Grisha Perelman, where are you?

Elusive Proof, Elusive Prover: A New Mathematical Mystery

Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world’s mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought. More... (http://www.nytimes.com/2006/08/15/science/15math.html?pagewanted=1&ei=5087%0A&en=695da381d228c886&ex=1156046400&adxnnl=0&adxnnlx=1155960840-Jp3UDJuvOuiy9EMDOM3r4Q)

http://mathworld.wolfram.com/news/2003-04-15/poincare/

and please go look at http://www.mtnmath.com/willbe/what.pdf and the mountain man info... manifolds and such...

Holey Riemannian manifolds, Ian (snakedude*)...!...
... more ... tomorrow ... :-) ...

S.

spiderman, batman and *snakedude!

After reading through one of the brief explanations of this, I have only one question: Given that we know that spacetime is (at least) 4-dimensional, why does a proof of how geometry in three-dimensional space matter?

“Math is really about the human mind" from Ian's article.

Imagine the mind as a mathematical structure ->- a structure which may be defined ->- and the absolute subjective truth of this statement is exposed.
Math is not absolute - it's an absolute within our particular flavour of Go..delian Universe (borne through serendipity, happenstance and environmental context).

SB.

After reading through one of the brief explanations of this, I have only one question: Given that we know that spacetime is (at least) 4-dimensional, why does a proof of how geometry in three-dimensional space matter?Hmmm ... maybe generalizability??? Don't know (at all) ...just yet... -though- think perhaps that complexity arises from levels of complexity *built upon the simple* - and that an effective solution of a simpler problem might generalize uppa'wards ... ... ... for sure - I'm guessin' - we'll be back to that idea ... it sure reminds me of one of my favourite scientific debates - the reconciliation in 1918 (by Fisher) of the warring camps - Mendel (simple Mendelian (doh!!!) genetics - 'peas and ruggedness') and Galton (complex multifactorial polygenic inheritance (in his case IQ)) ---[a bitter academic feud which commenced in 1868]--- and which ended with ~in effect~ ... ... ... Fisher's proof that the complex is built atop o'the simple ... more here (on ADDF) -> * (http://www.addforums.com/forums/showthread.php?p=247307&highlight=Fisher#post247307) <- ... ... ...

SB.

generalizability???From Kv's Wolfram link ... ... ... 'The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known even to 19th century mathematicians), n = 3 has remained open up until now, n = 4 was proved by Freedman in 1982 (for which he was awarded the 1986 Fields Medal), n = 5 was proved by Zeeman in 1961, n = 6 was demonstrated by Stallings in 1962, and n >= 7 was established by Smale in 1961 (although Smale subsequently extended his proof to include all n >= 5).'

sb.

After reading through one of the brief explanations of this, I have only one question: Given that we know that spacetime is (at least) 4-dimensional, why does a proof of how geometry in three-dimensional space matter?

Three dimensional geometry and the fourth dimension comes from ????

Space the finial frontier or the description of what is between my ears?


Duel puzzled and it may have caused a part if (I stand on my toes) think I should read the all of article, or make coffee, think I should think about it ?

if you are looking at three deminsional geometric thingie how many prespectives would be observed in three dimentions?

I think we live in a different place personally but this is fun to visit from time to time.


Dr. Morgan said the excitement came not from the final proof of the conjecture, which everybody felt was true, but the method, “finding deep connections between what were unrelated fields of mathematics.”

When I do this I get a diagnosis. . . apparent Hyperion they had done two and four even five but three was especially hard. . . . kind of like mathamatical hopscotch of the mind . . . . so that is the thing with the three dimensional biggie!



This may help ! Translation of sorts!
I got it off of one of kvrrds sources

***Quote This says it The n = 1 case of the generalized conjecture is trivial, the n = 2 case is classical (and was known even to 19th century mathematicians), n = 3 has remained open up until now, n = 4 was proved by Freedman in 1982 (for which he was awarded the 1986 Fields Medal), n = 5 was proved by Zeeman in 1961, n = 6 was demonstrated by Stallings in 1962, and n >= 7 was established by Smale in 1961 (although Smale subsequently extended his proof to include all n >= 5). ***End Quote

Too bad my Grandpa isn’t here he probably would be into all mathmatical figuring!



William Thurston of Cornell, the author of a deeper conjecture that includes Poincaré’s and that is now apparently proved, said, “Math is really about the human mind, about how people can think effectively, and why curiosity is quite a good guide,” explaining that curiosity is tied in some way with intuition.

All this time I thought it was associated with being nosy!



In the case of two dimensions, like the surface of a sphere or a doughnut, it is easy to see what Poincaré was talking about: imagine a rubber band stretched around an apple or a doughnut; on the apple, the rubber band can be shrunk without limit, but on the doughnut it is stopped by the hole.

Okay I do the wrong thing for a living here.



Asked about Dr. Perelman’s pleasures, Dr. Anderson said that he talked a lot about hiking in the woods near St. Petersburg looking for mushrooms.

I am sorry but this struck me a funny . . . . :p

Perhaps I should have tried this approach in high school geometry couldn’t have hurt my grades May have even helped! :rolleyes:

I am in danger of getting more diagnosis as I was laughing at a thread describing analog technology earlier and now donut holes in three deminsional space (which Gary doesn’t really understand) . . . . but I don’t find the stuff they play on TV (like that 70’s show) funny. . . .Gary thinks I am odd perhaps he has a point!




“He came once, he explained things, and that was it,” Dr. Anderson said. “Anything else was superfluous.”

Dyslexic pattern . . . . . once the general idea is out and been explained then why harp, figuring out weather or not you are right or wrong gives the rest of the world some thing to; so they won't be a bother while the next plateau is pursued .

Math is not absolute - it's an absolute within our particular flavour of Go..delian Universe (borne through serendipity, happenstance and environmental context).
Yeah, that's why I always hated math. At least physics, while relative, had absolutes. Even particle physics, where a particle is not a particle or a wave and is neither here nor there makes a certain amount of sense in that it's at least something (unless it's a neutrino, in which case it's almost nothing :) ). But seriously, regardless of how one might choose to mathematically define a photon, it carries the electromagnetic force, which is very real. Similarly, even if we can't observe a naked gluon, the strong force is still very real. Even without knowing whether a graviton exists (or whether Higgs might have been right), gravity as a force is there, it is not abstract. PV=nRT, E=MC^2, sigmaF=MA, etc etc.


