Thank you for reading my blog. I’m starting a new email newsletter to address two things that readers have mentioned.
Some say they enjoy the blog, but I post more often than they care to keep up with, particularly if they’re only interested in the non-technical posts.
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From The World Beyond Your Head:
The appeal of magic is that it promises to render objects plastic to the will without one’s getting too entangled with them. Treated at arm’s length, the object can issue no challenge to the self. … The clearest contrast … that I can think of is the repairman, who must submit himself to the broken washing machine, listen to it with patience, notice its symptoms, and then act accordingly. He cannot treat it abstractly; the kind of agency he exhibits is not at all magical.
Related post: Programming languages and magic
From JPL scientist Rich Terrile:
In everyone’s pocket right now is a computer far more powerful than the one we flew on Voyager, and I don’t mean your cell phone—I mean the key fob that unlocks your car.
These days technology is equated with computer technology. For example, the other day I heard someone talk about bringing chemical engineering and technology together, as if chemical engineering isn’t technology. If technology only means computer technology, then the Voyager probes are very low-tech.
And yet Voyager 1 has left the solar system! (Depending on how you define the solar system.*) It’s the most distant man-made object, about 20 billion kilometers away. It’s still sending back data 38 years after it launched, and is expected to keep doing so for a few more years before its power supply runs too low. Voyager 2 is doing fine as well, though it’s taking longer to leave the solar system. Surely this is a far greater technological achievement than a key fob.
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* Voyager 1 has left the heliosphere, far beyond Pluto, and is said to be in the “interstellar medium.” But it won’t reach the Oort cloud for another 300 years and won’t leave the Oort cloud for 30,000 years.
Source: The Interstellar Age: Inside the Forty-Year Voyager Mission
In Book VIII of Paradise Lost, the angel Raphael tells Adam what difficulties men will have with astronomy:
Hereafter, when they come to model heaven
And calculate the stars: how they will wield the
The mighty frame, how build, unbuild, contrive
To save appearances, how gird the sphere
With centric and eccentric scribbled o’er,
Cycle and epicycle, orb in orb.
Related post Quaternions in Paradise Lost
Every positive integer is either part of the sequence ⌊ nπ ⌋ or the sequence ⌊ nπ/(π – 1) ⌋ where n ranges over positive integers, and no positive integer is in both sequences.
This is a special case of Beatty’s theorem.
In the Star Trek episode “All Our Yesterdays” the people of the planet Sarpeidon have escaped into their past because their sun is about to become a supernova. They did this via a time machine called the Atavachron.
One detail of the episode has stuck with me since I first saw it many years ago: although people can go back to any period in history, they have to be prepared somehow, and once prepared they cannot go back. Kirk, Spock, and McCoy only have hours to live because they traveled back in time via the Atavachron without being properly prepared. (Kirk is in a period analogous to Renaissance England while Spock and McCoy are in an ice age.)
If such time travel were possible, I expect you would indeed need to be prepared. Life in Renaissance England or the last ice age would be miserable for someone with contemporary expectations, habits, fitness, etc., though things weren’t as bad for the people at the time. Neither would life be entirely pleasant for someone thrust into our time from the past. Cultures work out their own solutions to life’s problems, and these solutions form a package. It may not be possible to swap components in and out à la carte and maintain a working solution.
Adult heights follow a Gaussian, a.k.a. normal, distribution . The usual explanation is that many factors go into determining one’s height, and the net effect of many separate causes is approximately normal because of the central limit theorem.
If that’s the case, why aren’t more phenomena normally distributed? Someone asked me this morning specifically about phenotypes with many genetic inputs.
The central limit theorem says that the sum of many independent, additive effects is approximately normally distributed . Genes are more digital than analog, and do not produce independent, additive effects. For example, the effects of dominant and recessive genes act more like max and min than addition. Genes do not appear independently—if you have some genes, you’re more likely to have certain other genes—nor do they act independently—some genes determine how other genes are expressed.
Height is influenced by environmental effects as well as genetic effects, such as nutrition, and these environmental effects may be more additive or independent than genetic effects.
Incidentally, if effects are independent but multiplicative rather than additive, the result may be approximately log-normal rather than normal.
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 Men’s heights follow a normal distribution, and so do women’s. Adults not sorted by sex follow a mixture distribution as described here and so the distribution is flatter on top than a normal. It gets even more complicated when you considered that there are slightly more women than men in the world. And as with many phenomena, the normal distribution is a better description near the middle than at the extremes.
 There are many variations on the central limit theorem. The classical CLT requires that the random variables in the sum be identically distributed as well, though that isn’t so important here.
