Monday, July 28, 2008

Syncopation


The syncopated beat of the blues
Will make you move those feet in your shoes.
It’s got a rhythm everyone feels
Somewhere between the toes and the heels.
And faster than you can say “Let’s dance!”
You’re jumping up and taking the chance.
Well, syncopation’s centuries old.
It started in the classical mold.
And though it had been known all along,
It really shone in popular song.
When Mr. Joplin wrote ragged time,
The syncopation made it sublime.
And still today we’re hearing the beat
Of syncopated tunes on the street.
It figures into rap and hip-hop,
That little hesitation or stop
That comes from variations in stress
That syncopation is, more or less.

Friday, July 25, 2008

Newton, Apples, etc.

Ideas Great and Dumb is more about the ideas than the people who advanced them, but once in a while, it's fun to look at the individuals who contributed so much to our intellectual history.

Newton was certainly one of the most interesting characters in the history of science. There's a story that he once boiled his watch while staring at the egg. That would make him one of the first world famous total geeks.

It is true that Newton spent a year and a half at his family's estate in Lincolnshire when Cambridge University was closed due to plague in 1665. During that time, he discovered that white light can be decomposed into a spectrum by use of a prism, invented the reflector telescope, generalized the binomial theorem to work with any exponent, invented calculus, and demonstrated that the orbit of the moon around the earth is governed by an inverse square law of gravitation. Not bad for a school vacation. Upon Newton's return to Cambridge, his professor, Isaac Barrow, resigned his post and recommended Newton for the job.

Meanwhile, Newton's calculations for the moon's orbit were slightly off, due to his using an inaccurate number for the radius of the earth. Newton tossed the work in a drawer, and it remained there for 20 years. One day, Edmond Halley (namesake of the famous comet) approached Newton about the lunar orbit problem. Newton began rifling through his papers looking for the old work. This led to the observation that while all of Europe was looking for the law of gravity, Newton had lost it.

With Halley's prompting and support, Newton published his body of findings in a tome called Philosophiae Naturalis Principia Mathematica, or simply Principia, in 1687. That pretty much secured his reputation as one of the greatest scientific minds in history.

And the apple? As far as we can determine, that story is true. Newton's thinking about gravity was at least partly inspired by seeing an apple fall from a tree.

By the way, my particular inspiration for this rhyme, and to some extent the entire IGAD project, was a set of tapes from The Teaching Company called The Birth of the Modern Mind:The Intellectual History of the 17th and 18th Centuries, by Alan Charles Kors.

Monday, July 21, 2008

Isaac Newton


(To the tune of The Major General's Song, from Gilbert's and Sullivan's The Pirates of Penzance.)
Play Audio
Newton:
I am the very model of an “Age of Reason” know-it-all.
I’ve lots of arcane knowledge though I’m hesitant to show it all.
My academic record’s unimpressive and a trifle vague,
I left school when the university was closed because of plague
But lest you think I spent my days indulging in depravity,
At first I thought of calculus, and something I call gravity.
I demonstrated light’s a rainbow when it shines into a prism,
Formulated all the laws of physics known as classicism.
Chorus:
Formulated all the laws of physics known as classicism.
Formulated all the laws of physics known as classicism.
Formulated all the laws of physics known as classi-sassi-cism.
Newton:
I showed that force is equal to the mass times the acceleration,
And concluded energy obeys the laws of conservation.
Thus, with all my knowledge, though I hesitate to show it all,
I am the very model of an “Age of Reason” know-it-all.
Chorus:
In short, with all his knowledge, though he hesitates to show it all,
He is the very model of an “Age of Reason” know-it-all.

