1. Why does Pi appear in Einstein’s theory?
2. The 182-year-old tortoise. Still active.
3. A new class on Buddhist economics.
4. How many years of austerity will be needed?
by Tyler Cowen on March 14, 2014 at 12:47 pm in Uncategorized | Permalink
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#6: Ancient aliens, of course. Why else would that me magnetized? The aliens used super magnets to transport them to the mountain.
And obviously aliens, who are capable of travel between stars, would use rocks in their buildings once they got here.
But I think you are missing the obvious – how did they make the super magnets move? It is simple really – that is why wooly mammoths are extinct. The little gray bastards worked them all to death pulling their magnets.
It is.
3. this just seems confused. The economics assumption that ‘more is better’ is less of a metaphysical claim than a practical necessity for making optimization problems have a unique solution. You could just as easily make a 2-good production possibilities set with one of the goods being “Zen”, to show the trade off, with the assumption “more zen > less zen” so you get forced to the feasibility boundary.
The article itself made my eyes glaze over, but there is a legitimate question about “less is better” economics. What if humans became marginally more monkish. That is slightly less interested in status signals and slightly more interested in leisure time used for monkish pursuits.
If that happened, would the economy stall or shrink? If it does shrink, would that be a bad thing given the change in preferences?
The comment thread at #6 wins the dumb award for March, no doubt about it.
It’s about what you would expect considering the rest of the content of the site.
1. Sorry to be a party pooper. Linking Einstein’s birthday to Pi day is an Americo-centric coincidence . In Germany and rest of the world , Einstein’s birthday would be 14.3 , not 3/14. And they cannot celebrate Pi day on 3/14 ( since days come before months for them and 31.4 cannot exist in April) and ca only celebrate Pi day on 3.1.4159 , i.e Jan 3rd , 4159.
If we think about it we really have to wonder what the logic of putting months first is . Was it just a way to be different from the Anglo-saxon tradition?
Shedding (no) more light on this:
http://www.theguardian.com/news/datablog/2013/dec/16/why-do-americans-write-the-month-before-the-day
Chinese dates and the ISO8601 international data-interchange standard put the largest units first – YYYY-MM-DD – much like the digits of Pi themselves. This diverges from both legacy US and European conventions, but is so computer-friendly (date strings sort sensibly!) and logical for use in cross-cultural communications that I strongly expect it will win out eventually. So the annual 03.14 Pi party is back on, americo-phobic and illogical-legacy-ordering party-poopers notwithstanding!
Indeed, you see this ordering frequently in the United States. It hasn’t taken over, but it’s on the way up.
There is a deeper logic here in moving from the general to the specific. The American MM-DD standard observes this pattern (where the year is usually understood as the current year), while the European DD-MM-YYYY approach goes the other way.
Well, that’s a nice idea and everything, but surely it founders on the American pattern with the non-implied year, which is not YYYY-MM-DD, but MM-DD-YYYY.
I’ve never been one to ‘celebrate’ Pi Day (beyond saying “Happy Pi Day to you too”), but I might have to do something for next year’s: 3-14-15
4 significant digits! 9 if you include a time element: 3-14-15 9:26:53 (you can do something twice that day)
The Chinese of course do names the same way, starting with the family name and then the personal name. That is like their date arrangement a much better order because then names can be ordered, e.g. put into a phone book or a list, without needing to be reversed and have a comma added. E.g. Smith Adam is automatically the way you’d want it to look in an alphabetical listing or phone book.
And their concept of addresses is the same, e.g. the White House is at USA, DC, Pennsylvania Ave 1600, again enabling the searcher to start from the widest search and zoom in on the specific.
It’s a smarter, more logical way to conceive of dates, names, and locations. Culturally, some people suggest that it reflects the Chinese emphasis on the group and locating the individual within the group, in contrast to the Western emphasis on the individual and putting oneself at the center of the universe and then locating everything relative to oneself.
Terrible article, but it did (indirectly) lead me to this, so not all is lost?
“Cookies, elevator, french fries, truck; don’t say ‘petrol’ or you suck.”
http://www.straightdope.com/columns/read/1632/why-do-the-british-pronounced-the-letter-z-zed
4. “The calculations published in The Government Debt Iceberg are not some irrelevant machinations of US boffins trying to frighten us into reducing the size of government.”
