Thursday, July 20, 2006

Gold and Fool's Gold

Gold
Perhaps the highest density known is reached in neutron star matter (see neutronium). The singularity at the centre of a black hole, according to general relativity, does not have any volume, so its density is undefined.

The most dense naturally occurring substance on Earth is iridium, at about 22650 kg·m-3.

A table of densities of various substances:


So of course seeing this new posting and the ideas of what the gold nugget "is," is supposed to be here in our thinking is of course. Being clarified in terms of how we look at the LHC, most defintiely. Having expert opinion on this is always important. for sure.

Fool's Gold ?

Who is not without some blemish on the "heart values" when it had been held to a goal like truth, and had gone astray? It just matters that you try, and that you hold this value in front of your eyes, as you progress through life.

I was at a loss for what would describe "this beginning" and having looked at what is attained in the "Pascalian triangle", how could I not learn of the spiral induced numbers that lie at the very heart of such creations.

You have to understand what the basis of what this triangle is based upon. I gave clues here.

Some fractorial mathematical based idea, exposed to the matters, as crystaline objects of perception unfolding? Wolfram?

NPR's Richard Harris reports on the beauty of mathematics

How are some things built, that you would ignore "the mathematics at the basis of experience." Having such a geometrical basis is very important. I may call it "Algebraic equations" of Dirac(Lubos take note:), but it is more then that, and it is in the emergence of strings, that we recognize where the conditions are, as the strings basis? You had to understand "the entropic" as well as the CFT issues from the blackhole state? What are the initial conditions?

If I say microseconds, you should immediately assume it is after the big bang.:)Topological "geometrics" eh? :) is much different, then what we see classically of the 3+1? You remember "Klein's ordering of the geometries," of course? Right?

Gold in the Landscape?

I was looking for a specific posting on "Fool's gold" so I thought of Clifford's at Cosmic Variance and the post he created. A specific comment that I made. No, this does not imply anything against Clifford. :)

Here you might refer to the points between Lubos and Bee, about the "initial conditions?" It's "beyond" the placement of what is held in microseconds, and the arrow of time. What! Before time began?

So where is that? What already existed?

However, don't be fooled! The charm of the golden number tends to attract kooks and the gullible - hence the term "fool's gold". You have to be careful about anything you read about this number. In particular, if you think ancient Greeks ran around in togas philosophizing about the "golden ratio" and calling it "Phi", you're wrong. This number was named Phi after Phidias only in 1914, in a book called _The Curves of Life_ by the artist Theodore Cook. And, it was Cook who first started calling 1.618...the golden ratio. Before him, 0.618... was called the golden ratio! Cook dubbed this number "phi", the lower-case baby brother of Phi.


What a Cosmologist Wants From String theory by David Wand


I mean have tried to instill a good foundational perspective of what happens, and what is percieved, in terms of the joining of microsperspective views in regards to the nature of the cosmo?

So what is not revealled here in "my thinking" although we have been directed to the process of the "collidial views" imparted by expert opinion and further glossed by Q's blog building to face this thinking process? :)




A debate/dialogue is always a good thing to initiate, and I have not be too lucky to have somebody to run against my thinking. It's a relief Q. As you say, "I am looking for truth."

So where I am going to go from here? :) Should I go?

Well science has this thingy about experiment and beyond that, beyond the standard model, what thinking shall I introduce? Something "beyond the 3+1" perhaps? :)

Wednesday, July 19, 2006

Tomatoe Soup is Physical?

Spacetime in String Theory, by Gary Horowitz


Of course, one get's to thnking about where all this theoretical stuff is taking us, and the result of such conclusions become interesting in having consumed the model assumptions? Having Grokked it?

So how did you get "here" in the "mapping and finding of treasure" in recognition of thoughts that manifest and had taken us on ths wild journey?

Very simply we should see that the "fifth dimensional referencing" is based on a legitmate processes used to extend our thinking beyond what it assumes of 3+1. It existed in "other states" before this? Yes/No? :)

So what we have taken for real in our 3+1 now holds our mind in thinking beyond what it has as a "resulting frame of reference?" We do not ignore the science behind such thinking, as it is progressive in terms of the "theoretical stance" we take. Is it right or wrong? Well that remains to be seen.

