Tag Archives: math

Romancing the Sphere

Some may find this unique table helpful in understanding spheres.

Beyond the purely mathematic, this fully symmetrical regime may also find application in physics, sociology, ontology and economics.

Note: Using the diametric mode for calculations (mentally or on paper) can be quicker than employing the formal (radial) convention, especially when working with hyper-dimensional domains, exponential growth scenarios, or when one is in need of an easier way to factor between domains of differing dimensionality.

Diametric dimensionality

If you would like a personal, complimentary copy of this chart in PDF format (8.5″x11″ – but infinitely scalable) use the form below. Comments optional.


All versions since 2004 have reflected the much needed repair of the broken symmetry found in the 0-sphere definition under the prevailing n-sphere generalisation.

If you prefer the formal mode for transforms between exterior and interior space, simply use •r/d instead of •D/2d.

If you’re a student, check with your professor before applying these principles in your work. If you are the professor, just use your best judgement …and maybe get a second faculty opinion. 😉

Jan. 19, 2011 – Image updated from 2004 version to new 2011 version.

Jan. 22, 2011 – Minor aesthetic changes; image updated.

Jan. 23, 2011 – Diametric ext values adjusted by -1; image updated.

Oct. 26, 2011 – Minor text/aesthetic changes; explicatory notes added.

Dec. 28, 2011 – Declared dimensions as a single-character variable (d);
image not updated — use request form below for most current version.

Jan. 10, 2012 – Image updated.


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Filed under Economy, Life, Reason, Science

The Advent of Monolithic Man: Addendum Notice

An addendum to The Advent of Monolithic Man was added on this date.

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Filed under Science

Why I’m Not Concerned About the Ultimate Fate of Israel

ahmadinejad-un2No matter how obnoxious the rhetoric coming from Iran’s president, it’s difficult for me to imagine that Israel would not be able to respectably defend itself (and more) in any major conflict with the Persian state.

The reputation of Jewish scientists, as a whole, is well established. Despite comprising only 0.25% of the world’s population, Jews have nevertheless managed to rack up a considerable collection of Nobel—and other—prizes in Science.

Nobel Prize for Chemistry — 20% of total

Nobel Prize for Physics — 26% of total

Nobel Prize for Physiology/Medicine — 28% of total

Kyoto Prize — 26% of total

Wolf Foundation Prize — 34% of total

US National Medal of Science — 38% of total

* jinfo.org (2009)

Allied efforts during the First World War were greatly enhanced by the work of a Jewish chemist named Chaim Weizmann who invented a way to more easily manufacture acetone, a key ingredient in cordite-based explosives. Weizmann later went on to become the first President of Israel.

During the Second World War, the work of Jewish physicists like Albert Einstein, Robert Oppenheimer, Leo Szilárd, Niels Bohr, Albert Michelson, Wolfgang Pauli, Felix Bloch, Edward Teller, Lev Landau, and many others, made possible the harnessing (and unleashing) of nuclear energy.

I certainly hope that a third war will not make it necessary for such talented individuals to demonstrate what they might be able to come up with next.

Psalm 92 speaks of those times when David/Israel were/are/will be under fire from many sides, beset by numerous enemies. And it seems that every time this occurs, new revelations about the nature of matter and energy do indeed arise. Or, as it says in the psalm:

Psalm 18:16  (18:15 in some versions)
Then were seen the channels of the waters,
and the foundations of the world were laid bare
at thy rebuke, O LORD, at the blast of the breath of thy nostrils.

The word ‘waters’ can be synonymous with power or energy, which,
along with the foundations of the world (matter), will be revealed
when the encompassing enemies of Israel are rebuked by G-d.


Filed under Conflict, Reason, Science