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Monday, May 04, 2009

Filling the Universe with Sand

One of the "Silicon Avogadro Spheres" at the National Physical Laboratory (NPL), Teddington, UK. See:Counting Atoms in a Sphere

Stefan writes...
To measure means to count. We measure a length by counting marks on a ruler, and a time span by counting ticks of clock. We compare the quantity we want to measure to multiples of a standardized quantity, the unit of measurement, such as the metre, the inch, or the second......


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Discrete mathematics, also called finite mathematics or decision mathematics, is the study of mathematical structures that are fundamentally discrete in the sense of not supporting or requiring the notion of continuity. Objects studied in finite mathematics are largely countable sets such as integers, finite graphs, and formal languages.

Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages. In some mathematics curricula, finite mathematics courses cover discrete mathematical concepts for business, while discrete mathematics courses emphasize concepts for computer science majors.


Reductionism seems to be the ability to measure in powers of ten, and then, we get to a point where everything is all smeared out. So energy at some point becomes the determination of what any particulate could be measured, and yet, we would say that it is like using sand to fill the universe?

I have been intrigued by the idea of a "kitchen measure of a teaspoon of sorts" as well as to what water fills any glass to it's brim. Thinking, that such a substance while pertaining to the measure of something, can have space in between, with which it can fill? Yet, it does not flow over? How much before it does, and we say that this measure is what the spirit of these walking bodies shall qualify too? The soul at 21 grams?

The title of the movie comes from the work of Dr. Duncan MacDougall, who in the early 1900s sought to measure the weight purportedly lost by a human body when the soul departed the body upon death. MacDougall weighed dying patients in an attempt to prove that the soul was material, tangible and thus measurable. These experiments are widely considered to have little, if any scientific merit, and MacDougall's results varied considerably from 21 grams, but for some people this figure has become synonymous with the measure of a soul's mass [1]The Soul=λόγος,θυμος,ἔρως


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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


"Kepler Conjecture is speaking about cannon balls. Tom Hales writes,"Nearly four hundred years ago, Kepler asserted that no packing of congruent spheres can have a density greater than the density of the face-centered cubic packing."


Turning now to Archimedes’ reckoning, he proceeds to fill up the (then) known universe with sand by considering a succession of spheres, each 100 times the diameter of its predecessor in the succession. He uses a fact well known to Greek geometers: the ratio of the volumes of two spheres is the third power of the ratio of their diameters. The Sand Reckoner


The Stomachion

A computer-enhanced image of a 1,000-year-old manuscript reveals the faint traces of a copy of Archimedes' Stomachion treatise. It had been overwritten by monks in the 13th century. (Rochester Institute of Technology, Johns Hopkins University/The Archimedes Palimpsest)


It was chance that led Dr. Netz to his first insight into the nature of the Stomachion. Last August, he says, just as he was about to start transcribing one of the manuscript pages, he got a gift in the mail, a blue cut-glass model of a Stomachion puzzle. It was made by a retired businessman from California who found Dr. Netz on the Internet as a renowned Archimedes scholar. Looking at the model, Dr. Netz realized that a diagram on the page he was transcribing was actually a rearrangement of the pieces of the Stomachion puzzle. Suddenly, he understood what Archimedes was getting at.
See:στομα'χιον

See Also:Archimedes Palmpsest

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See:
  • Historical Approach of the Sand Reckoner
  • 13th Sphere of the GreenGrocer
  • Loosing Sight of Discrete Geometry
  • 5 comments:

    Phil Warnell said...

    Hi Plato,

    A nice little follow up piece on what Stefan had written about. As you can tell my greatest interest of course was the role that Archimedes had in all this and ancient Greece in general with the beginnings of the atomic outlook or the discreteness of matter. What I am of course the most keenest on is how all this was lost or put to the side for almost two thousand years before picking up the threads and followed again. For me that was two thousand years wasted and as I said I can’t help but wonder where would we all be today if that civilization would have continued from the discovery aspect of things.

    The general opinion is that we have today less than ten percent of what was written in antiquity, with much of that being mostly religious or philosophical works. So again I am lead to wonder if for all practical purposes are we perhaps at best only a century or two beyond what those of Archimedes time and place had achieved. What I find as even a greater concern is if you presented an average person today with the problem of the king’s crown what would be there reply in terms of solution? Even more important if I were to ask a staunch supporter of say the Green movement how many of them could offer a solution and execute it and would they fare any better than the more general average? The question of course are people confident and trust their futures to what they understand as knowledge or what they believe to be knowledge, since most have little ability to discern for themselves. Arun reminded me we are always at the bring of another dark age and what is really the truth is for most they have never left it,

    Best,

    Phil

    Plato said...

    Hi Phil,

    By introduction of the Crown, yes, I see now where your analysis resides.

    It has become an exercise for me of moving forward then from what is shown under the idea of a measure( Democritus), and more toward what ingenuity does when we are deep in thought. What is natural then?

    What we gain access too while we do not realize it? It is connecting to that which becomes the way in which we might say "how is it such thinkers can become and present ole ideas, in new ways?"

    I point that out in the new post today.

    Much as you have done with presenting the Crown for examination, or Pirsig. I was somewhat engaged in politics, but thank you for some new material to consider.

    I have not forgotten your comment on the Green movement(Carbon Foot printing) but need some time to think here.

    Truth is "more then" what the scale can represent to me at the most ideal and psychological basis for the person's growth toward reality.

    It begs the question of what the heart and truth represent in measure(a feather) that you will say this way is the way I shall conduct my life on principle.

    There shall then be no regrets then.

    The measure in air and in water are the realization of mind working to affect its conduct on earth, as it is in heaven. You see?:)



    Best,

    Plato said...

    Just as in the work on stratospheric temperature, it took scientists from two normally distant fields to fully tap the information flow from soil moisture studies—and add one more job title to the resume of the cosmic ray.Cosmic weather gauges

    Phil Warnell said...

    Hi Plato,

    If one thinks of it there is a limit for they have calculated the greatest amount of sand that can fill a space which is finite and that be the Swartzchild radius, after which all the space disappears with only the sand to remain. So should we ask is there a limit to space or a limit to the amount of sand which can be held within it? This is the paradox that is not understood and for which explanation is struggled for. It is also to ask what to call what’s contained between the horizon of one limit and the point of the other? So the largest sphere one can construct has no physicality we are familiar with, yet preserves all the qualities of it except one, which is time the one thing that we can’t produce an artefact to represent as to measure, for nothing can be constructed represent it simply as it cannot be contained yet still all existence depends.


    Best,

    Phil

    Plato said...

    Hi Phil,

    You are giving me the parameters with which I must hold perspective?

    Defining the Space your Living InNone of what I relay there has been negated, while living within the confines of those same parameters? You have to move outside the box cosmologically.

    I am defining the space with which our views had been reduced to a four dimensional view.

    It always remains dynamical no matter the distinction of the space, microscopically or cosmological, we describe?

    The universe has been wrapped in this microscopic view and remains dynamical even at that level.

    Best,