English translation please. Who are these boffins? Is Tyler Cowen one?
#4. It’s gonna be grim for everybody, but maybe most of all for government. The days of government as Santa Claus are over.
Where’s our man ummmm when we need him?
5. “How people in ancient times were able to move such massive stones is a complete mystery.”
Such a tiresome trope. A single person working alone can move stones weighing many tons with simple principles (leverage, wedges, etc). However, these megaliths are still interesting given the location.
6., rather
4. Question if governments need more austerity based on falling birth rates then how do governments increase birth rates?
Ok, if we have austerity and falling wages for the working & middle class, what is the easiet way for them to cut consumption? Have less children and be like the East Asian economies like Singapore.
Sounds like vicious circular function leading to mother of all liquidity traps! What can stop it. (The closest the West had been in this position was in the 1930s and that was not a good solution.)
#3: My prediction is that students will learn neither economics nor Buddhism.
“Why does Pi appear in Einstein’s theory?” is a remarkably dull question. The interesting question is why Pi pops up all over the place in science and maths when the issue in hand has nothing to do with circles or spheres.
In a lot of those cases the answer is that there is a circle or sphere lurking in the question in some non-obvious way. For instance, the sqrt(pi) in the normalization of the Gaussian function comes from the observation that the 2-D Gaussian, whose integral is easy to calculate, is a surface of revolution of the 1-D Gaussian. Most of the rest of pi’s (seemingly) random appearances go back to certain infinite series or continued fractions that converge to some multiple of pi. Anything that depends on those constructs, such as the solutions to certain kinds of differential equations, gets a pi smuggled in through that vector.
My memory is not good, but I’m pretty confident that one can sort out the 1D gaussian without any reference to the 2D. If so, your explanation doesn’t really hold water.
As for “most of the rest” you seem to be taking forever to admit that indeed circles and spheres have nothing to do with it.
Euler’s formula connects logarithms and complex analysis and trigonometry so deeply that you should expect both pi and e to show up all over the place in science and math. If you find one you should not be surprised if the other lurks nearby. The circle is the unit circle in the complex plane, if you like.
Nice try. I’m not entirely persuaded, but nice try. We’d then have to ask why e and Pi should turn out to be so intimately related. (I write as someone who on being shown that e^(i*Pi) = -1 actually clapped the teacher. The mad things we do at sixteen, eh?)
“If so, your explanation doesn’t hold water.” Fail. She just showed you where the circle was hidden. Just because you don’t look at it, doesn’t mean it isn’t there.
You’re simply being pig-headed and wrong: an explanation has been contrived that is no explanation at all. If the 1D Gaussian can be sorted out without reference to the 2D Gaussian (and you haven’t denied it, have you?) then dragging in the 2D Gaussian is just a little card-sharping.
It doesn’t matter whether you can “sort out” the 1-D Gaussian in some other way. The fact remains that because of the surface of revolution relationship between them, if one of them doesn’t have a factor of pi in it, then the other will. The relationship to circles was there all along; it’s just hidden.
As for “the rest,” like I said, there are two main causes: circles and series. Of course, if you want to dig a little deeper, you could always observe that the series that converge to pi are related to the derivatives of the trig functions (through the Taylor series), which brings us right back to the unit circle, so in a way the two explanations are actually related to one another.
To respond to your point below about Euler’s formula, write out the Taylor series for exp(i*x), and you will see the series for cos(x) and i*sin(x) interleaved, so Euler’s formula is just another manifestation of the relationship I mentioned in the previous paragraph.
I guess none of this precludes the phenomenon being an “interesting question.” All I’m saying is that it’s not very hard to answer.
I was drunk.
“Why does pi pop up when the context has nothing to do with circles?” It doesn’t. But sometimes the connection to circles is hidden. General relativity is a pretty good example of that – what does gravity have to do with circles? The point of #1 is to explain the connection to circles in one particular (and independently interesting!) case where that connection is not superficially apparent, but simple and fundamental once apprehended.
