The Lumber Room

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Archive for September 2009

The Decline and Fall of The Decline and Fall

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(Yes, this post is written just for the title. More details would be received gratefully.)

Over a period of 17 years from 1770 to 1787, Edward Gibbon wrote The History of the Decline and Fall of the Roman Empire. It was, among other things, a mammoth history (6 volumes, 71 chapters) of the last days of Rome, which for Gibbon apparently meant several centuries. (The book covers over thirteen centuries of history; here’s an outline.)

The work received instant praise. Adam Smith’s letter to Gibbon is typical:

“I cannot express to you the pleasure it gives me to find that by the universal consent of every man of taste and learning whom I either know or correspond with, it sets you at the very head of the whole literary tribe at present existing in Europe.”

The Decline and Fall became the model for all historians that followed — including its pessimism (history as “little more than the register of the crimes, follies, and misfortunes of mankind”), its overarching narrative, and its indictment of religion.

It became a literary monument of the 18th century, and one of the works that every educated man was expected to have read, a part of every bookshelf. Churchill (“I devoured Gibbon. […] I rode triumphantly through it from end to end and enjoyed it all”), Carlyle (“how gorgeously does it swing across the gloomy and tumultuous chasm of these barbarous centuries”), Virginia Woolf (“not merely a master of the pageant and the story; he is also the critic and the historian of the mind […] We seem as we read him raised above the tumult and the chaos into a clear and rational air”)… everyone read The Decline and Fall and spoke of it in the highest terms. (Gandhi read it in jail, and considered it an inferior version of the Mahabharata.) It was read by doctors, politicians, lawyers, novelists, even Sanskrit professors.

But then times began to change. Education stopped being the reading of “classics“, and became the learning of “subjects”. Today, no one I know has read The Decline And Fall, nor considers it worth the time.

Written by S

Sun, 2009-09-06 at 02:21:27 +05:30

Testing irreducibility using prime numbers

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Here’s a simple and nice test for irreducibility in {\mathbb{Z}[x]} that N told me about a year ago. (I just noticed this lying around while cleaning; I don’t have a year’s buffer like Raymond Chen.) Apologies for the ugly formatting; you’ll have to trust that the result (Theorem 1, or Corollary 8) is more beautiful than it looks. :-)

Actually I’m not sure why I wrote this originally, given that it’s all already well-explained in the originals and even partially on Wikipedia. Perhaps my proofs are different or simpler or I was bored or something.

1. Irreducibility test

In its simplest form, the test can be stated as follows.

Theorem 1 Given a polynomial {f(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_o} with integer coefficients, let {G = \max_{i}|\frac{a_i}{a_n}|}. If there exists an integer {m \ge G+2} such that {f(m)} is prime, then {f} is irreducible.

For example, with the polynomial x^2 + 3x + 1, we have G = 3, and f(5)=f(G+2)=41 is prime, which proves that it is irreducible. (We could also evaluate f at e.g. 7, 8, 9, or 10 to get the same conclusion.)

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Written by S

Sat, 2009-09-05 at 22:01:44 +05:30

Conscious consumption

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Late-night sleepy ramblings; please do not read :p

I have been taking a break, and it has helped me gain some perspective. Or so I thought.

Like some who might be reading this, I subscribe to a large number of blogs. Google Reader says 106 subscriptions, but a few of them are aggregators which combine the updates from several blogs.

For about three months (since June 10th, I think), I have not been reading them, nor reading the news. I’m not exactly sure why… it started as a day’s break (which was a big deal), then became four days (which was an even bigger deal), then it got easier and easier. Probably, I thought I was taking a break from (parts of) the internet in order to catch up with (parts of) my life. It didn’t work, of course. I merely found other sinks in which to dump my time. (I spent more time on Wikipedia than ever before, read more actual books than I had in the last couple of years, and so on.)

I did, however, discover a couple of things.

One is that Google Reader stops updating the count of unread items at “1000+”. (It also automatically marks items more than 30 days old as read, and, as I have “only” about 1500 items a month, I don’t know if it counts to “2000+”.)

The other is some general observations about what our lives have become.

It seems that the meanings of words like “recreation” have become somewhat quaint. Now “entertainment” is not always something to indulge in because one requires relaxation, or because it is a rewarding pursuit in itself, but simply “because it’s there”.
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Written by S

Sat, 2009-09-05 at 02:49:44 +05:30

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