Newton:
I showed the orbit of the moon obeys the law of inverse squares.
(Ok, the radius was slightly off, but that’s just splitting hairs.)
Gravity’s a force that operates between a pair of masses.
Spectra are what happen when you shine white light through certain glasses.
Due to this, most lenses will diffract like bubbles made of soap,
So I invented a device called the reflector telescope.
About binomial theorem I am teeming with a lot o’ news.
In fact, I’ve got a formula for any exponent you choose.
Chorus:
In fact, he’s got a formula for any exponent you choose.
In fact, he’s got a formula for any exponent you choose.
In fact, he’s got a formula for any exponent you choo-choo-choose.
Newton:
I have invented integral and differential calculus.
I’ve proven the hypotheses of Kepler and Copernicus.
So now I’m back at school in Cambridge to resume my education.
This concludes my brief report on how I spent my school vacation.
Chorus:
So now he’s back at school in Cambridge to resume his education.
This concludes his brief report on how he spent his school vacation.

Sunday, July 20, 2008

Podcast now available

You can now listen to the rhymes in Ideas Great and Dumb by subscribing to the RSS feed (http://ideasgreatanddumb.blogspot.com/feeds/posts/default) via iTunes, Google Reader, Bloglines or other RSS Podcast compatible readers.

Friday, July 18, 2008

Theories About Theories

It’s very tempting to think that science is the best means for understanding physical reality … what’s really going on in the universe. After all, science has given us so many useful by-products. Who can argue with the light bulb, the car, or the computer? But is it really reality we’re observing?

Think of the fable of the blind men and the elephant. Each touched a different part of the elephant, and came away with a completely different idea of what an elephant was. The man who touched the trunk thought the elephant was like a snake, but the man who touched the legs thought it was like a tree, and the tail man thought the elephant was like a rope. Each of them drew conclusions based on observations of a very limited part of the whole elephant. Moreover, their ideas of an elephant are shaped by where they came from, as well as by what parts of the elephant they touched. The man from the swamp thought the elephant very dry and rough. The man from the tundra thought the elephant very bald and unprotected. Our perception of reality is shaped as much by past experiences as by the current observations.

The other point usually overlooked with the blind men and the elephant parable is that each man understood the elephant by likening it to something already familiar … snakes, trees, rope, etc. We learn about the universe by fitting new knowledge into an established, intuitive framework. For centuries, physics could be understood by thinking of forces acting on particles.

Theories are cognitive inventions which seem to explain the world. But explanations are simply that which leads to understanding, and understanding is a very subjective, human phenomenon. To understand something means to have a model of how it behaves that enables us both to explain past observations and to predict future behavior. So explanation is the process of creating a metaphor … a mental model which corresponds to the observed world in important ways.

Moreover, we only perceive a tiny fraction of all the information available about anything in the universe. Our whole ideas of objects, planets, stars, etc. is just a mental model we’ve constructed from the scant bits of evidence we’ve been able to observe. So any conjectures about what these things are like or how they behave is really a stretch.

Viewed in this way, the heliocentric model of the solar system bears the same relationship to the actual solar system as the abstract idea triangle does to any roughly 3-sided object in reality. It is an abstraction and simplification, to allow us to grasp cognitively what is, in fact, a complex phenomenon.

There is little doubt the earth moves around the sun, but what this actually means is that the mathematics of describing the motion of the planets relative to each other and the sun is simplest when we think of the sun as being at one focus of the elliptical orbits. Both simplicity and mathematics are themselves products of how our brains work. So all we really know is that our brains find it easier to understand and predict the motion of the planets if we think of it as a heliocentric system. This is a far cry from saying “This is real.”

Imagine a universe in which the sun and planets all revolve around the earth, just as the pre-Copernicans believed. Imagine these orbits are composed of cycles and epicycles, just as the pre-Copernicans supposed. Suppose the effect of this combination of cycles and epicycles is that the planets and sun are always in the same positions, relative to each other, as they are in our universe. What, then, is the difference between that universe and ours? None! They are identical in every respect. Planets and stars do not obey laws. The laws are our attempts to understand and describe their behavior. But understanding and description are cognitive tools, not characteristics of nature.

