In the time I’ve been doing this blog, I’ve written 68 stories with little end in sight. However, of the 68, I’ve been comfortable with 67 of them. The problem one was the one about Ockham’s Razor. It was the one I didn’t quite get from my head.
I know nothing much about anything scientific. OK, I know a bit, the normal stuff I’ve gleaned from life like the freezing point of water (in Fahrenheit or Centigrade) and assorted practical science, but real hard stuff is not for me. I tried very hard to read Steven Hawking’s “A Brief History of Time” and it really was interesting for a page or two and then I was lost.
I used to feel the same way in Hebrew School as a child, or any language class or even most math classes beyond the basics. I can read a balance sheet, and I understand about money, but that’s practical. So science is definitely not my thing.
So, on April 23 I wrote:
In two recent experiences, the movie “Contact” with Jody Foster, and a book I was “reading” (listening to on my MP3 player, in this case a British mystery called “Dust”), there were references to Ockham’s Razor. Knowing this was not a Gillette, I had to dig farther. I knew within the context in which these were found that it referred to the idea that the simplest solution to a problem is probably the correct one. I decided to investigate, and here’s what I found:
Ockham's Razor is the principle proposed by William of Ockham in the fourteenth century: ``Pluralitas non est ponenda sine neccesitate'', which translates as ``entities should not be multiplied unnecessarily''.
In many cases this is interpreted as ``keep it simple'', but in reality the Razor has a more subtle and interesting meaning. Suppose that you have two competing theories which describe the same system, if these theories have different predictions than it is a relatively simple matter to find which one is better: one does experiments with the required sensitivity and determines which one give the most accurate predictions. For example, in Copernicus' theory of the solar system the planets move in circles around the sun, in Kepler's theory they move in ellipses. By measuring carefully the path of the planets it was determined that they move on ellipses, and Copernicus' theory was then replaced by Kepler's.
But there are theories which have the very same predictions and it is here that the Razor is useful. Consider for example the following two theories aimed at describing the motion of the planets around the sun
The planets move around the sun in ellipses because there is a force between any of them and the sun which decreases as the square of the distance.
The planets move around the sun in ellipses because there is a force between any of them and the sun which decreases as the square of the distance. This force is generated by the will of some powerful aliens.
Since the force between the planets and the sun determines the motion of the former and both theories posit the same type of force, the predicted motion of the planets will be identical for both theories. the second theory, however, has additional baggage (the will of the aliens) which is unnecessary for the description of the system.
If one accepts the second theory solely on the basis that it predicts correctly the motion of the planets one has also accepted the existence of aliens whose will affect the behavior of things, despite the fact that the presence or absence of such beings is irrelevant to planetary motion (the only relevant item is the type of force). In this instance Ockham's Razor would unequivocally reject the second theory. By rejecting this type of additional irrelevant hypotheses guards against the use of solid scientific results (such as the prediction of planetary motion) to justify unrelated statements (such as the existence of the aliens) which may have dramatic consequences. In this case the consequence is that the way planets move, the reason we fall to the ground when we trip, etc. is due to some powerful alien intellect, that this intellect permeates our whole solar system, it is with us even now...and from here an infinite number of paranoid derivations.
For all we know the solar system is permeated by an alien intellect, but the motion of the planets, which can be explained by the simple idea that there is a force between them and the sun, provides no evidence of the aliens' presence nor proves their absence.
A more straightforward application of the Razor is when we are face with two theories which have the same predictions and the available data cannot distinguish between them. In this case the Razor directs us to study in depth the simplest of the theories. It does not guarantee that the simplest theory will be correct, it merely establishes priorities.
A related rule, which can be used to slice open conspiracy theories, is Hanlon's Razor: ``Never attribute to malice that which can be adequately explained by stupidity''.
As I guessed, the simplest solution to a problem is probably the correct one.
The first paragraph and the last line were mine. The middle part was lifted from Wikipedia, a great source of all knowledge, although not always correct, but an easy way to get answers. I didn’t understand what I wrote but I figured my readers are simple folk like me.
Wrong, I have at least two “scientific types” who have happily responded to my ramblings, and I feel I have to come clean.
First was my Cousin, Gary Floam, a very religious person and a man schooled in Computer Science, who has made a living for these past 35-40 years in the computer programming business.
He said, “When I was reading your Ockham’s Razor post, I kept substituting "God" for "space alien". Was this your half-intention?
Concerning universal gravitation, we have no idea how it works. In Newton's day, this "action at a distance" was a mystery. Einstein said something about space being bent by mass, and this explains gravity, sort of. It is certainly not a more simple explanation than Newton's but Newton's predictions were found to be a little bit wrong and Einstein's explanation puts, say the orbit of Mercury, more where we see it to be.
Scientist have been looking for something that makes gravity work. They posit something called "gravitons", but we haven't found them yet.
Right now gravity is something that just happens. There may be something about the universe that makes it want to obey the Newton/Einstein equations, or it may be the particular will of God or a space alien, or we may read in tomorrow's paper that there are gravitons after all.
Then came a response from Dr. Joel Cohen, from the University of Denver, a scientist for sure, a physics Ph.D. and a computer expert.
Joel said “I enjoyed your blog post about Ockham's razor, especially your references to Copernicus, Kepler, and planetary motion.
When I first retired I was looking for something to do with my time and eventually decided to explore ancient mathematical astronomy and how it evolved up to the time of Copernicus, Kepler, and Newton. I was particularly interested in Kepler because I wondered how he could formulate his three laws of planetary motion (including motion in elliptical paths) given the planetary data that was available at that time. Kepler was a very interesting and crazy character. He was interested in astrology and had other theories about planetary motion before he settled on the final three laws. At one time he claimed to understand God's geometric plan for the solar system, and connected the motion of the six planets that were known at that time with the five Platonic solids. Surprisingly, the approach gave reasonably accurate results. While I eventually understood how he discovered his three laws of planetary motion, I was not able to find out to my satisfaction how he used the actual observational data. Eventually I moved on to other things.
By the way, my real hero in all of this is Isaac Newton. Newton put planetary motion on a firm mathematical footing and along the way invented calculus. Newton was able to show that assuming gravity acted according to an inverse square law, it was possible to prove mathematically that the planets moved in elliptic paths and followed Kepler's other laws. But he did something that was even more remarkable. He was able to show that if planets traveled around the sun in elliptical paths according to Kepler's theory, there had to be a gravitational force between the sun and the planets which acted in an inverse square way. In other words, Newton was able to infer the mathematical form of gravitational attraction without ever being able to measure it. Great science.
Although Newton understood the mathematical form of gravitational attraction, he never really understood what gravity is. This was left to Einstein's general theory of relativity which describes gravity in terms of curvature of space. In this case, the theory is much more complicated, but doesn't tell us much more about the motion of planets.
I'm looking forward to seeing you. Let's talk about this.
So now I have been “caught” by two people and I am helpless to answer. By writing this confession I hope to vindicate myself.
I have no idea what I said and I promise never to say it again!
No comments:
Post a Comment