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Prime Numbers II

In yesterday's entry, I discussed a recent proof devised by a professor at the University of New Hampshire that there are "bounded gaps" between prime numbers. Specifically, Yitang Zhang has established that there are infinitely many pairs of primes that differ by 70 million or less.

There are two fascinating things about this tidbit about which I wish to comment today. First, who the heck is Yitang Zhang? Second, infinity and size.

Who the heck?

One might naively expect the burning questions of a recondite field to be settled by the elites of the relevant expertise.  Andrew Wiles, the fellow who proved Fermat's Last Theorem correct (though in a way that can't "fit into a margin") was a Royal Society Research Professor at Oxford University, specializing in number theory. Before that, he had been a professor at Princeton University in the early 1980s and a Guggenheim Fellow at the Institut des Hautes Etudes Scientifiques in France in the late 1980s.

Do…

Prime Numbers I

All right. Let's really put our geek hats on and talk about prime numbers.

A little over a year ago I wrote about an enjoyable evening I spent watching the musical Fermat's Last Tango, a fictionalized (and lyrical) presentation of Andrew Wiles' successful effort to prove that Fermat was right about a certain famously generalized form of the Pythagorean theorem.  For purposes of the musical, Wiles is renamed Daniel Keane.

Anyway, one of the conjectures that has acquired a good deal of importance in elite math-geek circles since Wiles' success is something called the "bounded gap conjecture" concerning prime numbers.

As a refresher, a prime number is any number higher than 1 that can be divided only by 1 and itself.

There are lots of prime numbers amongst the lowest counting numbers, but they thin out as one gets into the higher ones.

1 is by stipulation not a prime. Two and 3 are both primes. The first integer above 1 that isn't a prime, then, is 4. …

Remembering the Civil War

On this Memorial Day weekend, we might well think especially of the war that gave rise to Decoration Day, in time so renamed.

Nancy Pearl has made the observation that every generation of Americans since the end of the civil war has re-written that war in fictional form to reflect its own "dreams, desires, fears, and beliefs."

The nineteenth century was not over yet when Crane wrote RED BADGE OF COURAGE.

Forty years after Crane, Mitchell's GONE WITH THE WIND gave us a crystallization of nostalgia for the antebellum society of Tara and the O'Hara clan.

Twenty years after that, MacKinley Kantor wrote ANDERSONVILLE, a novelization of the horrors of life in that prisoner-of-war camp.

Identifying more recent books is easy. Deciding which of the more recent ones deserve to be mentioned in the same breath as those is more difficult. COLD MOUNTAIN by Charles Frazier, can make a strong claim. Pearl mentions others.

On a trip through Virginia a few years ago, I notic…

Interactive Data Language

The human mind likes its data visually presented.

Thus, the demand for Interactive Data Language, a computer language used to create high-quality graphics.

It began life as the product of Research Systems Inc., and that company's founder, David Stern. In 1981 the company released a variant for VAX/VMS, the architecture that Digital Equipment Corporation  was using.

Although IDL's earliest use was in astronomy and the space sciences, it soon proved adaptable to such fields as medicine and nuclear physics. According to Liam E. Gumley of the University of Wisconsin, Madison, the language is used in "monitoring and controlling the plasma field of a nuclear fusion tokamak."

I wrote about this (including the above paragraph verbatim) for eHow back in September 2010.  Some Q-and-A operation called Brothersoft picked up on my explanation a year later: Brothersoft.

It was a neat challenge trying to master the…

Dylan Ratigan

According to an unimpeachable source, a recent episode of The Daily Show, Dylan Ratigan has retired from his career at television news.

To get TDS' take on it, go to the second segment here. It's about 8:30 and some unavoidable ad segments in.

So I looked back at less amusing news sources and found that Ratigan actually left MSNBC almost a year ago.

Though I'm not one of his biggest fans, (if I were of course I would likely have noticed his departure sooner), I have mentioned him before. In the blog that I closed down when I opened this one.

I wrote a couple of entries there poking some fun at one of Ratigan's colleagues at MSNBC, Charles Gasparino.

Here is one of them.

You'll note that when Gasparino was pulling his bizarre tantrum, it was Ratigan who played the role of the responsible and somewhat exasperated adult.

As it happens, that's the role he plays on the piece in The Daily Show as well.

I hope things go well with the farm.

Stock Buybacks

Thinking this through.

