## Education and the Question of Intuition

An intuition pump is a thought experiment structured to allow the thinker to use his or her intuition to develop an answer to a problem. The phrase was popularized in the 1991 book Consciousness Explained by Tufts philosophy and neuroscience professor, Daniel Dennett.

We argue in this education-completing book, that our intuitions are puzzling in a way that “intuition pump” talk does not cope with at all.

Let’s go immediately to the example of simple versus compound interest in basic finance.

You borrow \$100.00 for a year at an annual interest of 100%, without compounding and hence simple. A year passes and you owe the lender the initial \$100 plus one hundred percent of this amount (i.e., another hundred). In a year, you owe \$200.00, and every year thereafter, if the lender is willing to extend the loan, you owe another hundred to “rent” the initial hundred.

This is written as A+iA, where A is the initial amount (i.e., \$100.00) and i is the interest. This can be re-written as A(1+i)n where n is the number of years. Thus, if n=1, you owe: A(1+i), which is 100×2 (i.e., the \$200 we just saw). There’s nothing tricky in this.

You then are introduced to compound interest (i.e., where the interest accumulates interest). You can see where compounding by 6 months (semi-annually, or half a year) or 12 months involves dividing the n (the exponent over 1+i) by 12 months, two half-years or 365 days. You could routinely go to days and hours and minutes and seconds and nanoseconds and you could calculate interest payments compounding for each case.

But here is where your intuition falters and fails: suppose you compound continuously?

You get to the number e as growth factor where e=2.71823

Simple algebra does show that at 100% interest, \$100 of a loan becomes \$100 multiplied by e1 (hundred percent=1) or just e (i.e., you owe \$100e).

This gives you \$271.82.

So what has happened?

At one hundred percent simple interest you owe \$200.00 to the lender. Continuous compounding means you owe \$271.82. Instead of owing \$100 in interest, you owe \$171.82. Your interest bill has gone up by \$71.82 or about 72 percent.

Does that seem intuitive? Probably not.

How could one ever apply an “intuition pump” to this arithmetic? We get to the 72% increase in interest by using e which has nothing very intuitive about it. Thus it’s not clear that “intuition pumps” will work here.

You use compound interest arithmetic to get a number which you would never have been able to estimate based on standard intuition since like the 22/7 or 3.14 for π (pi), there’s nothing to “recommend” 2.71823 in and of itself. This means that the link between computational arithmetic understanding and your “gut” or “sixth sense” is feeble at best.

By exploring this way of thinking you could deepen your “meta-intelligence” (i.e., perspective-enhancement). The British economist Pigou (Keynes’s teacher) says that people have a “defective telescopic facility” (i.e., have a poor or even erroneous sense of time-distance).

How one might strengthen one’s sense of time-distance or “far horizons” is not clear.

## Words and Reality and Change: What Is a Fluctuation?

Ludwig Boltzmann who died in 1906 was a giant in the history of physics.

His name is associated with various fields like statistical mechanics, entropy and so on.

A standard physics overview book called Introducing Quantum Theory (2007, Icon/Totem Books) shows a “cartoon” of Boltzmann which says, “I also introduced the controversial notion of fluctuations.” (page 25)

In common parlance, some common synonyms of fluctuate are oscillate, sway, swing, undulate, vibrate and waver. While all these words mean “to move from one direction to its opposite,” fluctuate suggests (sort of) constant irregular changes of level, intensity or value. Pulses and some pulsations suggest themselves as related.

Expressions like “Boltzmann brains” refer to this great physicist Boltzmann and you can find this notion described here: “Boltzmann Brain.”

Notice that the word “fluctuation” occurs four times in one of the paragraphs of the article “Boltzmann Brain,” as you can see:

“In 1931, astronomer Arthur Eddington pointed out that, because a large fluctuation is exponentially less probable than a small fluctuation, observers in Boltzmann universes will be vastly outnumbered by observers in smaller fluctuations. Physicist Richard Feynman published a similar counterargument within his widely read 1964 Feynman Lectures on Physics. By 2004, physicists had pushed Eddington’s observation to its logical conclusion: the most numerous observers in an eternity of thermal fluctuations would be minimal “Boltzmann brains” popping up in an otherwise featureless universe.”

You may remember perhaps you’ve also heard the term, perhaps on a PBS Nova episode on quantum fluctuation.

In the classic history of science book, The Merely Personal by Dr. Jeremy Bernstein (Ivan Dee, Chicago, 2001), one encounters the word fluctuation all over:

“This uniform density of matter …and fluctuations from the average are what would produce the unwanted instability.”

“So Einstein chose the cosmological constant…” (page 83 of Bernstein’s book)

Suppose we allow our minds to be restless and turn to economics to “change the lens” we are using to look at the world, since lens-changing is one of the pillars of Meta Intelligence.

What do we see?

In 1927, Keynes’s professor Arthur Cecil Pigou (died in 1959) published the famous work, Industrial Fluctuations.

In 1915, twelve years earlier, the famous Sir Dennis Holme Robertson (died in 1963) published A Study of Industrial Fluctuation.

The word fluctuation seems to be migrating to or resonating in economics.

The larger point (i.e., the Meta Intelligent one): is the use of this word a linguistic accident or fashion or is something basic being discovered about how some “things” “jump around” in the world?

Is the world seen as more “jumpy” or has it become more jumpy due to global integration or disintegration or in going to the deeper levels of physics with the replacement of a Newtonian world by an Einsteinian one?

The phenomena of change—call it “change-ology” whooshes up in front of us and a Meta Intelligent student of the world would immediately ponder fluctuations versus blips versus oscillations versus jumps and saltations (used in biology) and so on. What about pulsations? Gyrations?

This immediately places in front of you the question of the relationship of languages (words, numbers, images) to events.

The point is not to nail down some final answer. Our task here is not to delve into fields like physics or economics or whatever but to notice the very terms we are using across fields and in daily life (i.e., stock price fluctuations).

Notice, say, how the next blog post on oil price dynamics begins:

“Our oil price decomposition, reported weekly, examines what’s behind recent fluctuations in oil prices…”

The real point is to keep pondering and “sniffing” (i.e., Meta Intelligence), since MI is an awareness quest before all.