Puzzling Plural/Pluraling Puzzle

A stray thought:

• Question: What is the correct plural of Attorney-General? Is it (a) Attorney-Generals? Or (b) Attorneys-General? Or even (c) Attorneys-Generals?
• Answer: I genuinely don't know and haven't looked it up (not yet anyway). Option (a) sounds most right to me, but I've heard (b) used on occasion. I threw in (c) just for the heck of it.

Three-Dimensional Space

The accomplishment of any task requires space in three dimensions: physical space, temporal space and psychological space. If any one of these dimensions is missing, or inadequate, the task cannot be possibly be accomplished at all or optimally.

Unfashionable Pursuits

It's about 30 years since Freeman Dyson sounded a warning about the problem of fashions in science. It is still relevant. He offered, as an alternative, the nurturing of Unfashionable Pursuits.

You and Time

If you don't manage time, time will manage you.

A Base-ic Solution

The "obvious" and wrong answer to yesterday's question is 80%. It's wrong because it ignores the base rate information that we have been given, namely that 85% of the city's cabs are Green and 15% are Blue. Again, Bayes' Theorem is the standard mathematical technique to unravel this problem. But here's a simple, common-sense solution:

Suppose the city has a total of 100 cabs. This means 85 are Green and 15 are Blue. The witness correctly identifies the colour of a cab 80% of the time and wrongly identifies the colour of a cab 20% of the time. In other words, of the 85 Green cabs, the witness would, on average, identify 68 of them (80% of 85) as Green and 17 of them (20% of 85) as "Blue". Likewise, of the 15 Blue cabs, the witness would, on average, identify 12 of them (80% of 15) as Blue and 3 of them (20% of 85) as "Green". So overall, out of these 100 cabs, the witness "sees" 29 of them as Blue (17 "false" Blues plus 12 true Blues). Therefore, the probability that the cab involved in the accident was Blue rather than Green is 12/29, or approximately 41%.

Back to Base-ics

Another base rate problem (from Chapter 10 of Judgment under Uncertainty: Heuristics and Biases - "Evidential impact of base rates" by Tversky and Kahneman):

A cab was involved in a hit and run accident at night. Two cab companies, the Green and the Blue, operate in the city. You are given the following data:

(a) 85% of the cabs in the city are Green and 15% are Blue.

(b) A witness identified the cab as Blue. The court tested the reliability of the witness under the same circumstances that existed on the night of the accident and concluded that the witness correctly identified each one of the two colours 80% of the time and failed 20% of the time.

What is the probability that the cab involved in the accident was Blue rather than Green?

Fooled by Positiveness

The following question comes to this blog from The New England Journal of Medicine (1978), via Randomness (1998) by Deborah J. Bennett, via Fooled by Randomness (2005, 2nd edition) by Nassim Nicholas Taleb:

If a test to detect a disease whose prevalence is one in a thousand has a false positive rate of 5 percent, what is the chance that a person found to have a positive result actually has the disease, assuming you know nothing about the person’s symptoms or signs?

Almost half of the respondents (consisting of "20 house officers, 20 fourth-year medical students and 20 attending physicians, selected in 67 consecutive hallway encounters at four Harvard Medical School teaching hospitals") answered 95%. Only 11 participants got the correct answer: approximately 2%.

This isn't a trick question, but it is a tricky question because most people fail to take into account the prevelance of the disease (i.e., it afflicts, on average, one in every thousand people). In more technical language, we are dealing with conditional probabilities and not just marginal (i.e., non-conditional or simple) probabilities. The standard mathematical technique to deal with such problems is Bayes' Theorem (named after its discoverer, the Reverend Thomas Bayes). But that requires a whole lesson, or series of lessons, on its own.

Here's a simple, common-sense approach to the problem:

To begin with, assume that the test yields no false negatives. Suppose we test a randomly selected group of 1000 people. Based on the given information, we would expect just one of these people to have the disease and therefore give a true positive test. We would expect 5% of the remaining 999, or roughly 1000, healthy people to also test positive, i.e., about 50 false positive tests. In other words, out of the 51 positive tests, only one would be a true positive. Therefore the chance that a person found to have a positive result actually has the disease is 1/51, or approximately 2%.

