Skippy Records » mathematics

Dollar cost averaging: making hay while the sun shines or doubling down?

Dr. Skippy — Fri, 23 Apr 2010 20:17:58 +0000

Over at Scientific Clearing House, Carson posted a pretty proof of the how dollar cost averaging is an optimal investment strategy. Unfortunately, I think the conditions for this optimization aren’t practical because they are far too optimistic about one’s ability to choose to invest in appreciating assets.

In a long winded comment, I take delight in making the following perverse equivalence between an honest work-ethic idiom and foolish gambling practice,

Under these optimistic assumptions, DCA [dollar cost averaging] is equivalent to the idiom: make hay while the sun shines. Downward price fluctuations are viewed as opportunities to use the same resources to make even more of a good investment. Under less certainty, this is what gamblers call doubling down–when you are loosing, bet more so when you win, you make up your previous losses.

I have advocated DCA as a reasonable investment strategy to friends of mine, but I am increasingly skeptical about the assumptions. It is starting to seem more like doubling down and less like making hay.

Tagged: dollar cost averaging, investment, mathematics

Learning and games

Dr. Skippy — Tue, 12 Jan 2010 23:00:48 +0000

EO Wilson: “Games are the future in education. I envision visits to different ecosystems that the student could actually enter…with an instructor. They could be a rain forest, a tundra, or a Jurassic forest.” (hat tip GG). Games are the way humans did it for thousands of years (up to a few hundred ago); they are how we will do it in the future. To acquire the complex science, math, social, economic, etc. skills that a crowded, connected fast moving world requires, we will have to get to a superior mix of fun, curiosity and content with simultaneous mental, physical and emotional engagement integrated and pushed to the limit. The “golden age” of pounding the 3Rs into kids orderly and quietly sitting at rows of desks will fade away as the dark age of the beginning of ubiquitous education…

Tagged: education, games, mathematics, science

Misunderstanding the long tail

Dr. Skippy — Tue, 01 Dec 2009 17:23:28 +0000

The Economist blows it! (I don’t get to say that very often.) On page 79 of the Nov 28 – Dec 4 2009 issue, there is an article (a world of hits) that misrepresents and misunderstands the ideas behind Anderson’s Long tail and proceeds for 2 more pages to build a story on the misunderstanding. This is not just useless reporting, writing and thinking, it is damaging and a sad illustration of mathematical and analytic carelessness.

I am sure Anderson and others will jump on the many errors here. I just posted this rant in the comments section of the online version of the article…feel much better now

The mistake seems to be not understanding that long tail statistics come from underlying dynamics. In particular, books and movies are small hits before they are big hits. The difference between the long tail and the big hits (possibly call it “tall head”) is how fast a book or movie becomes a hit and how big of a hit it becomes. It is difficult to propose a dynamic in which the bottom and middle of the distribution grow where the big hits don’t get bigger as well. Anderson never proposes such a fundamental shift in underlying dynamics.

There seems to be a complete disconnect between the statistics and the market dynamics producing the statistics in this article.

To say that the long tail ideas predict the demise of the hit is sloppy (or ignorant?). In fact, as technologies that enable access to the long tail become more efficient and capable, there may be an argument that the outcome will be that big hits get bigger. The tall head may grow taller since all tall head items start out with no following at all and grow from long tail-dom–the place where broad cheap access is changing our access most.

Hits will always be big (seems like I wouldn’t need to write a sentence that dumb on purpose!) and big hits will always make big money. The point of the long tail is that there are now opportunities to make significant money on less popular items (e.g. books and movies in the long tail.)

Tagged: long tail, mathematics, the economist

Mathematics education: Calculus or statistics?

Dr. Skippy — Mon, 13 Jul 2009 17:15:21 +0000

The attracting force of all mathematics education should be shifted from calculus to probability and statistics. Advanced mathematics students in high school should be taking Pre-stats instead of PreCalc or APStats instead of APCalc. Arthur Benjamin nails it in this TED talk. This point is vital for competing successfully in the future. It is important for our business decision makers, community planners, disaster planners, economic and political strategists, and all consumers of democracy, investment products, real estate and career opportunities. It is key to understanding uncertainty and risk. The amount of data we have on our complex world is only an advantage is we know what to do with it, how it tells stories of causation and optimal decisions. I love teaching calculus and admire its deep relation to fundamental physical laws, but I want to live in a world shaped by the voices of many skilled statisticians.

Tagged: calculus, eduction, mathematics, probability, statistics