Monday, October 09, 2006

Box Counting or "Points" on the Strings Length?

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory! Author Unknown


We understand I think the relevance in regards ot the cosmological views that GR helps us understand in the curvatures inherent as an expression of the cosmos.

What we may have trouble with is the value we may assign such curvatures taken down to the quantum regime. This may seem incompatible, yet, the dynamical nature of the energy is never really that far from speaking from the particle/energy inhernet in nature, as a energy determinant value?

Why would you treat the quantum realm any different then you would the cosmological one, if the assumption is that GR is predicted?



Fractal Dimenison-Tree Silhoutte

I like to think of the "roots and the rings of history" here so that you may see the comparative value of thinking of the "building blocks" not so much as "boxes" but as energy values related to the circle.




There really was a reason to fear pathological entities like the Koch coastline and Peano's monster curve. Here were creations so twisted and distorted that they did not fit into the box of contemporary mathematics. Luckily, mathematics was fortified by the study of the monsters and not destroyed by them. Whatever doesn't kill you only makes you stronger.

Take the Koch coastline and examine it through a badly focused lens. It appears to have a certain length. Let's call it 1 unit. Sharpen the focus a bit so that you can resolve details that are ⅓ as big as those seen with the first approximation. The curve is now four times longer or 4 units. Double the resolution by the same factor. Using a focus that reveals details 1/9 the first focus gives us a coastline 16 times longer and so on. Such an activity hints at the existence of a quantifiable characteristic.

To be a bit more precise, every space that feels "real" has associated with it a sense of distance between any two points. On a line segment like the Koch coastline, we arbitrarily chose the length of one side of the first iterate as a unit length. On the Euclidean coordinate plane the distance between any two points is given by the Pythagorean theorem


Planck time and what new physics would we have shown once we got down to these lengths? The energy of discernation has deluded us into what was once uncertainty has now QGP idealizations and the inherency of the thinking along side of high energy considerations.

Discretium and continuity are not at odds here just that the "realm of thinking" is limited to the GR suppositons about what the world is in cosmological discretium views? Yet, we know at such levels, the "continuity" of the energy has taken over. The coast lines appear fuzzy, yet in "box counting" it doesn't seem that way. What are it's limitations then, when our views meet uncertainty about what discribes the coast line? Shall we now refer to the days, weeks, months, as an energy valuation of the circle, in the trees root and the history it contains?

Pick a "ring/circle" of the tree and tell me what happen during that time?

Saturday, October 07, 2006

From Modelling to Experimentation?


Moving to higher energies, the expected fluxes of neutrinos become smaller, that even a cubic kilometer detector is not able to detect them. Larger volumes can be achieved by replacing optical sensors by acoustic detection. The reason is that acoustic waves can propagate over larger distances than light and allow wide spacing of detectors, and therefore larger detector volumes.


From Modelling to new thoughts on experimental processes and approach to the physics involved, it is important that one understands how this approach is considered. Not to loose sight of the relationship to high energy consideration and it's particle shower effect from such interactions.

Without some comprehension of RHIC valuation in production uses what was to be gained from cosmic particle collisions? What future in LHC inclusion of microstate with out some association to particle entities as a result of those collisions?

Reductionist processes leads to comprehension values that if let unnurtured, would not have allowed such model comprehension to exceed current limitation of thinking?

"String theory and other possibilities can distort the relative numbers of 'down' and 'up' neutrinos," said Jonathan Feng, associate professor in the Department of Physics and Astronomy at UC Irvine. "For example, extra dimensions may cause neutrinos to create microscopic black holes, which instantly evaporate and create spectacular showers of particles in the Earth's atmosphere and in the Antarctic ice cap. This increases the number of 'down' neutrinos detected. At the same time, the creation of black holes causes 'up' neutrinos to be caught in the Earth's crust, reducing the number of 'up' neutrinos. The relative 'up' and 'down' rates provide evidence for distortions in neutrino properties that are predicted by new theories."

Friday, October 06, 2006

That "light Bulb" was the Sun?