Will "gravity waves" one day prove to be right/wrong, or shall we ignore them all together?? What have we spent in order to "refer too this thinking" as we see often of string theory? That it is a "waste of time and is fantasy induced" states of realization?

How did you get there to find your treasure trove? :)

Sunday, July 16, 2006

Star Lite Public Outreach



In regards to the QGP(Quark Gluon Plasma) I thought such a creation important from the ideas of what happens in assessing any beginning?



This thought arose from what was revealled in terms of "Microstate blackhole" production and the circumstances from such gold ion collisions.

If we are lead experimentally to such a place, then what may we say of "reductionistic circumstances" and it's relation to the beginning of the universe?



In my GRand Quantum conjecture, such thinking to have established the origins of "quantum perception" along with the understanding of GR and it's curvatures?

Who would of thought such "an application" and ignore what is driving the perspective around blackhole hole creation? It's "microstate properties?"

Andy Strominger:
This was a field theory that lived on a circle, which means it has one spatial dimension and one time dimension. We derived the fact that the quantum states of the black hole could be represented as the quantum states of this one-plus-one dimensional quantum field theory, and then we counted the states of this theory and found they exactly agreed with the Bekenstein-Hawking entropy.


I pointed out "Strominger" in this case to help direct the "existance of perception" simultaneously of what is being related, not only in our early universe, but from the understanding of what "quantum perception" is doing in relation to reductionistcally driven physics?

Such a "relation and assumption of microstate blackholes," helps to direct supersymmetrical ideas, to what the "collapse of the blackhole is doing" in terms of the creation of this quark Gluon plasma state.

Are they the same in terms of what happens in the cosmological blackhole and what is created in the collider?

Ask a Astrophysicist

The Question:Can you explain to me what quantum gravity is, and if so how does it relate to black holes?

A quantum theory of gravity would involve particles passing 'gravitons' back and forth among themselves. This quantum theory would probably be a more accurate description of gravity, and might be accurate enough to describe the extreme conditions found at the center of a black hole.


They both from what I have understood so far would have needed to account for the "classifications" Strominger had pointed out for us?

What is Blackhole Entrophy?

Suppose we have a box filled with gas of some type of molecule called M. The temperature of that gas in that box tells us the average kinetic energy of those vibrating molecules of gas. Each molecule as a quantum particle has quantized energy states, and if we understand the quantum theory of those molecules, theorists can count up the available quantum microstates of those molecules and get some number. The entropy is the logarithm of that number.

When it was discovered that black holes can decay by quantum processes, it was also discovered that black holes seem to have the thermodynamic properties of temperature and entropy. The temperature of the black hole is inversely proportional to its mass, so the black hole gets hotter and hotter as it decays.


One would have had to conclude that the "energy states" are very importnat here, as well as the nature, and the way such a process is related in terms of those reductionsitic energy derivations?

Who is Boltzman? What is Chaos?

In the presence of gravitational field (or, in general, of any potential field) the molecules of gas are acted upon by the gravitational forces. As a result the "concentration of gas molecules" is not the same at various points of the space and described by Boltzman distribution law:


The "energy and decay(gravitonically considered and extended from the implication of GR)" have to be reconciled in our understanding of the blackhole, in regards to the nature of the microstate blackhole perceptions? The "evidentry" particle creations exemplify the energy distributions?

Thursday, July 13, 2006

GRand Quantum Conjecture



My continued looked into the "fluids dynamics" had me wonder about the superfluid anomalies. How would the "sphere look" if it collapsed and allowed information to travel through it, based on what has been given here for perspective, when the "state of equillibrum" is arrived at?

In regards to 3, let's just say the assumption is from a theoretcial standpoint, that microstate blackholes "are created." They are created in "cosmic particle collisions" as well?

This is the premise from which I work, and how I gave "how particles are created," a beginning(dimensional referencing), and a basis from which all science becomes "evidentary" in the particle creations.

Exotic physics finds black holes could be most 'perfect,' low-viscosity fluidVince Stricherz, University of Washington

Son and two colleagues used a string theory method called the gauge/gravity duality to determine that a black hole in 10 dimensions -- or the holographic image of a black hole, a quark-gluon plasma, in three spatial dimensions -- behaves as if it has a viscosity near zero, the lowest yet measured.

