Archive for May, 2011

May 31, 2011

To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.

Richard Feynman


May 30, 2011

Oil in the Fields by Paul Duncan

May 29, 2011

Japanese dream

May 29, 2011

In 1949, the total value of listings on the New York Stock Exchange was $150 billion. In 1984, the total value of all US public equities was $2,000 billion. In 2005, the total value of Big Board listings was $20,000 billion, plus $3,000 billion listed on NASDAQ.

Then, from Oct 2007 – Oct 2008, US stock market capitalisation lost $7,000 billion.

various sources including several versions of The Intelligent Investor


May 28, 2011
  • dt is a moment of your life
  • ∫ dt is the moments as they accumulate

  • is the whole thing and what it meant.


May 28, 2011

Jorinde Voigt via basetimesheightdividedbytwo


May 27, 2011

Whenever a government assesses “the” value of a property for tax purposes; whenever you project figures in a pitch to investors; whenever an accountant writes a single number on a line that isn’t referring to Cash Itself — a distribution has collapsed.

I put “the value” in scare quotes because one number can’t express an asset’s worth. Even if dollar-value-to-me is a 1-D concept — a dubious proposition itself — there are still many other players who value the asset differently. And those valuations could change with new laws, market conditions, reading a book and getting a crazy idea, etc. It all depends. It’s a function; it’s multi-dimensional; it has a topology; different opinions = different metrics, and so on.

Anyone who has done accounting in the real world knows intuitively that Numbers Aren’t Facts. Numbers are opinions. Numbers are estimates. Numbers are vague, but less vague than the alternative.

Let me delve into the economics of one imaginary ambiguous valuation for the more scholarly readers.

Family Farm

Imagine a farmer who owns land in Montana and has worked it all his life — never considering selling the farm because he loves farming, is a farmer, sees himself as a farmer, and wouldn’t know what to do with himself if he didn’t farm. He wants to pass the farm on to his kids, but the property will be subject to taxes as it passes from hand to hand.

How much should the government tax his land asset? They have to estimate the worth of the property and then charge a fair, fixed percentage that they would charge to anyone else. But there is no single worth of the property. It’s worth different amounts to different people, for different reasons.

  • In the hands of his kids, and in his hands, it has sentimental value.
  • In a farmer’s hands, it has agricultural value as well as the utilitarian pleasure the farmer gets from working the land.
  • In a real estate developer’s hands, if the developer does everything right and sells a good number of lots, the property will be worth a lot of dollar bills.
  • In a rich fool’s hands, the property is worth as much as he thinks it’s worth.
  • In a rich sentimentalist’s hands, the property is worth whatever s/he has to pay to acquire that beautiful thing.
  • In a conservation fund’s hands, the property’s worth will fluctuate with the carbon price, donations (which in turn will fluctuate with certain segments of the economy), grant money, the fund’s ability to obtain other nearby properties, the priorities and opinions of the Board of Directors, and the migratory patterns of endangered species.

By the way, I could also add this family farm story to my list of noncommutative phenomena in business — because the price to develop farmland into a subdivision isn’t the same as to go the reverse direction. (Similarly for conservation or any different use of the land.)

The farmer may want to live in his own universe where he works the land, his kids work the land, their own little economy — but the tax man’s assessment will definitely look at what other people outside that universe are willing to pay for the property.

Econ 101

A Marshallian supply & demand graph from Econ 101 makes the point. This is a 1-D chart so it doesn’t capture the full variegation of the stories I sketched above. But it shows more detail than a single number “the” value of the property.

The farmer only has one of “good X” to sell, so supply is inelastic.

In Econ 101, the market clearing price is the price which makes all units ship. In this graph there are multiple prices which would make all units ship, so there is no single market price.

In the family farmer situation, the farmer doesn’t even want to put his place up for public auction. But the ambitions and tastes of some rich guy or group of rich guys can still sway how much tax the farmer pays handing the property over to his kids. The farmer can choose whom he sells it to (and refuse to sell to a developer for instance), but that preference has no effect on the tax rate.

The family farm story isn’t the only case where a unique asset has to be assigned “a” single value.

  • Selling a restaurant — will the next owner sell alcohol there?
  • Shares of Bear Stearns around February 2008.
  • Any of the hot potatoes the Fed scooped up during the financial crisis. (google “mark to market” or “fair market value” for illiquid securities, it’s a controversial issue)
  • Any asset I buy for use in my business. Obviously I wouldn’t buy $10M of factory equipment if I didn’t think they would be worth much more than $10M to me. But their value in a liquidation would have to be lower, especially if the buyers know the liquidator is under time pressure and can’t use the stuff any other way.

Everything is connected — fortunately or unfortunately.

May 26, 2011

As David Foster Wallace saw it, irony could critique but it couldn’t nourish or redeem.

May 25, 2011


May 24, 2011

At my secondary school, the high-scoring wide receiver was more popular than the fat lineman. And the fat lineman was more popular than the team statistician. But you couldn’t really compare the wide receiver’s popularity to that of the actor who got most of the lead roles. They were admired in different circles, to different degrees, by different people. With so little overlap, a hierarchy must treat them as separate rather than comparable.

So popularity = a partial order (and, possibly, an inverted arborescence or join-semilattice). Sometimes there is a binary relation  between two people such that one is-more-popular than the other. Sometimes you just can’t say. And no such relation exists. (neither geoff ≻ ian nor ian ≻ geoff)

Transitivity did hold at my school, so if you were more popular than geoff, you were by extension more popular than anyone than whom geoff was more popular. ( ari, shem, zvi: arishem and shemzvi implied arizvi)

And, by definition, even I was more popular than the nullset. (thanks, mathematics)