Phasing

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Physicists have just built an enhanced version of an experimental atomic clock based on a single aluminum atom that is now the world’s most precise clock, more than twice as precise as the previous pacesetter based on a mercury atom.

The new aluminum clock would neither gain nor lose one second in about 3.7 billion years! WOW! Read more here or here.

It's dead letter week on Foolish Notions, just because. Here's no. 1:

Sir,

According to the Law of Conservation of Matter, every atom is continually recycled in the universe and never lost. In other words, we breathe the same atoms as those breathed by Galileo (approx 4.3 x 109 atoms per breath). Similarly, we drink – in every glass of water – some atoms of Adolph Hitler’s urine, while, on a lighter note, we also drink some atoms of Jennifer Lopez’s body fluids (provided they have had sufficient time to disperse). Conversely, Jennifer Lopez is drinking – in every glass of water she swallows – some of my body fluids. I would, therefore, like to ask Jennifer (if, indeed, she is prone to brush over this esteemed organ) if she would like to try the undiluted variety … purely for the purposes of scientific investigation. Of course.

Yours

R.H. Schmitt

If you’re a luddite like me (all my analysis code these days is written in octave-2.1.73 and octave-3.0 (better octave-forge support)) and you have a propensity o,  you may have encountered this error:

</code>

octave:1> chi2cdf(4000,4000)
 ***MESSAGE FROM ROUTINE D9LGIT IN LIBRARY SLATEC.
 ***FATAL ERROR, PROG ABORTED, TRACEBACK REQUESTED
 *  NO CONVERGENCE IN 200 TERMS OF CONTINUED FRACTION
 *  ERROR NUMBER = 3
 *
 ***END OF MESSAGE

 ***JOB ABORT DUE TO FATAL ERROR.
0          ERROR MESSAGE SUMMARY
 LIBRARY    SUBROUTINE MESSAGE START             NERR     LEVEL     COUNT
 SLATEC     D9LGIT     NO CONVERGENCE IN 20         3         2         2

error: exception encountered in Fortran subroutine xgammainc_
error: evaluating assignment expression near line 54, column 15
error: evaluating if command near line 53, column 5
error: evaluating if command near line 52, column 3
error: called from `gamcdf' in file `/usr/share/octave/3.0.1/m/statistics/distributions/gamcdf.m'
error: evaluating assignment expression near line 42, column 7
error: called from `chi2cdf' in file `/usr/share/octave/3.0.1/m/statistics/distributions/chi2cdf.m'

<code>

This is related (as above) to the library D9LGIT. Certainly in my case, and probably in general, there is another way to solve the problem. The gamma functions that underpin all of it will probably have nice asymptotics in any regime that triggers the error.  There’s scuttlebutt that this problem is better handled by the GSL library with hooks to Octave – it may be implemented “upstream” in the current Octave 3.2.

In the case of

chi2cdf

, for k sufficiently large (look here to determine “large” for yourself),

chi2cdf(x,k) and normcdf(x,k,sqrt(2*k))

will generate essentially equivalent results. The absence of  incomplete gamma functions in

normcdf

make it more general (and inapplicable for small k).

(Recital was OK. Finished one more application problem. Everything else that happened since the last update is trivial.)

I failed a practice AMC 12 (2007 B); I could only answer 1-12 and 23 (and got them all right, but that’s still not AIME qualification). (I also failed 2007 A because I remembered Vieta incorrectly and didn’t notice that 3 = 1 x 3.)

I’m also failing at electricity (well, potential/capacitance and currents).

Why am I becoming (more) stupid? >_<

We have an Algebra 2 quiz tomorrow, and I have the feeling I’m going to get 11.5/12 again. I’ll just have to check more. After that, I’ll ask Mr Mallon about not taking precalculus at MSJ, instead taking AP Stats and AoPS Precalculus and possibly AoPS Calculus. (Maybe Spivak’s Calculus. I’m not sure yet.)

I also hear on AoPS that USPhO (F=ma) results come back tomorrow. Apparently the cutoff was 13.75 last year, and will probably be lower this year. I answered 15 (and would have gotten one more correct if I didn’t solve that one right before we had to put our pencils down). Maybe I’ll make it. Who knows?

Author and journalist Christopher McDougall begins his journey with one simple question: “Why do my feet hurt?”  McDougall was an avid runner whose running days seemed to be ending due to acute foot pain.  Cushioned shoes and orthotics did not seem to help.  Running is simply bad for you, claimed most sport doctors.  But then, McDougall stumbled across the story of the Tarahumara, or, in their own language, Raramuri, which directly translates to “running people.”  These indigenous people from the Copper Canyon region of Mexico, an area known for its harsh beauty (Copper Canyon is the deepest canyon in the world).  They hunt their prey by exhaustion: they chase their prey for several miles to tire it out and then can catch it and kill it.  Also, they competed in one of the most difficult ultra-marathons (100 miles plus at a time) in the world and shattered the world record.  Then, disenfranchised by the modern world, disappeared back into the canyons.  Not only are the Tarahumara excellent runners, they are also known for serenity, and peaceful, good-hearted nature. Oh yeah, and the winner was 50 years old and ran in tire-soled sandals. ” So why, if these guys can do all this into their fifties, why can’t I run 3 miles,” McDougall asks.  The answer, he finds, is in the shoes, or lack thereof.  We evolved to run great distances in our bare feet, not oddly shaped shoes (I’ll post about the science of barefoot running one of these days).

Born to Run

He then embarks on a quest to find and learn from the mysterious Raramuri the way to run.  To do so, he must evade dangerous Mexican drug cartels,  deal with outrageous long-distance runners, and find the elusive tribe itself!  The result is Born to Run: A Hidden Tribe, Superathletes, and the Greatest Race the World Has Never Seen. This book is part adventure, part running guide, part history, and part science.  I enjoyed this book so much that I polished off this book in a single night.  Without a doubt, this is the most fun book I have read in a long time.

Grade: A

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