Philosophy 167: Class 12 - Part 5 - The Optics: an Experimentum Crucis, the Relationship between Hypotheses and Experimental Results, and Newton's Wish for a Natural Science Supported by the Greatest Evidence.

Smith, George E. (George Edwin), 1938-


This is from the same little notebook. This page is describing how to grind lenses. The next page is even more interesting because it looks at lenses and asks the following question. How do you detect imperfections in them? What do you do in terms of, looking at rays coming through them, and imperfections to work back to the imperfection in the lens?
Nice little problem. You think your lens isn't perfect. How do you test, not just whether it's not perfect, but to figure out all the imperfections so you can go back and grind them out? Okay this is again, while he’s an undergraduate, 1664 period. Before he gets serious in optics, and i'm doing it as an introduction to his work in optics.
Probably what got him interested in optics was Isaac Barrow doing a series of lectures on optics, called the Optical Lectures. And presumably Newton attended, we don't know that for sure again, time and again we don't know what Newton did with his life. We can only guess at what got him going.
I'm gonna cover, this is from the very first paper on light and colors. I'm going to read out the portions that are marked. And then show you in the next slide the diagram of it. Then I began to suspect whether the raise, after their trajection through the prism, did not move in curved lines.
And according to the more or less curvity, tend to diverse Parts 10-2, diverse parts of the wall, and it increased my suspicion when I remembered that I had often seen a tennis ball struck with an oblique racket describe such a curved line. I trust that all intrigues you slightly.
This is his writing in English, do understand. For a circular as well as a progressive motion being communicated to it by that stroke. And parts on that side, where the motions conspire must press and beat the contiguous air more violently then on the other. And there a sight, a reluctancy and reaction to the air, proportionally greater.
He's describing how a curve ball works. And correctly. And for the same reason, if the rays of light could possibly be globular bodies. Now you see where the hypothesis of particles comes from, and by their oblique passage out of one medium into another acquire a circulating motion. They ought to feel the greater resistance from the ambient ether on that side where the motions conspire and thence be continually bowed to the other.
I'm not gonna continue with that. I'm gonna jump down. The gradual removal of these suspicions at length lead me to the experimentum crucis, experiment of the cross, Christian cross. Crucis is not a classical Latin word at all. It's a word that comes with Christianity. And the term is Francis Bacon's but Newton almost certainly got it from Robert Hooke's Micrographia, where it's used in several places.
Led me to the experimentum crusis which was this, I took two boards and placed one of them close behind the person at the window. So that the light might pass through a small hole, and made in it for the purpose, and fall on the other board, which I placed at about 12 feet distance, having first made a small hole into it also for some of that incident light to pass through.
Then I placed another prism behind the second board so that the light trajected through both boards must pass through that also, and be again refracted before it arrived at the wall. This done, I took the first prism in my hand, and turned it two and from slowly about its axis.
So, much as to make the several parts of the image cast on the second board successively pass through the hole in it, that I might observe to what places on the wall the second prism would refract them. And I saw by the variation of those places that the light tending to the end of the image towards which the refraction of the first prism was made, did in the second prism suffer a refraction considerably greater than the light tending to the other end.
And so the true cause of the lengths of that image. The original weary was why the image is oblong in one direction. The true cause of the length of that image was detected to be no other than that light consists of rays of differently re frangible, which without any respect to a difference in their incidence, or according to their degrees of re frangibility transmitted toward diverse parts of the wall.
And of course it becomes, light consists of rays of different colors and those colors are each separately re frangible. The experiment is shown down here schematically, not of course by Newton. This is in an exposition. And you can see that as he rotates this, he's going to get different colors hitting the second hole.
And those different colors hit the second prism and they displace differently, because they're now nearly monochromatic. He ends up as part of this actually measuring the index of refraction for the lights of different colors, and shows their variability all the way through. With it, he explains chromatic aberration.
Going through the lens, they diverge and the colors at the end end up showing on the edges of the object. He also explains why he has to have a reflecting telescope because this doesn't happen with reflection. Isn't that nice? Only happens with refraction. Another experiment he does is to take the light of different colors, separate them, take them through prisms, bring them back together again and create white light out of them.
All of which convinces him that light consists of constituent light rays of different colors that have separate properties. And he was interpreted as saying, of different particles describing paths as rays. He expressly says over the course of this, rays are an abstract description of a path part of light travels.
But they took the part of light to be a particle and thus the controversy ensued even though he kept saying no, no, no, that's not what I mean. Now I'll get to the thing at the top in just a moment. I trust you see that's a fairly beautiful experiment.
What you do not see is he published maybe eight or ten experiments for every one of them, there are four or five experiments he doesn't publish that cross check the ones he does. This is a different experimenter from the ones you guys just wrote about in your preceding paper.
Newton gets a good result and then tries to show it's an artifact. In every way he can think of to make sure it's really robust. He apologizes in that first paper for reporting only a handful of the experiments trying not to bore people. You look at the actual optical papers, it's remarkable how much patience he has doing experiment after experiment.
