Thursday, December 5, 2013

An apology the world will little note nor long remember

Something I missed recently, but I'll include it here in case you missed it too:  coinciding with the 150th anniversary of the Gettysburg Address on 19th November, a retraction of an 1863 newspaper editorial dismissing the speech as “silly remarks”.

“We pass over the silly remarks of the President. For the credit of the nation we are willing that the veil of oblivion shall be dropped over them and that they shall be no more repeated or thought of.” With these stinging words did the Patriot & Union of Harrisburg, Pennsylvania achieve infamy in the annals of journalism, by panning the presidential speech that lives as one of the most treasured orations in the English language.

Three weeks ago, the successor paper Patriot-News revisited this unkind judgement, suggesting that their predecessors were perhaps under the influence of partisanship, or of strong drink - whilst wittily observing that “the world will little note nor long remember” the paper's apology.

This is all good fun, but ahistorical, of which more below.

Lincoln at Gettysburg (unknown date)
First, here's the full text of the Gettysburg address. [1]

Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.

Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.

But, in a larger sense, we can not dedicate - we can not consecrate - we can not hallow - this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us - that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion - that we here highly resolve that these dead shall not have died in vain - that this nation, under God, shall have a new birth of freedom - and that government of the people, by the people, for the people, shall not perish from the earth.

Now to the question of how the Patriot & Union came to overlook history being made that day. It's worth reading “Living on the wrong side of history? The Harrisburg Patriot & Union's notorious 'review' of the Gettysburg Address”  from Patriot-News website.

This deals with the issue historically, and discounts the playful suggestion that their 1863 predecessors were under the influence of strong drink. In the first place, the newspaper's own reporter described the President's speech in Gettysburg like this: "The President then arose and delivered the dedicatory address, which was brief and calculated to arouse deep feeling."  But the crux is that the Patriot & Union supported the Democratic party, and was hostile to Lincoln, his conduct of the war, and his war aims. Moreover, the paper’s editors had been in put in jail for sedition a year before. So there was stuff going on.

As a final thought, I've often wondered if Lincoln really believed that the world would little note, nor long remember, what he said that day.  He well knew he had crafted a masterpiece … surely he entertained the hope that the world would recognise this?

[1] This is the text most often reproduced. There are others, see Abraham Lincoln Online.

Of logarithms, fraudsters and exoplanets

Pristine log tables. Well-thumbed would be better.

Suppose you need to multiply 263.4 by 351.2 you would nowadays use a calculator, but when I was at school in the 1960’s we used logarithms.  Logs to their friends.  In a book of log tables we would look up the log of 263.4 and the log of 361.2, add the two logs together, then look up the result in an antilog table, and bobs your uncle. Not as quick as a calculator but easier than multiplying.  We each carried around a well-thumbed book of log tables, yet one thing we all failed to notice was that the pages for numbers beginning with 1 were more well-thumbed than pages for numbers beginning with 9.  Or if we noticed we never asked ourselves why. But a character called Newcomb did, in 1881. For he it was that discovered Benford’s law and in the process proved Stigler’s law (Stigler’s law being that in science, laws are always named after the second person to discover them; and in this case the second person to discover the law was Benford.) 

Benford's law states that in most lists of data, the first digits of the numbers follow a pattern of probability, where 1 is the commonest first digit, and 9 the least common.  Take for example a list giving the heights of the tallest buildings. Almost one third of the buildings in the list will have a height whose leading digit is 1. Next most frequent in the leading position is the digit 2. And so on, till you come to 9 which is likely to be found as the leading digit in only 4.6 per cent of buildings.

Or rivers. Look at Wikipedia’s list of world rivers longer than 1000 km. You'll find a table giving length in km, length in miles, drainage area in km², and average discharge in m³/s. At my rough count, it contains five hundred numbers, of which only 18 start with a 9.


Benford's law also applies to financial data, a fact unknown to most fraudsters, who tend to suppose that the best way to insert phoney entries into a list of expenses or transactions, is to make up numbers at random, with as many starting with 9 as starting with 1. But Benford’s law soon finds them out. And the spooky thing is, it matters not whether the transactions are in pounds, euros or dollars.

Exoplanet with two suns and an exomoon. But is it real?

I've read the Wikipedia article on Benford’s law which purports to explain why this should be so,  and I can't follow it as it involves high level maths.  But no matter, all this is by way of working out how many exoplanets have been discovered.

I recently mentioned that the Kepler mission found over two thousand planets orbiting other stars. Now it's important to note that these haven't actually been seen in the usual sense of the word. They have been seen in strings of data, indicating very slight periodic dimmings in the brightness of a star. From this data scientists have inferred size of a planet, distance from the star, and other factors.

But inferences can be wrong. In some cases the data could perhaps result from another phenomenon entirely, and have nothing to do with a planet at all.

And according to this week’s New Scientist, that’s where Benford’s law comes in. 

Thomas Hair at Florida Gulf Coast University wondered if Benford's law would hold true even beyond the solar system, and examined data from an online catalogue that lists 755 confirmed exoplanets and nearly 3500 planet candidates. Planet masses are given in multiples of Earth's or Jupiter's mass. He found that whichever of these two units is used, the figures closely fit Benford's law, making it highly likely the supposed planets really are out there. "The close fit with Benford's law gives a confirmation to experts' belief that most of the candidates are valid," he says. 

I wish I still had my log tables so I could check that well-thumbed business for myself. I looked in vain on the web for an image of a used copy to put at the top of this post. For fun, I've spent the last half hour reminding myself how to use logs. If you too last used them in the 1960’s take a look.