isomorphismes

People think mathematicians are brilliant because they talk about things like C* algebras or B-splines or A-modules or D-branes or … really any combination of unexplained letter with abstract noun. (Extra points if the letter is Greek!)

But when I think of really genius ideas, I think of things like:

• stairs. If stairs don’t exist, who is going to think “I need to invent stairs”?
• alcoholic beverages. We trivialise that somebody must have just drank some rancid stuff and thought it was good.
  
  But no, people had invented sophisticated methods of getting particular tastes long before modern chemistry. When natural philosophers were still talking about phlogiston, Bordeaux already had fine wine down to a science.
• rope
• buckets, bowls, pots
• handles on mugs
• screws, bolts, nuts
• ball bearings!
• sponges with a scratchy pad … and how do they make those scratchy pads anyway?
• mitred joins, moulding, wainscoting
  
• sewing. I guess you notice pretty quickly when you sew stuff that many small stitches are super powerful, even with a thin thread. But who’s going to never have thought of the concept of a needle and thread before and suddenly think of it?
• weaving. Warp, weft … have you seen these old tapestry machines? They’re the predecessor of the modern computer.
  
• the invention of a chair. Again, suppose no chairs exist. Who is going to think of one and how?
• toilets.

Let me go a little deeper into several of the brilliant things about modern toilets.

1. First of all there are the two hinged things, which are stacked in the right order. First one being — not only so your butt doesn’t touch the bowl (because they could just make a bowl with a flat ring on top of it, not make it detachable)—but so anyone who pees from a height doesn’t have to splash onto where everyone sits.
   
   Second hinge controls the cover—which is a great idea because not only will stuff not fall into the toilet, but residual smells will be kept in. Let’s say your toilet is clogged, for instance. Then keeping the cover down is the best thing you can do for your comfort. By the way: without looking at your toilet, try to draw a diagram for how a series of hinges could control two separate toilet covers, and be bolted into the bowl.
2. But the true genius is putting water in a bowl. Not only does it give you a way to evacuate the crap, but it reduces the smell.
   
   Smells, of course, are volatile particulate matter that are flung off into the air from your poop, and reach your nose. (Which means that every time you smell poop, poop is getting on your towel, toothbrush, …. I don’t understand why people put showers, toothbrushes, and baths in the same room as where they poop — I mean it’s convenient for plumbing, but I would rather have my poop be as far away from my toothbrush as possible. Well, until I can design and live in my dream house, I have one of those cheapo toothbrush covers.)
   
   So how can we cover up an entire piece of poop — it could have lots of shapes, we don’t want to have to touch it, we want to cover all of it with no errors, and we want to compress the poop particles so that they don’t fly off the turd. WATER. Yes. Next time you go in a pit toilet or port-o-let at a concert or camping, hyperventilate before you go in, cover your nose, and wish that they had poured gallons of water into the bank before everyone pooped in it.

That’s leaving aside the efficient manufacture of commodes and the sewage system, which I’m sure are both marvels of their own. You think about something like New York City, it’s a human habitation of 6 million people, each taking maybe 5-10 dumps per week (well, in good times). That’s 30–60 million pieces of crap every week that nobody wants to see or smell ever again.

Imagine you just dug a hole in the side of a hill, Hobbit-style, in a natural clearing. Suppose, too, that you’re close enough to a lake or stream that you can get water to your house easily. (Or it rains enough and you bought some huge rainbarrels.) Then what the crap are you planning to do with all of the crap you generate?! That’s a conundrum for ya.

@UnlearningEcon lamented the deviations-from-Pangloss framing of neoclassical economics. Normal economic theories take perfection (optimality) as a starting point and ask how real-world “market imperfections” differ from the putative abstract-free-market ideal. (That “the free market” is an abstract ideal can be verified by first going to an actual bazaar and then listening to the way pundits use the term “free market” or “private enterprise” as in versus “government”.)

If you’ve spent too much time with your head in a book rather than participating in actual commerce, it can be hard to even conceive of another frame.

Here’s an alternative theory, just as wrong and just as simple & parsimonious as the Panglossian-private-enterprise frame:

• Every rich person has some business that’s making them rich.
• No rich person will enter a contractual relationship that makes them poorer.
• The only way for a poor person to obtain wealth is to perform a service for a rich person.
• So the service must increase the efficiency of the rich person, add new customers, draw more sales from existing customers, or make the same work get done for lower cost.
• Therefore, the rich always get richer. The poor may or may not get richer.

Of course, the real world deviates from this theoretical ideal in some respects.