Opportunity

"The opportunity of a lifetime must be seized within the lifetime of the opportunity."
- Leonard Ravenhill

Randomised by Folly

Reading:

Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by the talented Mr. Taleb

Time

Some thoughts on the characteristics of Time as a resource:

• Time can only be acquired and utilised in finite quantities.
• Time is completely inelastic.
• Time is free (but not cheap).
• Time, in and of itself, is a neutral quantity; it only takes on certain characteristics based on how it is used.
• Time is the only resource that everyone has exactly the same quantity of, no more, no less.
• Time is the universal currency: everyone, everywhere, is spending it on something.
• Time is the only resource that is essential for every undertaking.
• Time has no intrinsic value - on its own it's worthless,
• Time only becomes valuable when it is used or spent on something of value.
• Time can never be created or destroyed.
• Time can't be killed, only wasted on worthless activities.
• Used, Time's potential value is limitless.
• Unused, Time's actual value is worthless.
• Time can't be stopped (or started).
• Time can't be stored.
• Time can't really be "saved".
• Time can't be transferred.
• Time can't be traded.
• Once gone, Time can't be replaced.
• Time can't be substituted.

Ben's Blog

Ben Horowitz is probably the only management guru (I'm sure he'd hate to be called that) who uses rap lyrics as epigraphs. Certainly, he's the only tech management guru who does. And yet "guru", in the tech/geek sense, is precisely what he is: sharp, knowledgeable, the go-to guy of tech management. He and Marc Andreessen are co-founders of the new tech venture capital firm called (what else?) Andreessen Horowitz. The firm's domain name is A16z.com (get it?).

PHD

PHD = Piled Higher and Deeper (Cham, J. G.)

(Un)Known Unknowns

In his latest book The Bed of Procrustes (see excerpt), Nicholas Nassim Taleb continues to explore the theme of the limits of human knowledge and the consequences of misunderstanding those limits.

Towards the end of his extraordinarily long and productive life, Peter F. Drucker was asked whether, in retrospect, there was anything he wished he had done that he had not been able to do. "Yes," he replied, "quite a few things. There are many books I could have written that are better than the ones I actually wrote. My best book would have been one titled Managing Ignorance, and I'm very sorry I didn't write it."

Perhaps Taleb's new book provides yet another step towards the achievement of Drucker's unfulfilled objective.

Mistaken monopolies

It was indeed a decade of budding African political thought although, seriously, not one could be called a political philosophy. There is no denying that the independence generation of leaders in Africa aspired [...] to establish themselves as philosopher kings or at least as men of thoughtful persuasion. After independence the major topic for rallies [i.e. anti-colonialism] was removed. A new rallying point was necessary and the personality of the leader himself was the obvious choice. In this process, it would appear, the leaders confused the monopoly of power with the monopoly of wisdom, and set about to create quotable dicta.
--From the essay "Zambian Humanism" in The Musakanya Papers.

Just one glimpse into the brilliant mind of the late Valentine Musakanya.

Freedom!

If the comments by some of the readers of The Economist's latest article on the trial(s and tribulations) of Mikhail Khodorkovsky are anything to go by, Mr. Khodorkovsky, once Russia's richest man (and now very possibly its poorest given some rather hefty alleged unpaid tax bills), suffers from acute spiritual schizophrenia. Opinion seems split roughly down the middle as to whether the man is the incarnation of one of the holy archangels or of the devil himself.

What is not in doubt, however, is the eloquence and power of the statement he made on the virtues of a free society.

Five Books

"Nobody reads any more these days."

The words of one of the owners of a second-hand bookshop I visit from time to time. The fact that this is being said as I am handing her some money in exchange for some books is lost in the ironical wash.

So. Is it true? Does nobody, apart from a few (fool)hardy individuals who are members of a bibliophilic species rapidly approaching extinction, read any more "these days"?

I think not.

The format and technology of reading has certainly changed, but the reading matter is still there. Think websites, blogs, Twitter, Kindles and iPads.

Speaking of these new formats and technologies, how's this for an idea to put old wine into new wineskins? Set up a website where experts, or enthusiasts (a much more agreeable description in my view), recommend the best five books (yes, books) on their subjects. And the quote-unquote business model? Small commissions on every resulting Amazon sale. Both ingenious and simple, is it not?

Behold: Five Books.

Here are Walter Isaacson's best five books on Einstein, for example. He modestly leaves out his own excellent biography.

All change

On this day, in this election, at this defining moment, change has come to America.

The Supremacy of Theory

Einstein on the supremacy of (correct) theory:

Suddenly Einstein interrupted the reading and handed me a cable that he took from the window-sill with the words, "This may interest you." It was Eddington's cable with the results of the famous eclipse expedition. Full of enthusiasm, I exclaimed, "How wonderful! This is almost the value you calculated!" Quite unperturbed, he remarked, "I knew that the theory is correct. Did you doubt it?" I answered, "No, of course not. But what would you have said if there had been no confirmation like this?" He replied, "Da könnt' mir halt der liebe Gott leid tun. Die Theorie stimmt doch" ("I would have had to pity our dear God. The theory is correct all the same").
– Ilse Rosenthal-Schneider, Reality and scientific truth. Discussions with Einstein, von Laue and Planck (1980).