June 2012
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Graphical Axioms from the nCatLab
If you don’t read the n-category café’s wiki project, you are missing out.
Definition. A Frobenius algebra in a monoidal category is a quadruple (A,δ,ϵ,μ,η) such that
(A,μ,η) is a monoid,
(A,δ,ϵ) is a comonoid, and
the Frobenius laws hold: (1⊗μ)∘(δ⊗1)=δ∘μ=(μ⊗1)∘(1⊗δ).
In terms of string diagrams, this definition says:
The first line here shows the associative law and...
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“Calculus is topology.
The reason is that the matrix of the exterior derivative...”
– Peter Saveliev
May 2012
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Smart Risks
One misconception I got from the academic theory of finance is that risk and reward go together. You take on more risk, you get more reward. This is formalised in CAPM theory as a higher expected return associated with a higher standard deviation of investment returns.
In the real world, ∃ many stupid risks—mistakes, bad ideas, not doing your homework, believing people you shouldn’t...
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“I’m tired of things improving incrementally through experience. I just...”
– Josh Gondelman
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“What is the world made of?…There are twelve basic building blocks.
Six...”
– Alberto Güijosa
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on the Obligation to Consider Others' Opinions
I noticed a contradiction within myself. I was emailing with someone about the financial morass of ≥2008, and he said:
“I didn’t read any more than the first paragraph of that article, because I could already tell I wasn’t going to agree with it.”
On the one hand, that sentiment sets me on edge. How can you write off what the author’s saying without reading it? On...
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“It takes ~20 observations to verify your first significant digit of the mean...”
– Karen Kafadar
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“You may have heard that attitude is everything. Perhaps. How you view the world...”
– “Sonshi”, summarising Sun Tzu’s Art of War
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the Begats
The word < is normally defined to mean less than in some quantifiable sense. For example, considering the set {3,6,1441}, one could say that 3<6<1441.
But in the abstract language of partially ordered sets, < is reinterpreted many ways — to mean proper subset of ⊂ (contained by), divides, “is hotter than” or … any transitive relation — even begat.
...
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Climate Statistics
httpness: (studying statistics) Can there be a different standard deviation up and down?
isomorphisms: Yes. it's called a semideviation. (Or a quasinorm.) There are a lot of people who argue that semideviations and quasinorms are more natural than standard deviation and norms.
httpness: So that's not a normal distribution?
isomorphisms: Whatever distribution you're using, there are different measures of dispersion on that -- standard deviation, downside risk / semideviation, interquartile range, kurtosis, etc.
httpness: I was just thinking about temperatures. The standard deviation changes depending on the time of year, and the chance of unseasonably warm or cold days changes too.
httpness: Here's an example of what I mean. let's say during the summer there _is_ a standard deviation and it's the same up and down. But at another time of year there could be more chance of a very warm day, and at a third time of year there could be more chance of an unseasonably cold day.
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“I am often amused by the progressive bias [in favour of] smaller [investment...”
– Bond Girl (@munilass)
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Infinite Data
Since people liked my last opinion piece on #big data, here’s another one.
Imagine there was a technology that allowed me to record the position of every atom in a small room, thereby generating some ridiculous amount of data (Avogadro’s number is 𝒪(10²³) so some prefix around that order of magnitude — eg yoctobytes). And also imagine that there was a way for other scientists...
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Watch ideas of “pure reason” without emotion send us in the wrong direction
D. Hume & A. Smith didn’t take such an impoverished view of rationality
funny images of successful people with no purpose
stories of people with high “EQ” (emotional intelligence / people skills)
an excerpt from I Am A Strange Loop where Doug talks about the enduring feeling of oneness he...
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“The [academic] job market is brutal, we all know that. Grad school is a gamble,...”
– boiler
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I feel vindicated in several ways by the Netflix Engineering team’s recent blog post explaining what they did with the results of the Netflix Prize. What they wrote confirms what I’ve been saying about recommendations as well as my experience designing recommendation engines for clients, in several ways:
Fancy ML techniques don’t matter so much. The winning BellKor/Pragmatic...
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I can afford to consume each of
chocolate
cheese
tea/coffee
fruit
multiple times per week. I think that qualifies me as Pretty Goddam Lucky.
