Magic Numbers / your Reality is a shadowy, unreliable reflection of the True Reality: the Positive Whole Numbers

Copyright (c) Xavier Borg - Blaze Labs

In this rather lovely and marvelous wiggle.gif (which I sincerely hope wiggles for you), the individual marbles are nucleons -- each either a neutron or proton, in the atomic nucleus. If this particular tetrahedron arrangement were rotating above a mirror surface -- the same arrangement of marbles twinned below it -- it would represent a nucleus with a "Magic Number" of 50 nucleons, and thus would be a nuclide (what they used to call an isotope) with an unusually long time-stable life before any radioactive decay turned it into anything else.

Magic Numbers, and atoms whose nuclei have a Magic Number of protons + neutrons, represent one of many bizzare intimacies between pure whole-number arithmetic and mathematics, and the behavior of the Real Physical World as we have actually measured and perceived it. 2500 years ago in his mystical mathematics cult in Italy, Pythagoras would have understood everything about Magic Numbers, and in fact would yawn to be told that moderns have discovered that Magic Numbers describe this startling time stability deep in the nucleus of atoms. Pythagoras would say (in Greek): "I told you so."

But mainly I just think Xavier Borg's wiggle.gif is real pretty. If he catches me filching it, I hope he doesn't get mad.

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post to the Ionizing Radiation Garage & Basement Scientists:
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In "The Character of Physical Law," Nobel physicist Richard Feynman asks why Nature so thoroughly and slavishly obeys extremely simple mathematical rules. His answer: Nobody knows, but we should all be very grateful.

I've never seen these Magic Numbers mentioned on the List, but since I bumped into them, I thought I'd pass them along, and troll for the List's knowledge about and experiences with them. The underlying math is just high-school algebra.

But the integers in this sequence turn out, quite surprisingly, to be the numbers of nucleons (protons + neutrons) of nuclides which have great stability -- unusually long duration before radioactive decay, compared to neighboring nuclides with close numbers of nucleons, but not exactly these Magic Numbers.

How important is this odd link between high-school algebra and radioactive decay? It earned the 1963 Nobel physics prize for its discoverer, Maria Goeppert Mayer. Her discovery and prize were the cherry on a lifetime of slammed doors as she sought paying jobs in the all-male physics world of her native Germany and her adopted USA. In an age when chemistry and nuclear physics were barely distinguishable, she worked on new methods of separating fissile isotopes at Los Alamos for the bomb project.

The buzzwords for her discovery are Magic Numbers and the Mayer-Jensen Shell Model of the nucleus. (This doesn't refer to electron shells, but to the 3D billiard-ball "packing" scheme of nucleons in the nucleus.)

It should take this bunch about ten minutes to zip past my primitive grasp of the math and physics of Magic Numbers, but as the integers in this sequence grow, try to identify familiar nuclides with these numbers of protons + neutrons in their nuclei. (Or maybe they're not familiar, because they're so time-stable -- they just sit there and don't set off radiation detectors.)

The Magic Number integer sequence is designated OEIS A018226 on the very nifty collection of all known integer series (like Fibonacci, etc.), ATT Labs's On-Line Encyclopedia of Integer Sequences.

(They got about 135,000 sequences in their database, and if you want, OEIS will turn any sequence into musical notes on your choice of instruments. This one's not a particularly pretty tune.)

Because of their importance as stable nuclei, Magic Numbers begin and end with

2, 8, 20, 28, 50, 82, 126

but there's the science-fiction possibility that some lab could someday cook up a nucleus with a larger Magic Number of nucleons, which would not decay and vanish in a gazillionth of a second, but be stable.

The sequence is generated by two different formulas,

(n(n^2 + 3n + 2)) / 3 for n = 1, 2, 3

and (n(n^2 + 5)) / 3 for n > 3