If you’re using a reader, you can subscribe to the new site at http://feeds.feedburner.com/TheEndeavour.

I’ll keep this site up for a while, but new posts will be to the new address.

]]>Take a male honeybee and graph his ancestors. Let B(n) be the number of bees at the n^{th} level of the family tree. At the first level of the tree is our male honeybee all by himself, so B(1) = 1. At the next level of our tree is his mother, all by herself, so B(2) = 1.

Pick one of the bees at level n of the tree. If this bee is male, he has a mother at level n+1, and a grandmother and grandfather at level n+2. If this bee is female, she has a mother and father at level n+1, and one grandfather and two grandmothers at level n+2. In either case, the number of grandparents is one more than the number of parents. Therefore B(n) + B(n+1) = B(n+2).

To summarize, B(1) = B(2) = 1, and B(n) + B(n+1) = B(n+2). These are the initial conditions and recurrence relation that define the Fibonacci numbers. Therefore the number of bees at level n of the tree equals F(n), the n^{th }Fibonacci number.

This is a more realistic demonstration of Fibonacci numbers in nature than the oft-repeated rabbit problem.

]]>If you call a person enterprising, you have in mind someone who takes risks and accomplishes things. And Enterprise has been the name numerous ships, real and fictional, based on the bold, adventurous overtones of the name. But Cyndi Mitchell says when she thinks about enterprise software, the first words that come to mind are **bloatware, incompetence, and corruption**. I wouldn’t go that far, but words like bureaucratic and rigid would be on my list. In any case, enterprise has a completely different connotation in enterprise software than in USS Enterprise.

Scott Hanselman: What’s it like for Mac Developers, an nterview with Steven Frank

.NET Rocks: Miguel de Icaza and Geoff Norton on Mono, mostly about .NET development on the Mac

Also, there are a lot of Mac-related talks on the GeekCruise podcast. The talks from January 2007 were directed at a general audience new to the Mac.

Hanselman’s podcast talks about some of the cultural difference between Microsoft and Apple customers. For example, Mac users update their OS more often and complain less about OS changes that break software.

]]>- Immediacy
- Personalization
- Interpretation
- Authenticity
- Accessibility
- Embodiment
- Patronage
- Findability

**Daniel Pink** has a related list in his book A Whole New Mind. (Here’s an interview with Pink that gives an overview of his book.) Pink says the skills that will be increasingly valued over time, and difficult to outsource, are:

- Design
- Story
- Symphony
- Empathy
- Play
- Meaning

In The World Is Flat, **Thomas Friedman** says four kinds of people are untouchable, that is, immune to losing their job due to outsourcing. These are people who are

- Special
- Specialized
- Anchored
- Really adaptable

In Friedman’s terminology, special means world-class talent, someone like Michael Jordan or Yo-Yo Ma. Anchored means geographically anchored, like a barber. For most of us, our best options are to be specialized or really adaptable.

**How do these three lists fit together**? You could see Kelly’s and Pink’s lists as ways to specialize and adapt your product or service per Friedman’s advice.

- Meet your customer’s emotional needs (design, authenticity, patronage, empathy).
- Make things convenient (immediacy, accessibility, findability).
- Bring the pieces together, both literally (personalization, symphony) and figuratively (interpretation, story, meaning).
- Be human (embodiment, play).

A work is beautiful to the extent that it displays at the same time both complexity and unity.

From Acquired taste, World Magazine, February 9/16, 2008.

]]>Mr. Chebyshev may have the honor of the most variant spellings for a mathematician’s name. I believe Chebyshev is now standard, but his name has been transliterated from the Russian as Chebychev, Chebyshov, Tchebycheff, Tschebyscheff, etc. His polynomials are denoted T_{n}(x) based on his initial in one of the older transliterations.

With medical testing, the prevalence of the disease in the population at large matters greatly when deciding how much credibility to give a positive test result. Clinical studies are similar. The proportion of potential genuine improvements in the class of treatments being tested is an important factor in deciding how credible a conclusion is.

In medical tests and clinical studies, we’re often given the opposite of what we want to know. We’re given the probability of the evidence given the conclusion, but we want to know the probability of the conclusion given the evidence. These two probabilities may be similar, or they may be very different.

