Dalo

I am very surprised at this affirmation and would be very interested in references and links.

I certainly agree with you on this. Anyway, if I had to judge the value of my ideas by their popularity I would look first at my reputation. I am glad I do not. But both reputation and views do give some information about the interests and the convictions of the users of this forum. As such, they are fairly decent indicators.

This is what I said in the first post of this thread. There is no theory of vision, that I know of, that makes use of the wave theory of light.

you should definitely do that. How would such a diagram look like, drawn on scale?

I did, but you find my view apparently so strange that you simply ignore it. Imagine your size, as an observer, and that of the sun. Forgetting about perspective, how much would the sun rays need to converge for you to see (half of) the sun?

Please remember that you are thinking in terms of ratios given by perspective. Seen like this I can only agree with all of you. What I am saying is that our perspective, which is certainly unavoidable as far as we are concerned, does not explain space. Objects become smaller with distance, seen from our perspective. But seen from the other side, it is us who are becoming smaller and smaller. At the same time, when we try to think about it, we cannot deny that neither the distant objects nor ourselves have shrunken to a point.

That's what I would like to know. Anyway even that wouldn't help. How much would the sun rays need to converge to reach the eyes of an observer on earth? Almost parallel would not cut it I'm afraid.

Aren't you changing the theory?

- I do not! - you do too!

show me, or if you think I will not listen, show the world.

Yes, draw a diagram... of the sun, earth, the observer, and keep the same ratios as far as size is concerned.

Except that I already know what a sin function is, and what is meant with "continuous" and "discrete" in mathematics. One certainly needs a minimum of knowledge of mathematics to "philosophize" about mathematics, or any other branch of science., but one certainly does not need to be a specialist. In fact, being a specialist might just be a hindrance in such a case.

Again, this is only correct if one consider details that only specialists learn to understand after years of formation and experience. But the idea that we cannot understand the universe sounds like some form of obscurantism, or elitism. Whatever the good intentions behind it. This is a view that is easily reached within the context of Quantum theory. The idea that Nature does not comply with our intuition and logic is a metaphysical stance that has reached the status of a scientific dogma.

This is the biggest mystery of all. And if one thinks about how the world looks like in perspective, and how it does from another perspective, one can only wonder how it it is possible that we see the sun "in its totality", meaning, the parts facing us. The sun rays can only reach us in a parallel way because of our perspective. If we remember how much larger the sun really is, and we still cling to the idea of parallel rays, then we would be a dust speck on the path of the sun, and the few rays getting bent through the atmosphere would show us nothing but a bright speck. That is the mystery of space, and how we see it and experience it. Before the relativity of time, maybe Einstein should have started with the relativity of space.

This is a very extreme position. Only mathematicians and physicists can understand the principles on which Nature works? I will certainly agree with your view if you mean by that that mathematical proofs cannot be expected to be understood by non-mathematicians, or chemical proofs by non-chemists. To deny that would be denying that there is something as science and that not everybody has the same level of understanding of deep processes. There is a very large distinction though whether Nature is to be incomprehensible for all but a minority of experts. It would destroy the idea that Man can understand the universe, even if he does not grasp all the details.

I don't think so. Anyway, I'm glad we agree on something Yes, it would certainly be very interesting. But let's not forget that we got to this point because of the concept of wave and particle. And Quantum Mechanics which aims at superseding both concepts and uniting them in "wave-particle". But even before that, we were discussing how to render the phenomenon of polarization using the theory of light as a particle, instead of as a wave, and how difficult that was.

You shouldn't be so sure. The philosophy of Mathematics, just like any other philosophical terrain, is very diverse. So I won't claim universality for my own convictions. Concerning continuity, the best example is the circle. Maybe you should think about how it is expressed mathematically, and how it was the start of the method of exhaustion among the Ancient Greeks, the geometrical counterpart of Calculus. And how Calculus itself defines a continuous value by ever closer discrete ones, in the form of reals. Maybe you think that reals are continuous, which is of course correct as long as you consider them as concepts. But any real you will ever use in any calculation will still be a discrete value. You may also think about the concept of limit, which can be nothing else but a discrete value towards which other values may grow without touching it, by taking ever increasing or decreasing but discrete values. You may also want to think about the concept of infinity and ask yourself if it is a pure mathematical concept. After that, and after having thought about many other issues treated by the philosophy of Mathematics, maybe you will be willing to admit that the issue is much more complex than you initially thought. Please do not confuse the practice of mathematics with its philosophy.

It is more than engineering, it is the indication that mathematics cannot be considered simply as number crunching. The continuous is something that the human mind adds to the mathematical discrete. I would think it is pretty obvious that mathematics understood as independent from the human mind cannot render the continuous. The way you understand mathematics is too rich and generous, but at the same time unjustly ignoring the role of the mind and the imagination.

Er, yes. A sine function is built with discrete values which have been smoothed out by the human mind or imagination. Just like a circle which is rendered as a polygon. Try inputting a continuous value in a computer or calculator.

In mathematics everything is discrete, while it is continuous in nature and in our mind. Calculus is an attempt to render the continuous while using discrete values.

So, in the end, it is all a mystery? We have to accept a wave concept which can only be mathematicized by punching in discrete values. We construct therefore a wave with "particles" or points, then we appeal to the human imagination to turn the static functions into a dynamical concept. But when we are asked about the particles or points themselves, it becomes too complicated? Pleochroism is a very interesting phenomenon. It could explain Bragg's experiments and the disappearance each time of the beam or its mirror reflection. A beam or a reflection only seem to disappear, in fact they have taken on a dark color and become indistinguishable from the unlit background. Of course, it still does not solve the problem of two different directions.

why is that?

I will accept those figures, which means that light cannot "squeeze" between the gaps. In that, my mental model was wrong, just as you said. Maybe you will help me ameliorate my mental models even more by explaining to me the case in which polarization takes place in what used to be called tourmalin, and which, just like Land's Polaroid sheets,is completely transparent. Because, I have also to admit that my mental model of "gaps" is necessarily complemented by a model of not-transparent, opaque, crystals or surfaces. I see, now that I have read the patent application more carefully, that I was wrong. Just like tourmalin or calcite, the crystals are transparent. That makes the idea of absorption and transmission really obscure in my head. Also, I have to insist on the necessity for me to understand how a variable polarizer is fabricated constructed. In fact, I am sure that if that became clear, we would probably conclude our discussion more swiftly.

I am really sorry about that. I did refer to the Malus experiments from your link. I do not understand this reaction. If I missed something that you said that should have stopped all my questions, then please be so kind as to state it one last time. If this is the post you wanted me to react to, then I must say I am not sure I understand it. Maybe it is evident to people with enough physical knowledge, but I do not really see any difference between what is supposed to be a wave, and what is supposed to be a particle. The idea that a particle has probability of x% to pass through is completely alien to me. I understand statistical probabilities and am willing to accept the metaphorical use of the expression, but a single particle has, as far as I am concerned, no probability of going through, except if this probability concerns our own knowledge of it. Maybe it has nothing to do with the issue we are here discussing, but that reminds me of Schroedinger's cat.

From the patent application: "The die-members and the mass 10 in Fig. 1 may be deemed to show the parts greatly magnified as the die-members in practice are spaced apart a distance not much greater than the least dimension of the polarizing bodies" In fact, it would seem that we were, or at least I was, all wrong about the polaroid sheets, at least in this version. There are gaps everywhere, and not only in one direction or the other. We are dealing with discrete crystals, also transparent, and not with continuous, opaque surfaces.