A Crayon Physics Paradox Photo Phinish

Newton's Ocean prodded me into some additional thoughts in his comments about the Crayon Physics Paradox post. He could be correct that I might be trying to force a square peg (math) into a round hole here (non-math). I'm still holding out hope for a math person to look at my distinctly non-math graph and say something like, "It's quite simple, the answer lies in an equation where you take the the sum of the limit of virtual reality as it approaches real reality..." I have a fancy for imposing math on non-math. Not a good quality for a guy whose worst grade in college was in calculus.* But then again, perhaps the CPP is just psychology.

However, I still see a bit of life in this near-dead horse, so I'm giving it another beating with my club:

Imagine a foot race between two contestants, each on opposing sides of a field with a Finish Line in the middle. On the one side is a completely primitive human with no technology (or only crude technology at best like sticks and rocks). On the other end of the field is the first Texas Instruments calculator, clunky, huge, and only capable of simple math. When the starter pistol sounds each opponent races towards each other, vying to cross the finish line first, but also at risk of colliding with the opponent who is running head on. As they race head-onwards, each one becomes more and more like the other. The human assumes mechanical, electrical and technological properties. The calculator assumes human properties and becomes more "life like". As they get closer and closer to the finish line it becomes more difficult to distinguish the two. The one who reaches the finish line first wins(?) but also, as soon as he/it crosses the line, he/it becomes indistinguishable from the opponent, for all practical purposes.

The endorsment deals and broadcasting rights for this event would be huge! Stay tuned folks, don't touch that dial.

The Fine Print

*I deserve some slack, however. The teacher was on foreign exchange from China and his command of English was worse than my command of Chinese.

Nicolas Bourbaki: The Greatest Mathematician who NEVER Lived

Nicolas Bourbaki is the greatest mathematician who NEVER lived.  He produced outstanding advances in set theory, algebra, and topology among many others. Bourbaki published 40 volumes of work. Though he waxed and waned, he was a steady contributor for 50 years after the 1930s, especially in France.  But he's never drawn breath or put pencil to paper.  He never existed.

In fact, Nicolas Bourbaki wasn't a mathematician.  He was a conspiracy.

I'm not a mathematician, but I'm interested in math.  And I'm not paranoid, but I'm partial to my share of conspiracies (and I don't care if they are watching me!)  So that makes him my kind of historical figure and, apart from Newton,  Nicolas Bourbaki stands as my favorite math guy. 

He was invented in the 1930's by five students who wanted to rewrite the standard math text under the cloak of secrecy! [Insert the sound of the Twilight Zone here].   They operated for years, publishing under a pseudonym and adopted persona.  They were highly exclusive and had rigorous standards for their approach to their work.   They recruited in secrecy.  The academic community assumed that there was some brilliant, quirky recluse operating in his own bubble and cranking out brilliant work.  Turns out there were a bunch of brilliant, quirky recluses operating in a bubble.  The ruse eventually ran its course and the final Bourbaki publication was in 1983.

The story is much better told at Planet Math.  

Because this appeals to me on so many levels, I fashioned Sir Robin Louis Baack*, the antagonist in my novel "A Body at Rest", after Nicolas Bourbaki*.    In the novel, Sir Robin is the head of an academic secret society bent on destroying Cambridge University.  Oh man, there's going to be some trouble coming from the House of Baack.  Big trouble.

The Fine Print

*Twelve bonus points to you if you figured out that these two are anagrams (leaving out the "sir").   No, wait.  I'm just giving ten bonus points.  I mean, come on!  They have all the same letters in their names, just rearranged...Hey now!  Don't get snippy with me.  I'll knock it down to 8 points.  I will.** 

**I mean it.

When virtual reality approaches real reality

Crayon Physics is the best thing since sliced bread.  Why?  Because it closely simulates reality. Very closely. You digitally draw a crayon box, it falls, hits a CG board, then tilts, falls, knocks a CG ball which then rolls off of an edge.  The virtural springs spring like springs, virtual gravity pulls like gravity, virtual pendulums pendulate(?) like pendulums.  The "cool factor" lies in how close it approaches reality.

But why don't I have the same awe, fascination and intrigue about real reality?  Why not spend hours taking a ball, dropping it on the table, and watch it roll to the floor?  Some real life games capture this (marble contraptions, hot wheels tracks, etc...) but they have a different intrigue somehow.   A real pendulum that gets knocked by a box doesn't have the same wonder of its virtual counterpart.  But why shouldn't it?    The "cool factor" of computer simulation/games/CG increases exponentially the closer it gets to "Reality", but then takes a sudden dive when the line of reality is crossed.  This is why a very realistic, but virtural, Crayon Physics ball dropping seems cooler than a real ball dropping.  

But shouldn't it be different?  Why shouldn't the cool factor increase (assymptotically?) just after it crosses the line into real reality?  Why shouldn't a real ball dropping hold even more fascination that the CG one?  Why not this?

I'd like somebody more mathematically adept to help me describe what is happening at the points on the two graphs where the red line crosses the dashed line. It seems that calculus infinitesimals and geometric asymptotes are playing a role here, but I'd be very grateful for your help and thoughts on that. (The truth? This call for cooperation and community is just a thin veil that tries to cover for my laziness. But I would be thankful nonetheless!)