Attaching units to numbers reduces the chance of mistakes. For example, if you’re about to add 3 pounds to 7 feet, you’ve probably done something wrong. (The result would be 10 what?) In engineering, this is called “dimensional analysis.”
In computer science, the analogous discipline is strong typing. In strongly typed programming languages, a function that expects a floating point number will complain bitterly if you pass in a JPEG image instead.
When I’m doing math, I’ll sometimes start out with back-of-the-envelope scribbling until I start getting confused. Often the way out of my confusion is to be explicit about function domains and ranges, very much like strong typing in programming.
But sometimes natural typing isn’t enough, and it helps to create artificial distinctions. For example, torque and work both have units of force times distance, but it would be a mistake to add torque and work.
Sometimes it helps me to imagine numbers having different colors. Say I’ve got a function f(x) and I imagine that it takes in red numbers and produces blue numbers, while another function g(x) takes in blue numbers and produces green numbers. That helps me keep straight that expressions like g(f(x)) are OK, but expressions like f(x) + g(x) are probably not.
The March 6 Nature podcast has a story about the Large Hadron Collider. The LHC is expected to gather 15 petabytes (15,000,000 gigabytes) of data. One of the people interviewed said that 15 petabytes of data would require a stack of DVDs the height of Mount Blanc.
You probabily have someone else’s cells growing inside you.
In a phenomena known as microchimerism, mothers pass some of their cells onto their children, and vice versa, during pregnancy. That’s not too surprising in itself. What is more surprising is that these cells can reproduce for decades. It’s not uncommon to find female cells in a grown man, or male cells in a woman who gave birth to a son.
See “Your Cells Are My Cells” in Scientific American, February 2008.
Edward Hallowell coined two great terms in his book Crazy Busy: C-state and F-state.
C-state is clear, calm, cool, collected, consistent, concentrated, convivial, careful, curious, creative, courteous, and coordinated.
F-state fractures focus, is frenzied, feckless, flailing, fearful, forgetful, flustered, furious, fractious, feverish, and frantic.
Multitasking leads to F-state and activates different parts of the brain than C-state. Just giving F-state a name and being aware of it helps to back out of it.
E. T. Jaynes gave a speech entitled A Backward Look to the Future in which he looked back on his long career as a physicist and statistician. The speech contains several quotes related to my recent post on what a probability means.
Jaynes advocated the view of probability theory as logic extended to include reasoning on incomplete information. Probability need not have anything to do with randomness. Jaynes believed that frequency interpretations of probability are unnecessary and misleading.
… think of probability theory as extended logic, because then probability
distributions are justified in terms of their demonstrable information content, rather than their imagined — and as it now turns out, irrelevant — frequency connections.
He concludes with this summary of his approach to probability.
As soon as we recognize that probabilities do not describe reality — only our information about reality — the gates are wide open to the optimal solution of problems of reasoning from that information.
Sun Microsystem CEO Jonathan Schwartz posted an article on his blog this morning about UT’s Ranger supercomputer.
Schwartz calls Ranger the world’s largest supercomputing cloud, and no doubt by some definition it is. The world probably has dozens of largest clusters depending on how you define the term.
Charles Petzold describes on his blog how he wrote his book The Annotated Turing, a commentary on Alan Turing’s seminal computer science paper. The book is scheduled to be released June 10. Petzold began by literally cutting and pasting pieces of Turing’s paper. He worked on the book away from his computer for the first couple months.
As a programmer and author, Petzold has no aversion to using computers. He says “I gave up handwriting … sometime around 1982 when I first learned WordStar on my Osborne 1.” But he discovered that he thought more deeply about the subject of his book when he wasn’t distracted by typesetting issues. He’s a technical wizard, but he makes selective use of technology.