It is easy to see the difference in viscosity between a jar of honey or molasses at room temperature and a glass of water. The honey is much thicker and more viscous, and it pours very slowly compared with the water.

Using string theory as a measuring tool, Son and colleagues Pavlo Kovtun of the University of California, Santa Barbara, and Andrei Starinets of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, have found that water is 400 times more viscous than black hole fluid having the same number of particles per cubic inch.


Your points in conclusion,I, II, III

I-yes
II-yes
III- from my conclusions as well.

Again in above quote, I am defining the leading perspective on blackholes as they are being theoretically defined now, and will be subject to experimentation soon?:)

Now again "backreaction in the laval nozzle" is up for inspection here as we delve deeper into the nature of the blackhole.

Nature in Analog Models

Analogue models of (and for) gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing) and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity).


"Analogistical behaviors" help to push perspective, where before, our theoretical explorations had ran dry?

Q:
These wormhole like 'blackholes' do not lead to other pocket universes, unless we choose to call another sector of space a pocket universe, like Europeans first called the land across the Atlantic the 'New World' or Australia 'Another World' yet still clearly part of this World we call Planet Earth.


If we are to think that the overall context can be apllied to this universe, then such evidence "should be obtainable" as to the nature of such a beginning? But even still, to your point and aspect within this universe, we are looking for accontable methods to such dark energy creation?

Plato:
Every picture held in mind is a link to other pictures


Each event in regards to gravitational collapse would be indicative of what can be "put back into this universe" and sustain it?

Lubos Motl:
The mechanism behind sonoluminiscence remains a bit controversial. Claiming that a thermonuclear fusion occurs during sonoluminiscence is among the more conservative explanations. The physicist Claudia Eberlein argued that the correct explanation is that the imploding bubbles create sonic black holes and the flashes are the counterpart of Hawking radiation as the sonic black hole evaporates. You should not think that this is an example of a very, very low energy quantum gravity because the sonic black holes have no connection with the scales of gravity. It is not a supercollider in a glass of beer. But let me admit that as an undergrad, I was excited by this proposal, at least for a few minutes, but I apparently forgot the details of that encounter.


So by developing this picture of the "bubble collapse in sonofusion", and let's forget about the energy produced from such bubbles and focus on the geometrics of such a collapse. That's my point.

Lubos Motl:
Janice Granhardt has pointed out a press release that is two days old and arguably much more serious and potentially far-reaching than the news about "sonofusion" we described yesterday.


That is part of my conjecture as well as the "unification factor" in my GRand Quantum perceptions.:)That if you remember Kip thorne's plate 27 you will understand that information from the collapse had to be sent over a great distance for us to make sense of the geometrical dynamics that are unfolding from that time and place.

So you look for the gravitational waves that Webber initiated, and Kip Thorne encouraged in our measures of what is actually being transmitted. Kip Thorne is the father of the LIGO program?

You must remember gravitational waves have not yet been verified, yet the theory of GR implicitly tells and is about gravity. It was thus taken further in my conclusions having understood that the creation of this infomration would allow one someday "to map" this very collapse in terms of the gravitonic information left in the bulk?

This is "Dimensional orientated" from a beginning(11dimensional view?), from which evidence is "the 3+1."

That's outside the box thinking? :)Cosmologists work "inside," as Clifford of Cosmic Variance once said?

How then is such a gravitational heat generated from the boundary conditions(blackhole), which grows ever smaller in that collapse, and our energy valuations go higher to supersymmetical realizations? The present volume calculated in the extension of our universe would have to be in concert with the volume before such a collapse was to be expected?

This "total energy value," assuming the universe is flat teeter's on the brink of ?:)

Total dark energy would have to account for this and supernova events contributing as well as, particle collisions that go on all the time?

So if space is not really empty, then what is it supposed to be filled with? Quantum harmonic oscillator and zeropoint?

See:
  • Charlatan's Who Use Graviton
  • Tuesday, July 11, 2006

    Singularities must be Rewritten?