Three dimensional geometry and the fourth dimension comes from ???? \

Einstein showed that what we think of as three dimensional space is really four dimensional space-time. It's not that space and time are functions of each other, they are actually the same thing. The only difference is that there appears to be some law of the universe that causes time to be one-way, at least in our region, which is almost certainly tied to why entropy always increases. In fact, the definitions of time and entropy are fairly intertwined to that extent. In non-physics terms, it's like saying that there is nothing that man can build that time cannot wash away.

Anyways, at relativistic distances and timescales, space and time operate as different parts of the same thing. A strong gravitational field will bend space and time, and at the event horizon of a Black Hole, spacetime is bent to the point that time itself freezes (and quite possible reverses on the other side, but there's no practical way of observing that because all of our physical equations work with time going in a certain direction).

In fact, even referring to time having a direction is probably wrong. Time is a dimension, objects moving in the T dimension have a vector that happens to move in the same direction. One theory in quantum electrodynamics considered that particles and antiparticles were actually one single particle caught in a time loop, although I don't know if this bore out.

We know that time is related intrinsically to mass, matter, and gravity, as well as entropy. It is also related to distance, as lightspeed over distance determines causality. I wish I understood the Higgs field better, because it supposedly describes how mass came about, but until someone manages to find good evidence for how to fit quantum and relativistic models of spacetime together (string, supersting, and M-theories don't count), then who knows?

apparent Hyperion they had done two and four even five but three was especially hard
Hehehe, yeah, apparently 3-D space is actually fairly hard to comprehend...there's a part of me that thinks that much of the difficulties in the Standard Model (particle physics) and the various quantum oddities arise specifically because they're using three dimensional math to describe four dimensional behavior (not that I'm going to try to describe the Standard Model in four dimensions, I think I'd go crazy trying).




Of course, if the crazy M-theory people are right, spacetime is 11 dimensional and this entire universe is just one small manifold of a larger topology. My feeling is that until you can get general relativity, which people need to remember is the only high-level physics theory that actually works for all observations, to work in 11 dimensions, I'm not buying it. The only possible explanation that would work for me in that sense would be if the observable universe were a black hole within the larger 11 dimensional topology. This actually makes a lot of sense when you look at a black hole in spacetime and not just space. It occupies a region of spacetime originating at a massive, cataclysmic singularity and extending to an event horizon beyond which nothing known to physics can escape, an event horizon which could not even be observed. Within a black hole, time could be unidirectional, because at least one dimension would have to be bent in such a way if nothing were to escape. In fact, such a black hole would even have its own speed limit, the limit below which nothing could escape, which would explain the limitation on light. If photons could move faster, they would escape the horizon, and we would not observe them. In fact, even the possible scenarios by which the universe could end resemble those of a black hole, we could grow so large that we dissipate, we could collapse in on ourselves, or we could reach a steady state.

Of course, the problem with that theory is that spacetime itself would be defined by how the singularity (the big bang) bent the larger 11 dimensional topology, and by definition we cannot know what said topology would have resembled, because we are cut off from it, and thus as far as the laws of physics are concerned, our universe is the universe for all intents and purposes for all points in spacetime covered by this black hole. It would mean that there would be, by the very definition of our universe, information which could not be known (what lay beyond the event horizon).

Holy **** - Did I just informally prove Goedel right?

If proving the ocnjecture allows space tro be explained in terms of geometry, the addition of time will allow the explanation of how things change. I thikn that is kind of fundamental.

The errie thing is that it is a little reminiscent of Kepllers theory of "perfect solids". Maybe Keplers dead- end was not so far off track afterall.

I hope the fellow who solved this decides to reappear. It would give me warm fuzzies to know that he was rewarded for what had to be some very difficult work.


ME :D

A 'stub' to return to soon ... the three dimensions of our Universe are of 3,4 and 13 ...more to follow...

..:-)...

sb.

It's not that space and time are functions of each other, they are actually the same thing.

Hyper where were you two weeks ago when I was in chat? :rolleyes: They thought I was making up the fact that without space there would be no time because they are the same thing? They thought I was making it up!

Wrong section perhaps for me probably should keep my time asyc. my mind seems to work better that way!



Hehehe, yeah, apparently 3-D space is actually fairly hard to comprehend...there's a part of me that thinks that much of the difficulties in the Standard Model (particle physics) and the various quantum oddities arise specifically because they're using three dimensional math to describe four dimensional behavior (not that I'm going to try to describe the Standard Model in four dimensions, I think I'd go crazy trying).

Going crazy can I watch? ;)

Most excellent point going on here! The three dimensional describing the four well perhaps the going crazy thing too I have trouble with the more abstracts of mathematical stuff but I figured that is attributing to my lack of formal education in that area (okay in general )





Within a black hole, time could be unidirectional, because at least one dimension would have to be bent in such a way if nothing were to escape.

sdrawkcab = mirror image which one is which :confused: (equal vs. opposite ~ dark vs. light) up + down = Anti-time!

“No Hair Theorem.” - guess once in a black hole weather or not one has hair doesn't matter!


Hawkins looking glass (http://encarta.msn.com/encyclopedia_761556019/Stephen_Hawking.html)

***Source Quote
Since 1974 Hawking has studied the behavior of matter in the immediate vicinity of a black hole from a theoretical basis in quantum mechanics. Quantum mechanics is a theory that describes how subatomic particles behave and how matter and radiation interact. He found, to his initial surprise, that black holes—from which nothing was supposed to be able to escape—could emit thermal radiation, or heat***End Source Quote

:eek: Late great wtffry moment . . . . .this ain’t supposed to be happening quick Robin back to the theorymobile!

Source quote conti***
Several explanations for this phenomenon were proposed, including one involving the creation of virtual particles . . . . . .Empty space is full of virtual particles fleetingly “created” out of nothing, forming a particle and antiparticle pair that immediately destroy each other.***End Source Quote

Saves time . . . . . . . :faint:

Then we have the uncertainty theory = which is where I spend most of my time uncertain but I don't think that is what they mean.

is we can never be certain but we sure try . . . no that isn't it either.

Oh yea some thing about we can't really be certain where a particle is!

Encyclopedia meaning~ impossible to measure both the position and energy of a particle precisely. (Close enough to all three)


***Source QuoteHawking proposed that when a particle pair is created near a black hole, one half of the pair might disappear into the black hole, leaving the other half to radiate away from the black hole. To a distant observer, the radiation of the leftover particle would appear as thermal radiation . . . . . ***End Source Quote

Half of space enters a black hole the other half stays here. Two kids twins time and aint~dividing jelly beans that ain’t there. . . . . one for you , one for me, one for you, one for me!

