Thanks for all the..

I remembered once, in Japan, having been to see the Gold Pavilion Temple in Kyoto and being mildly surprised at quite how well it had weathered the passage of time since it was first built in the fourteenth century. I was told it hadn't weathered well at all, and had in fact been burnt to the ground twice in this century."So it isn't the original building?" I had asked my Japanese guide.

"But yes, of course it is," he insisted, rather surprised at my question.
"But it's burnt down?"
"Yes."
"Twice."
"Many times."
"And rebuilt."
"Of course. It is an important and historic building."
"With completely new materials."
"But of course. It was burnt down."
"So how can it be the same building?"
"It is always the same building."

I had to admit to myself that this was in fact a perfectly rational point of view, it merely started from an unexpected premise. The idea of the building, the intention of it, its design, are all immutable and are the essence of the building.

The intention of the original builders is what survives. The wood of which the design is constructed decays and is replaced when necessary. To be overly concerned with the original materials, which are merely sentimental souvenirs of the past, is to fail to see the living building itself.

—Douglas Adams, Last Chance to See

Its that time of the year where a lot has changed but the intent still survived. I have a lot of things to be thankful for (my consciousness shall send messages to that effect) .It also begins a season of festivities around here which I consider to be the best on this side of the sun..

Happy Thanksgiving !

Quote du Jour

Masters and mistresses are very necessary to compensate for want of inclination and exertion, but whoever would arrive at excellence must be self taught.

-Thomas Young

Mantra of the Day

Say what you know, Do what you must, Come what may........

The Pleasure of Finding Things Out

I left a previous post saying I have a gut feeling that this can be solved for general cases (It was proved for triangles and I extended it to cyclic quadrilaterals). Now I got it. The attached equation shows the relationship between the Area and Perimeter for any convex polygon

as a function of the number of its sides (denoted by n)

In one form it amounts to saying that a circle is the most democratic of all convex shapes (every point is equidistant from the center..wish that was true for the states of a country).  Or to put it another way to max out the area you need all of your sides to be equal. Nothing else will do to max it out (maybe you knew that in grade school,). This time I convinced myself of its veracity.

"In the course of my law reading I constantly came upon the word "demonstrate". I thought at first that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when I demonstrate more than when I reason or prove? How does demonstration differ from any other proof? 

I consulted Webster's Dictionary. They told of 'certain proof,' 'proof beyond the possibility of doubt'; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understood demonstration to be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have defined blue to a blind man. 

At last I said,- Lincoln, you never can make a lawyer if you do not understand what demonstrate means; and I left my situation in Springfield, went home to my father's house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out what demonstrate means, and went back to my law studies."

                                                                        -Abe Lincoln

Food For Whatever...

"Nevertheless, I do not think for a minute that science will ever provide the consolations that have been offered by religion in facing death. The finest statement of this existential challenge that I know is found in 'The Ecclesiastical History of the English', written by the Venerable Bede sometime around A.D. 700. Bede tells how King Edwin of Northumbria held a council in A.D. 627 to decide on the religion to be accepted in his kingdom, and gives the following speech to one of the king's chief men:

Your Majesty, when we compare the present life of man on earth with that time of which we have no knowledge, it seems to me like the swift flight of a single sparrow through the banqueting-hall where you are sitting at dinner on a winter's day with your thanes and counsellors. In the midst there is a comforting fire to warm the hall; outside, the storms of winter rain or snow are raging. This sparrow flies swiftly in through one door of the hall, and out through another. While he is inside, he is safe from the winter storms; but after a few moments of comfort, he vanishes from sight into the wintry world from which he came. Even so, man appears on earth for but a little while; but of what came before this life or of what follows, we know nothing.

It is an almost irresistable temptation to believe with Bede and Edwin that there must be something for us outside the banqueting-hall. The honor of resisting this temptation is only a thin substitute for the consolations of religion, but it is not entirely without satisfactions of its own."

 -- Steven Weinberg, "Dreams of a Final Theory"

A Masterpiece

This article is the best so far on the subject by one of my fave authors.

Some excerpts to whet you appetite just in case you think the article is too long

What he underestimated was the total unabashed complicity of the upper class of American capitalism. For instance, he knew that the big Wall Street investment banks took huge piles of loans that in and of themselves might be rated BBB, threw them into a trust, carved the trust into tranches, and wound up with 60 percent of the new total being rated AAA.

We have a simple thesis,” Eisman explained. “There is going to be a calamity, and whenever there is a calamity, Merrill is there.” When it came time to bankrupt Orange County with bad advice, Merrill was there. When the internet went bust, Merrill was there. Way back in the 1980s, when the first bond trader was let off his leash and lost hundreds of millions of dollars, Merrill was there to take the hit. That was Eisman’s logic—the logic of Wall Street’s pecking order. Goldman Sachs was the big kid who ran the games in this neighborhood. Merrill Lynch was the little fat kid assigned the least pleasant roles, just happy to be a part of things. The game, as Eisman saw it, was Crack the Whip. He assumed Merrill Lynch had taken its assigned place at the end of the chain.

The models don’t have any idea of what this world has become…. For the first time in their lives, people in the asset-backed-securitization world are actually having to think.” He explained that the rating agencies were morally bankrupt and living in fear of becoming actually bankrupt. “The rating agencies are scared to death,” he said. “They’re scared to death about doing nothing because they’ll look like fools if they do nothing.”

The changes were camouflage. They helped distract outsiders from the truly profane event: the growing misalignment of interests between the people who trafficked in financial risk and the wider culture.

He agreed that the main effect of turning a partnership into a corporation was to transfer the financial risk to the shareholders. “When things go wrong, it’s their problem,” he said—and obviously not theirs alone. When a Wall Street investment bank screwed up badly enough, its risks became the problem of the U.S. government. “It’s laissez-faire until you get in deep shit,” he said, with a half chuckle. He was out of the game.

It was now all someone else’s fault.

Something for nothing. It never loses its charm.

My Connection With Brahmagupta

The above is an excerpt from a magazine called Pi in the Sky to which I was introduced by Danesh Forouhari back in 2006. Danesh one day sent me his contribution  involving triangle inequalities which can be seen here in issue #10.  

I deduced some stuff which is basically laid out above (extended the same theorem to cyclic quadrilaterals)  and Danesh graciously sent it over to the editorial folks who published them in their latest issue.  I am happy to  add a really small drop to the ocean that was explored by Brahmagupta & company when they were at Ujjain

The next challenge is to generalise the same result for cyclic polygons (have a feeling it could be deduced but not sure exactly how..). This makes my day :)

Quote Du Jour

There is something fascinating about science. One gets such wholesale returns on conjecture out of such a trifling investment of fact.

—Mark Twain, Life on the Mississippi

Indianapolis,1956

The dream they saw in 1956, I hope, shall come true today. Its quite nice to be at a cusp of history where you can tell your kids (maybe yours too) that we were here in the land where "pursuit of happiness" can end in finding one..

and it rained..

It rained yesterday.After a long time, it rained. It was a very nice saturday for curling with a good book and coffee listening to the pitter,patter of the drops with the tick,tock of the clock.Perfect time for a zen moment when I was listening to this track

"You miss too much these days if you stop to think."

- U2, "Waiting for the End of the World"

The trick here is to think without thinking? This portal has some answers to that