My father gave me life, but Coperni taught me how to live it

I am become death, destroyer of worlds...Therefore, get up and attain glory. Conquer your enemies and enjoy a prosperous kingdom. All these (warriors) have already been destroyed by Me. You are only an instrument, O Arjuna.
Bhagavad Gita, chapter 11, verses 31-33

Never since the Carpenter's son has there been a man like Coperni. Coperni called astronomy the pinnacle of mathematics - and believed heaven to be the most beautiful object possible to study. "Among the various literary and artistic pursuits which invigorate men’s minds, the strongest affection and utmost zeal should, I think, promote the studies concerned with the most beautiful objects… these dealing with the universe’s divine revolutions.. What indeed is more beautiful than heaven, which of course contains all things of beauty?"
He also quips poetry. "For us who are borne by the earth, the sun and the moon pass bye / And the stars return on their rounds, and again they drop out of sight"

To begin with, Copernicus was a late bloomer. At a time when young men were sent to University at about age fourteen or fifteen (women were not permitted), Copernicus did not begin until he was almost nineteen. The typical student went to university for three years and then started to seek fame and fortune. Copernicus attended his undergraduate university for four years, did not earn a degree, and then studied at three other universities for the next eight years. He spent a total of twelve years as a university student. Today we would call such a student a slacker. In Copernicus' era such a prolonged sojourn was highly unusual.

Second, there is not even a whiff of ambition emanating from Copernicus' life, nothing to indicate that he might pursue a line of inquiery that would be revolutionary. Most of the other titans.. Leonardo, Brahe, Galileo, and Newton - had ambitious streaks and outsized egos, and each was eager for acclaim and recognition. Not Copernicus. He was a retiring hermitlike scholar who wanted nothing more than to be left alone.. After finishing his studies, Copernicus followed the path of least resistance and took a position as the personal assistant to his uncle.. an influential prince-bishop in the Church who wanted to groom Nicolaus to be his successor guaranteeing a life of riches and power. Instead, Copernicus opted off the fast track at the age of thirty seven, left his uncle's side, and spent the rest of his thirty-three years as a comfortable but minor cleric. He did not even bother to take the relatively easy step necessary to become a priest, ignoring pressure to do so from his superiors and friends.
- Copernicus Secret

GH Hardy - A Mathematicians Apology

Though this is a picture of Sir Isaac - in his stunning regalia, right before he is about to hit up the club and drop it like it's hot - he's an example of someone mystified by the domain of numbers, and GH Hardy attempts to explore this domain in his essay. Alright forget it - I'm just going to talk about what's interesting about it. Here goes:
I was about fifteen when my ambitions took a sharper turn. There is a book by 'Alan St. Aubyn' called A fellow of Trinity, one of a series dealing with what is supposed to be Cambridge college life... There are two heroes, a primary hero called Flowers, who is almost wholly good, and a secondary hero, a much weaker vessel, called Brown. Flowers and Brown find many dangers in University life, but the worst is a gambling saloon in Chesterton run by the Misses Bellenden, two fascinating but extremely wicked young ladies. Flowers survives all these troubles, is Second Wrangler and Senior Class, and succeeds automatially to a Fellowship (as I suppose he would have done then.) Brown succumbs, ruins his parents, takes to drink, is saved from delirium tremens during a thunderstorm only by the prayers of the Junior Dean, has much difficulty in obtaining even an Ordinary Degree, and ultimately becomes a missionary. The fiendship is not shattered by these unhappy events, and Flower's thoughts stray to Brown, with affectionate pity, as he drinks port and eats Walnurts for the first time in Senior Combination room.
Now Flowers was a decent enough fellow, but even my sophisticated mind refused to accept him as clever. If he could do these things, why not I?
What's intriguing is 1) [not mentioned in this paragraph] but from a young age he viewed math as a competitive type sport.. and 2).. math was his claim to fame - his way to gain fellowship. But digging deeper here's something more intriguing 3) what about poor Brown, who, perhaps through no fault of his own, is not 'genetically protected via Nature' from Drink.. more likely to succumb.. and all of a sudden his life is in ruin, graduate's second class, and is not given the World's esteem like Flowers. Talk about unfair, and talk about idiot pretentious Flowers, who doesn't realize this. What's more interesting is this is just the way humans and society works, the succumbers 'work themselves out' - and those who can survive stay - though perhaps thinking it is through sheer will that they have become who they are. This gets into moral responsibility - which is a conundrum for philosophers = the more humanity discovers how we are not equal - how their are imbalances - and how addicts, 'manics', the messed in mind are inclined to odd behaviors - the more problems arise from this because people must face their prejudices ( "we are not all angels and our souls do not fly free - E.O Wilson"). It's sort of humerous that perhaps people with some sort of trait charactertized by lack of moral revolt in performing certain acts are killed rather than 'fixed/understood' when they commit crimes - another topic altogether.