***All underlining in sources mine!


Holy **** - Did I just informally prove Goedel right?

Hehehe ! I have those holy **** moments in here every once in a while! Normally mine are holy **** I think I have a clue what they are talking about, normally just enough of one to create choas, confusion and uncertainity! (mostly my own, but I do share)Think we could get them to re-name this section “Holy sh*t ADD” :p

Think we could get them to re-name this section “Holy sh*t ADD” :pNo, but I think we could always name it "A thousand monkeys at a thousand typewriters"

... could only make 1000 novel works of Shakespearian majesty if the realm of possibility were finite.
An infinite number of possibilities would noT permit us to regenerate Shakespeare - our Universe (as conjured by our minds) is structured.

So highly structured that random cannot be encapsulated.

3,4,13.

... :-) ... sb.

The mind must have some constraints - its underlying structure exposes those 'shortcomings'.

From the out ward universe to inward universe . . . . . . . or is it all the same . . . . .the same but different?

my highlights below.

time
http://searchsmb.techtarget.com/sDefinition/0,290660,sid44_gci552553,00.html

Isaac Newton believed that time is continuous, and that it flows at an unchanging rate everywhere in the universe. This was accepted by most scientists until the Michelson-Morley experiment around the end of the 19th century, from which it was discovered that the speed of light is the same regardless of the direction of propagation, and regardless of the motion of the source. Albert Einstein considered this result an axiom, from which he derived the special and general theories of relativity. According to relativistic physics, the rate at which time passes depends on the relative motion between observers, and also on the strength of a gravitational or acceleration field.

space
http://whatis.techtarget.com/definition/0,289893,sid9_gci962691,00.html
In mathematics, space is an unbounded continuum (unbroken set of points) in which exactly three numerical coordinates are necessary to uniquely define the location of any particular point. It is sometimes called 3-space because it contains three distance dimensions. If a continuum requires fewer or more than three coordinates (dimensions) to uniquely define the location of a point, that continuum is sometimes called n-space or n-dimensional space, where n is the number of dimensions. Thus, for example, a line constitutes 1-space and a plane constitutes 2-space. When time (http://searchsmb.techtarget.com/sDefinition/0,,sid44_gci552553,00.html) is considered as a dimension along with the usual three in conventional space, the result is sometimes called 4-space, 4-dimensional space, time-space, or space-time.

a comparison
http://www.bun.kyoto-u.ac.jp/~suchii/comparison.html
<B>
Newtonian Space-and-time, Neo-Newtonian Spacetime, and Spacetime of Special Relativity
<HR>

<TABLE height=421 width="95%" align=center border=1><TBODY><TR><TD width="19%">�@</TD><TD width="16%" bgColor=#ccffff>Newtonian space-and-time
</TD><TD width="34%" bgColor=#ffffcc>Neo-Newtonian spacetime
</TD><TD width="31%" bgColor=#ccffcc>

Minkowski spacetime (special relativity)

</TD></TR><TR><TD width="19%">absolute temporal separation
</TD><TD width="16%" bgColor=#ccffff>OK
</TD><TD width="34%" bgColor=#ffffcc>OK
</TD><TD width="31%" bgColor=#ccffcc>NO
</TD></TR><TR><TD width="19%">absolute spatial position
</TD><TD width="16%" bgColor=#ccffff>OK
</TD><TD width="34%" bgColor=#ffffcc>NO
</TD><TD width="31%" bgColor=#ccffcc>NO
</TD></TR><TR><TD width="19%">absolute velocity
</TD><TD width="16%" bgColor=#ccffff>OK
</TD><TD width="34%" bgColor=#ffffcc>NO
</TD><TD width="31%" bgColor=#ccffcc>NO, except for the velocity of light
</TD></TR><TR><TD width="19%">absolute acceleration
</TD><TD width="16%" bgColor=#ccffff>OK
</TD><TD width="34%" bgColor=#ffffcc>OK, if "inertial" motion is introduced (by definition)
</TD><TD width="31%" bgColor=#ccffcc>OK in the sense that noninertial motion can be distinguished; and if an inertial frame is chosen, the magnitude of acceleration can be defined as an invariant quantity.

But otherwise absolute magnitude of acceleration is meaningless except for zero.


</TD></TR></TBODY></TABLE>Added March 23, 2001: The preceding comparison needs supplement; John Earman (World Enough and Space-Time, 1989, ch. 2) pointed out six kinds of classical space-time:


Machian space-time, which assumes absolute simulataneity and a Euclidean metric structure for each instantaneous space (i.e. a slice of space-time at an instant), and in which a relative distance between two particles is invariant.
Leibnizian space-time, which adds time metric to Machian space-time, and consequently relative velocities and accelerations also become invariant.
Maxwellian space-time, which adds a standard of rotation to Leibnizian space-time; that is, you choose a rigid frame and declares that this is nonrotating. This makes the difference between linear motion and rotation, and rotation of an extended body becomes invariant, although acceleration in general of a body is not meaningful.
Neo-Newtonian or Galilean space-time (now familiar to you), which is obtained by adding inertial structure to Maxwellian space-time, and acceleration becomes invariant.
Full Newtonian space-time, which assumes absolute space in addition to Neo-Newtonian space-time. Thus velocity also becomes invariant.
Aristotelian space-time further assumes a single spatial origin (see Aristotelian Space (http://www.bun.kyoto-u.ac.jp/~suchii/arist.space.html)) , so that a distance from the origin (i.e. the center of the universe) becomes invariant. However, in this context you have to ignore both the "natural" difference between celestial region and sublunar region, and the finiteness of the universe, contrary to Aristotle's own assertion! Earman's idea is a "modernized Aristotelian view", for limited use only.
In any case, this finer distinction throws some good light on the classical debates on relationism-absolutism of space and time. </B>

Carl Sagan was on the Science channel last night. "Atoms and their components, the neutron, the proton, and electrons are the smallest components that exist." Hopefully, everyone knows that science has made a lot of progress since then...


SpacetimeFrom Wikipedia, the free encyclopediaJump to: navigation, searchFor other uses of this term, see Spacetime (disambiguation).
In physics, spacetime is a mathematical model that combines three-dimensional space and one-dimensional time into a single construct called the space-time continuum, in which time plays the role of the 4th dimension.
According to Euclidean space perception, our universe has three dimensions of space, and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a good deal of physical theory, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.
In classical mechanics, spacetime is a mere formal option, but in special relativity, space and time are inseparable. The notion of space depends on the observer, as instantaneous events depend on a reference frame.
Spacetime is also vital to general relativity, an extension of special relativity that takes gravitation into account.
How many dimensions are needed to describe the universe is still an open question. Speculative theories (such as string theory) predict from 10 to 26 dimensions, but all dimensions other than the usual 4 (3 spatial and 1 temporal) matter only at subatomic scales.