    From Dr. Kip Thorne, Caltech 01 On Relativity-Plate 24

    I have given examples why the singularities have to be rewritten. I explain the value of the KK Tower as well. As well, it's relationship to curvature of the universe. Following through that discussion I hope I reveal the thinkng that has been garnered through my own research and understanding.

    If the initial states at the beginning of the universe are to be in concert with particle reductionism, and the particle creations that I have exemplified in how particles came into being, then, the understanding of what can be transmitted through the blackhole is extremely important as a valuation of what appears over time?

    So we have this universe and the temperature of the WMAP and the cosmic background?

    You have to know what the entropic realizations say about this time(now), as well as what is gravitationally being exemplified at this junction of the universe in terms of geometrical curves.

    Are the expansitory revelations being realized as I relate entropic and temperature valuation to the existing universe? What about the beginning then, and our supersymmetical realization?

    It was much simplier then?:)

    So looking for similarites in expression ask that "lagrangian methods" be established in terms of how the "weak field measure" in context of the Sun/earth relation, also speaks too, what is transmitted in the high energy collisions "outflows" as well?

    Image and text from NASA Solar System

    The Quark Gluon Plasma revealled the anomalies for us to consider the "jet outflow" of all that is being propelled back into this universe? Much like this image that is being reproduced. The beginning has then been established in my point of view:)

    Particle creation helps to exemplified this position.

    You would have to understand this geometrical progression as well?

    If you seat yourself in the terms of high energy considerations, how shall this geometry be expressed? Topological undertanding would need to be examined as you progressed to the basis of the singularity with the way I am seeing. The way I am directing one's view to that singularity in terms of the Quark Gluon Plasma.

    High energy photon recognition helps us in this regard as well?

    Monday, July 10, 2006

    First floor Completed



    Finishing the first floor framing on the ground level entry, on Friday, my son had his first floor trusses delivered. I got to take a little break this weekend, spending sometime with my grandchildren and taking time off regular work.



    While doing this, his father-in-law helped to place these first floor trusses. Looking down upon the layout today I was quite impressed by the work they had done.

    Today I went in about seven in the morning, and finished up a "to do list" that has been haunting my son. These small things have been accumulating, while moving ahead with the pace of construction.

    Getting these out of the way today, we will start laying the plywood on the first floor and begin framing again starting tomorrow morning.

    Hopefully all this will be done by the 18 July.

    Dreaming of Another Vacation



    All this work has me dreaming of another vacation. As I was scanning my pictures, I couldn't help think of the "landscape" pictures other people had taken.



    From our vacation last year. Taking the Gondola lift up to the top, gives one a good clear view of the Banff Spring's Hotel and the surrounding terrain.

    Thursday, July 06, 2006

    Lisa Randall's Theoretical Insights



    The picture above was shown because of another picture in which I thought deserved comparison. The reason for this, would help the mind understand how such an image could be explained in a "easy and suttle way?"

    So look at this picture above and then at the one to follow.



    The very ideas are of extra dimensions are very progressive, and are not without some history. Some people will label anything as crackpot, without undertanding the history of these discussions.



    I was thinking here of Banchoff, and the imaging that he deals with. While he is speaking from a mathematical position that imaging of a 2d screen does wonders in how 5d perception are presently engaged in the veryday world of computer screens and the like.



    But to think about the picture painted by Dali, it is not without it's mathematical inclinations, that a painter like him may wonder about the "elevation" to spiritual thinking, with such thought embued with our look at the mathematical world, with which we assign our "spiritual principles?"

    Tuesday, July 04, 2006

    When Is a House A Home?

    This phrase up top of this blog entry is catchy is it not?

    Starring: Kevin Kline, Kristen Scott Thomas, Hayden Christensen, Jena Malone, Mary Steenburgen, Mike Weinberg, Scotty Leavenworth, Ian Somerhalder, Jamey Sheridan, Scott Bakula, Sandra Nelson, Sam Robards, John Pankow, Kim Delgado, Barry Primus Director: Irwin Winkler

    The fact that the "ole fabric" of our thinking can be torn down and rebuilt in a better format, after much careful thought and considerationCan it not be worthy of what you can put back into what you want your house to be?