The analogy between false positives in medical testing and false positives in clinical studies is helpful, because the former is easier to understand that the latter. But the problem of false conclusions in clinical studies is more complicated. For one thing, there is no publication bias in medical tests: patients get the results, whether positive or negative. In research, negative results are usually not published.

]]>Textbooks typically rush through the medical testing example, though I believe it takes a more details and numeric examples for it to sink in. I know I didn’t really get it the first couple times I saw it presented.

I just posted an article that goes over the medical testing example slowly and in detail: Canonical example of Bayes’ theorem in detail. I take what may be rushed through in half a page of a textbook and expand it to six pages, and I use more numbers and graphs than equations. It’s worth going over this example slowly because once you understand it, you’re well on your way to understanding Bayes’ theorem.

]]>Whether most published results are false depends on context, but a large percentage of published results are indeed false. Ioannidis published a report in JAMA looking at some of the most highly-cited studies from the most prestigious journals. Of the studies he considered, 32% were found to have either incorrect or exaggerated results. Of those studies with a 0.05 p-value, 74% were incorrect.

The underlying causes of the high false-positive rate are subtle, but one problem is the pervasive use of p-values as measures of evidence.

Folklore has it that a p-value is the probability that a study’s conclusion is wrong, and so a 0.05 p-value would mean the researcher should be 95 percent sure that the results are correct. In this case,** folklore is absolutely wrong**. And yet most journals accept a p-value of 0.05 or smaller as sufficient evidence.

Here’s an example that shows how p-values can be misleading. Suppose you have 1,000 totally ineffective drugs to test. About 1 out of every 20 trials will produce a p-value of 0.05 or smaller by chance, so about 50 trials out of the 1,000 will have a significant result, and **only those studies will publish their results**. The error rate in the lab was indeed 5%, but the error rate in the literature coming out of the lab is 100 percent!

The example above is exaggerated, but look at the JAMA study results again. In a sample of real medical experiments, 32% of those with significant results were wrong. And among those that just barely showed significance, 74% were wrong.

See Jim Berger’s criticisms of p-values for more technical depth.

]]>It’s remarkable that he can even ask the question. Can you imagine someone asking with a straight face whether there have ever been major screw-ups in, say, software development? And yet it takes some hard thought to come up with examples of really big blunders in math.

No doubt there are plenty of flawed proofs of false statements in areas too obscure for anyone to care about. But in mainstream areas of math, blunders are usually uncovered very quickly. And there are examples of theorems that were essentially correct but neglected some edge case. Proofs of statements that are just plain wrong are hard to think of. But Mark Dominus came up with a few.

Yesterday he gave an example of a statement by Kurt Gödel that was flat-out wrong but accepted for over 30 years. Warning: reader discretion advised. His post is not suitable for those who get queasy at the sight of symbolic logic.

]]>The problem is that the Windows clipboard only holds the most recent thing you copied. Jeff Atwood posted an article a few days ago called Reinventing the Clipboard where he recommends a utility called ClipX that extends the clipboard. After you install ClipX, typing Ctrl-Shift-V brings up a little menu of recent clippings available for pasting.

I’ve been using ClipX for a few days now. It’s simple and unobtrusive. The only slight challenge at first is remembering that it’s available. One you think to yourself once or twice, Oh wait, I don’t have to go back and copy that again, you’re hooked.

]]>- GroupBar provides the desktop snapshot feature I mentioned.
- Microsoft Scalable Fabric is a tool for organizing documents and task switching.

I haven’t had a chance to use either of these tools yet. If you try them out, let me know what you think.

]]>The easiest way to build a brand is to sell fear. The best way, though, may be to deliver on hope while aiming for love…

People don’t want fear, they want faith. They want to buy something they can place their trust in to alleviate their fears. Replacing the term fear with faith makes the three levers more parallel, stating each in terms of positive aspiration. With this edit you could summarize Seth Godin’s marketing advice as follows.

Now abide faith, hope, and love. But the greatest of these is love.

I think I’ve read that somewhere before.

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