Strong Law of Small Numbers

I got a tiny glimpse into the beautiful, mystical quality of number theory, having read about the Strong Law of Small Numbers. Simply put, there aren’t enough small numbers (or distinct signifiers) to meet demands placed upon them. This is not merely a mathematical observation; it has applications elsewhere.

Consider, for example, the limited number of small numbers (only 100 numbers have just one or two digits) that are positioned at the beginning of the number line. That’s not very many numbers bearing useful, distinct meanings compared, for example, to words. That limitation often poses a problem because numbers are reused a lot in different contexts where distinct meanings are lost — making things that aren’t truly equivalent look as though they are. Put another way, one-fourth of the first hundred whole numbers are prime, and one-tenth are perfect squares. Distinctions like these become increasingly rare farther up the number line, and large numbers themselves lose utility as bearers of meaning separate and distinct from each other.

This problem occurs all the time: the disappearance of new, toll-free 800 numbers, the fragmentation of the zip code system, the necessity of new area codes to meet demand of new users (and now ubiquitous ten-digit dialing). Outside of numbers, all the short, memorable domain names are spoken for. Pharmaceutical companies can’t coin new drug names without exhaustive searches and marketing studies. Logo designers have trouble creating simple, distinctive logos that haven’t already been used. Trademarks and trade names increasingly run afoul of each other. Acronyms now assume dozens of meanings depending on context. And an increasing likelihood exists that someone sharing another’s name will become famous (or infamous).

Perhaps these examples are neither here nor there to the average reader. That’s probably true in some respects. But the usefulness of small, memorable bits of information to designate something is linked to cognition. A famous study called The Magical Number Seven, Plus or Minus Two observes that humans are typically limited in their ability to remember and/or perceive (these are related tasks) more that seven distinct bits of information. Trying to memorize a string of numbers more than seven (the length of a phone number without the area code) is difficult. Similarly, the ability to perceive more than a few colors (the color wheel is divided into six primary and secondary regions; addition of tertiary regions increases the number to twelve) or more than seven musical pitches (the diatonic scale is seven distinct pitches). Trying to remember more than seven people met at a party or meeting poses a problem as well.

As I say, it’s a tiny glimpse into number theory, with a curious applicability to or isomorphism into cognition. Make of it what you will.

Near-Complete Disapproval

With so many news websites and blogs devoted to endless, and largely pointless, discussion of politics (don’t they ever learn?), there is no reason for me to add my lousy, ill-informed two cents to that din. So I’ve mostly eschewed politics in favor of things not discussed in other blogs. However, I can’t pass up the opportunity to remark how remarkable it is that both the U.S. President and the U.S. Congress have sunk to all-time lows in their public approval ratings.

President George W. Bush and the U.S. Congress registered record-low approval ratings in a Reuters/Zogby poll released on Wednesday, and a new monthly index measuring the mood of Americans dipped slightly on deepening worries about the economy.

Only 29 percent of Americans gave Bush a positive grade for his job performance, below his worst Zogby poll mark of 30 percent in March. A paltry 11 percent rated Congress positively, beating the previous low of 14 percent in July.

My appreciation of all things political is fairly limited, since my approval ratings (of them) have hovered around zero for years and I stopped paying attention. Potential for the new Democrat-controlled Congress was always a pipe dream, considering how diplomatic and economic factors so far outweighed anything Congress could realistically impact through legislation (which, BTW, is its job, right?).

So it’s with no great satisfaction that I note that the American public seems to be coming closer to my level of dissatisfaction. I wonder if the minority who approved of things aren’t mostly made up of the top quintile who earned 50.5% (more than half) of all U.S. wealth, as contrasted with the bottom quintile who only account for 3.4%. The superrich have lots about which to be glad.

Soundbite TV

I haven’t blogged on the utter wasteland that is television, in large part because it seems too obvious to even the most uncritical mind to be worth the bother. Sure, one can learn things or even be entertained (such as TV claims to do); I don’t deny that. But a couple questionably salutary effects, which can be accomplished better through other means, don’t make up for the immensely destructive character of the medium and its content. When I say to people that “TV rots your brain,” I’m not being funny or ironic, although that’s how most people take it. It’s sort of like pointing out to a smoker that cigarettes kill: they know, but the comment is somehow transmuted into a joke.

As a kid, just like most kids, I watched TV all the time, and as a result, I have a veritable storehouse of useless information in my head. I’d call it ephemera except that it never really goes away. These days, I watch so little TV that it’s tantamount to watching none. For instance, I’ve never seen a single episode of such critically lauded shows as 24, The Sopranos, Arrested Development, Grey’s Anatomy, The Family Guy, 30 Rock, or Sex in the City, just to name a few that have gotten a lot of press and won some awards. I don’t know anything about most of the celebrities recently made famous by TV, either. I’ve seen just one episode of a number of other shows — enough to know that I’d never watch them again. I rather regret seeing the entire first season of Lost on DVD. So it’s with this fundamental lack of familiarity with the medium (from the last ten years of so) that I offer an assessment of two new styles of narrative that have recently come into their own.

Smoke Flavoring

Barbeque is one of those smells, like burning leaves, that immediately triggers olfactory memory and a host of associations. An outdoor public market in Rochester, NY, where I used to live, has a smoke house, and the smell of charred meat created such a sensation that omigod did I want some of that stuff right away. Barbeque isn’t a comfort food exactly, but something about it is so primal and satisfying that I’m always sure to try the ribs or brisket on a menu.

I was in Rochester recently, and although I didn’t go to the public market, I did go to its newest restaurant sensation: Dinosaur Bar B Que. (Franchises also exist in Syracuse and New York City.) Gotta say, it rates full and complete approval on the basis of the sampler I had. That was barbeque done right, the traditional way, in a smoker, without too much sugar in the sauce.

Which brings me to my wider point. Some chemist has figured out how to distill the smoke flavor in a bottle, which is now a typical ingredient in barbeque sauces such as this one. Maybe that’s an OK accomodation for the backyard barbeque enthusiast, but I’ve been to a variety of rib joints and barbeque shacks that use liquid smoke as part of their house sauce. Although liquid smoke may be a distillation of the real thing, boy oh boy does it ever taste artificial when added to bottled sauce. It’s sort of like an orange LifeSaver, which doesn’t really taste orange at all but is some chemical approximation of what an orange tastes like.

Which brings me to an even wider point: at what point should we insist upon authentic experience rather than experiences mediated and distilled through some process? Would you rather be in love or take a pill that gives you the approximate feeling of being in love? Would you be happy to take a virtual vacation or would you rather see and experience the real thing? Or on the flip side, do violent video games (or flight simulators, or drag racing games) stimulate in some of us at least a desire for real life thrills from violent and/or risky behavior?