I would guess that most people who find this dull, just aren’t into theoretical physics. 🙂
I am not a very good mathematician but I have thought up a few sequences here and there, and I could translate high-level bridge hands into some beautiful discrete mathematical descriptions (but so could 90 percent of the 2 or 3 million living mathematicians who are more skilled and talented than me). That being said, I would be shocked, shocked, shocked if pi could not be made to show up at a sevenfold or better rate than expected by “homo mediocritus mathematicus” (i.e. someone who understands math at a slightly less thick rate than me)in properly explained theorems, sequences, numerical distillations, you name it, than one would expect when first making acquaintance with said theorems, sequences, hypotheses, numerical distillations, et cetera.
e and gamma on the other hand – well, e anyway – are much more surprising when they show up in any non-trivial application, (surprising to me, anyway). I welcome a rebuttal from any of the top 3 million mathematicians in the English speaking world.
“It doesn’t.” Oh yes it does: you are avoiding the question, not answering it.
“what does gravity have to do with circles?” The simple, symmetrical way to represent 3D space is with spherical co-ordinates – s’obvious, and because it’s obvious it’s not remotely interesting.
“most people who find this dull, just aren’t into theoretical physics”: no doubt some of us have grown out of our youthful interest in such things – perhaps even because we find that too many physicists can’t answer a straight question but would rather indulge in evasive, smug, self-congratulation.
You: Pi comes up when there are no circles to be found. I’m interested in those cases, not cases where there is a hidden circle.
Me: There is always a hidden circle.
You: No there isn’t.
Give me an example then. I hope you can, but I doubt it. I’m aware of a couple dozen examples where the connection to circles is not superficially apparent, but nonetheless exists upon some digging (and several such examples have been pointed out to you). I’m not aware of any examples where no connection to circles can be found. That’s a pretty good p value. Also, if pi showed up in a case that were truly independent of circles, it would be very, very (infinitely?) surprising. My prior for this situation is correspondingly low.
“too many physicists can’t answer a straight question” Sure. This is equivalent to saying at least one physicist is an asshole. This is true of any field. In my experience (grad school) physicists do significantly better than average on this score.
5. Perhaps 50-60 years ago, “modern” instrumental music was less appealing for general audiences than choral music, but that kind of distinction doesn’t seem to be the case anymore.
Yes, non-musicians may have a better understanding of singing and choral music than they do of instrumental performance and instrumental music, but the range of contemporary musical styles played by classical orchestras, chamber ensembles and soloists includes much that non-specialists audiences seem to find attractive.
I’m basing this on programming, sales, broadcasts and the like and I understand how few copies a classical release has to sell to be in the Billboard top twenty in any given month, but that’s equally true for new classical music for any kind of ensemble. Vocal music is NOT selling significantly more than instrumental music by any available measurable standards.
3. I would object to the phrase Buddhist Economics. This seems to be a course in Hippy Bullsh!t taught by someone with no obvious link to Buddhism at all beyond a rather naive belief that they can believe any Hippy Bullsh!t they like and call it Buddhist. The same criticism of which applies to most of their texts by the look of it.
Comments at #6 are pure comedy. They’re even debating whether the Tower of Babel was before or after the flood. If the Bible came in bullet point cheat sheets, they’d still get it wrong.
# 6. Clearly, those rock formations are not man-made. Another “Bosnian Pyramids” silliness.
4. History will mostly forget that the statists had to invent what is obviously impossible — a liquidity trap for a monetary sovereign — in order to avoid acknowledging the inexorable descent toward the event horizon of a government that consumes more than the economy can produce, which, if not necessarily the logical endpoint of their policies, seems to be the practical outcome of their budgets in an increasing number of cases.
Today’s cynicism can be tomorrow’s practicality, and one might cynically wonder today whether tomorrow we’ll shake each other’s hands and retire to our respective ideologies across new borders, all of us safe in the knowledge we’re doing the right thing.
#3: I think we should just include a lot of examples of internalities in Ec 101, taught alongside externalities. Internalities are the bigger market failure anyway.
Implied value of anti-hypertensives (based on value of life): high
Willingness to pay for anti-hypertensives: low
So is CS from the drugs low or high? Kids get that.
Real Buddhist Economics would of course have something about metapreferential utility functions, or perhaps empty utility functions.
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