    It is as though this has to be put out there for minds to consider? Like all possibilties, the diversities of the home in which we all live, is as unique as it is to the very life that is lead through the living of it.

    When you go back to the homes in where you grew up, how is your perception against what you will see that day? It seems, it was always bigger then what I had expected it to be. Time changes this. "Time," puts it back into perspective?

    So what is home for one, might be different in the way the one would interpret a house. Would be vastly different in how this house will be the measure of all homes? Will be the measure of "what home is," in life?

    In his novel Ulysses, James Joyce includes a lengthy discussion about Hamlet, referring to it as one of a select few important artworks that outshine the rest.

    "Art has to reveal to us ideas, formless spiritual essences. The supreme question about a work of art is out of how deep a life does it spring? The painting of Gustave Moreau is painting of ideas, the deepest poetry of Shelley, the words of Hamlet bring our mind into contact with the eternal wisdom, Plato's world of ideas. All the rest is the speculation of schoolboys for schoolboys."


    To be, or Not to Becomes from, "The Tragedy of Hamlet, Prince of Denmark"

    To be or not to be, that is the question:
    Whether 'tis nobler in the mind to suffer
    The slings and arrows of outrageous fortune,
    Or to take arms against a sea of troubles,
    And by opposing end them. To die: to sleep;
    No more; and by a sleep to say we end
    The heart-ache and the thousand natural shocks
    That flesh is heir to, 'tis a consummation
    Devoutly to be wish'd. To die, to sleep;
    To sleep: perchance to dream: ay, there's the rub;
    For in that sleep of death what dreams may come
    When we have shuffled off this mortal coil,
    Must give us pause: there's the respect
    That makes calamity of so long life;
    For who would bear the whips and scorns of time,
    The oppressor's wrong, the proud man's contumely,
    The pangs of despised love, the law's delay,
    The insolence of office and the spurns
    That patient merit of the unworthy takes,
    When he himself might his quietus make
    With a bare bodkin? who would fardels bear,
    To grunt and sweat under a weary life,
    But that the dread of something after death,
    The undiscover'd country from whose bourn(e)
    No traveller returns, puzzles the will
    And makes us rather bear those ills we have
    Than fly to others that we know not of?
    Thus conscience does make cowards of us all;
    And thus the native hue of resolution
    Is sicklied o'er with the pale cast of thought,
    And enterprises of great pitch and moment
    With this regard their currents turn awry,
    And lose the name of action.-Soft you now,
    The fair Ophelia, - Nymph, in thy orisons
    Be all my sins remember'd.


    For me there was always an interactive feature about what the photon could do in terms of describing it's "state of existance" and if this were the case, then how would you have applied such a measure?

    Light-matter interaction
    Low energy phenomena  Photoelectric effect
    Mid-energy phenomena Compton scattering
    High energy phenomena Pair production




    So while we have held the romantic to heart, what "beat in measure" would any in/out going state signify, if the calculation of the photon is "gravitationally considered?" Shall it be so static and discrete that we forgot how raelly smooth these heartbeats really are?

    What Dreams May Come

    When Chris enters the house, he finds that she doesn't recognize him. Pale, gaunt, and miserable-looking, Annie isn't fully aware that she's dead. He talks to her gently, pretending to be a neighbor, before he is able to gain enough of her trust to reach her for a moment. In guilt and disbelief, Annie screams and pushes him away, and a saddened Chris realizes he has failed. He tells his insane wife a last good-bye, and leaves the house. The Tracker consoles him, and Chris tells him he has given up.

    "But," he adds, "Not the way you think."

    He asks the Tracker to give his love to his children, and re-enters the house. Taking his wife's hand, he tells her he won't leave her. He's decided to stay forever in hell and join her in madness rather than leave her again. Somehow, this sacrifice reaches Annie when nothing else can, and she and Chris pull each other out of the miasma of hell, narrowly escaping.


    What Dreams May Come is a 1978 novel by Richard Matheson about the afterlife.

    While some may never have considered the strength of the matter states, and what they hold for us in our decisions, it is of some relevance that the "lighter constituents of gravity" defined in a equilibrium state, are significant, if ever held in context of the "hell's of damnation inferno?"

