Monday, March 22, 2010
On the Physical Logic of the Complex Plane
On the Physical Logic of the Complex Plane
A quote from Lincoln on the sciencechatforum.com thread today under Physics called singularity.
It is quite likely that new mathematics will be required. However math is the least of our problems. Math is merely a language. The issue is a model that represents reality. Then the theoretical physicists and/or their mathematically-inclined colleagues will work out a way to solve the equations.
There are mathematicians who derive consequences of mathematics in a vacuum. Then voracious physicists descend like locusts to see what they can steal to make things easier to calculate. And, occasionally, people will need to invent the math to be able to solve their problems. One example given for this is Newton, who need calculus to calculate things. (I'm not a sufficiently-educated Newton historian to know precisely the order in which he did all this during that couple of years when he was waiting for the plague to burn itself out in London.)
One thing that is true is that no new math will solve the singularity problem as is. The problem is the model, not the math to solve it.
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I have finally made the leap in understanding the unity of mathematics of our day in itself which may catch up to the models I have proposed- I too thought it would take a new mathematics but although slow our mathematics if very powerful- and at some place, in many models, the math and the models are the same thing. As far as the intelligibility of teaching and learning these heights of understanding the world what we seem to be really looking for is the unification of the diverse branches of mathematics itself rather than some application or background calculation. Oddly, few seem to readily accept the alternative models or stray to far from the long steep learning curve of our gains thru a succession of academic gifted students and teachers. Some research, some teach, but few combine both well.
The complex calculus as a rewarding and most beautiful thing, the contour calculus which ties much of mathematics together. It serves no good purpose to operate so as to teach by a principle or model alone and not the answer a prioi at the end of our journey in the back of books. The essential thing here- and each of us is responsible for our philosophic position - is that the world is stable to a point and finite in some of its functions- and these between realms or domains as if a linear continuum contain points on that continuum which may or may not diverge as with any place we deal with the infinite and zero, with horizons and singularity. Our inability to frame the singularity problem is more one of philosophy than models.
Is it not abstract enough that we imagine some higher dimensional structures and even those filled with so called "holes" of part reaching out to ideal infinity so as to have them return again in structures of a multiplicity of density? That things are simply connected such that a loop may reduce toward a point and not have an internal region which is really the same as that outside- consider all ideas of the very small as reflecting the very great- this the source of wider topologies. Yet the world can be more complicated than even the non-euclidean and presumably finite use of this terrain. To say GR breaks down at some level is just to restate that there is a problem to be solved on the nature of singularities, an empty tautology perhaps of what we assume is the given state of the reality of all models.
It is no priestly secret that most of the advanced made in the last few centuries that apply to physics at least for the experts of theory and not necessarily the expertise of the engineers that this involves the complex plane. Is the symmetry of Maxwell's equations that surprising when the mathematical formalism of Cauchy solved it before hand? And how far away are we from an intelligible idea that the unbalanced monopoles therein may not be there also in these higher complex quadratics structurally right under our nose? Here we may need a new formalism of materialization of what it actually means to be a pure particle or wave.
We should explore grids like pi/e ratios in the flatland of such dynamic matrices of space- and there be one law of motion of the zeta functions to describe things not two that have not gone beyond the grounding symbolism of our formalism.
* * * This said I continue the poetic and metaphysical parts of the posts with such things and similar things on my mind. It will not just take a new Newton or Gauss or Riemann or Einstein- but a whole new lineage of such mentors to make the needed breakthroughs who at least inspire and not stiffle the next creative and gullible generation of physicists and mathematicians. * * *
Is that Love's Linear Analysis or Infinitesimal Calculus Leonard Edgar Otto 21 March 2010 spring
Our dreams are so similar as to be confused
that we distrust the empty "is", see as abuse
Honest intentions that say "I Love You" and
our faith in each other unhealthy agnostic to everything
Confusing change and chains for the source of timeless Love
some squared acceleration although primes exceed the squares
We already there who missed the boat, overshot the
first fall together creatively into false vacuums of
Annoying presence and persistent orbits of mere friendship
No one can be wide awake at early morning classes of
spherical trigonometry nor grasp its austere
Beauty, take to heart and use, topology down to earth for living
bare naked simplicity, singularity and continua not disturbed, perturbed
We are more the Cupid's arrows still yet moving by our heartbeats
* * *
Yet your ghost my world indifferent to your out of sigh seething cauldron
is not so forever far away Love's consequences do not catch up, return to us
Reality and the Good Lord slips through all dihedral angles
its empty shells return to sand, predestined all entangles
It hardly matters, dust in an urn or vessels embalmed and
set in holy ground as the sea gives up its copper waste and dead
That we got lucky and can't exhaust the final bank's unbalanced wages
Our first dreams also challenging our children, age appropriate the ages
some moral stance of all Love's that might have been our bonds, roles, children
Its open sesame street the agenda, one family diverse its children
who will look back and see it, the hoaky Sea Hunt moral message
What was theirs beyond the closing words today of Jerry Springer
How Mormon tabernacle choir the tame gyrations in Muscle Beach Bikini's
Until returns to farce the talking spherical horse and younger but dead actors, mangled ravens.
Crime goes free with hanging judges that law fills the territory, prairie
while the citizen army protects the planes and codes, demean the play as well the indians and cowboys while
We debate come Trinity the flying carpet bomb bey's over Mumbai
* * *
The Tree of Life Covers the Earth 21 March 2010 spring
In the braided rings of time the avatars as
shepherd moons vie for all the layered sky
Five or seven come eleven space to chase the
Trojan bodies where futures past and the past future
Craters made from echoes of the war to come
between the thirsty dirty dust along the Indus and
The troughs and sells of the Prophet's tears
heaven perpendicular, no parallels ten thousand household gods
From the Ganges Ghandi Gunga-din felt the non-violence
winds of Aether, a Baluchitherium he rode again and
History as it were returned as snowbound Lama down from the world's top
David and Goliath, Persia falls to Greece, Albion and the Bear and
So on goes the soliton sensed and fixed in prophesy the apocalypse
Each new Eden, even sword sliced Zion, the center chosen inheriting Hallowed Land
* * *
What profits man that he divines by prayer or reason cleft
deducing truth outside his dream that nothing else is left?
What have we done with our dominion over the Earth when
the roots were fossil real, whales elephants returned to sea and
All the beasts and chimera, ape man in the mind of sleeping God
half awakened now on Eearth recalled in cracks of broken vessels glued?
The golden fruit half and twice eaten so too the lodestone worms
our minds go beyond our skulls, beyond the holes in the canopy of stars
Although lighter than the angels, ghosts, and aliens, beyond forever's
our archangel wings awaken, command their clockwork fires
Let us praise the many lost and the few who found the way through the maze
even the demons are immortal in memory who stopped and built their kingdom
Tired and part way and free from the Lords of the trade routes
giving birth to angels with time to tame the wolves, plant orchards.
* * *
Gods In Retreat Half Fail 21 March 2010 spring
How absurd into dimensions shod of mystery so
the only analogies to trust those of geometry
Or in your simple faith thought obvious to the point
you think me full of nonsense, irrational
That you accelerating at light speed shrink me, make
me smaller in the distance, send me to ideal margins?
When I come closer to you, timeless and instantaneous
the greater shift of unities you face away dark side moon
My Hubble eyes can only see by your theory of rainbows
thought's small step tears in the empty sea of Moscow
As if Lenin made a pointless difference who lived or died
in retreat the skaters art for change sake on rocks not ice
The frontier is within the half-spin and spin twice
Adam half facing God, and atoms half shrinking science.
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