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Posts tagged with philosophy

philosophy & quantum mechanics

@jtc_19 asked:

The isomorphismes links (last three tweets) might be worth sharing with everyone. (I’ve been accused that this site is hard to browse—sorry!)

@isomorphisms haha, yep.

— Clark (@jtc_19) April 15, 2013

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By the way! OCW has course notes on the standard weird phenomena and also the standard interpretation of the physics. http://ocw.mit.edu/courses/linguistics-and-philosophy/24-111-philosophy-of-quantum-mechanics-spring-2005/lecture-notes/




Things I Failed

I’m bored of #ff meaning follow Fridays. Let’s do Failure Friday instead and talk about things we’e failed at.

  • I failed an arithmetic test.
  • I failed judo class.
  • I failed to attract interest with my CV.
  • I failed to be married or have a stable job by my 30th birthday.
  • I failed an entrance exam.
  • I failed most of my writing assignments.
  • I lost an important contest.
  • I lost a race. Badly.
  • I lost a client I thought I had secured.
  • I failed a client I thought I could help.
  • I failed to get paid what I thought I was worth.
  • I failed to be honest in a romantic relationship.
  • I failed to do anything cool for a few years.
  • I couldn’t walk on a mountain because I was so out of shape.
  • I failed to wear sunscreen.
  • I failed to read the prospectus.
  • I failed to get into my preferred university.
  • I failed to get someone to fall for me.
  • I didn’t know what I wanted or how to get it.
  • I failed to keep in touch with old friends.
  • I failed to impress people.
  • I failed to advocate for myself.
  • I failed to do things on time.
  • I lost Other People’s Money.
  • I failed to come up with good ideas.
  • I failed to give it my all.
  • I failed to lose weight.
  • I failed to meet expectations.
  • I failed to look “put together”.
  • I failed to stay organised.
  • I failed to Get Things Done.
  • I failed to cook a good dinner.
  • I failed to recognise the obvious signs.
  • I failed to learn what I was trying to learn.
  • Things did not go according to plan.

NB: I don’t intend Failure Friday as a pity party. It just bugs me when people try to act flawless and successful. Infinitely wise with inerrant self-command. Even apparent failures are successes in disguise. Sorry stories modulate into major key as the lessons learned were invaluable rungs on the ladder of upward progress so in the end it all worked out for the best.

What is that? You’ll probably just make people who are already down feel worse by doing that. And not make anyone feel better.




What is the object of the game of chess?

This was a rhetorical question our chess teacher used to ask us. It’s a reminder that even though materiel, position, and tempo are worthwhile achievements that advance your interests, the goal is to check-mate the King.

For example the Blitzkrieg or “Scholar’s Mate” doesn’t capture materiel or obtain an advantageous position. It just goes directly for the kill.

It’s worth asking this question whether you’re just out the gate or mid-game. Is there a way within a few moves that you could mate early? Never forget to look for that in the quest for materiel or position.

 

I use the question now in my life as a shorthand for

  • why am I doing this?

. Getting money, obeying authority, learning things, obtaining credentials (résumé builders”), maintaining a low weight—all are “good” goals which advance my interests. But why? What is it aiming towards? What am I really trying to do?

In chess the goal is well-defined, whereas in life one can choose one’s own goals. In particular they can be

  • continual (“Go for walks”)
  • or circular (“Raise kids, so they can raise kids, so they can raise kids, …”)
  • rather than once-and-done (“Get thin”, “Mate the King”).
  • (And they needn’t be zero-sum.)

I think that makes the question What is the object of the game of chess? even more important.

That’s something that helps me and I hope it helps you. I’m going to pause now for some quiet reflection.




Noncommutative & irreducible

  • a−a+b−b=0
  • a+b−a−b≠0

An organon of economic theory, contra Foucault, is that—just as a gas is nothing more than a composite of molecules—so is “a society” nothing more than a composite of individuals. (Although individuals vary considerably more than do atoms; a gas molecule can be characterised with only a handful of numbers.) “‘Society’ does not exist”—if I cared to google some more, I could I think find utterances by Prime Minister Thatcher, Alan Greenspan, Russ Roberts, and Ayn Rand, to this effect.

Is that rubbish? I only specialise in stage 17 of the industrial-steel treatment process because other people have specialised in stages 16 and 18. But if we tossed out Cartesian decomposability, we’d be tossing out science (=reductionistic experimental method), and mathematics, and logic itself … right?

http://upload.wikimedia.org/wikipedia/commons/9/9c/Sacrificial_scene_on_Hammars_-_Valknut.png

Here with the Borromean rings, as with cohomology elments, we get an example of a global property which is lost at the local level. Nothing is special about any of the individual rings. It’s the way they combine that’s special—not an independent Cartesian product, but a thoroughly intermeshed interlinking. The whole is more than the sum of the parts.