Plato:
It was important for me to reveal how I am seeing the cosmo. How the superhighway has been spoken too, in regards to the Langrange points.These points are lead to and from unstable orbits. Points, where gravity balances out between bodies, like the earth and the moon. These are not to be considered stable equilibrium points


It was Socrates' turn to look puzzled.
"Oh, wake up. You know what chaos is. Simple deterministic dynamics leading to irregular, random-looking behavior. Butterfly effect. That stuff."
Of course, I know that," Socrates said in irritation. "No, it was the idea of dynamic logic that was puzzling me. How can logic be dynamic



Now surely this is not the case? A "light bulb" is really the sun?

Some Orbits with theirLyapunov Exponents

Maybe just some analogy to what may have become the brilliant idea, was just looking hard enough into what the energy is doing? It found an "avenue or road" to allow for the transferance from "the place," where all ideas reside to become? Hence, "the nature of all things" which already exist, to have found it's way through the mind into a more briliant focus of what was determined of the energy now, becomes, the sun/idea? Worked hard enough to manifest into reality?


Artist's impression of the micro vortices observed in the Northern magnetic cusp by Cluster. It is the first time ever that such phenomenon is observed in space.


So I sit here wondering about where that energy had gone, and how and I am quickly transported back to the conditions of the early universe? "QGP! what you say?" How is that possible?

And from it we see the lagrangian views as points between the sun/earth relation that allow for easier transport(satellites in orbit) then other conditions if gotten into the flow of things?

A State of equilibrium? Que! Non?




Sample Orbits of the Standard Map
(x, y) → (x + y, y − 0.971635 sin (2πx)/2π)Different orbits are assigned different colors.

Tuesday, October 03, 2006

Monday, October 02, 2006

The Periodic Table of the Moon's Strata


Clementine color ratio composite image of Aristarchus Crater on the Moon. This 42 km diameter crater is located on the corner of the Aristarchus plateau, at 24 N, 47 W. Ejecta from the plateau is visible as the blue material at the upper left (northwest), while material excavated from the Oceanus Procellarum area is the reddish color to the lower right (southeast). The colors in this image can be used to ascertain compositional properties of the materials making up the deep strata of these two regions. (Clementine, USGS slide 11)
Clementine gravity experiment used measurements of perturbations in the motion of the spacecraft to infer the lunar gravity field


Like Grace, I choose to build an understanding of the gravity fields.

S-Band Transponder Doppler Gravity Experiment

The gravity experiment used measurements of perturbations in the motion of the spacecraft to infer the lunar gravity field. Clementine was equipped with an S-band microwave transponder and 2 S-band omni-directional high-rate antennas which were used for tracking by the NRL tracking station in Pomonkey, MD, and the NASA Deep Space Network. The frequency of the S-band transmission was measured every 10 sec, and the Doppler shift would give the relative velocity of the spacecraft towards or away from the Earth. Accelerations were calculated from changes in the velocity, and after accounting for the orbit, relative motions of Earth and moon, and Earth and solar gravity, these accelerations are converted to lunar gravity effects on the spacecraft.
The calculated lunar gravity field can be used to model subsurface lunar structure. The Pomonkey station could measure the velocity to an accuracy of 3 mm/sec, while the Deep Space Network stations could achieve about 0.3 mm/sec. Tracking was not possible on most of the lunar far side (120° to 240° long, -45° to 45° lat), when the moon was between the spacecraft and the Earth. In all, over 361,000 observations were made, approximately 57,000 at less than 1000 km altitude.


As our physical interpretation of this lovely pearl(earth) we live on has changed in the conceptual views of "times clocks and such," it became evident in GRACE that the world was quite different then what was first view from space in triumph.

As you might well know, all matter in the universe consists of small particles called atoms and each atom contains electrons that circle around a nucleus. This is how the world is made.
If one places an atom (or a large piece of a matter containing billions and billions of atoms) in a magnetic field, electrons doing their circles inside do not like this very much. They alter their motion in such a way as to oppose this external influence.

Incidentally, this is the most general principle of Nature: whenever one tries to change something settled and quiet, the reaction is always negative (you can easily check out that this principle also applies to the interaction between you and your parents). So, according to this principle, the disturbed electrons create their own magnetic field and as a result the atoms behave as little magnetic needles pointing in the direction opposite to the applied field*.



