalized to Osama and Saddam, viewers already understood that a manhunt could be a wartime activity, involving cruise missiles and high altitude bombers.

The American public was asked to believe the CIA had spooky insider knowledge that Saddam's chances of being in that secret bunker were greater than fifty-fifty.  Given the number of American lives that might be put in harm's way should Operation Iraqi Freedom proceed on schedule (which it did), the President and Secretary of Defense must be forgiven for trying.  Great cover story.

Of course in reality there was no such bunker and Saddam was not waiting around in Baghdad while CNN waited breathlessly for some explosions for the home-viewer voyeurs.  Whether the CIA really had any spooky insider knowledge was irrelevant as the only important order of business was to get some stealth bombers doing their thing on TV, being heroic and all, their pilots getting in harm's way.

As we see in Why We Fight, a postmortem documentary, the neighborhood was populated with ordinary civilians.  The "precision guiding" practiced here had nothing to do with geography or preventing the slaughter of these innocent "extras" in the Pentagon's show, and everything to do with surgically wiring US TV viewers to appreciate how supremely awesome and shocking the Beltway Goons could really be, so they'd pop popcorn and cheer for more, good patriots that they be.   What, no Saddam under that palatial tea cup?  It's a shell game! Bomb them all!  Go Team America.

The TV dupes and doofuses bought it, hook, line and sinker.  The myth of "trying to stop the war at Dora" was spun, whereas in reality it was planned as a curtain opener, with much more to come.  So much more.  The Attack Iraq extravaganza would be another one for the history books.  Many proud and heroic chapters would follow, with troops putting themselves in harm's way all over the map.

Wittgenstein & Buddhism