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:
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