But of course may I infer "floating ships" over mineral deposits that were conducive to transportation in regards to the superconductors, floating frogs and such? An "attenuator of a kind" for the strength's and weaknesses of such composite gatherings?

But anyway before this "energy is considered in it's matter formed," how did such asymmetrical breaking from the origins not have ocnsidered such constitutions built on the very matters of the moon or such, in it's construction? In the end the gravity field is worth what?

At SLAC and elsewhere in the 1990s, precision measurements probing quantum effects from physics at higher energy scales were very successful. Precision electroweak measurements accurately predicted the mass of the top quark before it was discovered at the Tevatron at Fermilab, and they were cited in the awarding of the 1999 Nobel Prize to Veltmann and t'Hooft, which recognized their work in developing powerful mathematical tools for calculating quantum corrections and demonstrating that the Standard Model was a renormalizable theory. The discovery and mass measurement of the top quark at Fermilab's Tevatron and the precise Z0 boson mass measurement from CERN experiments added to well established values for other Standard Model parameters, to allow predictions for the only Standard Model parameter not yet measured, the Higgs mass.



What is a coupling constant? This is some number that tells us how strong an interaction is. Newton's constant GN, which appears in both Newton's law of gravity and the Einstein equation, is the coupling constant for gravitational interactions. For electromagnetism, the coupling constant is related to the electric charge through the fine structure constant a



While the idea in my mind is "the extension of all elements demonstrated in some way arising from the standard model, what said that "this element or that" could not have been created from a oscillatory expression of the big bang, and the particles that issue forth, are not without some geometrical expression as "inhernet structures" of that table?



As a "resonantial value" of a point along the length of the string?

Dr. Timmothy Stowe's physicists periodic table



So you see, I had a vision about the future. A time when I will work in space deploying satellites. But what said that future would not ascertain the requirements when our fossil fuels will have to be disregarded? Change the way the planets inhabitants will look forward to the benefits of such conceptual changes?

So this is a fictional posting then, about that future.

CP Violation

The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann




ON a macroscale the blackhole is a understanding of when we investigate curvature parameters with regards to the nature of our universe in spacetime. We understand this right?

What are the "entropic valuations" being recognized as we look to a earlier time of when the QGP existed and then such manifestaion in the "matters states" have exemplified such characteristics as?


Both space and spacetime can either be curved or flat.


I am going to give you a quick summation of what GR is. It is about "Gravity." Now if you hold that in mind you should not loose any time with what I am telling you.

Now, how is it that we can see the dynamcial nature of the universe, yet, we would not consider the effect of the presence of microstate blackholes in regards to such gatherings in the space, of what we call "spacetime?" What would "such gatherings" show of itself?


A circle of radius r has a curvature of size 1/r. Therefore, small circles have large curvature and large circles have small curvature. The curvature of a line is 0. In general, an object with zero curvature is "flat."


Think about the "circle" and it's 2D view of what the blackhole is doing in 3D +time in context of many blackholes. I always refer to "one" so you can see the comparative view that I am having little success in transferring to you, in what I am seeing.

The curvature parameters are closely associated to the thermodynamic realizations. This is importnat not only on a cosmological level, but on a microstate as well.

Lubos explains that here.

Lubos:
There are lots of other examples what you can do to increase the number of black holes. Change the couplings so that the stars burn their fuel faster, and they will collapse into black hole faster. Reduce the gap between the Planck scale and the QCD scale, and nuclear collisions will be more likely to end up as black holes.

It is quite obvious that the change of virtually any parameter of the Standard Model (plus inflation) in the right direction (one of the two directions) will result in an increase of the number of black holes. How can you doubt such a trivial thing?


So there is something about the nature of our universe and the balance that it seeks to maintain of itself? Here we are, looking at events within the cosmo and "secular views of it's manfiestation" different then other locations within the universe. Yet not apart from it, or not indifferent to it's nature to be part of a larger picture?



Silicon Vertex Tracker. The SVT is the heart of the BABAR experiment at SLAC—in the photo, physicists are putting the finishing touches on improvements to the detector. (Photo Courtesy of Peter Ginter)
SLAC's BaBar collaboration has discovered that CP violation—an asymmetry between the behavior of matter and antimatter—exists even in a very rare class of particle decays. This result offers the most sensitive avenue yet for exploring matter-antimatter asymmetries, with implications for the future understanding of physics beyond the Standard Model.