Carl Sagan was on the Science channel last night. "Atoms and their components, the neutron, the proton, and electrons are the smallest components that exist." Hopefully, everyone knows that science has made a lot of progress since then...

Yeah, I saw that too. Makes me wish Sagan could be alive today (or in a few years, I guess) to see the LHC go online. I kinda wondered why they didn't add in a little segment on quarks, gluons, and quantum chromodynamics, sort of like how they add in newer graphics for some of the cosmological stuff. By the way, please tell me that those weren't the real elements in that table that he was using. I can't imagine that they'd put actual Uranium on there, but he was picking it up with a set of tongs...

There is no such thing as + or -
+ and - are artefacts of a geometry representing statistically probable +/- in proximity.
+/+ and -/- are essentially the same statistically improbable event.

Generalizing further - the concept of + and - can be derived from the simplest thing imaginable ...

_ (stored energy)
represent _ as - o -
imagine motion ...

random examples ...
- o -.....\ /...........o <
............o.................

- / \ <(both halves) ->- should be the same length ... ... ...

... however
o -
ie where
- o -
is highly improbable as
- and -
will occupy the same space ...

so - ->- - o - ->- negative o negative ->- - o - ->- -+-

...the fundamental -+- is a statistical property.
-+- is both the fundamental particle and also the fundamental component of logic ... 'logic has a shape' {see ADDF thread::evolutionary psychology}


~actually a paraphrase~
logic is fundamental to the all (nature) of our uuu?UUU?niverse

... time (rooting), sausages (vegetarian) (geometries) and 3,4,13 (evolution understood as a repeating pattern of superstructure built upon and copying the same basic fundamental shape - evolution as motion to complexity - complexity as potential energy stored (information content)) next ...

... home straight??? ...:-)... or is it?
... one never does know
... not around these parts?

SB.

From the out ward universe to inward universe . . . . . . . or is it all the same . . . . .the same but different?
...evolution understood as a repeating pattern of superstructure built upon and copying the same basic fundamental shape.
...evolution as a Universal rule - not restricted to just lil'ole' life... ... ...

sb.

ooo!
time is an artefact of a rooted structure mixed with a statistical distribution.
And the fundamental particle is a vegetarian sausage.
yupsy - time is a dimension ... ... ...

Wonder whether it can cook itself without the use of a timer???

SB.

time is an artefact of a rooted structure mixed with a statistical distribution.
And the fundamental particle is a vegetarian sausage.
yupsy - time is a dimension ... ... ...

Dimension . . . .Hmm I have always wondered the same thing about time that most do about a tree falling in the forest. If no one or nothing there to observe it does time really continue to exist . . . . . .



Wonder whether it can cook itself without the use of a timer???

Hmmmmm good question I know I shouldn’t attempt this my self!

~Thanks Tams!~
..~ *~. . . ~ *~
... . . ~ *~

Are we there yet???
One never knows ...
...not around these parts ...

..........CHAOS::EMERGENCE {solution}
(two sides of the same sausage {vegetarian})

Gert (http://www.mountainman.com.au/chaos_03.htm) Eilenberger, German physicist - who took up nonlinear science after specializing in superconductivity: "... Our feeling for beauty is inspired by the harmonious arrangement of order and disorder as it occurs in natural objects - in clouds, trees, mountain ranges, or snow crystals."

Guacamole (http://www.addforums.com/forums/showpost.php?p=329250&postcount=573) Kebab, ADDF member:"And what exactly are the properties up there on the crown of a tree - or the canopy of a rain forest? Maximal transduction of solar energy to mass ... high oxygen yields ... ... ... Maximal complexity - and 'beauty' ... ... ..."

Tams (http://www.addforums.com/forums/image.php?u=1891&dateline=1156637977) 823-phD(s) (permanent head damage after investigating the mental properties of Speedo avatar emulation ...:-)...), ADDF modium:
""""""""
"http://www.addforums.com/forums/image.php?u=1891&dateline=1156637977
George (http://hincapie.psych.purdue.edu/) 'googoo' Hollich, Infant Language Lab director:
"--> (http://hincapie.psych.purdue.edu/PDP_Primer/NChaos.html)Chaotic nature of Creativity::
---Neural Networks and Chaos theory::
-Two of the hottest words in psychology today are ... and Chaos.
---Chaos Theory::
-Complexity fills our world. From trees to crystals ... {eg snow}
---Chaotic nature of creativity::
... nature's inventiveness never fails to surprise. We can find no identical snowflakes ... indeed, it seems nature constantly evolves and reinvents itself anew each day. One might even conclude that nature exibits its own brand of creativity ...

Kevin (http://www.addforums.com/forums/showpost.php?p=327422&postcount=532) Sausage, ADDF member:
""""""""""""""""""""""""""""""""""""
""http://i79.photobucket.com/albums/j132/sb_camsci/Y_fundamental-benzene-IgX-virus_Y.jpg
Father (http://en.wikipedia.org/wiki/Father_Christmas) Christmas, beardy benefactor: "yay! ; It's Christmas!" :

""""""""""""""""""""""""""""""""""""""""""""""""""""""
"http://webdeveloper.com/animations/holiday/christmas/gifs/snow.gifhttp://webdeveloper.com/animations/holiday/christmas/gifs/snow.gifhttp://webdeveloper.com/animations/holiday/christmas/gifs/snow.gifhttp://webdeveloper.com/animations/holiday/christmas/gifs/snow.gif


... :-) ... SB. ...:-)...

...evolution as a Universal rule* - not restricted to just lil'ole' life** ... ... ... {from above}
*,** *Extremely important*

...evolution as a Universal rule* - not restricted to just lil'ole' life** ... ... ... {from above}
*,** *Extremely important*

Our evolution is in the hands of the same property which defines each snow flake as different --- and not in the hands of Bob {for short} (Boss of beardy bloke).

SB.

'Life (http://bepi1949.altervista.org/adams/adams.html), the Universe (http://bepi1949.altervista.org/adams/adams.html) and Everything (http://bepi1949.altervista.org/adams/adams.html)'
... solved ...:-)...
... sufficiently ...
...to allow it to continue... but ***insufficiently***
...to allow it to shut up shop...