What happens to the value of shares of public stock if the company buys some of the stock back in the marketplace?

Think of it first as a simple accounting matter, and let's assume for simplicity's sake that the actual or potential buyers of the stock in the marketplace (who constitute the market demand) know and care about the book value on the balance sheet: that is, the equity as defined by the formula Assets - Liabilities = Equity.

Suppose the company has 1,000 shares of stock outstanding, each selling for $50. Its market capitalization, then, is $50,000. 

Now, it uses some of its own cash (an asset) to buy back some of the shares of stock. This decreases the amount of stock still available to a would-be buyer.  So if 100 shares are retired and 900 are left, as a first approximation -- assuming demand for the stock stays the same, we might well expect the value of those to increase to $55.55 per.

BUT something else has taken place, too. The comp…

Hume's Fork

One of the passages in the writings of David Hume that sets out what is known as "Hume's fork" runs this way:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, relations of ideas, and matters of fact. Of the first kind are the sciences of geometry, algebra, and arithmetic, and in short, every affirmation which is either intuitively or demonstratively certain. That the square of the hypotenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers.

Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.

Matters of fact, which are the second objects of human re…

Altucher and Bitcoin

Sitting in a tree.

Kay eye ess ess eye en gee.

Altucher is happy that Bitcoin "is not dependent on any one person (for instance, a Federal Reserve Chairman) or on "complicated central bank operations."

Thus, he is selling his next book "bitcoin-only for a few weeks."

More here.

Good luck, you adorable young lovers.

More on Borgias and Machiavelli

I can't really write about the Borgia family -- as I did yesterday and as I am about to do again -- without deploying my favorite quotation from The Third Man.  Restraint in this matter would do grave violence to my nature.

Harry Lime, the worst racketeer in occupied Vienna, tells an old friend who has gone to a good deal of trouble to track him down, "Don't be so gloomy. After all it's not that awful. Like the fella says, in Italy for 30 years under the Borgias they had warfare, terror, murder, and bloodshed, but they produced Michelangelo, Leonardo da Vinci, and the Renaissance. In Switzerland they had brotherly love, they had 500 years of democracy and peace, and what did that produce? The cuckoo clock."

What were the 30 years of Borgian dominance Harry had in mind?   I suppose you might start the clock running in 1481, when Ludovico Sforza took power in the duchy of Milan. The fates of the Borgia and Sforza families were closely intertwined (another member …

The Borgias: The Hidden History

Meyer, the author of this book, now lives in England and seems to have no academic post, though he used to teach in the US -- apparently at three different colleges -- and has his MA from the University of Minnesota.

The Borgias is aimed at a broad audience and is not particularly academic in form. It has a thin set of endnotes and (given the subject) a very thin bibliography. I say that as a matter of transparency, not that I would hold that against him. My last book had neither of those.

One enthusiastic reviewer has called Meyer's book "an incredibly interesting and quite frankly brilliant read, and one I would wholeheartedly recommend to anyone interested in learning about the history of this fascinating family."

I won't review the book, I'll just quote the following passage, which concerns the relation between the Borgia family (especially Cesare) and the philosopher Machiavelli.

"Like everyone associated with Florence's post-Medici republic, [Ma…

If You Have to Explain It ... Don't

According to the FBI, as mediated by Vanity Fair, accused inside-info trader Jesse Tortora e-mailed the following to his buddies and co-conspirators:

"Rule number one about email list. There is no email list, fight club reference."

Okay, here's a rule. If you have to explain that your previous sentence (or, strictly, the first half of the sentence you're still writing) was a Fight Club reference, don't. Delete, abort, retry.

Especially since he didn't really get the allusion right, anyway.

David Friedman

I mentioned Friedman rather tangentially in yesterday's post, so I thought that before writing this one I should check up on what David F. has been up to lately.

Not much, it turns out. The last writing of his that I would describe as a contribution to the public intellectual's case for liberty was a contribution to an anthology edited by Andrew I. Cohen and Christopher Heath Wellman, Contemporary Debates in Applied Ethics. That came out in 2005 -- eight years ago.

Since then, Friedman seems to have been trying to turn himself into a novelist. His second novel, Salamander, a bit of medievalist fantasy, appeared in March 2011.