"BaBar has proven to be a fantastic instrument for exploring the origins of matter-antimatter asymmetries, allowing us to probe with exquisite precision very rare processes related to how the early universe came to be matter dominated," said David MacFarlane, BaBar Spokesperson and Professor at the Stanford Linear Accelerator Center.


So here we are having been given the example of CP violation above and here?

How is it that anything could be asymmetrical? :) So you introduce anti-matter and matter?


(ambigram courtesy John Langdon)
If we could assemble all the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.


As a observer Einstein made it clear that the observable universe has ideas attached to it. The "Pretty girl and the hot stove analogy" was compelling to those of us who recognized the values we may attach to life. "The Gravity of the situation?" How narrow our view of the world is when we feel the world is lost?

But the hope and inspiration is, that the world has a bright future when we undertsand the implications of our views. Our involvement in the "toposense of reality? We are "part and parcel" of it?

So, should we talk about the components of Heaven and Hell( my philosophical discourse on the nature of consciousness?)? You have to understand the picture and the dynamical nature this universe can say about it's entropic valuation?

While I may have understood Omega, it didn't come to the nature it is by not including a geomtrical perspective about the nature of that same universe.

That's my point. It had to arise from a earlier time and the manifestation is the matter states we are defining in correlation to the entropic valuations.

While you see these as macro-characteristics and the relation to blackhole in 3d+time, the result is, a explanation of matter states in "macrostylistic beauty" we see in the events of the cosmo.

If such inclinations to drive the energy to a ever smaller defined circle, as it gets smaller "the difference is" not so indiscernable that the events of the "particle showers" created are matter states that arise form the energy that was used.

You see?:)

The Ceiling

The deeper implications of such a thought from perspective is focused upward? Yet such perspective can be made from other positions? So some minds were flexible? Others, were just engineers? ;)

Understanding other worlds came naturally to him. Perhaps it was an inevitable consequence of being the child of Japanese Americans. His parents, though born in California, spent World War II behind barbed wire, guarded by people with machine guns: incarcerated by their own country as enemy aliens. Afterwards his father worked as a gardener, his mother a maid: two of the few jobs that were available to Japanese Americans. Kaku grew up poor, but one of the family treats was to visit the Japanese Tea Garden in San Francisco's Golden Gate Park. It turned out to be the place of a childhood epiphany. Wondering in the way that only a child does, Kaku looked at the carp swimming in a weedy pond and imagined how they would not be able to conceive of other worlds. "A carp engineer would believe that was all there is; but a carp physicist would see the ripples on the surface and start thinking about unseen dimensions," Kaku told me, laying the first of many lashes on his token engineer.


The "ceiling" is the perspective of the carp, not the perspective of the "carp physicist."

See:

  • Liminocentric Structures: Which Circle do you Belong Too?-Sunday, July 10, 2005


  • Ps: Some updates are curvature given for perspective. Think of a string, and any point on that string. What does the energy value of "that point" tell you in regards to the circle? The point on that string. It's just a way of looking at the string and the resonantial value assign along the string's length?

    Catching Nature in Action


    To capture the particles emerging from powerful proton-proton collisions at the LHC, scientists design and build huge, massive detectors. The CMS detector, about 50 feet tall, relies on an array of particle detection subsystems. The tracker (the subsystem at its core) records particle tracks with ultrahigh precision. The intermediate subsystem, the calorime-ter, determines the energy of the particles escaping the collision. The outermost devices identify muons, heavy electron-like particles that can travel long distances.
    Graphic: CMS collaboration


    LHCf is a different type of experiment, using the LHC's protons as a source that simulates cosmic rays. It will study how colliding protons cause showers of particles, in particular photons. Analysis of these showers will aid in the interpretation and calibration of large-scale cosmic-ray experiments, which can cover thousands of square kilometers of ground


    See:

  • The wonders of Quark-Gluon Plasma
  • Saturday, September 30, 2006

    Are Strangelets Natural?