    It is with some hope, that "the higher realization" of spirituality, will bring us to the father's house? When you roll your eyes upward, it is not so very far away is it?

    So of course as one descends into the hells of what has held us most in life(quark Gluon Plasma) and tamed for us to the conclusion of the way it is? Then, the plight of suffering was wholesomely considered, as Robin Williams sought to get his wife from the choice she had made?

    While it is in some Catholic minds, the sin, it was more the damnation one could have attributed to the minds conclusion i that religious thinking? That it was then locked in what it could no longer take in life, took along with them, in death? But in "cleaning up life's work, as it never seems to conclude whole fully(the medicine wheel) until the realizations are always there for us to think about as parts of the whole? Robin's "choice" with his wife to reincarnate?

    Robin Williams seeing the "beauty of life" saw it in the heaven's making? Certain realizations abundant, and very swift, in every thought form held there for Robin Williams. We should of "held off on our judgements" one might say in life, also made so quickly without recourse?

    Backfill Complete

    As you can see in the background there are some things that were installed.





    Underground wiring, water line and sewage line. His lagoon sytem will be completed further on when the contractor is brought back. As well as the driller will be here to dig their well.

    As you can see the backfill here completed , took about 10 t0 12 truckloads of gravel. The thing here is, as the gravel was layed inside the foundation walls, it needed to be compacted as it was being dumped. So using a 450 compactor this was layed out about a foot at a time, to make sure the inside compaction was solid.



    There are reasons for this as the type of heating system that will be used are tubes laid out in the concrete, and by using a on demand boiler, the heat will be radiant from that floor. I find this much better then the forced air heating system.

    This of course has moved us into the construction stage, with our first wall up, two days ago, while we are near completeing the main floor. We hope this to be done by Thursday, as the main floor design trusses will be delivered then.

    This stage then will allow us to move into the second floor construction.

    Saturday, July 01, 2006

    Dimensional Referencing



    While the basis of the cosmic string lying in ruins in terms of verification that others went after, it does noes not in anyway reduce the impoirtance of how Andrey Kravtsov's animation can be less in our assumption of the supersymmetrical universe?

    It's as if the neurons are connecting, in the vast universe, to bring parts of itself to linking in some "visionary image," that mankind has connected, from one thought to another.

    Never mind about Jacque Distler's interlinking software capabilites, as this has been going on for sometime now, here, and on other forums.

    Even the term Trackback is new, while this neuronical developement was understood in terms of Andrey Kravtsov's computer imaging, it becomes even more apparent, as the images I bring forward take their place in our thinking.

    There is more to follow for sure.

    They call them trackbacks." I just call them a continuation of the interlinking that is going on in the universe.:) Wordful quotation, or in imagery, we can track it to the source eventually?

    Phase Changes

    It's a way of seeing dynamical movement and phase states? If Alice didn't step into mirror world, what would Young's experiment have meant in relation to path integrals?


    G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1). You have to realize that such emergence into the views of universal formulations, has to have some associative response from the quantum world to see that such relevance in the cosmological particpations could have ever pointed to the motivation of these universes coming into being, that it would go through a phase transformation relevant to each particle discription? Is this correct? This presented itself in a "way of seeing" that stretches the mind imaginations tht I wonder have I indeed gone off the deep end.


    Columbus, or the Greeks, over some "edge" and be done with it? :) No there are always greate rimagnations working to solve the fantasies that Dirac may of set in motion for Feynman.

    So "Toy models" are created to house the systemic movements. From this, calorimetric instruments are developed.

    Now we change the way we have been doing things and the following paragraph makes more sense?

    We had to break out of the moulding with which society has cast itself. It requires "greater ingenuity and imagination" to go beyond the standard model.

    Shall we forget about Dirac's abilties besides writing to the algebraic equations, or Feynman's extension of the matrices, to toy models?

    Ant World


    Three dimensions are all we see -- how could there be any more? Einstein's general theory of relativity tells us that space can expand, contract, and bend. If one direction were to contract down to an extremely tiny size, much smaller than an atom, it would be hidden from our view. If we could see on small enough scales, that hidden dimension might become visible.


    Some actually testng that has been postulated to look at what may be anywhere between the "inaccessible Planck length and infinity."