"Mountains of Ice about me to Melt"

Betwixt you and me, There exists a poem, Which I write about, On my own.
About numbers, The Pythagorean Flux,
Paintings, Patterns, Gee-Willickers-Shux!
Dont you know, From the Gods of Old,
Everything created, was in Numb3rs mold!
Life, trees..Man with his Urn,
3 Billion years, of DNA pattern!
The Sun, The Moon, The Earth, Our Sky,
The System Repeats, Higher and Nigh!
There's even a rumor, Helen was just a metaphor
What the Trojans stole, Was a repeating decimal!
A repeating pattern, The diameter to Circle relation!
So beautiful was the discovery,War was the Summation!
Let us listen to Senaca, And new relations uncover,
"Our life's a sorry affair, Without something new to discover!"
And we'll heed Van Gogh, who said when he was candid
"True Art is never finished - Only Abandoned"
And Lastly if it's true, Man just creates order from chaos-
Read me and my blog, So now two won't be Lost!!
- F.W. Westaway

Cosine - Sine - lovers wedded to graviation?

"Let us now consider, for a little while, how wonderfully we stand upon this world. Here it is we are born, bred, and live, and yet we view these things with an almost entire absence of wonder to ourselves respecting the way in which all this happens. So small, indeed, is our wonder, that we are never taken by surprise.. I think to a young person.. the first sight of a cataract or mountain would occasion him more surprise than he had ever felt concerning the mean of his own existence -- how he came here; how he lives; by what means he stands upright; and through what means he moves about from place to place. ." - Faraday, on the Various forces of nature

Curious is the flight of the stone as it descends to the ground - curious is the descent of urinary projectiles as it forms an arch - juvenile amusements aside, it certainly is an interesting reflection to consider how important the cosine and sine functions are. They form beautiful wiggle waggling curves, and it makes one wonder if we weren't being sucked into the center of the earth at 9.8 m/s, if this beautiful curve motion downwards we would've evolved shape-brain cell-recognition patterns for.

As a fun thought, consider the magnitude of the earth, for every reaction there is an equal and opposite. 6 Billion people are applying a force (ma) against the earth while it pushes back. It's able to endure this. and more than that, it is still able to maintain it's inertia while it carries us around the sun now and we notice none of it. Moreover, imagine how big is the sun, how big are others, how big is the galaxy, and the invisible attractions pulling it every which way. Then think of the atom in one finger, somehow it knows to listen to the force of gravitation from some spot millions of miles below the earth(the center), rather than the feeble attraction from that colossus star in the center of the solar system we call the sun (Helios sounds better). There must be more gravitational particles whispering sweet somethings to it from that spot below the earth right now... as opposed to those that managed to make their way here at the speed of light from the sun.

I am a believer with Booker Washington that the biggest sin is speaking simply to speak. so I will skip rambling and relay my ardours - I believe our fascinatioin with certain shapes are entirely and obviously predicated on our earthly living habitations, and our evolved recognition shape cells obviously reflect this - common sense, but interesting are the incites. Chimps can recognize chimp faces the same way we our own species. Bees similar (I believe, have to research the link) More mysteries await the one who thinks more about this.

I love math

Like a storm cloud that perfumes the horizon, sounds of thunder and bolts of lightning scare the flocks as they run in terror - dark as this it seems is the feeling as I open a new chapter to master. I inhale and prepare for battle with my pen.
Differentiate this polynomial - is that all you've got?
Draw a curve sketch and mark horizontal and vertical asymptotes? Please.
State the 3 requisites for Rolles theorem, state the formal definition for dy, then guesstimate the change in x for this function from 10 to 10.1 - like taking candy from a baby.
I'll dominate this like Achilles, who after he slayed Hektor, roped him, attached him to his carriage, then dragged his dead corpse in circles around his village - as the citizens of Troy watched and gasped in terror.

me, parading around with the corpse of my homework

The Grandeur that was Archimedes, and the Glory that was Rome

There's something about an activity that can entrance one so willingly that even war itself cannot distract him. This was the case for the bearded man above. His glory was so great Plutarch, that sage of sages, describes him in a passages and also describes his death. The man is Archimedes.

The granduer of archimedes (plutarch):

" Archimedes..possessed so lofty a spirit, so profound a soul, and a wealth of scientific inquiry. He believed the business of mechanics and every utilitarian art as ignoble and vulgar [and] gave his zealous devotion only to those subjects whose elgance and subtlety are untrammeled by the necessities of life.. [he was] continually bewitched by some familar siren dwelling within him, he forgot his food and neglected the care of his body; and how, when he was dragged by main force, as often happened, to the place for bathing and annointing, he would draw mechanical figures in the hearths, and draw lines with his finger in the oil with which his body was annointed, being overcome by great pleasure and in truth..