We now know we will never know
... c-o-o-l ...!...!...!...
:-)
... yay! and It's Christmas!!! ... total b-o-n-u-s ...!...!...!...

Hey Cray!
Can you work with this guy?

http://bepi1949.altervista.org/images/panic.jpg

...:-)... SB.

~my attempt~
hmmm ... ... ...

.!.!.!...:-)~ ....!.!.!.
... DON'T PANIC! ...

Post#001300

SB.
...:-)...

the numbers...
...it's in the numbers...
the Golden ratio (http://mathworld.wolfram.com/GoldenRatio.html),
Fibonacci (http://mathworld.wolfram.com/FibonacciNumber.html) series,
and realm of the 'Complex (http://mathworld.wolfram.com/ComplexNumber.html)' ... ... ...
....to...name...but...a...few... ... ... ...

...3...4...13...
Sausages (http://mathworld.wolfram.com/SausageConjecture.html) {vegetarian}

I believe that Perelman withdrew from the academic mainstream because of his inability to tease apart rrr{eality} from RRR{eality} ... tell ya' though - best not to try!

Ooo can I call that the 'big' con jecture ... ... ...?...

He wouldn't have been able to pick up the medal - if he believed his work here not to be done ... silly Perelman - your work could get mankind out of all sorts of Perilman ... mandude ... 'choose life' ... you rock ... dudeman!!! ... ... ...

... :-) ... SB.

Actually - I wonder whether he just couldn't bear time away from his pad of paper ...
Woody Allen and Oscars ... Greg Pearlman and Fields ... ADDers either do not turn up ... or are late ... ... ... {for a very important date}'

' so we're told - except -- ADDers don't do important ...

~you see~

... we're on a rock in the middle of nowhere ...

and about all that's going for us

~is that~

... it's a pretty rock ...

Perel
man.

Peril
man.

ADDF thread:: (http://www.addforums.com/forums/showthread.php?t=31836)Poincaré #22 (http://showpost.php?p=329636&postcount=22)

...evolution (3,4,13) (switch between kinetic energy[E in E=mc"] and potential energy[m in E=mc"]) as a Universal rule - not restricted to just lil'ole' life... ... ...

ADDF thread:: (http://www.addforums.com/forums/showthread.php?t=28559)Evolutionary Psychology #576 (http://www.addforums.com/forums/showpost.php?p=329805&postcount=576)

~and c~ ... :-) ... How about?' the basis of time, c defined by the statistical distribution introduced in ADDF thread:: (http://www.addforums.com/forums/showthread.php?t=31836)Poincaré #21 ... :-) ...

SB.

' ??? wtf[fry]

#13 03
probability distribution ->- time and speed of light

time and speed of light ->- derive from the same physical property
'verb'

geometric topologies ->- derive from the same physical property
the fundamental particle call it ->->- _ (http://www.helloIamthefundamentalparticle.bigbang) -<-<- ...:-)...
'noun'

ytf(fry){sausages}[vegetarian]?

::Note::
noun:PE
verb:KE

#13 04
Does the speed of light slow down as time slows down?

...:-)...
...:-)...SB.
...:-)...SB....:-)...

-c-o-o-l- ...!...!...!...

::Note::
PE
potential energy
KE
kinetic energy

Hey Ergie!
Gert (http://www.mountainman.com.au/chaos_03.htm) Eilenberger, German physicist - who took up nonlinear science after specializing in superconductivity ... But why did he do that? - was he unhappy?
~or perhaps ...?... just maybe ...

superconductivity ->- absolute zero [cold] ->- fundamental particle [all m no E in E=mc" ->- _ ->- through emergence _ becomes more than _ ->- through 3,4,13 emergent evolution _ (Y) ... builds into superstructures ->- emergent evolution leads to entities with new properties - with highly structured 'chaotic' patterns ->- nonlinear (http://chaos.aip.org/chaos/staff.jsp) science (http://www.Chaos_Journal_of_the-AmericanInstitute_of_Physics_devoted_to_NonlinearP henomena.CLICK_nonlinear)

SB.

hello ... :-) ...

Poincaré had a very close relative (cousin, I think) who was also a
Poincaré - who became the President of France.
1 in 3 Frenchmen think it was the same guy.

OK - so I only asked 3 Frenchmen ... but what the heck!

SB.

We'll never know -
... but on the basis of the rather *excellent* Wiki (http://en.wikipedia.org/wiki/Henri_Poincar%C3%A9)-Poincaré write-up ...
I have never been more certain of an individual's status as an ADDer.

Poincaré *is* the definitive academic ADDer
... have a look at WikiWacky(Jabber)Wocky - and you'll see what I mean ... ... ... Julie Henrietta Poincarrierbag was an ADDer ... ... ... honest!

SB.

wicked!

...:-)... and *thanks* Ian - I've a new favourite French scientist from the 20th century specializing in theoretical mathematical physics ... ... ... hmmm!!! ... {don't ask!}

Poincaré *is* the definitive academic ADDer And I get it...his attitude.
I bet it was hard for him to release this theory only to be scrutinized by idiots.
He already explained it once so everyone else has to catch up - or not.
He'll respond when someone takes it further or perhaps finds a flaw.
He doesn't need the general scientific community's opion for affirmation.
I wonder who he might have respect for...
I wonder if these results have become obvious to him...
I wonder if he reads this forum and will come back and tell me to go pound sand...

#13 03 call it ->->- _ (http://www.helloIamthefundamentalparticle.bigbang) -<-<- ~or~ at the other end

call it ->->- string -<-<-

sb.

but but but....Time is an illusion to help us gauge the passing of events. Does the speed of light slow down as time slows down? Relativity. If I'm moving along at the speed of light, then light is standing still relative to me. There is no RRReality to time. Time dilation. It falls into the mundane calculation frenzy to facilitate stuff in that old box.
The big step here is that some tedious calculations further verify the past and predict the future.
Just as good as throwing that dart - random walk?
Time and the speed of light describe frequencies.
So string theory falls into just being a more sophisticated way of describing/calculating some rrreality, not RRReality.
RRReality is NOW and the alignment between points at a given time = 0.
This alignment is what facilitates sentience - percieving what IS at the points of alignment.
ying yang biorythms...
Garçon! Sangiovese for everyone...

http://upload.wikimedia.org/wikipedia/commons/9/97/JdlV_osc_15.144.gif (http://en.wikipedia.org/wiki/Image:JdlV_osc_15.144.gif)
I just don't know...