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“The accounting double-entry system … has survived relatively unchanged for...”
– Rick Young, Reflections on accounting structure and principles
So accounting reduces to a set of propositions with the fixed form of a triple:
(∃ thing, value of thing, claimant of thing)
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What is calculus about?
W Gilbert Strang, a really excellent lecturer who sees teaching as central to his purpose in life, has made his complete calculus course available for free here. He has also summarised the basics of calculus, using simple words and examples, boiling the subject down to 2.5 hours here.
Calculus is not all there is to post-secondary mathematics. But it does symbolise “difficult! complicated!...
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Things That Are Nice
hot water
clean, dry clothes
breathing mindfully
taking walks
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You have options, you know.
You don’t have to listen to the experts.
You don’t have to read the newspaper.
You could do yoga without paying anyone.
You could take a job that pays less than what you were offered elsewhere.
You could forgo the university credentials and just start reading things that interest you. You could spend 3 hours a day reading.
You could stop trying to get a “real job”....
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Big Data vs Quality Data
theLoneFuturist: I'm not certain why learning Hadoop isn't more attractive to you. If you are fine with R, doesn't having lots of data interest you?
theLoneFuturist: Don't get me wrong, there are probably unexciting tasks associated with big data, but you'd then get to run your algorithms over big data. And lack of data is an often cited problem for learning/adaptive algorithms. But of no interest to you?
isomorphisms: The BIG DATA fad seems to be based on "let's turn a generic algorithm loose on exabytes!"
isomorphisms: No matter how the data was gathered, what its underlying shape/logic is, what's left out.
isomorphisms: For example twitter text analysis. At a high level I might ask "How are attitudes changing?" "How do people talk about women differently than men?" "Do attitudes toward Barack Obama depend on the state of the US economy?" Questions whose answers aren't easy to turn into just a few numbers.
isomorphisms: My parody of a big-data faddist's response would be all the sophistication of: listen twitter | Hadoop_grep Obama | uniq -c | well_known_sentiment_analysis_algo. Hooray! Now I know how people feel about Obama! /sarcasm
isomorphisms: In the 'modelling vs scavenging' war (cf Leo Breiman) I'm more on the modelling side. So I find some aspects of the ML / bigdata craze unsavoury.
isomorphisms: But the emergence of petareams is certainly a paradigm shift. I don't think the Big Data faddists are wrong in that. That environmental difference will change things as surely as cheap computing power changed statistics. (Why learn statistical theory when you can bootstrap?) As far as the art of the possible -- more clickstreams being recorded makes more analysis doable.
isomorphisms: Anyway, to answer your question, no, having a lot of data doesn't interest me.
isomorphisms: I'd rather have interesting data than lots of it.
theLoneFuturist: Thing is, interesting data is probably a subset of big data. Mechanically define/separate interesting and you can get it.
isomorphisms: Definitely not, think about historical data.
isomorphisms: For example Angus Maddison's estimates of ancient incomes; the archaeological or geological record; unscanned text (like the Book of Kells, are you going to OCR an illuminated manuscript? You would miss the Celtic knots)
isomorphisms: Even if stuff were OCR scanned properly and no problems with tables, the interpretive work that historians do would be hard to code up in an algorithm. To me they dig up much more interesting information than the petabytes of clickstream logs.
isomorphisms: Or these internal documents they just found from Al-Qaeda? Which would you rather have, 100 GB of server logs or 10 kB worth of text from Osama bin Laden at a crucial moment?
isomorphisms: Also, we talk about text being "unstructured data", how about "I smell sulphur coming from over there" (during an archaeological dig) or "This kind of quartz shouldn't be at this depth in this part of the world" or, you know, "Hey look are those dinosaur footprints?"
isomorphisms: The kind of stuff a fisherman might notice. THAT'S unstructured data.
theLoneFuturist: Sure, though if enough historical records get scanned, they too become the dread big data. I do catch your point, though.
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on Dauphin County, Pennsylvania's bankruptcy... →
This is the kind of thing I wish I would have learned about in government class. Instead of talking about irrelevant abstractions—the structure of government, utopias, immigration, constitutions, “international affairs”, long-dead pamphleteers, and quaternary sources that collapsed the complexity of historical debates—we should have been talking about stuff that actually...