a thought of being
cannot be what being is
within or without
Tag Archives: Steinman
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.
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.
Request a PDF version:
Gravity is a non-waveform phenomenon.
Light responds to gravity at the speed of light.
Gravity is atemporal but its effects cascade through time.
— from Steinman’s “Attributes of G”
Filed under 10 Words or Less, Science
The Advent of Monolithic Man
The word ‘monolith’ denotes something that is massive and uniform. As such, it can be applied to anything from a large, continuous piece of stone to a person of towering, unique intellect – someone who stands alone in his or her field of endeavour. In the latter case, there is perhaps no more perfect an example than that of the late professor Albert Einstein.
Had he not existed, we would not have GPS systems because the satellites can only be coordinated using the principles enshrined in his theories of Relativity. We might not even have television because he was the one who defined the photoelectric effect. Let’s not even tread into the more esoteric worlds of gravitational lensing, Bose-Einstein condensates, or the Einstein-Podolsky-Rosen paradox.
At the conclusion of 1999, Time magazine declared him to be the Person of the Century. FDR and Gandhi were mere runners-up.
Whether a matter of sheer coincidence or some bizarre manifestation of destiny, the name Einstein may have held a clue about the potential of this singularly impressive individual.
EIN + STEIN (German) =
ONE + STONE (English) =
MONO + LITH (Latin) =
A note about the cover shot from Time:
The iconic image of Einstein on our cover was taken in 1947 by the legendary photographer Philippe Halsman. Einstein was not fond of photographers (he called them Lichtaffen, or light monkeys), but he had a soft spot for Halsman. Einstein had personally included the photographer on a list of German artists and scientists getting emergency U.S. visas to evade Nazi capture. Halsman recalled that Einstein ruminated painfully in his study on the legacy of E=mc²: talk of atomic war, an arms race. “So you don’t believe that there will ever be peace?” Halsman asked as he released the shutter. Einstein’s eyes, Halsman said, “had a look of immense sadness…a question and a reproach in them.” He answered, “No. As long as there will be man, there will be war.”
Most people don’t have the time or patience required to understand the physics of Einstein, so I’m posting this practical explanation of what could be called Basic Relativity, as opposed to Einstein’s Special or General theories of Relativity.
It was derived in very much the same way that Einstein initiated his own theories – through rigorous, logical thought experiments and a healthy dose of creative intuition. (Generally, for Einstein, the formal mathematics to support his theories came in the secondary stage of his theoretical explorations.)
So, here’s a straight-forward, logical statement on Relativity (in 10 words or less) that doesn’t break any physical laws and which can even be seen to underpin many of those accepted rules – including the absolutely fundamental inverse square law. The principle (along with a simple mathematical proof) was developed by an amateur cosmologist in 2005.
Steinman’s theorem simply states:
“Matter is to energy as time is to space.”
matter : energy = time : space
m : e = t : s
m / 1 : e / 1 = 1 / v : v / 1
(v is velocity or acceleration)
e = mv²
(in the ultimate case, e = mc²)
UPDATE: December 1, 2009
In response to requests for additional information on this topic, here is an addendum posted by Mr. Steinman to a related IOP [Institute of Physics] discussion group thread on LinkedIn…
I can fully understand that it’s difficult to grasp the concept:
“Matter is to energy as time is to space.” ~ But that’s the way things work.
In Gary’s [Dr. Navrotski’s] earlier response, he cited E(k)= ½mv² (the kinetic energy of a rigid body in motion) which aligns perfectly with Einstein’s Relativity. (Note: It is “½m” because the other half of the mass would be contributed in any collision by the body which is struck, à la Newton’s Third Law.)
The key to my challenge [as defined in the IOP discussion] was the word “absolute”, since this is when c embodies the most acute aspect of the accelerative component and reveals itself as absolutely central to nuclear reactivity.
Though the matter of “why” is addressed in the logical statement, the following may help to identify “how” c creeps into the calculation:
In a four-variable equation, you need to resolve at least two of them in order to extract any significant meaning.
The first thing to test is an absolute. Ideally, you’d want to interject a constant that satisfies two of the four variables.
There’s only one universal constant ( c : speed of light in vacuo) that applies to two of the four variables (in this case, time and space) without any need for statistical uncertainty (in Newtonian G uncertainty is 1.0 x 10^-4; the Planck and reducedPlanck constants have an uncertainty factor of 5.0 x 10^-8).
So, plug in the appropriate, defined, universal constant ( c ).
But you can’t plug c directly into both the Time and Space placeholders without a very minor adjustment:
For Time, it must be stated as the amount of time required for light to travel one standard unit of distance ( 1 / c ). For Space, it is the distance traversed by light in one standard unit of time ( c / 1 ). This reflects the interrelated nature of space and time as a true continuum.
This works regardless which set of standard units is used.
(Note: It may help to view time as latency; how fast something DOESN’T happen.)
After cross-multiplying the equation, you get e = mc², which conforms precisely to Einstein’s Relativity principle for mass-energy equivalence.
The nine-word statement (“matter is to energy as time is to space”) can serve as an answer to the original question (Why c² in e = mc² ?) or it can be viewed as a description of Relativity in its most fundamentally naked form.
While the logic of equating m/e to t/s will seem completely obtuse to most readers, the simplicity of the proof is inescapable.
Simple, but not overly so. (Some do find it maddening.)
Viewing things through the prism of “matter is to energy as time is to space”, you will find that none of the established laws are broken ~ only gently bent.
Filed under 10 Words or Less, Reason, Science