*~*Time is an illusion to help us gauge the passing of events. Relativity. *~*

*~* If I'm moving along at the speed of light, then light is standing still relative to me. There is no RRReality to time. Time dilation. *~*

*~* Time and the speed of light describe frequencies. *~*

*~* So string theory falls into just being a more sophisticated way of describing/calculating some rrreality, not RRReality.*~*

*~* RRReality is NOW and the alignment between points at a given time = 0.
This alignment is what facilitates sentience - percieving what IS at the points of alignment. *~**~*
What if that fundamental particle is both noun and verb?
So ... time is required in order for events to pass - 'time' for man is a surrogate for this other fundamental 'time' ... ... ... for us (ADDers) ... for sure ... 'time is an illusion ... {what you said}'
*~*

*~*
If the fundamental particle which defines {(ugh!!!) --- OK} TTTime (external true objective time) not tttime (our own internal perception of time) ... both makes up the 'free particles {actually waves e.g. solar energy}' [KE rich] and us (too) 'bound waves {particles}' [PE rich] ... we are the results of the (eventually {that is} several stages up the pattern ?stage VII? from N) first movement in evolution away from the pattern ... ... ...
:: Stage I ::
1(wave) ->- [3,4,13[1']]
:: Stage II::
1'(*not* wave) ->- [3,4,13[1']]
If we're moving at the speed of light - the oscillation of the fundamental particles trapped within us will be resonating identically with waves Stage I-1. Time will slow. rrr and RRR merge. Mass increase.
So TTTime{c too???} and RRReality are inseparable???
*~*

*~*
... describe frequencies of oscillation of this fundamental particle ... ie _ ->- Y
... the Y is the fundamental and it forms into its perfect superstructure (at the other end) - a perfect superstructure - which is a manifold with surfaces which string theorists call 'branes'.
I believe {from my education on ADDF) - that branes collided resulting in ->- the 'Big Bang'.
This idea may be generalized back down to the fundamental particle.
From above - this is kinda' what I'm getting at in post # 21
->->->-
... however
o -
ie where
- o -
is highly improbable as
- and -
will occupy the same space ...
->->->- ->->->- ->->->- big bang.
I guess I'm sayin' that ...
... the pure superstructure formed from the fundamental particle - which gave rise to the Universe - gave rise to the Universe (the big bang) - when a statistically improbable event occurred - that is - in effect the + and - sat at exactly the same point in space.
freakin' ADDer thought
->- this is the basis underlying emergence
--- it's just that emergence (ordinarily) - does not involve such large superstructures (by ordinarily - I'm talkin' in the rrreality which we inhabit) ... in a way - emergence (dependent on the stage of evolution) - involves 'bangs' ...:-)... of varying sizes ... big, medium, little ... ... ...
*~*

*~*
... a more sophisticated way of describing rrr and RRR ... ... ... maybe ... but if it gets us closer - cool! ... I just wonder whether it gets us closer than is immediately obvious ... ... ... any chance that anybody'd like to help me derive c {1,079,252,848.8 km/h} {in a vacuum} {not cleaner}.
*~*

*~*
rrreality is NOW ... if NOW exists within tttime
... NOW can exist within TTTime {too} -
if TTTime could reduce to zero - this wouldn't be true ... I think NOW requires some passage of some notional construct which has the properties of 'time' ... ... ...
TTTime can slow (but not to zero - close (very close) (I think) - but to zero - (?no?))
- strong alignment to the idea of absolute zero - k{el}v(in} - I know {sorry!}
... which ?cannot be reached?
... and to the idea of superconductivity ... {from above (Gerty)} ... ... ...
[quote]
"...RRReality is NOW and the alignment between points at a given time = 0."
I think so - RRReality cannot end.
... ... ... rrreality {on the other hand} *will* end {for us all} ... unless we all {the planet's subsp. sapiens population ... buys into speciation into sp. neosapiens {aka ADDer}}*
*~*

SB.

*deadly serious.

Time is an illusion to help us gauge the passing of events.

Okay but if time was merely an illusion would every cell in my body be fooled?(considering their short attention span and all)

In my mind :
Time is relative not absolute!


Time is motion which takes space to accomplish. Time isn’t part of dimension it is the other way around dimension is time dependent! Dimension has to have space and time to exist???! Some thing like that now I am confusing myself again darn :eyebrow: .

Oh wow - we are scaring me...
fundamental particle is both noun and verb? this is the duality of light. Can one exist without the other?

Now Randy hasn't participated in any of this [ and he would kick my *** if he knew how much time I spent here... ] and I posed this question to him:
Would you get more sun if you're moving or if you're standing still?

As a noun, I'd say more when you're moving - you happen to be contacting more particles.
As a verb, it doesn't matter because it's continuous. Which was Randy's off-the-cuff response (no math or science education).
[ I get stuck on this broken waves/frequencies. They would all have to be synchronized to your rate of movement for it to be continous? not today. it's too much. for me. I've been crying for a couple of hours now. Plus son#3 is sad about losing his girl and he's playing R. Kelly 'If I could turn back the hands of time' and then that interview with God and then that revelation sparked by DB Coop and Nova...and these posts ]
wahhhhhhhhhhhhhhh. little creatures touching resonating chords... [ throat = chord ]

If we're moving at the speed of light - the oscillation of the fundamental particles trapped within us will be resonating identically with waves Stage I-1. Time will slow. rrr and RRR merge. Mass increase.
So TTTime{c too???} and RRReality are inseparable???
Mass reaches infinity. Does TTTime legitimize RRReality?
But the speed of light. Which light? Any light? Our sun's light - which ties us to this galaxy.
Isn't the distance of the stars calculated relative to the speed of light?
What if the speed of light is different somewhere else?
Would the calculations we know be pertinent there?
Relativity to our frame of reference.
"can't think - brain dumb - inspiration won't come"
Maybe it's a coincidence that light exhibits this duality and somewhere else the duality would be with something else. Like no light, just sound. Science fiction. An ADDer may know things but knows it won't be taken seriously and so disguises it as sci-fi?

Tammy: Time is relative not absolute!


Time is motion which takes space to accomplish. Time isn’t part of dimension it is the other way around dimension is time dependent! Dimension has to have space and time to exist???! yes, but not to exist - to be described. Man, I feel like scrambled eggs.