Not saying that the world is Borromean or something as simplistic as that. But just like Cantor’s laughably small example of a three-part system (ω,ω²,π∙ω) disproved Nietzsche’s unfounded assertion (in The Eternal Return) that “Any complex system must return to its original state” (naïve conception of infinity) without suggesting that Society is a three-part system,—we might take the existence of a tiny primitive with global-non-local properties as at least evidence against the Great Organon, and possibly pointing the way toward a theory in which “society” can have a meaning beyond “collection of individuals”.

 

Echoes of financial crisis. If you removed 30% of the banksters (and attorneys) from the problem centres (wherever they were!) in the instigation of the financial crisis, would we have averted an O($10 trillion) destruction of wealth? Or is it the incentives (echoes of Richie/Rosen’s “entailment structures”)? Or the “culture” (and can we give this meaning?) in which Gordon Gekko-worshipping


acolytes of capitalism buy and resell a Panglossian view of price-as-value-added where success comes only to those who serve the most? vision of capitalism—if indeed that replaced some earlier less casino-like culture to investment banking (http://www.tubechop.com/watch/923989).

But this sounds too vague and hand-wavy. A dystopian “system” that controls free-willed individuals? Constituted of “military-industrial-lobbying-banking complexes” and shadowy networks of faceless vice-presidents—but when one asks those who propound this woolly claptrap to point to specifics or give an atomistic description of what they think is going on, they can’t! Proving of course that their accusations are baseless.

http://3.bp.blogspot.com/_j1PMRiUP1iY/TU40j-3vIKI/AAAAAAAABlE/NMP3fCwksyw/s1600/penroseTriangle3.png

Where could anyone ever hope to find the tools to make a rigorous theory out of it?

(Source: math.cornell.edu)










The category of categories as a model for the Platonic World of Forms by David A Edwards & Marilyn L Edwards

  • Thales (7th cent. BC) made the first universal statement (proof w/o regard to the gods or mythology, just from pure reason)
  • pre-Greek mathematics was essentially engineering maths.
  • I owe ya a post on the illiterates in chapter 2 of James Gleick’s The Information. He tells the story of some illiterates in outer Soviet Union. According to the tale, they basically do not abstract at all. No abstract reasoning, no properties ascribed to members of a class, and so on.

    It sounds kind of idyllic in the way of NYT tales of the Pirahã or Jill Bolte Taylor’s story of losing the logical half of her brain. I’m not sure if Thales set us on the path to Hell or Heaven.
  • “Plato set for himself the [goal] of extending geometry [beyond] triangles and circles and such, to all of human thought. He failed, but his vision has come to pass.”
  • Why did Lawvere succeed where Plato and Whitehead failed?
  • He had Descartes’ already-abstract notion of a function, along with
  • Eilenberg & Mac Lane’s notions of category and functor.
  • The definition of function for infinite sets is already implicit in the choice of “which set theory”.
  • Category theory, unlike earlier formalisations (think Peano arithmetic and Goedel’s proof), is stable to the “meta” step: you do 2-categories, you do n-categories … the abstraction is ultimately a k → k+1 kind of deal rather than a “And this is the ultimate finality!” kind of deal.




In 518 BC, Pythagoras journeyed west … interview with the … ruler Leon of Phlius while both were attending the Olympic Games. Prince Leon was most impressed by Pythagoras’ range of knowledge and asked in which of the arts he was most proficient.

Pythagoras replied that, rather than being proficient in any art, he regarded himself as being a “philosopher”. Prince Leon had never heard this term before—it had been newly coined by Pythagoras—and asked for an explanation.

Pythagoras said: “Life may well be compared with these pan-Grecian Games. For in the vast crowd assembled here, some are led on by the hopes and ambitions of fame and glory, while others are attracted by the gain of buying and selling, with mere views of profit and wealth. But among them there are a few, and they are by far the best, whose aim is neither applause nor profit, but who come merely as spectators through curiosity, to observe what is done, and to see in what manner things are carried on here.

“It is the same with life. Some are slaves to glory, power
and domination; others to money. But the finest type of man gives himself up to discovering the meaning and purpose of life itself. He, taking no account of anything else, earnestly looks into the nature of things. This is the man I call a lover of wisdom, that is, a philosopher. As it is most honourable to be an onlooker without making any acquisition, so in life, the contemplation of all things and the quest to know them greatly exceed every other pursuit.”

free translation by A.H. Louie of anecdote recorded in Marcus Tullius Cicero (c. 45 BC) Tusculanae Questiones - Liber Quintus, III: 8-9

What a self-serving view! I regard my own addiction to philosophy as base and irrational. I can think of many ways in which it’s made my life worse and none in which it’s provided a benefit for anyone else.

Yet it’s not at all infrequent I read philosophers claiming they’re better than other people—without proof, of course.

(And if you try to take the route of philosophy → natural philosophy → technology: well first you’re avoiding the question of whether pure thought is per se valuable, and second neither Thomas Newcomen nor Robert Conrad were natural philosophers.)