Anyway, you could go on and on with Flowers and this particular story, because it's very interesting. But the Gold of Hardy's thing is how he describes math, he suggests math is simply patterns (which it is) and that there is a beauty to this (like beauty to poetry, which is a pattern of words, which don't neccessarily have to hold truth to reality, he gives an example). Math is just like a painting - the derivative of sin is cosine, cosine's is - sin. sin squared plus cos squared is 1.. etc. there are patterns to the paintings, which are neat and fun to pick out. I came across his essay by accident earlier, having brought the wrong volume of a book and opening to his essay on the first flip, and then also I read of two mathematicians who claimed this essay in particular is why math 'grinds their gears;.
Anyway, interesting interesting.

Pythagoras offers tips from the grave

Pythagorean Persevering Spirit.

Words of wisdom from the grave - a letter from Lysis to Hipparchus, saved from historical death via transcription by Copernicus in his Revolutions of the heavenly spheres written in 1500. Lysis was a follower of Pythagorus, and here, shockingly, he tells Hipparchus if he wishes to continue teaching mathematics/philosophy without any adjusting of his pupils, he is "as good to him as dead".

Lysis compared those who preached the lofty precepts of philosophy without laying a type of 'cleansing of the spirit' to pouring fresh water down a mucky well. "Pure water is mixed with filth, and the result is a mix of waste."

Imagine every professor ever starting his class for the first 3 days saying:
"These first 7 days the syllabus is as follows - nothing for today, nothing for tomorrow, and nothing this entire week. Past this - what I will be doing is giving you information so prized by the ancients countless hours of toil and persevering spirit were needed to unearth these treasures. You can either sit here, and let it go to waste, and I waste my time and you yours, or you may listen and be initiated. You must cleanse the stains on your heart of terrible habits, obstain from beastly drugs, and inhale these words as if they come directly from Minerva herself. You will not be given these secrets as you are, there is a reason you are average and not great. But if you 'get up and attain glory' - work to change and show you are eager - you will be initiated, and with persevering spirit and hard work things will be reveiled to you which now lie hidden.
Lysis to Hipparchus: Greetings!

After the death of Pythagoras... it is not fitting to hand out to everyone what we have obtained through so much labor. In the same way as it is not permitted to reveal to profane people the mysteries of the Eleusinian goddesses...The value of our labor, indeed, is to rehearse continually: How much time we have consumed in removing blemishes which persisted in our breasts; so that at last after five years we have been able to master his precepts. In the same way that dyers, after washing, fix the color with an astringent, so that they might hold the color indelible, so the color does not pass away thereafter...

There are some, in truth, who, imitating his doctrine, make much of it in the wrong context, not as is seemly to instruct young men. Hence, they make the pupils importunate and arrogant, as they mix the genuine precepts of philosophy with turbulent and impure attitudes. It is as if someone pored pure and clear water into a deep well full of mud: he stirs up the mud and loses the water's clarity. So it happens to those who teach or are taught in that manner. Deep and dark tangles occupy the heart and the mind of those who were not correctly initiated, and they impede all gentleness and right reason in the soul. In this tangle there are found all manner of vice which feed in them. They keep reason away and do not allow it to come forth. We shall name first, as mothers of those ingredients, incontinence and greed. For they are both most prolific. Incontinence breeds all sorts of illicit things, incest, drunkenness, outrage, unnatural pleasures, and certain violent forces which drive one to death and destruction. Lust drives certain ones even to relations with their mothers and daughters, whom it also leads even against law, state, city, and rulers. It hurls them into traps so that it forces them into perdition. From avarice arises robbery, murder, sacrilege, poisoning, and other vices of that kind. Therefore it is fitting to remove by fire, sword, and any means those who are influenced by shadows of this forest. Once we understand innate reasoning--freed from these influences--we will have implanted the best and most fertile fruit for him.

