The Navier-Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have yet to prove that in three dimensions solutions always exist (existence), or that if they do exist they do not contain any infinities, singularities or discontinuities (smoothness). These are called the Navier-Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics, and offered a $1,000,000 prize for a solution or a counter-example.
His stunning conclusion?
“The amount of information that can be stored by the ultimate laptop, 10 to the 31st bits, is much higher than the 10 to the 10th bits stored on current laptops. This is because conventional laptops use many degrees of freedom to store a bit whereas the ultimate laptop uses just one. There are considerable advantages to using many degrees of freedom to store information, stability and controllability being perhaps the most important. Indeed, as the above calculation indicates, to take full advantage of the memory space available, the ultimate laptop must turn all its matter into energy. A typical state of the ultimate laptop’s memory looks like a plasma at a billion degrees Kelvin — like a thermonuclear explosion or a little piece of the Big Bang! Clearly, packaging issues alone make it unlikely that this limit can be obtained, even setting aside the difficulties of stability and control.”
Ask Lloyd why he is interested in building quantum computers and you will get a two part answer. The first, and obvious one, he says, is “because we can, and because it’s a cool thing to do.” The second concerns some interesting scientific implications. “First,” he says, “there are implications in pure mathematics, which are really quite surprising, that is that you can use quantum mechanics to solve problems in pure math that are simply intractable on ordinary computers.” The second scientific implication is a use for quantum computers was first suggested by Richard Feynman in 1982, that one quantum system could simulate another quantum system. Lloyd points out that “if you’ve ever tried to calculate Feynman diagrams and do quantum dynamics, simulating quantum systems is hard. It’s hard for a good reason, which is that classical computers aren’t good at simulating quantum systems.”
Bold emphasis added by me.
The issue of computer language would have been to reveal the deeper implications of the cosmos, while we entertain the “phase changes the universe will go through.” While we may think of the blackhole used as a weapon on April fools day, what use the Ipod in Mission Impossible III if it were to melt into a superfluid and bring forth all the ills of the past? It ‘s in the supefluid state that all of the information of the past makes it’s way again into this universe, and supplies the dark energy for the current state of the Universe?
Hey I got one for you. You remember mission impossible. Well in this case, your only able to use the ipod once, then it turns into a super liquid.
While we consider newer technologies what use to “see the sun in a different way” now that we understand the range of “the window of the universe” now incorporates gamma ray detection, it forces upon us the end result of Tscan compiled data?
The Tip of the Pyramid and Quantum Gravity
I like to compare it to wandering in the desert, and stumbling over a tiny pebble. When we push away the sand, we find that this “pebble” is actually the tip of a gargantuan pyramid. After years of excavation, we find wondrous hieroglyphics, strange tunnels and secret passageways. Every time we think we are at the bottom stage, we find a stage below it. Finally, we think we are at the very bottom, and can see the doorway.
One day, some bright, enterprising physicist, perhaps inspired by this article, will complete the theory, open the doorway, and use the power of pure thought to determine if string theory is a theory of everything, anything, or nothing.
Only time will tell if Einstein was correct when he said, “But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.”
Tscan (“Trivial Scanner”) is an event display, traditionally called a scanner, which I developed. It is a program that shows events graphically on the computer screen.
It was designed to be simple (“trivial”) internally, and to have a simple user interface. A lot of importance was given to giving the user a large choice of options to display events in many different ways.
Tscan proved to be a very useful tool for the development of fitters. A particularly useful feature is the ability to show custom data for every photpmultiplier tube (PMT). Instead of the usual time and charge, it can show expected charge, scattered light, likelihood, chi-squared difference, patches, and any other data that can be prepared in a text format.
Multiple rings of Cerenkov light brighten up this display of an event found in the Super-Kamiokande – neutrino detector in Japan. The pattern of rings – produced when electrically charged particles travel faster through the water in the detector than light does – is similar to the result if a proton had decayed into a positron and a neutral pion. The pion would decay immediately to two gamma-ray photons that would produce fuzzy rings, while the positron would shoot off in the opposite direction to produce a clearer ring. Such kinds of decay have been predicted by “grand unified theories” that link three of nature’s fundamental forces – the strong, weak and electromagnetic forces. However, there is so far no evidence for such decays; this event, for example, did not stand up to closer scrutiny.