Johannes Kepler ...
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Greetings in the day of the King ... the day of Thor, the Thor-day, the Thursday ...
And enjoying the Happy Majestic Music of Johannes Strauss and the Angelic Perfect music of Johann Sebastian Bach ... we introduce and speak about Johannes Kepler as well other actors ... like Walter Russell or Harold Scott M. Coxeter and others.
I want to begin with ... some words about the ... Golden Mean, the Divina Proporzione ... called in Latin ... De Divine Proportione.
Most people ... never mind ... and consider this problem very simple ... but ... they do not consider is the solution to a problem of Optimization.
Proposing the problem like, "What is the Optimal distance between two extremes, a and b, to place a point c ... such that the distance from a to c ... is optimal (not maximal)?"
It is evident that have no sense to introduce functions ... but is sufficient to consider the proportion,
Kepler also extend the concept building a triangle over the segment ...
and extending the Panorama ... we reach up to the Great Pyramid internal Triangle ...
After this introduction ... we can say speak about the ... Donald Coxeter.
Please consider that him is a modern Mathematician ... he born in 1907 and die, recently in 2003. However, he works intensively in Sacred Geometry ... including of Course the High Dimensions.
I want particularly catch your attention on Mr. Thorold Gossett who was an Attorney that does not find clients and dedicate to Mathematics.
After an extensive research on the Web, I find finally its article ... titled, "On the Regular and Semi-regular Figures in Space of N-dimensions", published in the excellent but discontinued Journal ... titled, 'Messenger of Mathematics', where English Professor Godfrey Harold Hardy, speaks frequently ... also on important topics like Riemann Function ... in his years.
The point is ... that The Geometry of High Dimensions ... not well covered by Professor Einstein ... is also based on the Platonic Solids ...
In fact, Professor Gosset (understanding someone with great expertise in Mathematics) ... explains and speaks about some ... High Brothers ... of the Platonic Solids ... which he call, 'n-ic Pyramid' ... 'n-ic Double Pyramid' ... (n-1)-ic Check ...
He propose some theorem:
* In space of n dimensions there are four regular figures.*
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* *From Kepler Triangle we comment about Multi-dimensional Platonic Solids ... now we back to Kepler and its comment on Gravity ...
It is fair and interesting ... to say that Johannes Kepler also works on Gravitation ... like Einstein ... like Galileo ... as well Newton, of course.
He, Kepler comment some aspects of the Gravitation ... in its '*Astronomia Nova*' which was the most know Kepler work as well translated in English ... first than any other.
Kepler say,
"Gravity is the mutual bodily tendency among kindred bodies towards unity or contact ... so that the earth draws a stone much more than the stone draws the earth ... If the earth and the moon were not kept in their respective orbits by a spiritual or some other equivalent force, the earth would ascend towards the moon one fifty-fourth part of the distance, and the moon would descend the remaining fifty-three parts of the interval, and thus they would unite. ... "
This is very fascinating ...
Because consider Bodies with (like Einstein did for time ... introducing proper time (See Landau Vol 2 - Theory of Fields)) ... a ... proper Gravitation ... Still considering the Sun ... that attract the Earth more than the Earth attract the Sun ... and the stone be attracted by the Earth.
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Now the final jewel ... or comment ... comes from Walter Russell ... in his Cosmogony about Gravitation.
He say that Radiation and Gravitation are partner forces ... like Electricity and Magnetism ... and is know that Magnetism and Gravitation are partners.
Now ... Humanity has not ... entered in the full understanding of Magnetism and Gravitation because they do not understand Multi-dimensionality ... which according to Kepler, Coxeter and Gosset ... are formed and composed by ... just to say ... Higher Platonic Solids ...
Humm ... If you understand these platonic solids ... we will ... in time ... unlock Gravity.
Professor George Gamov ... wrote a book about 'Gravity' too ... where he introduce some interesting concepts ... speaking at last ... about Waves.
both ... Professor Coxeter (a second actor in the book) and Professor Gamov a primary actor ... spoke about H. G. Wells, books ... and how Einstein Theory feels insufficient.
Like a final comment ... I can cite Professor Georges Lakhovsky ... in his book about 'Matter' ... and he explains ... like Archangels comment ... that the Sun is cold ... but the multiple irradiations that he send to Earth that in contact with the Atmosphere let the particles on it ... vibrate and produce its force and strength ...
The Solution to the domination of Gravity leads in Multi-dimensionality which is a concept directly involved with Time.
Thanks,
Giovanni A. Orlando. |