Cross checking. So I brought, I'll pass both of these out now, this is a collection of papers, but what's in here in the opening part are all of Newton's papers on light and colors from the early 1670's, I put them on supplementary material. And this is the Lucasion lectures on optics from 1670 to 72 edited by Alan Shapiro who's in the process, has been in the process for 25 years of editing the second volume of that.
The optical papers from the later period. And as he says, I saw him two weeks ago and I of course asked, how's it coming? Slowly. This is all hand written stuff crossed out, this is not, you don't start from it all typed out. It's got loose sheets, you've got to figure out how to organize them.
You've got a lot of work to do. This is a part of the very first letter that Oldenberg decided not to publish. Now this is a kid under 30 years old, your age more or less, publishing for the first time in his life in the prestigious philosophical transactions, and what's he say?
I shall now proceed to acquaint you with a nether more notable deformity in the rays wherein the origin of colors is unfolded. Now this is my bold. A naturalist would scarce expect to see the science of these become mathematical and yet I dare affirm that there is as much certainty in it as in any other part of optics, for what I shall tell concerning them is not a hypothesis,but most rigid consequence not conjectured by barely inferring tis thus because not otherwise.
Or because it satisfies all phenomena. The philosopher's universal topic. But events by the mediation of experiments concluding directly and without any suspicion of doubt. To continue the historical narration of these experiments would make a discourse too tedious and confused. And therefore I shall rather lay down the doctrine first and then for its examination, give you an instance or two of the experiments as a specimen of the rest, that was not published.
But it tells you very, very clearly what his view is of hypotheses, what his view is of experiments. That by the way tends to derive from Barrow. Barrow had a view that the distinction between a hypothesis and an established, experimentally established claim is a distinction of kind, not degree.
And Newton, his whole life had that theory. Doesn't mean that the things you establish by experiment aren't provisional, because subsequent experiments may show some sort of refinement, but he thought conjectures were one thing, results established from experiments were another. And that's where the controversy blew up because he couldn't understand why others couldn't see this.
Now of course part of the reason is his announcement here wasn't published, but you can also see why Oldenburg wouldn't publish. Here's a guy who's virtually unknown. Gets elected to a fellow of the Royal Society after this appears telling the other people who are doing science that they're jerks.
And it was, I think, Newton's view. He did not have a high view of most people. One other, this is in response to parties. This is being translated from the Latin, because parties not being English wrote in Latin but it's worth reading this whole thing again. An answer to this it is to be observed that the doctrine which I explained concerning refraction and colors consists only in certain properties of light without regarding any hypotheses by which those properties might be explained.
The word is explica by the way. For the best and safest method of philosophy seems to be first to inquire diligently into the properties of things. Establishing those properties by experiments. Then to proceed more slowly to hypotheses for the explanation of them. For hypothesis should be subservient only in explaining the properties of things but not assumed in determining them unless so far as they may furnish experiments.
For if the possibility of hypotheses, pause a moment. What do you do in the hypothetico-deductive method strictly logically? You show the hypothesis is possible because a consequence of it is true. You don't show it's true. You establish it's a possibility, and he's actually saying that. For if the possibility of hypothesis is to be the test of the truth and reality of things, I see not how certainty can be obtained in any science.
Since numerous hypotheses may be devised, which now seem to overcome new difficulties. Hence it has here been thought necessary to lay aside all hypotheses as foreign to the purpose that the force of the objection should be abstractly considered and receive a more full and general answer. I can show you other passages like this.
I've singled out the two most explicit. One of which was published, this one not published. People did not want to hear this. They didn't wanna hear it any more when the Principia appeared. That is, just as he told think of rays in the abstract, don't think of them physically, he said the same thing about forces and they had the same difficulties okay.
One last quote. This is a very important quote that I will come back to. I show you the Latin on the facing page. This was not public. This is in the optical lectures. Lecture three. And I'll just start yeah, I think you can read the whole thing but I'm gonna start from where I've marked it.
Thus although colors may belong to physics, the science of them must nevertheless be considered mathematical in so far as they are treated by mathematical reasoning. Indeed, since an exact science of them seems to be one of the most difficult that philosophy is in need of. Exact here, let us see what the word it should be accurada, I don't see.
Sorry, I'm not able to see what I want to see. Yeah, there it is, there it is. Accurada. So exact is simply the word accurada. Indeed, since an exact science of them seems to be one of the most difficult that philosophy is in need of, I hope to show as it were by my example, how valuable mathematics is in natural philosophy.
I therefore urge geometer's to investigate nature more rigorously, and those devoted to natural science to learn geometry first. Hence the former shall not entirely spend their time in speculations of no value to human life, that's the mathematicians. Nor shall the latter while working assiduously with an absurd method perpetually fail to reach their goal.
That's the philosophers, the natural philosophers. But truly with the help of philosophical geometer's and geometrical philosophers, instead of the conjectures and probabilities that are being blazoned about everywhere. We shall finally achieve a natural science supported by the greatest evidence, and the words there are science of nature, supported by the most firm, firmaton evidentius.
Okay? That's, and I'll come right back. That's a vision he had in 1671 or 72 and it's realized in the Principia, okay? It's not realized ever in his work in optics. He never really managed to see how to do a totally integrated math and physics in the case of the optics.