1. Ego projects. Sometimes a rich person wants to indulge in an ego project—like starting their own fashion label, “investing” in a “startup”, or retiring from business to write a blog or perfect the craft of 17th-century viola restoration.
2. Bad, lying employees. Hiring managers sometimes make mistakes and hire someone who said they would make the operation more efficient, but actually costs more than they’re worth.
3. Vacations and big houses. A few large purchases do transfer wealth from rich to poor for consumptive purposes. However, it can be shown that when a continuum of houses and vacations trade in continuous time, the real [def.] economic [def.] returns to hillbillies exchanged for house-building go to booze and marijuana with plim → 1.

One misconception I got from the academic theory of finance is that risk and reward go together. You take on more risk, you get more reward. This is formalised in CAPM theory as a higher expected return associated with a higher standard deviation of investment returns.

In reality, ∃ many stupid risks—mistakes, bad ideas, not doing your homework, believing people you shouldn’t believe, taking on a job without negotiating a floor for your own compensation first, or investing in a company that was bound to tank.

Recently, academics have undercut the premise that risk goes hand-in-hand with reward. Perhaps this pill is easier to swallow after seeing “dumb money in Düsseldorf” vacuum up synthetic CDO pyrite (AAA mortgage bonds) spun from BBB bonds—and then find out, publicly, along with the rest of investment Narnia, that the rewards were nowhere near commensurate with the risks.

I’ve seen this play out a little more in private equity, where models of price paths are less influential than common sense, gut reactions, and balance-sheet research.

I don’t know as much about trading. But I’ve read between the lines on the EliteTrader forum and its cousins, and got the sense that, as academic papers that study the matter report: most day-traders lose money on expectation. Their trading capital approaches $0 faster than would be expected merely by the drag of trading fees on a statistical mean of zero profit.

Warren Buffett, the world’s best living investor, is in a business where risk and reward are inverted from the CAPM model. (He’s written about it plenty so I won’t repeat him.)

Steve Schwarzman, another of today’s most successful investors, says in this lecture that he focusses on figuring out every possible angle beforehand, not making any mistakes, controlling every risk and making sure he wins. I’ve read similar things in interviews where Mark Zuckerberg or Peter Thiel talk about “making their own luck”. A lot of questions and decisions go into running a business, and I find it entirely credible that getting that right increases the chances of success—that if an omniscient Arjuna were starting a company today, he would have a very high chance of success (again, what does “chance” mean? Where do the “possible worlds” come from?)

Insurance and reinsurance companies, though they may serve a social function, aren’t actually concerned with actuarially converting risk into reward. They’re interested in collecting as many large premia as possible for risks that will never harm their balance sheet. Why do you think they have three times as many claims adjusters as actuaries? Si guarda al fine.

Michael Price, one of the stars of The Vulture Investors, bought a loan to a bankrupt company for 47¢ on the dollar, covered 15¢ immediately with cash, plus 45¢ in bonds plus 23% of the post-bankruptcy company. He needed the bargaining skills and the capital to buy out other bondholders and negotiate a good rate for 

One last classic example: McDonald’s. Ray Kroc saw a huge return on investment but only took smart risks, doing less of the hard work and spending more time being successful. Mr. Kroc didn’t finish college with a bright-eyed hope to be the world’s greatest entrepreneur (cf. YCombinator). He sold Dixie cups for 17 years before he saw an opportunity—in a B2B space—with high returns and low costs. (Selling malt mixing machines back when malts were the profit centre for burger joints—a malt might cost as much as sandwich + fries, or even as much as sandwich+fries+coffee.) The malt mixer business was a classic play; it would earn 100% checkmarks from a Business 101 textbook. Only after Ray Kroc saw another opportunity related to the business he was in, did he buy up the MacDonald Brothers’ restaurant and multiply it out. Again, this is a textbook private-equity move: find a proven business where somebody has completely figured out how to make money hand over fist, such that the only other thing they need is more money. (Obviously this is very different from an entrepreneur with an idea who just wants some money or thinks their failing idea would be saved if only they had more money.) You provide the money and collect the multiplied profits, i.e. you take on the easy part of the problem, negotiate the terms so you get a huge return on solving it, and then you’ve done little work for great reward. That’s a “smart risk”, not a correlation of risk and reward.

We could probably go back and forth with examples of titanic companies. (Sure, Ted Turner threw massive sums into a money pit for over a decade before seeing TNT and its siblings become profitable.)

But still I think the overall message of risk~reward is wrong. There are smart risks, and there are dumb risks. Don’t expect that just because you did something risky, that the return will be good. Work smart, not hard. Cover your *rse and check yourself before you wreck yourself.