Archive for June, 2012

Sustainable Yield?

Tuesday, June 12th, 2012

Murray Bourne at ‘squareCircleZ’ has a great post on modeling fish stocks as an interesting applied example for a math class.

In addition to helping students find interest in understanding the mathematics, this can also help people to really see why when fisheries scientists say that a particular harvesting practice is probably unsustainable.
My only caution would be to note that while it makes sense to avoid what the model says is unsustainable it doesn’t necessarily go the other way, and in fact sometimes what looks like a plausible model can give undue confidence in a belief that a certain harvesting rate is sustainable when in fact it is not.
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Information Geometry

Tuesday, June 12th, 2012

I have been trying to read some of John Baez’s[1] series on “Information Geometry” (here at Part 11), part of which has now also been summarized by Sean Carroll.[2]

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More Philosophical Whining

Tuesday, June 12th, 2012

Jim Holt, in the NYTimes (via 3Qdaily) says “Physicists, Stop the Churlishness“.

Oh come on! This ‘churlishness’ is all just part of the ‘game’ that has been going on *between* philosophers ever since the beginning.

And philosophers themselves have never been slouches when it comes to applying that ‘churlishness’ to philosophy in general – especially in comparison with real science.

Russell: “The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.”

Nietzsche:”Gradually it has become clear to me what every great philosophy so far has been: namely the personal confession of its author and a kind of involuntary and unconscious memoir; also that the moral (or immoral) intentions in every philosophy constituted the real germ of life from which the whole plant had grown.
…(but)…
among scholars who are really scientific men things may well be different – ‘better’, if you like – there you may really find something like a drive for knowledge…”

But I would give Democritus a bit more credit than some other commenters have done. Coming up with a plausible hypothesis is a worthwhile contribution, even if the necessary step of testing it is left for someone else to do later (and even if “later” in this case means two millennia). His atoms actually do serve quite well to explain the proportions of reagents in chemical reactions. And after what early chemists thought to be the “atoms” turned out not to be? – well, we still have not quite completely abandoned the idea of truly elementary particles, so the idea of indivisible “atoms” still has legs to some extent.

Yes We Do (Have to Raise Taxes on the Rich)

Thursday, June 7th, 2012

I was surprised to see media claims that Bill Clinton was advocating an extension of the Bush tax cuts, but Robert Reich (who was there) explains that the comment was not about what should happen but what might happen as a result of legislative deadlock .

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Essay on Man

Tuesday, June 5th, 2012

Here are some favourite lines from Alexander Pope’s Essay on Man.

Know, then, thyself, presume not God to scan;
The proper study of mankind is man.
Placed on this isthmus of a middle state,
A being darkly wise, and rudely great:
With too much knowledge for the sceptic side,
With too much weakness for the stoic’s pride,
He hangs between; in doubt to act, or rest;
In doubt to deem himself a god, or beast;
In doubt his mind or body to prefer;
Born but to die, and reasoning but to err;

Learn each small people’s genius, policies,
The ant’s republic, and the realm of bees;
How those in common all their wealth bestow,
And anarchy without confusion know;

Slave to no sect, who takes no private road,
But looks through Nature up to Nature’s God;

Invention or Discovery?

Friday, June 1st, 2012

A current | LinkedIn discussion asks “Did man invent Maths or was it there all along waiting to be discovered?”. So I thought I’d take the return of that old question as a prompt to review and express some thoughts on the nature of the subject, of “truth” in general, (and of us).

In fact Elias Gourtsoyannis’ description of the views Lakoff and Nunez (which I guess I should make a point of reading!) sounds very like my own feelings on this issue – which also echo my (possibly not entirely faithful) reading of Alexander Pope’s “The proper study of mankind is man”.

As I see it, the rules of logic and axioms of set theory (from which all else in conventional mathematics can be constructed) are really as much expressions of how our minds work as of any external “reality” with which we have to deal.

And, as Colin says, when we find interesting new new tautologies to add to the body of mathematics (which consists of nothing else after all), the question of whether we are inventing or discovering is really just about the attitude with which we do so.

Of course, the reference to set theory as a foundation is merely an example. But most of the body of any mathematical system consists of tautological consequences of some small set of propositions which are taken as axioms.

I think that the part of mathematical activity which builds an edifice of theory on top of its axiomatic foundation is (contra the building metaphor) actually more a voyage of discovery than an act of invention. After all, once the axioms and rules are set, we have no choice to invent anything but what is already there.

But a claim for invention can surely be made about the axioms, and I believe, also about the rules of logic.