2014 World Class Mat Puzzle

There is a tradition of embedding a geeky problem in artwork of the FLL mat.  This year’s puzzle is printed in the SE corner of the mat:


This is a bit over the heads of the typical 9-14 yr FLLer given the math and physics involved so maybe it’s for the adult volunteers.  Some people realized that Plank’s constant is the only common number anywhere near 10^-44 power and then started combining other numbers to discover the number printed on the mat is the inverse of the product of G (the gravitational constant) and h (Plank’s Constant).

The Gravitational Constant ( 6.673×10−11 N·(m/kg)2 ) is used in Newtonian Physics to calculate gravitational forces between two masses.  Plank’s Constant ( 6.673×10−11 N·(m/kg)2 ) is a proportionality constant describing the relationship between energy and vibration frequency at the subatomic quantum level.  From Wikipedia:  “Planck discovered that physical action could not take on an arbitrary value. Instead, the action must be some multiple of a very small quantity (later to be named the “quantum of action” and now called Planck constant)”.

More speculation about this year’s FLL mat puzzle at Quora.

Specifically, we have figured out that the numerical portion is the Plank constant times the Gravitation constant, which is 4.4 X 10^(-44) m^5/s^3. Note, however, that the units are inverted.
Other potential clues are:

  • Why is the divisor bar hollow like that? Does that mean something?
  • Why the unconventional way of writing the units? m^(-5)/s^(-3) is the same thing as s^3/m^5. Does that mean something?
  • It is obvious that this has something to do with g*H. G&H are consecutive in the alphabet. Also, hg is the symbol for Mercury. Could either of those observations be on to something?
  • The theme for this year’s competition is “World Class Learning Unleashed”. I would *THINK* the puzzle would have something to do with learning, how we learn, why we learn, something like that. Remember, this is a competition for kids. Sure, a 10YO kid wouldn’t know hG, but the puzzles may be targeted for the coaches and parents???

A couple of my favorite theories:

Jay Wacker, physicist, phd+postdoc+faculty

19 upvotes by Akshit Kumar, Anonymous, Quora User, (more)
It’s about the value of the Cosmological Constant.If you simply take it at face value that the dude is being a moron and trivially obfuscating the value and call
 X = 4.44\times 10^{-44} s^3/m^5Then the combination
 \hbar^3 c^6 G_N X = 60~ \mathrm{ meV}^4
which is in the ballpark of the vacuum energy density of the Universe.

You may wonder I why I didn’t write out more significant figures, well the expansion rate of the Universe is only known to one or two decimal places, so if this is the case, the person would have to not respect significant figures — which aligns pretty well with their choice of using negative exponents in the denominator.


Christopher Pow, keeping it simple since 1974

6 upvotes by Abhijeet Borkar (PhD student in Physics (Astrophysics)), Skip Morrow, Joshua Engel, (more)
My thoughts.  First, I googled “cubic second”, and I find What is a cubic second?, which helps a bit, I think.  It tells me something about the quantity.  It might be a “steady increase in acceleration of” some unitless quantity.  A constantly accelerating acceleration.  But of what?  It seems very strange that something that’s accelerating could be found to be accelerating its acceleration by such a miniscule amount.  Perhaps it is a “constant” only because our current measurement of the effect yields this number, but we are actually measuring an acceleration of an acceleration that’s slowing down — approaching zero.  That is one explanation I can think of for why the number is so small.  I think perhaps the symbol separating the m^-5 and s^-3 is not division.  I don’t find any references for a division symbol that has a hollowed center. 

I experience BSOD at this point.  Not sure what to do with m^-5.

EDIT: Continuance…

The hollow-line symbol could be interpreted as a Vinculum (symbol).  That doesn’t help much.  “Vinculum is Latin for “bond”, “fetter”, “chain”, or “tie”, which is roughly suggestive of some of the uses of the symbol.”

But I learned the word for the symbol that represents division among many other things.  So yay.

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