You indeed, Hipparchus, had learned these things from no little study. But you have preserved little, O good man, having tasted Sicilian luxury--which you should have regarded of no value. Many say you philosophize publicly, which Pythagoras forbade, who, relinquishing the short treatises in his will to his daughter, Dama, ordered her not to give them to anyone outside the family. Although able to sell them for a great price, she did not. She held poverty and the instructions of her father more dear than gold. It is said that the dying Dama left this trust of faith to her daughter Vitalia. For we males are omitted in wills by the master, but we are the bearers of our profession.

If you will correct yourself, I shall receive joy. If not, you are as good as dead to me.


A man's encounter with an Algebra book
And now we are together, O mysterious tome, whose Arab name breathes a strange mustiness of occult lore and claims kindred with the sciences of almagest and alchemy. What will you show me? Let us turn the leaves at random. Before fixing one's eyes on a definite point in the landscape, it is well to take a summary view of the whole. Page follows swiftly upon page, telling me nothing. A chapter catches my attention in the middle of the volume; it is headed, Newton's Binomial Theorem.The title allures me. What can a binomial theorem be, especially one whose author is Newton, the great English mathematician who weighed the worlds?
What has the mechanism of the sky to do with this? Let us read and seek for enlightenment. With my elbows on the table and my thumbs behind my ears, I concentrate all my attention.
I am seized with astonishment, for I understand! There are a certain number of letters, general symbols which are grouped in all manner of ways, taking their places here, there and elsewhere by turns; there are, as the text tells me, arrangements, permutations and combinations.
Pen in hand, I arrange, permute and combine. It is a very diverting exercise, upon my word, a game in which the test of the written result confirms the anticipations of logic and supplements the shortcomings of one's thinking apparatus.It will be plain sailing,‘ said I to myself, ‚if algebra is no more difficult than this.‘
I was to recover from the illusion later, when the binomial theorem, that light, crisp biscuit, was followed by heavier and less digestible fare. But, for the moment, I had no foretaste of the future difficulties, of the pitfall in which one becomes more and more entangled, the longer one persists in struggling. What a delightful afternoon that was, before my grate, amid my permutations and combinations! By the evening, I had nearly mastered my subject. When the bell rang, at seven, to summon us to the common meal at the principal's table, I went downstairs puffed up with the joys of the newly initiated neophyte. I was escorted on my way by a, b and c, intertwined in cunning garlands.


Tomorrow, we may have a quiz in regards to guestimating square root functions (square root of 26 for example). You just use the equation for a tangent line for the square root function ( 1/2 root x as the slope - and then plugin y - 5 = m (x - whatever)... for 26.. you use 25 because you know the square root is 5.. do y - 5 = m (26-25).. and m is like 1 /10th.. so basically the guess is the square root of 26 is about 5 and 1/10th or so.. which is reasonable. So it's a nifty way to do it. There's going to be more on the quiz, it's our 7th, but I'll that up later. The latest section covers concavity.. telling whether a function is increasing or decreasing at x values.. just via being given a function.. f(x) = 5x^4 + 3x^2 + 4.. and via tricks determine where it increases/decreases/inflects/etc.

We had our midterm last Friday, and I'll see how I did on it next time. I was ready when I took it, so hopefully not so bad.Now that was that for starters, give me a second and my next post will be more fun.

Below is just something aesthetically pleasing I found, how the wiggle of the cosine function looks, and basically making stones out of it and building it high makes humans gasp in awe. check it