If you look at that Amazon page to which I just linked you, you'll find the book description. But in case you're feeling lazy, I'll reproduce it here:

Magister Coelus, the College’s young and brilliant theorist, finally has a student capable of learning theoretical magery at the level at which he can teach it. He invites her to help him wit…

Stefan Molyneux and Me

Stefan Molyneux seems to be the hot new thing among young anarcho-capitalists. Not old fuddy-duds like me.

He is the author for example of Universally Preferable Behavior, a book that attempts to expound a rationally impregnable (and secular) ethical system.

I have not read that, or anything else of Molyneux's. I leave to those who have read it to pass on its merits.

I do not rely entirely upon secondary sources, though. I did spend some time listening to one of his podcasts, the beginning of a comprehensive course on philosophy he offers here.  That particular link leads you to a forty minute effort to introduce the subject matter of the remainder of a series. The gist of it, if I understand it at all, is that philosophy, in the sense in which Molyneux proposes to use the term for the duration of the course, the sort of philosophy he hopes to teach, is: a lot like empirical science -- indeed it is empirical science, writ large -- such that any inferences a philosopher reaches m…

Risk in non-quantitative terms

But let’s leave the mathematics aside for a moment and discuss risk in intuitive terms.


It seems clear enough that as we move from one broad asset class to another we’ll see a trade-off.U.S. Treasury bonds are safer, and produce a much lower return, than do corporate stocks.
Can we get more granular? Can we look within the world of corporate stocks and define subsets of that asset class, and find the same trade-off at work?
There are various sorts of risk. There are risks associated with the economy as a whole (the risk that the whole ocean will dry up so all the boats will find themselves on the bottom); the risk associated with specific markets or products (the risk that the horseless carriage will hurt all the buggy whip manufacturers); and the risk associated with one specific firm due, for example, to the excellence or incompetence of its managers. These are known as systemic risk, market risk, and idiosyncratic risk, respectively.
How might you protect against systemic risk? We’…

Great Chain of Being

One of the points that Lovejoy makes in the book of that title I mentioned last week is the importance, in the Neo-Platonist conceptions and in the later development of the "chain of being" metaphor, of what he calls the principle of plenitude. This is the underlying notion that everything that can exist must exist, that creation would not be possible at all were it to leave gaps.

The value of this idea for a certain type of theodicy is clear enough.

This caused theological difficulties when these ideas were absorbed into Christianity.  I'll quote a bit of what Lovejoy has to say about those difficulties:

"For that conception, when taken over into Christianity, had to be accommodated to very different principles, drawn from other sources, which forbade its literal interpretation; to carry it through to what seemed to be its necessary implications was to be sure of falling into one theological pitfall or another."

The big pitfalls were: determinism on the on…

Exobiology

According to a new calculation by Alexei Sharov and Richard Gordon, life must have pre-existed the planet Earth.

You can find the study here.  You can find some of my own earlier uncredentialed speculations about related matters here.

Sharov and Gordon are both properly credentialed. Each is a Ph.D. with a research role with prestigious (though non-academic) institutions. Nonetheless, there is a good deal of speculation in their work, as one might imagine given the subject.

The gist is that they infer that genetic complexity increased at an exponential pace: it doubles every 376 million years.  If that is right, then life originated roughly 9.7 billion years ago (give or take 2.5 billion). And if that is right then it could not have originated on earth. Radiometric dating puts the age of the earth at roughly 4.5 billion years.

So on their guesstimations, life must have been already 5 billion years old before the earth was formed.

Their calculations also indicate that it would have t…

Andrew Wakefield and an Epidemic in Wales

I've blogged about Andrew Wakefield before. Here, for example.

Today, I'll only link you to a discussion in SLATE of the public health situation in Wales, for which he may bear some responsibility.

Bernie Madoff and Stock Options

We'll resume our discussion of stock options from where we were here. The above photographed felon will come into our discussion soon enough.

Options can be part of broader strategies that limit exposure in either direction. You can combine puts and calls to create a “collar” around the market price of the underlying stock, limiting both your own profit and your own risk.
The word “straddle” has connotations similar to “collar,” suggesting that options allow the straddler to be on both sides of the same underlying asset at the same time. Yet “straddle” has a more aggressive sound to it.
As it happens, Bernie Madoff used to tell prospective clients that he was following an options-based straddle strategy. Of course, he wasn’t following any strategy, but he needed to sell a story, and that was it.
Such a straddle strategy, by the way, can work when carried out legitimately. It can do roughly what Madoff claimed that he was using it to do – produce a slow-but-steady stream of equity …