This is a lot of what Elkhart Tolle's book is about.
If there were nothing but silence, you wouldn't know what it is. Only when sound appears does it come into being. this is your tree falling and the cat in the box. schroedinger's.
What we percieve externally as space and time are ultimately illusory, but they contain a core of truth. They are the two essential attributes of God, infinity and eternity.
So Being is having presense and awareness of the now. Presence being pure consciousness.
The mind is a logical structure (navigating and extrapolating memory) facilitated by the physical structure (neurons and company) which requires time to exist. And we need to use it for day to day living. But to not think and to just Be your part of everything. This is what he calls enlightenment.
If you remain in conscious connection to the unmanifested then we value, love and respect the manifested and every life within it as an expression of the one life beyond form. wonderful stuff.
He also has great advice and how to get rid of pain. accept it, change it or walk away. no dwelling allowed.
He quotes Buddha, Jesus, Rumi, and uses Zen, Chi and Karma and more.

I've gone back and forth in this email adding and removing and then it timed out and some stuff was lost and I couldn't tell you what it was right now....

gotta go watch son#3 and football....

It's a good thing we are all not verbose....

I love this guy (http://www.imanet.org/technotes/stnewsb.asp).

The whole "step away from the rat race" stance is so... apropos.
Ray Vaughn

http://www.tufts.edu/programs/bend/research/images/ratplus.jpg (http://www.tufts.edu/programs/bend/research/ratmaze2.htm)

snakes and rats ...:-)...

... you're reinventing Chinese astrology ...

... I'm a {cheeky} monkey ...

SB.

... Thanks Ian ...

The seven (http://en.wikipedia.org/wiki/User:Mpatel/sandbox/Clay_Mathematics_Institute) Millennium Prize problems are:

P versus NP
The Hodge conjecture
The Poincaré conjecture
The Riemann hypothesis
Yang-Mills existence and mass gap
Navier-Stokes existence and smoothness
The Birch and Swinnerton-Dyer conjecture


... these guys all relate to manifolds, recursion and supersets{superstructures} ...

SB.

I guess folding the donut in half and eating it and shooting the rubber band across the room at a loved one was not part of the equation. . . . .I see the rubber band apple shrinkage thing in my head but when I think of the donut I think of folding it in half -gotta get rid of the hole- . . . .that as far it goes then I think eating it (that gets rid of the hole tooo) with some coffee beverage, not hungry for rubber bands though! Probabaly why geometry was not my string suite. . . . .right before lunch!

Form Ian's source . . . .

Ball said he was not at liberty to disclose those incidents, but he did add, “He has a different psychological makeup, which makes him see life differently.”
(end quoet)


Part of a post that I never posted. . . . trying to be good . . . . refrain from inciting riots . . . . .overt objections . . . . .you know ADD stuff that happens by accident because (who knows why –some people just can’t handle it -shrug)


“The Executive Brain”
Elkhonon Goldberg (forwarded by Oliver Sacks)
Page 180

Our culture traditionally approaches neurological disorder as a deficit a loss. This is reflected in our terminology: aphasia – loss of language; amnesia loss of memory. Hypermnesia and hyperverbality, when they occur are viewed by society as a mnemonic or literary gift, not as a pathology. But if the norm is defined as the population average, then talent is by definition a deviation from the norm. The relationship between talent and psychopathy has intrigued and beguiled both clinicians and those afflicted (or blessed)

It is common to distinguish in neurological and neuropsychological conditions between “negative” and “positive” symptoms. Negative symptoms reflect the loss of some thing that should normally be present, such as the ability to walk, talk, and see things. Positive symptoms reflect the presence of some thing that is not part of normal cognition, such as hallucinations or tics. Negative symptoms are more readily comprehensible, easier to conceptualize, measure quantify and subject to rigorous scientific examination. Positive symptoms are usually more elusive more mysterious but also more intriguing and challenging. They hint at an inner world that is different and not merely impoverished – at the presence of a neurological condition which not only robs but also endows.
(end quote)

~Under lining and bold mine~

To simply look at the negative while ignoring the positive was once seen by me as non-productive my opinion has now been upgraded to taking the easy way out of studying (or having) neurological diversities.

Oops to far . . . . .

Maybe this Perelman is simply high functioning "neuro diverse" like some of us which is how he figured it out . . . but also why he is "strange" maybe most people suck as far as he is concerned . . . .High functioning Autisics are supposed to be good at that sort of thing -math goemetry- progrming - not people - social -lites ya know . . . . - and the ones I know of are really good at patterns, puzzles, but different types of patterns than dyslexics tend to be good with. . . . hard to explain . . . .still having weird brain day- maybe because it is night!

Think I will crash for the night!

I may need the mighty Cray to assist me on the next point ... ... ...
ADDers don't do photographs (appearance within).
Don't do smiles on request.
Only smile if happy.
ADDers don't do pictures.
Look vaguely uncomfortable ... stiff ... with the obvious thought 'please let this be over' echoing around their voluminous brains ... ... ...

... .... ... wait a minute ... ... ...
if I am not mistaken ... I may just have delivered the perfect description of this cheeky chappy --- but who is this mysterious mathematical genius?

http://upload.wikimedia.org/wikipedia/en/b/b1/Grigori_Perelman.jpg

... oh! and look to the eyes ... :-) ... he isn't present here - he's looking straight through the camera into his mind ...

G. Perelman {photograph above courtesy of WikiP}

SB.

...ps... did I mention that all ADDers have beards -<- joke {honest Tams}

This guy ain't pretend --- we're seeing him straight up in this picture ... ... ... His world is purely abstract - he sees no need for anything which does not add to the beauty of his inner realm.

... when I think of the donut - I think of folding it in half
-gotta get rid of the hole-
. . . .then I think eating it (that gets rid of the hole tooo) That may well be it ... really sounds like it.
Look at some of these shapes - and they're kinda' like a hexagon with a hole - where the hole has been stabilized.
It looks as though - the hole is necessitated by the structure of the fundamental - but the emergent structure fails unless the hole is stabilized.

Also - the hole may be filled by another emergent structure - but that structure has the same problem - kinda' like just shifting the problem down a layer of abstraction.

Need a picture ... I'm talking ...
<()> where <> is akin to the 6 membered ring of benzene ... 3,4,13 ... and a solution might be ...<(<()>)>... level II in evolution {3,4,13} ... Stabile described the mind harbouring 'black holes' ... I think that this is what T and K meant ... ... ...

Black holes of mind

Black hole and Stabile 'search' ... kicks off here ... ADDF thread::NLP #25 (http://www.addforums.com/forums/showpost.php?p=106954&postcount=25) ... and progresses on in that thread.