    Thus RHIC is in a certain sense a string theory testing machine, analyzing the formation and decay of dual black holes, and giving information about the black hole interior.



    It is important that you look at the date of this article following, and what has subsequently arisen from "then to now." The title of this post asked a legitimate question and it was answered in response to the disaster scenario's presented to the LHC "recenty?" Check the date on it? Not so recent?

    Discovering this raised the conclusiveness about what was comparative to the cosmic ray collisions. This lead us to believe, the microscopic blackhole creation was safe. Becuase it happened all the time in the space above us. Just as we may see the aurora borealis in our observation in the interaction with the sun, so too, in cosmic particle collisions in ways beyond the standard model.

    So looking back?


    SCIENTISTS ARE OFTEN ACCUSED of trying to play God. But obviously they can't really mimic the feats of the putative Creator of the Universe, and make a universe in the laboratory. Or can they? Before you snort in disbelief, you should know that some serious cosmologists have considered the idea. Indeed, one of them has already had a shot at creating a universe--albeit inside a computer. The idea dates back to the late 1970s, when Andrei Linde, now at Stanford University, and Alan Guth of the Massachusetts Institute of Technology separately came up with the concept of "inflation". According to this idea, an incredibly short, violent burst of expansion occurred around 10-32 seconds after the birth of the Universe. Propelled by concentrated vacuum energy, inflation boosted the size of the Universe from one billionth the width of a proton to the size of a grapefruit. That's what the theorists claim, but showing that inflation really did take place like this is hard... unless, of course, someone can recreate the right conditions in the lab and watch what happens. Linde and his colleagues have already done a dry run on a computer. "Setting up the simulations was hard work, and only on the seventh day did we finish the first series," he reported in Scientific American in 1994, adding in Strangelovian terms: "We looked at the shining screen, and we were happy--we saw that the universe was good!" This isn't enough for Linde: he wants to do it for real. But theory suggests that matter has to be squeezed to densities similar to those in the primordial Universe before such fields appear. No-one has the faintest clue how to create such densities, yet. Linde is sanguine about the dangers involved, if it ever becomes possible. "You can think of our Universe as being like a smooth surface, with one part of it inflating like a balloon. The new universe will be connected to ours by just a tiny passage--what we call a wormhole--the size of a subatomic particle." Quite how we'd know we'd succeeded isn't obvious, but at least there seems little danger of someone tumbling into the new universe by mistake, or anything nasty getting out.


    THis one post includes "lots of link"s from the accumulation of my thinkng as a layman. I had gathered these as they unfolded, to help me understand what was introduced to me some time ago by Paul on the question in regards to the "Disaster Scenario at LHC."

    Now in regards to "new physics" one needed to see what would come out of such collisions that would be produced, so one had to indeed follow that thinking which I did. How far from the truth of it was what was generated in the public eye distant from what was published by the reputable scientists?

    Well you would have to judge for yourself, and "my excuse," well it has been provided for me, so one can say as a layman I am really distant from the current thinking.

    So yes before Cosmic Variance and the disaster scenario, it was in our conversations that "Mooreglade of Superstrintheory.com forum" introduced the article of "A Blackhole Ate My Planet" which lead too "Fate of our Planet"

    So you see, between then and now, I was able to construct accordingly as I was exposed to the information in regards to "both ways" to which Lubos implies in that statement in comment link?

    Okay. Now the stage has been set.

    What has been Lubos been saying?

    That the connection in "B's question" again sets the stage for further thoughts?

    That's just the way of it and who better then student who will make way for further insights, whether it be "Lubos or B?"

    In the past my mistake was made to "mirror" Lubos with Peter Woit, because I needed to see what the others may offer in regards to the positions they adopted. Or, another example would have been Smolin and Susskind, who bounced off each other. Or, Gell-mann or Feynman. Or maybe even Plato and Aristotle shhown in the picturte at the top of this Blog?

    IN the above case with Peter Woit, I did not learn much? The counter arguments as to why strings were failing in the road to experimental validation(sure we were preoccupied with it's validity then), and how this message was being put out there.

    Be sure that more senior people agree with me that it is trivial to falsify that conjecture, including Susskind, Vilenkin, Banks, and others who have looked into it.