Last night I checked a few books out from a library. One was Milton’s Paradise Lost and another was Kuipers’ Quaternions and Rotation Sequences. I didn’t expect any connection between these two books, but there is one.
The following lines from Book V of Paradise Lost, starting at line 180, are quoted in Kuipers’ book:
Air and ye elements, the eldest birth
Of nature’s womb, that in quaternion run
Perpetual circle, multiform, and mix
And nourish all things, let your ceaseless change
Vary to our great maker still new praise.
When I see quaternion I naturally think of Hamilton’s extension of the complex numbers, discovered in 1843. Paradise Lost, however, was published in 1667.
Milton uses quaternion to refer to the four elements of antiquity: air, earth, water, and fire. The last three are “the eldest birth of nature’s womb” because they are mentioned in Genesis before air is mentioned.
For the last fifteen Wednesdays I’ve been posting links to technical notes. This is the end of the series.
You can find most of the links from previous Wednesday posts on one page by going to technical notes from the navigation menu at the top of the site.
When people sneer at a technology for being too easy to use, it’s worth trying out.
If the only criticism is that something is too easy or “OK for beginners” then maybe it’s a threat to people who invested a lot of work learning to do things the old way.
The problem with the “OK for beginners” put-down is that everyone is a beginner sometimes. Professionals are often beginners because they’re routinely trying out new things. And being easier for beginners doesn’t exclude the possibility of being easier for professionals too.
Sometimes we assume that harder must be better. I know I do. For example, when I first used Windows, it was so much easier than Unix that I assumed Unix must be better for reasons I couldn’t articulate. I had invested so much work learning to use the Unix command line, it must have been worth it. (There are indeed advantages to doing some things from the command line, but not the work I was doing at the time.)
There often are advantages to doing things the hard way, but something isn’t necessary better because it’s hard. The easiest tool to pick up may not be best tool for long-term use, but then again it might be.
Most of the time you want to add the easy tool to your toolbox, not take the old one out. Just because you can use specialized professional tools doesn’t mean that you always have to.
Related post: Don’t be a technical masochist
The origin of the word idiot is “one’s own,” the same root as idiom. So originally an idiot was someone in his own world, someone who takes no outside input. The historical meaning carries over to some degree: When you see a smart person do something idiotic, it’s usually because he’s acting alone.
The opposite of an idiot would not be someone who is wise, but someone who takes too much outside input, someone who passively lets others make all his decisions or who puts every decision to a vote.
An idiot lives only in his own world; the opposite of an idiot has no world of his own. Both are foolish, but I think the Internet encourages more of the latter kind of foolishness. It’s not turning people into idiots, it’s turning them into the opposite.
For this week’s resource post, see the page Stand-alone code for numerical computing. It points to small, self-contained bits of code for special functions (log gamma, erf, etc.) and for random number generation (normal, Poisson, gamma, etc.).
The code is available in Python, C++, and C# versions. It could easily be translated into other languages since it hardly uses any language-specific features.
I wrote these functions for projects where you don’t have a numerical library available or would like to minimize dependencies. If you have access to a numerical library, such as SciPy in Python, then by all means use it (although SciPy is missing some of the random number generators provided here). In C++ and especially C#, it’s harder to find some of this functionality.
Last week: Code Project articles
Next week: Clinical trial software
Sometimes it’s rational to walk away from something you’ve invested a great deal in.
It’s hard imagine how investors could abandon something as large and expensive as a shopping mall. And yet it must have been a sensible decision. If anyone disagreed, they could buy the abandoned mall on the belief that they could make a profit.
The idea that you should stick to something just because you’ve invested in it goes by many names: sunk cost fallacy, escalation of commitment, gambler’s ruin, etc. If further investment will simply lose more money, there’s no economic reason to continue investing, regardless of how much money you’ve spent. (There may be non-economic reasons. You may have a moral obligation to fulfill a commitment or to clean up a mess you’ve made.)
Most of us have not faced the temptation to keep investing in an unprofitable shopping mall, but everyone is tempted by the sunk cost fallacy in other forms: finishing a novel you don’t enjoy reading, holding on to hopelessly tangled software, trying to earn a living with a skill people no longer wish to pay for, etc.
According to Peter Drucker, “It cannot be said often enough that one should not postpone; one abandons.”
The first step in a growth policy is not to decide where and how to grow. It is to decide what to abandon. In order to grow, a business must have a systematic policy to get rid of the outgrown, the obsolete, the unproductive.
It’s usually more obvious what someone else should abandon than what we should abandon. Smart businesses turn to outside consultants for such advice. Smart individuals turn to trusted friends. An objective observer without our emotional investment can see things more clearly than we can.
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This posted started out as a shorter post on Google+.
Photo above by Steve Petrucelli via flickr