“Our toasters can probably read our chances of developing diabetes too with 10% over chance success.”
s33 questions the validity of reading thoughts via fMRI, using his ever-full bag of entertaining metaphors.
Meme Engine "statistics"
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Arthur Benjamin in one of the shortest TED talks I’ve actually found interesting, suggesting a new direction for grade-school math education.
To the point: he suggests working up to a thorough coverage of Statistics, as opposed to Calculus like we do now.
He may have a point about applicability. Understanding the stories in our media, or how advertisers (or politicians) can manipulate and spin data could all be covered using statistics. Practically, I think I like his suggestion.
Aesthetically though… to me, Calculus is beautiful and powerful. It melds the exactness of algebra with continuity and infinitesimals. And calling Calculus “inapplicable to life” would certainly not be right! (though maybe to the average person’s everyday experience…)
Stats on the other hand has always felt ugly to me as a theory. It’s so… uncertain! Statistical significance stacks ugly stats on ugly stats. I once made the comparison to my brother that Galois theory was like smoothly pouring a cup of water from a pitcher, while my (Statistics-like) Analysis courses felt like filling the glass by placing it beside the sink, turning on the tap and trying to splash the water in. Epsilon’s and Delta’s would splash everywhere.
Though I don’t know how I’d come down on “Calculus vs Stats” in high-school after carefully weighing the options, I can say that for me the aesthetics of the math I did get to study enticed me to pursue it. Stats would not have done so.
Zipf’s Law
This is pretty interesting… Zipf’s Law (which is actually an empirical, statistical observation, not a law) is a law about frequency distribution in big data sets. The law compares frequencies of the most commonly appearing pieces of data, and asserts that “The number of appearances is inversely proportional to the frequency ranking.”
The example that seems to be used most often is how words, letters, or even common phrases seem to distribute using Zipf’s Law in large enough collections of written language! For example…
Say we have a novel of several hundred pages, and the most commonly appearing words are “the”, “and”, “for”, “her”, and “princess” in that order. Zipf’s Law then claims that “and” will appear half as many times as “the” (because it’s second most common), and “princess” will appear one fifth as many times as “the” (because it’s fifth most common), etc.
This prediction is apparently borne out quite regularly counting words in natural language (or letters, or phrases), yielding a frequency histogram like the one shown above, and leading some to speculate that (since language is meaningful), the pattern seen in Zipf’s law is an indicator of Meaning.
Other sets of data claimed to conform to Zipf’s Law:
- City population ranges, worldwide or national.
- notes (pitch and duration) or note combinations in a piece of music.
- email recipients, connectivity of routers, requests for various webpages.
- information content of “junk DNA” in the human genome.
Given the association of Zipf’s Law to Meaning, the fact that Junk DNA follows a Zipf-like distribution leads some to think that there’s a meaning or a purpose in the “junk”. Though it seems a bit of a stretch, I think that finding evidence through a statistical correllation like this is not entirely out of line. Hmmmmm…
What Is the Human Genome?
Some wonderful things in this article:
- Application of platonism to a real life example (and analysis).
- Suggestion for a statistical method for displaying the “most accurate” human genome.
- A look under the hood of a “rockstar” science concept.
The human genome that researchers sequenced at the turn of the century doesn’t really exist as we know it.
The Human Genome project sequenced “the human genome” and is widely credited with setting in motion the most exciting era of fundamental new scientific discovery since Galileo. That’s remarkable, because in important ways “the human genome” that we have labeled as such doesn’t actually exist.
cosmin4000, istockphoto
Plato essentially asserted that things like chairs and dogs, which we observe in this physical world, and even concepts like virtues, are but imperfect representations or instances of some ideal that exists, but not in the material world. Such a Platonic ideal is “the human genome,” a sequence of about 3 billion nucleotides arrayed across a linear scale of position from the start of chromosome 1 to the end of the sex chromosomes. Whether it was obtained from one person or several has so far been shrouded in secrecy for bioethical reasons, but it makes no real difference. What we call the human genome sequence is really just a reference: it cannot account for all the variability that exists in the species, just like no single dog on earth, real or imagined, can fully incorporate all the variability in the characteristics of dogs.
Nor is the human genome we have a “’normal” genome. What would it mean to be “normal” for the nucleotide at position 1,234,547 on chromosome 11? All we know is that the donor(s) had no identified disease when bled for the cause, but sooner or later some disease will arise. Essentially all available whole genome sequences show potentially disease-producing variants, even including nonfunctional genes, in donors who were unaffected at the time.
Ira Glass, Andy Bloch
"How to Count Cards"
This American Life #466
100 seconds on how to count cards in Blackjack. Though this is a nefarious example, it seems to me a wonderful study on how to package something difficult (statistics) in an easy-to-use, user-friendly way without losing very much of the power in the original math.
This American Life host Ira Glass provides the explanation with help from Andy Bloch, of the MIT blackjack team. Find the full episode here.
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Science... technology... literature... it's all philosophy when you dig deep enough isn't it? Here you'll find my thoughts on all sorts of ways to discard your preconceptions and see things in a new light. "Hear Here" links you to my audio-clips from great radio shows or podcasts on science, philosophy or the arts.