You can never find a line in real life, because a line is an idea … an abstraction from actual edges and boundaries we find in reality. In the same way, a scientific explanation is an abstraction that fits the observed facts. The planets don’t revolve around the sun in elliptical orbits. They are all just moving bodies in space, whose distances and orientations change in relation to one another. The ellipse is an idea we invented to make things predictable. If another theory fit all the observations just as well, it would be just as true. Two theories which explain the same phenomena with the same verifiability are equally valid.

When you try out a new piece of computer software, you can find out all about it by watching how it behaves, experimenting with different actions to see what reaction the software has, etc. By doing this, you can come up with a very detailed and complete description of every aspect of the software’s behavior. Yet this says nothing about what the software is actually doing internally, or what its developers intended.

NOTE: This does not imply there’s any validity to the so-called intelligent design! Currently, it’s very difficult to make any critical assessment of science without being regarded as a defender of creationism or the so-called intelligent design theory. Nothing could be further from the truth. But science itself has become an authority, and we should always question authority. (Says who?)

One of the cornerstones of science is the experiment. The scientific method, including the experiment, is often thought of as a foolproof means for ascertaining truth. But there are flaws in this. For one, the experiment proves that a given result is possible … that it might happen. It doesn’t prove that the result will always happen. No matter how many times we demonstrate that oil and water don’t mix, we can’t prove that they never mix.

Moreover, in the scientific method, the experiment is a hypothesis test. We make a conjecture about some phenomenon, and then experiment to see if the conjecture holds up. But we only do experiments on ideas that we already consider to be plausible. In a sense, we’re filtering out things that don’t seem scientific, and only experimenting with those things that fit the belief framework. In particular, we assume causality to apply in all situations, since causality is the basis of experimentation. So if there could possibly be phenomena which don’t behave causally, they will simply be dismissed as observational errors.

Within a belief framework, the theory seems plausible and valid, and consistent with the rest of the framework. Outside the framework, however, the theory may seem irrational. This is not unlike fantasy fiction. We accept that Frodo may have a ring that makes him invisible because it’s within the natural order of the universe Tolkien created for his stories. So saying the ring works by powerful magic is a perfectly sound explanation in that universe. Our own universe is, of course, not completely knowable, so we create stories of how things behave to satisfy our own curiosity. In one set of stories, everything may be purely mechanical. The universe is a giant machine that runs according to definite, if unknown, principles. Another set of stories may have the universe a place of mystery and unpredictability, subject to the whims or moods of some controlling being or beings.

If you happen to believe a supreme being created the earth, than the earth becomes evidence of that being’s existence. We can see the circularity of the logic when it’s stated this way, but in general, belief systems form a context in which we interpret all experiences, and the experiences themselves then reinforce the context. That’s why something that violates our expectations of how the world behaves is so surprising.

But that’s pretty much the history of science, isn’t it? Violated expectations? We’re constantly revising theories and replacing them with new ones. That fact alone should convince us that, as convincing and practical as our scientific knowledge is, we don’t have a lock on reality yet.

References:

Monday, July 14, 2008

Theories

Audio

We started with a universe that came with no instructions,
And had to figure things out by assumptions and deductions.

The first snag we ran into was the drastic limitation
Of using just our senses as the means of observation.
For though our instruments can magnify both far and small,
The fraction that we glimpse is scarcely anything at all.

Some think the cosmos is like a machine that has no flaws,
And keeps on working perfectly by dint of natural laws.
But laws are just what we invent in order to explain
Our observations in a way that makes sense to the brain.

We understood that gravity’s a force of great attraction
That worked, as Newton told us, by an inverse square abstraction.
For centuries, that theory fit the purposes it served,
But now that model’s obsolete, and space itself is curved.

And though we learned the earth goes round the sun, not otherwise,
That viewpoint mainly differs in the math it simplifies.
For certainly it’s simpler just to plot the planets’ motion,
But simple‘s in the human mind, a quite subjective notion.

