Monthly Archives: November 2012

Eight fallacies of declarative computing

Erik Meijer listed eight fallacies of declarative programming in his keynote address at YOW in Melbourne this morning: Exceptions do not exist. Statistics are precise. Memory is infinite. There are no side-effects. Schema doesn’t change. There is one developer. Compilation

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Posted in Software development

A literal black swan

Nassim Taleb popularized the phrase black swan in his book by that name. Taleb uses a black swan as a metaphor for rare events with significant impact. Europeans assumed that all swans were white until explorers reached Australia and saw

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Winston Churchill, Bessie Braddock, and Python

Last night I was talking with someone about the pros and cons of various programming languages and frameworks for data analysis. One of the pros of Python is its elegance. The primary con is that it can be slow. The

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Posted in Python, Software development

Quantum superposition of malice and stupidity

Last night, several of us at YOW were discussing professional secrets, inaccuracies and omissions that are corrected via apprenticeship but rarely in writing. We were arguing over whether these secrets were the result of conspiracy or laziness. Do people deliberately

Posted in Business

Equivalent form of the Riemann hypothesis

The famous Riemann hypothesis is equivalent to the following not-so-famous conjecture: For every N ≥ 100, | log( lcm(1, 2, …, N) ) – N | ≤ 2 log(N) √N. Here “lcm” stands for “least common multiple” and “log” means

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Water signs

There are strange signs about water usage all over Melbourne. For example: Should I be worried? The typography implies I should. But unless you’re combining your own hydrogen and oxygen atoms, it’s all water recycled? Here’s another one. Again, the

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Shakespeare on adolescence

From The Winter’s Tale I would there were no age between ten and three-and-twenty, or that youth would sleep out the rest; for there is nothing in the between but getting wenches with child, wronging the ancientry, stealing, fighting. Related

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Approximation relating lg, ln, and log10

My previous post about logarithms has generated far more discussion than I expected. One valuable comment cites Donald Knuth’s TAOCP. While looking up the reference, I stumbled on this curiosity: lg x ≈ ln x + log10 x. In words,

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Digits in powers of 2

Does the base 10 expansion of 2^n always contain the digit 7 if n is large enough? As of 1994, this was an open question (page 196 here). I don’t know whether this has since been resolved. The following Python

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Posted in Math, Python

Rise and Fall of the Third Normal Form

The ideas for relational databases were worked out in the 1970′s and the first commercial implementations appeared around 1980. By the 1990′s relational databases were the dominant way to store data. There were some non-relational databases in use, but these

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Product of polygon diagonals

Suppose you have a regular pentagon inscribed in a unit circle, and connect one vertex to each of the other four vertices. Then the product of the lengths of these four lines is 5. More generally, suppose you have a

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Posted in Math

What is mathematics for?

“What is mathematics for? To delight the mind and help us understand the world.” From the back cover of Calculus Gems.

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Pure possibility

Peter Lawler wrote a blog post yesterday commenting on a quote from Walter Percy’s novel The Last Gentleman: For until this moment he had lived in a state of pure possibility, not knowing what sort of man he was or

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Posted in Creativity

How well do moments determine a distribution?

If two random variables X and Y have the same first few moments, how different can their distributions be? Suppose E[Xi] = E[Yi] for i = 0, 1, 2, … 2p. Then there is a polynomial P(x) of degree 2p

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The most interesting logs in the world

I occasionally get a comments from people who see “log” in one of my posts and think “log base 10.” They’ll say they get a different result than I do and ask whether I made a mistake. So to eliminate

Posted in Math