Saturday, 15 March 2008

Richard Feynman: part 2

As promised about a week ago, here is the second part of my reflection on the thought of physicist Richard Feynman. This post has been given an added relevance by the announcement during the past week of the award of the Templeton Prize to Fr Michael Heller, a Catholic priest, philosopher and physicist. Fr Heller's statement made on receiving the prize can be found on the Templeton Prize website at http://www.templetonprize.org/pdfs/heller_statement.pdf

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In Chapter 1 of his book The Character of Physical Law, Feynman presents the law of Gravitation as an example of Physical Law, and draws out from it a description of what a physical law is. At the end of the chapter, he gives a summary of his conclusions, saying that what he has presented about the law of Gravitation is also true about all other physical laws. I have added emphases to make clearer the separate points that Feynman makes:




"First, it is mathematical in its expression; the others are that way too. Second, it is not exact; Einstein had to modify it, and we know it is not quite right yet, because we have still to put the quantum theory in. That is the same with all our other laws - they are not exact. There is always an edge of mystery, always a place where we have some fiddling around to do yet. This may or may not be a property of Nature, but it certainly is common to all laws as we know them today. It may be only a lack of knowledge.

"But the most impressive fact is that gravity is simple. It is simple to state the principles completely ... It is simple, and therefore it is beautiful. ... It is complicated in its actions, but the basic pattern or system beneath the whole thing is simple. This is common to all our laws; they all turn out to be simple things, although complex in their actual actions.

"Finally comes the universality of the gravitational law, and the fact that it extends over such enormous distances that Newton, in his mind, worrying about the solar system, was able to predict what would happen in an experiment [in a laboratory]... Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organisation of the entire tapestry."



It should be noted that, when Feynman says that laws are inexact he is not saying that they are wrong or incorrect; rather he is saying that they are open to, and indeed at certain points need, the greater precision that comes with furtherance of scientific knowledge. The word inexact has been well chosen here.

In Chapter 2 of The Character of Physical Law, Feynman considers further the relationship between mathematics and physical laws. One point that Feynman makes in this chapter is that the mathematician deals just with "theory" (my choice of words here, not Feynman's) or language that is mathematics, whereas the physicist has to make a connection between "theory" or language and a "real world". Again, I include some emphases of my own, which will be referred to below:


"Mathematicians are only dealing with the structure of reasoning, and they do not really care what they are talking about. They do not even need to know what they are talking about, or, as they themselves say, whether what they say is true."

A mathematician will represent a quantity by "x", and, after that, it is not critical to him or her exactly what "x" represents.

"In other words, mathematicians prepare abstract reasoning ready to be used if you have a set of axioms about the real world. But the physicist has meaning to all his phrases....(In) physics you have to have an understanding of the connection of words with the real world. It is necessary at the end to translate what you have figured out into English, into the world, into the blocks of copper and glass that you are going to do the experiments with."


Feynman also points out the possibility that, what is the same thing in the "real world" of physics, can be expressed by different forms in the language of mathematics. So, the law of Gravitation can equally well be expressed as a formula describing the force between two objects at a distance or as a formula describing a potential field in which a number expresses a gravitational property of each point in space. These different formulations might be exactly equivalent scientifically, but Feynman suggests that they can be very different "psychologically" (Feynman's choice of word). This is because when you are trying to find out new laws, or see how the laws apply in new situations, one formulation might turn out to be much more useful to the physicist than another. He also refers to the idea of a kind of scientific intuition, or the use of models and pictures of reality, that can be used to arrive at a new physical law. These can help, he says, but the bottom line is that, the greatest discoveries then

"abstract away from the model and the model never does any good".

Feynman continues:

"This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way."

In concluding his chapter, Feyman writes:

"To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature .... If you want to learn about nature, to appreciate nature, it is necessary to understand the language [ie mathematics] that she speaks in. She offers her information only in one form; we are not so unhumble as to demand that she change before we pay any attention."

Feynman has deliberately, to use an expression I used in part 1, allowed the physics to speak for itself. However, now look at the emphases/emphases highlighted above and compare them to the philosophical expression of S L Jaki in his book Cosmos and Creator p.54:

"First, the material entities observed by science must be real, that is, existing independently of the observer ...Second, the material entities must have a coherent rationality. They must be governed by laws which can be formulated in a quantitative framework, and they must have a validity which transcends the limits of any particular time or location ...Third, those entities, because they are governed by consistent laws, must form a coherent whole, that is, must be subject to a consistent interaction ... Fourth, the form in which that coherent wholeness, or universe, does exist, cannot be considered .. a necessary from of existence. It is only one among countless others that are conceiveable. As to the question why such a universe does in fact exist, science has no answer....

"These four features of the universe are indispensable ... for making science possible."


So, I want to suggest, Feynman comes very close to offering what a philosopher might consider the necessary metaphysical conditions, that is, the necessary understanding of the way the world really is, for a self sustaining scientific enterprise just by letting the nature of the study of physics speak for itself ...

2 comments:

Mike Gottlieb said...

I have to admit that when I came to your blog it was with my atheistic hackles up and a critical eye. "Who is this religionist writing about Feynman, and what the heck does he have to say?" But as I read on I found nothing objectionable or even untrue, and in fact, I found what you wrote to be quite correct and insightful. Then I read the first part of your essay and discovered that it was also uniformly fair, which left me with a feeling of relief on the one hand, since I was expecting the worse, and disappointment on the other, as I was readying myslelf for a good fight. Oh, well!

Anyway, I just want to say that I like what you have written in your Feynman essay, and also I do not mind that (in the first part of the essay) you are using the (copyrighted) picture of Feynman printed on the cover of "Feynman's Tips on Physics," which I co-authored with Ralph Leighton, and Feynman (posthumously). So, keep up the good work! I look forward to reading your next installment.

In closing I wish to mention that I have posted some elementary (but not necessarily easy) physics exercises (with answers, and some solutions) on The Feynman Lectures website, www.feynmanlectures.info, which you might find useful for your students; many of these problems were used in the first term of the Caltech introductory physics course taught by Feynman in 1961-63, which was the basis of "The Feynman Lectures on Physics." You will find more exercises (with answers) in "Feynman's Tips on Physics," along with three lectures Feynman gave his freshmen students about problem-solving, a lecture about dynamical systems and their applications (with lots of interesting information about gyroscopes), and a historical essay by Matt Sands on the origins of The Feynman Lectures.

My colleagues and I are currently working on a project which (hopefully) will result in the publication of a much larger set of exercises and other ancillary material meant to accompany The Feynman Lectures, in order to make it more usable for its originally intended purpose as an introductory physics textbook.

Best wishes,
Mike Gottlieb
Physics Department
California Institute of Technology
---
www.feynmanlectures.info

Joe said...

Dear Mike

Thank you for your comment, which I have appreciated very much. It gives me confidence that I have understood Richard's thought accurately, for which I am grateful.

I was aware of possible copyright issues in using the photo - when I first started blogging I promised myself I would use only photos I had taken myself, in order to avoid possible infringements of copyrights, but I haven't stuck to that rule! In principle, I am happy to take down pictures on request, so thank you for the permission to leave up the photo.

In one of my future posts I intend looking at the lectures that appear in The Meaning of it all - this is why I gave an "alert" in my first post to look especially at the fourth post. I am expecting to engage more critically with Richard's thought at that point!

Many thanks again for your comment,and I hope you will feel able to contribute again, especially if you feel I have been inaccurate or unfair to Richard's thought in any way.