Pascal's Wager

When is a game worth the candle?

Fermat and Pascal founded the essential rules that govern all games of chance. T[he rules] can be used by gamblers to define perfect playing and betting strategies. Furthermore, these laws of probability have found applications in a whole series of situations, ranging from speculating in the stock market to estimating the probability of a nuclear accident.

A mathematical formula leads to infinity.

Pascal was even convinced that he could use his theories to justify a belief in God. He stated that "the excitement that a gambler feels when making a bet is equal to the amount he might win times the probability of winning it." He then argued that the possible prize of eternal happiness has an infinite value and that the probability of entering heaven by leading a virtuous life, no matter how small is certainly finite. Therefore, according to Pascal's definition, religion was a game of infinite excitement and one worth playing, because multiplying and infinite prize by a finite probability results in infinity.

— Simon Singh, Fermat's Enigma

Painting: Caravaggio: The Cardsharps 

Concentrate on the Best

Sturgeon's law is usually expressed thus: 90% of everything is crap. So 90% of experiments in molecular biology, 90% of poetry, 90% of philosophy books, 90% of peer-reviewed articles in mathematics—and so forth—is crap. Is that true? Well, maybe it's an exaggeration, but let's agree that there is a lot of mediocre work done in every field.

A good moral to draw from this observation is that when you want to criticize a field, a genre, a discipline, an art form . . . don't waste your time and ours hooting at the crap! Go after the good stuff or leave it alone. This advice is often ignored by ideologues intent on destroying the reputation of analytic philosophy, sociology, cultural anthropology, macroeconomics, plastic surgery, improvisational theater, television sitcoms, philosophical theology, massage therapy, you name it.

Let's stipulate at the outset that there is a great deal of deplorable, second-rate stuff out there, of all sorts. Now, in order not to waste your time and try our patience, make sure you concentrate on the best stuff you can find, the flagship examples extolled by the leaders of the field, the prize-winning entries, not the dregs. Notice that this is closely related to Rapoport's rules: unless you are a comedian whose main purpose is to make people laugh at ludicrous buffoonery, spare us the caricature.

—Daniel Dennett, Intuition Pumps and Other Tools for Thinking

Painting: Angelica Kauffmann (1740-1807), Phryne Seducing the Philosopher

Confused and Obscure v. Clear and Distinct

Large cat can mean Tabby, lynx or lion 

And therefore where there are supposed two different ideas, marked by two different names, which are not as distinguishable as the sounds that stand for them, there never fails to be confusion; and where any ideas are distinct as the ideas of those two sounds they are marked by, there can be between them no confusion. The way to prevent confusion is to collect and unite into one complex idea, as precisely as is possible, all those ingredients whereby it is differenced from others; and to these ingredients, so united in a determinate number and order, apply steadily the same name.

But this neither accommodating men’s ease or vanity—nor serving any design but that of naked truth, which is not always the thing aimed at—such exactness is rather to be wished than hoped for.

And since the loose application of names, to undetermined, variable, and almost no ideas, serves both to cover our own ignorance, as well as to perplex and confound others, (which goes for learning and superiority in knowledge,) it is no wonder that most men should use it themselves, whilst they complain of it in others.

Though I think no small part of the confusion to be found in the notions of men might, by care and ingenuity, be avoided, yet I am far from concluding it everywhere willful. Some ideas are so complex, and made up of so many parts, that the memory does not easily retain the very same precise combination of simple ideas under one name: much less are we able constantly to divine for what precise complex idea such a name stands in another man’s use of it. From the first of these, follows confusion in a man’s own reasonings and opinions within himself; from the latter, frequent confusion in discoursing and arguing with others.

 —John Locke; An Essay on Human Understanding

Painting: Salvador Dali, Galatea of the Spheres

The Best of All Invisible Things

To the King.

Sir, I do here most humbly lay this small present at your Majesties royal feet. And though it comes accompanied with two disadvantages, the meanness of the author and of the subject; yet in both I am encouraged by the greatness of your Mercy and your Knowledge.

By the one I am taught that you can forgive the most presumptuous offenders; and by the other, that you will not esteem the least work of Nature, or Art, unworthy of your observation.

Amidst the many felicities that have accompanied your Majesty’s happy Restoration and Government, it is none of the least considerable that Philosophy and Experimental Learning have prospered under your Royal Patronage. And as the calm prosperity of your Reign has given us the leisure to follow these studies of quiet and retirement, so it is just, that the fruits of them should, by way of acknowledgement, be returned to your Majesty.

There are Sir, several other of your subjects, of your Royal Society, now busy about nobler matters: the improvement of manufactures and agriculture, the increase of commerce, the advantage of navigation: in all which they are assisted by your Majesty’s encouragement and example.

Amidst all those greater designs, I here presume to bring in that which is more proportionable to the smallness of my abilities, and to offer some of the least of all visible things, to that Mighty King, that has established an Empire of the best of all invisible things of this world, the minds of men.

— Robert Hooke; Dedication to Micrographia: Some Physiologicial Descriptions of Minute Bodies made by Magnifying Glasses With Observations and Inquiries Thereupon; 1667

Illustration: Ant, from Micrographia