We keep inventing models that exhibit this causality
And if they work, we dignify them with the name reality.
A straight line’s one example. We all know a line, of course, is
The path a moving object takes when free of outside forces.

But objects do not obey laws as if they were just slaves.
We made up lines and laws to fathom how a thing behaves.
And likewise, the ellipse is just a shape that we invented.
There are no orbits out there on which planets ride, contented.

Our theories all are just like engineering in reverse,
To figure out how we might make a working universe.

Friday, July 11, 2008

Out of Time

We measure things by comparing them to other, more familiar things. We measure distance by seeing how many short things (e.g., inches, centimeters, etc.) can fit into a longer thing, and liquids by seeing how many ounces or cups the larger volume can fill.

Measuring time was a major challenge, both because of the usefulness of it, and because of the complex relationships of the available measurement units. The most obvious repeating events were days and lunar cycles. Unfortunately, neither of these fit nicely into a year. Trying to force them by defining a year as 12 lunar cycles, for example, just meant that the year had no relation to the actual position of the earth or, more importantly, to the seasons. Some pretty whacked out schemes were devised, like the Babylonian calendar of 19 year cycles with years of different lengths. Try keeping that in your DayTimer or Filofax!

In The Discoverers: A History of Man's Search to Know His World and Himself, Daniel Boorstin credits the ancient Egyptians with finally breaking the mind set of using lunar cycles, and noticing that the time between Nile floods could be divided up into 12 months of 30 days, plus 5 extra intercalary days. That was successful enough that the ancient Romans adopted it, with some modifications by Caesar, resulting in the Julian calendar. Further refinements were made under Pope Gregory XIII. This, the most widely used calendar today, at least for day-to-day purposes, is known as the Gregorian calendar. Other calendars are still used for things like finding the dates of Easter, Passover, Ramadan, etc., which is why these holidays occur on different dates every year.

In some ways, the field of astronomy owes its existence to the need for time measurement. And because astronomy depended on accurate measurements and records, it was one of the first sciences.

Monday, July 7, 2008

The Calendar

Audio

The ancient Egyptians
Were having conniptions
Because of the floods of the Nile.
They had no way to know
When it might overflow
(Which it does every once in a while.)
When the flooding did stop
They would plant every crop
In the hopes there would be time to reap.
For they harvested manually,
Knowing that annually
Crops could get lost in the deep.
They found it mysterious
The star we call Sirius
Signaled the start of the flood,
For it rose every year
At a time pretty near
To when they all got covered with mud.

Then they studied the moon
And observed pretty soon
It had cycles of waxing and waning.
These took near thirty days
Which a year, cut twelve ways,
Roughly equaled, with five days remaining.
And that was the reason
Predicting each season.
Was one of the calendar’s strengths,
Though it since has been changed
And the days re-arranged
Into twelve months of unequal lengths.
For a while it was Julian.
Gregorian’s truly an
Asset for scheduled living.
In four thousand B.C.
Nobody could foresee
What a valuable gift they were giving.

Wednesday, July 2, 2008

Horse Trading

Historian Barbara Tuchman, in The March of Folly: From Troy to Vietnam, describes an act of folly as a self-destructive act made by a group of people, even when a clear alternative is available, and at least some people at the time are aware of the self-destructiveness of the act. She uses Troy's acceptance of the legendary Greek gift horse as the prototypical example of folly.

Of course, in real life, things are rarely so clear-cut, and it's easy for historians to say "Well, obviously these people were right and these people were wrong." Still, it would have been pretty easy at least to examine the horse for signs of occupants. Given that there were a number of warnings about it, what would have been the harm?

The harm, apparently, was the risk of offending Athena, to whom the horse was dedicated. That brings a whole different dimension to the question of whether or not accepting the horse was folly. When you think you're at the mercy of powerful, inconsistent and self-serving gods, trying to make a rational decision is pretty tough.

Anyway, depending on whose perspective you have, the Trojan horse could be considered either a great idea or a dumb one.