But what specially grieved Marcellus was the death of Archimedes. For it chanced that he was alone, examining a diagram closely, and having fixed both his mind and his eyes on the object of his inquery, he perceived neither the inroad of the Romans nor the taking of the city. Suddenly a soldier came up to him and bade him follow to Marcellus, but he would not go until he had finished the problem and worked it out to the demonstration. Thereupon the soldier became enraged, drew his sword and dispatched him. Others, however, say that the Roman came upon him with drawn sword intending to kill him at once, and that Archimedes, on seeing him, besought and entraced him to wait a little while so that he might not leave the question unfinished and only partly investigated; but the soldier did not understand and slew him.- 100 AD, Plutarch, on Archimedes "

Restoring the Glory of his fall (cicero)

" When I was in siciliy in 75 bc.. I managed to track down his grave. The Syracusians knew nothing about it, and indeed denied that any such thing existed. But there it was, completely surrounded and hidden by bushes of brambles and thorns. I remembered having heard of some simple lines of verse which had been inscribed on his tomb, referring to a sphere and cylinder modelled in a stone on top of the grave. And so I took a good look round all the numerous tombs that stand beside the Agrigentine Gate. Finally I noted a little colume just visible above the scrub; it was surmounted by a spherre and a cylinder. I immediately said to the Syracusans, some of whose leading citizens were with me at the time, that I believed this was the very object I was looking for.

So one of the most famous cities in the Greek world, and in former days a great centre of learning as well, would have remained in total ignorance of the tomb of the most brilliant citizen it had ever produced, had a man from Arpium not come and pointed it out! http://www.math.nyu.edu/~crorres/Archimedes/Tomb/Cicero.html "

"He tortured and tormented Quantities in all possible ways - to make them confess their Secrets, and discover their Properties"

To strike out new lights, to adventure where no footsteps had ever been set before… this is the noblest Endowment that a human Mind is capable of.
-1736, Sir Isaac's Method of Fluxions and Infinite series Preface

I was going through L’Ptal’s book, (preface; cant find whole) which of course is interesting, but was incredibly struck with his first two postulates – 1) that all curves are just polygons with infinite sides. It means no wonder you can find a tangent to some point on a curve to guess how it’s changing, because the whole curve is nothing but infinite tangents. More over, what does that say about other curves, radiation?

I began to think about photons, and surfaces in general. All surfaces are ‘clouds’ of electrons, there is no solid edge. The beauty of the world around us is nothing touches ever, and this explains the mystery of magnets acting at a distance – it always acts this way, it’s just the distance is so small we can’t see it. But perhaps this gives new light to another particle theory for promoting radiation of the electromagnetic spectrum. If electrons are clouds, photons ‘packets of energy’.. these curves representing their boundaries or gradations of influence can be thought of as polygons infinitely small.

http://www.archive.org/stream/methodoffluxions00newt#page/n19/mode/2up

http://turnbull.mcs.st-and.ac.uk/history/Extras/LHopital_Preface.html

ps –another neat thing in the Newton preface is they don’t talk of calculus but the ‘philosophy of quantity’ – now that is interesting. The philosophy of quantity! Who talks like that! Crazy. And that makes it much more interesting. Quantity rules the universe, we have our own unconscious mechanism of gauging it – the philosophy of it is certainly worth a peek-see. also listen to this language!

" He had acquired a complete knowledge of the Philosophy of Quantity, or of its most essential and most general Laws; had considered it in all views, had pursued it through all its disguises, and had traced it through all its Labyrinths and Recesses; in a word, it may be said of him not improperly, that he tortured and tormented Quantities in all possible ways - to make them confess their Secrets, and discover their Properties. "

fun

Jacob Bernoulli: (left)

"I'm telling you man, when she asked you up for coffee that was your in"

Johannas Bernoulli: "Are you serious?! .
I just left and said no thanks.

Damn it!"

Lo-Pee-Tal

It’s 1696 France. Your walking down a cobbled stone path. A man greets you, you make small chat. You find out he’s headed to the congregation of oratory.. where he speaks.. then to his tutor jacob Bernoulli, with whom he meets, then to work on a theory of limits – which posterity will call by his last name. The man is Guillaume Francois Atoine de L'Hospital, "a man of the highest social distinction whose love of learning drove him to devote much of his short life to scientific writing"

Fast forward 323 Earth Sun orbit rotations – it's 2010. I’m sitting in a library with a book , whose text is using this man’s very theory to solve problems. Your trying to find a value for some relation but the normal method gives an irrational fraction. The man’s secret was a pattern – if the 0/0 fraction exists, take numerator and denominator’s derivatives, plug in the value your looking for – bam, you have it.

In notation

The guy - the jacob one - is the one in the pic.
who cares who did it.. neat trick nonetheless