    So where are we today in regard to strings? Lubo's reference to Banks, Vilenkin, and Susskind already asking these questions is a significant pointer to what has already transpired, and what days, weeks, years, have passed before we see this statement today?

    You see how this is done?

    Friday, September 29, 2006

    Historical Approach of the Sand Reckoner

    I should pave the way for how the thoughts that are unfolding this morning.


    But nothing afflicted Marcellus so much as the death of Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming up to him, commanded him to follow to Marcellus; which he declining to do before he had worked out his problem to a demonstration, the soldier, enraged, drew his sword and ran him through. Others write that a Roman soldier, running upon him with a drawn sword, offered to kill him; and that Archimedes, looking back, earnestly besought him to hold his hand a little while, that he might not leave what he was then at work upon inconclusive and imperfect; but the soldier, nothing moved by his entreaty, instantly killed him. Others again relate that, as Archimedes was carrying to Marcellus mathematical instruments, dials, spheres, and angles, by which the magnitude of the sun might be measured to the sight, some soldiers seeing him, and thinking that he carried gold in a vessel, slew him. Certain it is that his death was very afflicting to Marcellus; and that Marcellus ever after regarded him that killed him as a murderer; and that he sought for his kindred and honored them with signal favors.


    First off, as Plato I understand "the secret" of the Building of the Pyramids. Why and what it means as a model of comprehension about the building blocks of nature.

    So "carefully think in conclusion" about what this post means as you near it's end. For I had much more to say about it philosophically, but that would be stepping ahead to "now." :)

    Anyway


    Many physical quantities span vast ranges of magnitude. Figures 0.1 and 0.2 use images to indicate the range of lengths and times that are of importance in physics.


    A lot of people do not understand that if you look to the cosmo, you do not just look at what is evident from observation, but that your observation is increased, as you enhance your perceptions about the "real depth" of that universe.

    IN "LHC Factoids," presented by JoAnne of Cosmic Variance, some of the tantilizing ideas about the complexity of the information is being discussed. To me, this presents an opportune time to gain perspective from the "bottom up" discussed by Frank Wilczek .

    If the sand is melted into a lense or a diamond, what view had been established by Frank that you might say his lense "is" distorted? If you read the article you understand the context, but until then, what use any "mountain/pyramid to climb" if you did not understand the complexity of the information?



    Archimedes met an untimely death while deep in thought, pondering a figure he had drawn in the sand. He did not see the Roman soldier approach, sword in hand. The mosaic portrays this historical event


    About Dimension

    John Baez's link this morning in his comment is important for a lot of different angles... ummm... reasons?:)

    So when you are pointed towards the valuation of all these "sand particles," it not that you want to look like an "ostrich and bury your head in the sand," but that you want to retain perspective on the complexity of the "sand castles" that mathematicans like to build? So you tend to look for the technique concerning the point, breadth and width of the evolving statemntement of the projective geoemtries?


    A space is a collection of entities called points. Both terms are undefined but their relation is important: space is superordinate while point is subordinate. Our everyday notion of a point is that it is a position or location in a space that contains all the possible locations. Since everything doesn't happen in exactly the same place, we live in what can rightly be called a space, but points need not be point-like. Any kind of object can be a point. Other geometric objects, for instance, are totally acceptable (lines, planes, circles, ellipses, conic sections) as are algebraic entities (functions, variables, parameters, coefficients) or physical measurements (time, speed, temperature, index of refraction). Even so-called "real" things can be points in a space: people are points in the space of a nation's population, nations are points in the global political space, and telephones are points in the space of a telecommunications network.



    So of course you always start off with Euclidean perspective, and work from there. So, you have "one" grain of sand? One raindrop? One string? Okay, you get my point yet?

    The beginning of the Universe?

    I want people to realize where the strings fit in. I can't help but stress that such advances to "the cause" of what perception is necessary had to start off in a "avenue" like all things, this road leads to the universe we have today.



    Because it starts off in the analogy of "the string" makes this feature no less important then the "sargeant major" of Robert Laughlin's condense matter theorist view.

    See:


  • What are those Quantum Microstates-Tuesday, October 18, 2005


  • A Perspective on Powers of Ten?