(Source: ontoslink.com)




Conflicting Ideas of Probability & Likelihood in the Wikipedia article on Monopoles

In the Public Encyclopedia’s (present) discussion of the hypothetical existence of a magnetic monopole

http://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Em_monopoles.svg/1000px-Em_monopoles.svg.png

in nature, among the possible fundamental particles, exemplifies both (and maybe >2) “sides” in the debate over what probability means:

Magnetism in bar magnets and electromagnets does not arise from magnetic monopoles, and in fact there is no conclusive experimental evidence that magnetic monopoles exist at all in the universe.

…

Since Dirac’s 1931 paper[8] , several systematic monopole searches have been performed. Experiments in 1975[10] and 1982[11] produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive.[12]Therefore, it remains an open question whether or not monopoles exist.

Further advances in theoretical particle physics, particularly developments in grand unified theories and quantum gravity, have led to more compelling arguments[which?] that monopoles do exist. Joseph Polchinski, a string-theorist, described the existence of monopoles as “one of the safest bets that one can make about physics not yet seen”.[13]These theories are not necessarily inconsistent with the experimental evidence. In some theoretical models, magnetic monopoles are unlikely to be observed, because they are too massive[why?] to be created in particle accelerators, and also too rare in the Universe to enter a particle detector with much probability.[13] (According to these models, there may be as few as one monopole in the entire visible universe.[14])

http://upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Em_dipoles.svg/1000px-Em_dipoles.svg.png

Here are a few potential explanations of how one is to arrive at a probability number:

  • opinion — it’s just Joseph Polchinski’s opinion
  • frequentism — Europeans never observed a black swan before exploring the New World, therefore black swans have 0% chance of existing.
  • frequentism + how hard you’ve searched — the probability comes attached with a confidence number. If you’ve stayed within the city limits of Minneapolis your entire life, you should attach a low confidence to your search for tarantulas the size of your head. But we’ve tried very hard to find monopoles, and haven’t. So a “more confident” zero on that one.
  • Dutch Books — could we arbitrage Joseph Polchinski’s “sure thing” bet?
  • authority, credibility, expertise — who exactly is this Joseph Polchinski character, anyway? And who says he’s such an expert? Is he an interested party? I don’t believe what vested interests and biased sources say, even if it happens to be true.
  • propensity — good gravy, I don’t even get to invoke the famous “coin has an innate propensity to tend to certain heads/tails ratio” because it would get us nowhere in terms of “Do monopoles have a propensity to exist or not?”. Anyway propensity merely passes the buck even in the cases where it does make sense.
  • reason & facts — there is no conclusive evidence that monopoles exist, yet they haven’t been proven impossible. I will withhold my opinion and it would be unreasonable to assign a probability mass to either alternative. We’re simply somewhere ∈ [0%, 100%] at this time.
  • model strength — some of these models sound suspect. It’s constructed “just so” that there’s only one monopole in the universe? Very convenient for you, when you want to say monopoles exist and we just haven’t seen them yet. Pull the other one!

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All of the stochastic maths is done with the Kolmogorov axioms, i.e. it’s done with measure spaces with a fixed | finite | constant measure (= 100% of the probability mass) without connecting that to “how likely” a one-off event is. (Much like some maths you could pass off as financial modelling “is just” the theory of martingales = fair repeated bets.) But it needn’t have be called “likelihood”, it could have been “fuzzy truthiness” or “believability” or “motions of a fixed-volume-but-infinitely-divisible liquid”. As Cosma Shalizi puts it here:

Probabilities are numbers that tell us how often things happen.

Mathematicians are anxious to get on with talking about ergodicity, Markov transition matrices, and large-deviations theory. What you’re seeing in this block quote is the handoff between mathematicians and philosophers—essentially the mathmos say “You take it from here to the firm foundation” and philosophers, so far, haven’t been able to.

 

Is there a problem in practice due to not having a sound foundation on our concept of probability? Yes. It’s not secure to move forward with the rear flank uncovered. The lax attitude toward probability and “We’ll do the best with what we can” lets us make up numbers for the {pessimistic, neutral, optimistic} scenarios of our forecasting spreadsheets.

Think about when some consequential decision by a powerful group depends on the value of one parameter. It could be

  • the likelihood of Floridian home prices decreasing by more than 5% in a year,
    image
  • the likelihood of [foreign country X] attacking “us” in response to Y,
  • the likelihood of RHIC creating a strangelet and swallowing the world in a minisecond,
  • the likelihood of construction on the new power plant going over budget,
  • the likelihood of borrowing rates staying this low for another 5 years,
    image
  • the likelihood of real GDP rising at least 2%/year during the next 10 years,
  • the likelihood of our borrowing rate quadrupling
    image
  • the likelihood that your college degree will “be worth it” to you
  • the likelihood of this whole startup thing actually working.
    http://paulgstacey.files.wordpress.com/2010/09/startup_financing_cycle.png

and I get to either rely on

  • historical data (“home prices have always gone up before”, “we haven’t seen any problems with financial derivatives yet”, “correlation with a Gaussian copula has always worked so far”),
  • reason and facts (and multiply an endless debate among the experts),
  • or gut (throw in some numbers that sound pessimistic, optimistic, and neutral, and we’ll see how the forecast behaves).

We got nuthin’.