Comments on: The danger of giving homage to mathematical incompetence

By: The limits of disclosure : Dangerous Intersection

The limits of disclosure : Dangerous Intersection — Fri, 20 Jul 2012 17:33:09 +0000

[...] that this issue of communicating financial information to consumers is that so many of them are afflicted with innumeracy. I’ve spoken with many consumers as part of my law practice, and I must report that many of [...]

By: The real risk of an American dying in a terrorist attack : Dangerous Intersection

Thu, 21 Jun 2012 04:53:31 +0000

[...] if Americans weren’t so afflicted with innumeracy, we could accept the true (miniscule) risk of dying from a terrorist act, and focus on preventing [...]

By: Edgar Montrose

Edgar Montrose — Sat, 09 Jun 2012 00:10:39 +0000

This all ties together into the main point of this thread. Given that the world in which we live requires sophistication of thought greater than the capabilities of the average person, what do we do about it? There was a time in the past when much of the population was illiterate and uneducated. Literacy and education were necessary for success; not only for individual success, but for cultural success. The solution was that we educated people. It took a long time, but overall the literacy rate now is pretty high, and our culture has definitely benefitted from it.

The world has now become even more complicated, to the point where simply providing more education is no longer up to the task — some (quite a large number, actually) people will never understand “sextillions”, or even logical fallacies or basic statistics, no matter how much education they receive. In short, the magnitude of the problem has outgrown our ability to solve it by brute-force means. So what are we to do?

Perhaps the computer example above shows the way — when the problem becomes so large as to be untenable, such that the brute-force solution is a bigger problem than the problem itself, one must find simpler ways to deal with it. In the computer world, the solution was to address the problem indirectly, by understanding the fundamental underpinnings of the problem, and controlling them. So what is the analogous approach to enabling an unsophisticated populace to make sophisticated decisions without having to understand every aspect of those decisions?

I am sorry to say that I do not know.

By: grumpypilgrim

grumpypilgrim — Thu, 07 Jun 2012 21:58:26 +0000

Further on the above thread, the important point we should focus on is not that people are bad at math, logic or large numbers; the important point is that ignorance of these subjects can have troubling, sometimes even disastrous, consequences. Bush’s ignorance of basic logic (or his willful failure to employ it) was the proximate cause of death for 4400+ American troops and more than 100,000 innocent Iraqi civilians. It also resulted in the devastation of Iraq’s infrastructure, the looting of priceless objects from Iraq’s museums, and a massive financial debt for U.S. taxpayers (in the trillions of dollars, which per Edgar’s comment most Americans probably can’t begin to comprehend).

By: Edgar Montrose

Edgar Montrose — Thu, 07 Jun 2012 15:38:03 +0000

“You do realize that ‘a billion’ isn’t what it used to be, right? … Even ‘a trillion’ doesn’t take your breath away the way it once did. The good news about all this conceptual inflation is that the average person may soon be able to truly grasp the concept of infinity. The bad news is that we’re gonna be pondering it while living under a bridge.”

– Evan Morris, The Word Detective

By: Edgar Montrose

Edgar Montrose — Thu, 07 Jun 2012 15:29:20 +0000

That is why there is extensive error detection and correction built into all computer operations. Computers DO exhibit errors, but there are mathematical techniques to detect and correct them. (And they are far more sophisticated than simple redundancy.) The mathematical techniques are even aware of their own limitations, i.e., we can implement algorithms that deliver any desired level of error detection and correction performance. The tradeoffs are speed, complexity, and size.

By: Dan Klarmann

Dan Klarmann — Thu, 07 Jun 2012 03:04:58 +0000

One numerical example that impresses me is right in front of you. Let's say you have an average computer, with 4GB ram and a 2GHz clock. It only works if every value of every bit of memory (8x4x10⁹) is correct 2x10⁹ times a second. In an hour, your computer has to be perfect for 3,600 x 2x10⁹ x 8x4x10⁹ states, or 230,400,000,000,000,000,000,000 perfect states. We have come to expect it to do this unerringly for several years. And yet we complain when one of those states goes bad, and something crashes.

By: Dan Klarmann

Dan Klarmann — Thu, 07 Jun 2012 02:57:04 +0000

If you want really big numbers, delve into combinatorics. How many combinations of those planets would we have to check to see if any have contacted another? On the order of a sextillion factorial, or a number greater than the number of atoms in the universe.

By: Erich Vieth

Erich Vieth — Tue, 05 Jun 2012 16:20:56 +0000

Thanks, Edgar. Terrific illustration of an incredibly large number.

By: Edgar Montrose

Edgar Montrose — Tue, 05 Jun 2012 14:17:32 +0000

In addition to understanding mathematics and logic, I would add comprehension of large numbers. Not too long ago I was trying to explain to someone why it was unlikely that Earth had ever been visited by aliens, arguing that there are so many planets in the universe that the odds against even finding Earth are astronomical. My argument went like this, but I still don’t think that she was convinced:

- Number of planets per star: Current estimate is that there is somewhat greater than 1 planet per star, on average; assume 1 planet per star.

- Number of stars per galaxy: Estimates vary, as well, but 100 billion seems to be a reasonable number.

So the number of planets per galaxy is approximately 100 billion.

- Number of galaxies in the universe: Estimates vary from ~100 billion to ~1 trillion; use 500 billion as a reasonable number.

So the number of planets in the universe is approximately 100 billion planets-per-galaxy times 500 billion galaxies = 50 sextillion planets.

If we wanted to name all of those planets, and we assumed that there were 26 letters and 10 numbers available with which to do so (case-insensitive), then we would need to use 15-character names just to have enough unique names for all of them.

If we assigned a unique 15-character name to each planet, then we would need 750 billion 1-terabyte hard drives just to hold all of the names.