Silly Boy beseeches metaminds ... black holes of mind .... 'feed me' ...
... ADDF thread::Amen #192 (http://www.addforums.com/forums/showpost.php?p=133819&postcount=192)

Why?
Because the black hole {of mind} can be made sense of now - especialy when we factor in our discussions of virus from ADDF thread:: (http://www.addforums.com/forums/showthread.php?t=28559)Evol Psych ... ... ...

Because we're ever so close to working out the linkage between logical structure, logical structure of virus, logical structure of mind

Because - if we can arrive at a solid proof for 'logical structure of mind' --- then we're nearly there ... where??? though ... ... that'd be ...

'there on the stairs' ' right there' 'a little mouse with clogs on' 'well I despair' 'going clip clippety clop on the stairs' 'where?' 'right there' 'right there?' 'right there!!!'

SB.

... and the answer's gonna be something kinda' like a logical structure with properties kinda' like DNA in a virus --- replication, survival, mutation ... ... ... the selfish logical structure???

And ... ... ... looking up at the stars ...


Structure formation (http://en.wikipedia.org/wiki/Structure_formation) refers to a fundamental problem in physical cosmology.

Observations suggest that structure formation (http://en.wikipedia.org/wiki/Dark_matter#Structure_formation) in the universe proceeds hierarchically, with the smallest structures collapsing first and followed by galaxies and then clusters of galaxies.

Physical cosmology, as a branch of astrophysics, is the study of the large-scale structure (http://en.wikipedia.org/wiki/Physical_cosmology) of the universe and is concerned with fundamental questions about its formation (http://en.wikipedia.org/wiki/Physical_cosmology) and evolution.

Understanding the formation and evolution of the largest and earliest structures (ie, quasars, galaxies, clusters and superclusters) is one of the largest efforts in cosmology. Cosmologists study a model of hierarchical structure formation (http://en.wikipedia.org/wiki/Physical_cosmology#Formation_and_evolution_of_larg e-scale_structure) in which structures form from the bottom up, with smaller objects forming first, while the largest objects, such as superclusters, are still assembling.

sb.

Then virial (http://en.wikipedia.org/wiki/Virial#The_virial_theorem) theorem
The expression "virial" derives from vis,viris, the Latin word for "force" or "energy"....to...

{* (http://66.249.93.104/search?q=cache:dzmcmEX8st8J:media.wiley.com/product_data/excerpt/99/35273136/3527313699.pdf+virial+viral&hl=en&ct=clnk&cd=5)} <-<-<- ooo! the pain! from * (http://media.wiley.com/product_data/excerpt/99/35273136/3527313699.pdf)
virial meets viral ... meets DFT meets geometry ... meets stability meets topology
{but the pain ... feel the pain} ... :-) ...

sb.

... and smile whimsically ...

It's all about a simple fundamental which grows and makes a bigger mini-me, makes a bigger mini-me ... the structure formation (http://I_am_a_vegetarian_sausage_and_I_love_guacamole.oop sy) is simply a byproduct of ... ... ...

<()> ->->->-evolution->->->-

->->->-evolution->->->- <(<()>)> ->->->-evolution->->->-

->->->-evolution->->->- <(<(<()>)>)> ->->->-evolution->->->-
->->->-evolution->->->- <(<(<(<()>)>)>)>->->->-evolution->->->- {etc}

sb.

3,4,13{1'}

doughnuts ...
' then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut.'

As Homer once said ... {fridge empty} 'doh!!!' ... {food shelves bare} 'nuts!!!' ... ... ...
'doh nuts' ...
... the fundamental particle kinda' does this ->- <> -<- ... the hole is implicit in every superstructure ... built on every layer of abstraction ... from low to high ... moving up superstructures or supersets ... ... ... the Universal rule of evolution - simply the drive of the < kinetic energy loaded waves {there's no such thing as a free particle, Nova - you so were there, weren't you?} ... particles kick in as emergence occurs <> but ... the hole propagates ... always there ... shielded, but locked away - somewhere safe ... ... ... yupsy Tom and Kay - you got that right ... ... ...

doh!!! nuts!!! Too many bright sparks in this joint ... ... ...

How very ADD!

...:-)...

SB.

Would you get more sun if you're moving or if you're standing still?
... dark matter ...
gets more sun?
stands still?

sb.

... ... ... the Universal rule of evolution - simply the drive of the < kinetic
energy loaded waves {to form} particles ... the original 'emergence' <>
~aside~
The Virial Theorem (http://www.astro.cornell.edu/academics/courses/astro201/vt.htm)
The virial theorem states that, for a stable, self-gravitating, spherical distribution of equal mass objects (stars, galaxies, etc), the total kinetic energy of the objects is equal to minus 1/2 times the total gravitational potential energy. In other words, the potential energy must equal the kinetic energy, within a factor of two.
K.E. = - 1/2 P.E.
~aside~

~ALTERNATIVELY~

< = ?-? 1/2 <>KE wave (E in E = mc'')
PE particle (m in E = mc'')

... why do I always get my protons and my photons backwards?

The Virial Theorem (http://users.pandora.be/nicvroom/virial.htm) is based on two concepts:
The Total Kinetic Energy KE and the Total Potential Energy PE<dt> And the Virial Theorem states that: KE = -0.5 * PE
For more detail go to: http://math.ucr.edu/home/baez/virial.html by John Baez

In fact this documents states: "it (The Virial Theorem) is really the reason we think that dark matter exists." Universal theories rock!

</dt>SB.

<dd>
</dd>

Then we have (http://math.ucr.edu/home/baez/virial.html)

<t>< T >= -< V ><v>/2
<t><v>where</v></t><t> < T > is the time average of the total kinetic energy, and < V > <v>is the time average of the total potential energy. I always found this to be a bit magical. It seems surprising at first that such a simple law could hold so generally. But in fact, it's just a special case of something called the "virial theorem", which also applies to forces other than gravity, and impacts everything from astronomy to the theory of gases.

<t><v><t><v> Universal theories rock!

SB.</v></t></v></t></v></t></v></t>

The promise made some time back was that I'd get back to you when I understood.

I kinda' want to tell you {} and then realised that I think you {} and so - hey!
... stay cool! ... and for chrissake - get a dishwasher!!!

... for the record though there's rrreally - {{{nothing}}} to worry about
:-) ... but you know that ... ... ...... I once mentioned to Wheezie that she wouldn't believe me (about all of this) - heck!!! - might need a hand to wrap this into short form :-) ...

oi vey!!!
what's a girl to do?