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Misty concepts


Dalo

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37 minutes ago, Dalo 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.

The crystal structure means that light polarised one direction is absorbed more than light polarised at right angles. (Again, from the photon view, this is related to how the photons interact with the electrons in the asymmetrical crystal structure - but I doubt there is a simple explanation of that.) So you send unpolarised light in and you get polarised light out because the other polarisation is absorbed: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/polabs.html

There is another mechanism where crystals can polarise light: https://www.uwgb.edu/dutchs/Petrology/xls-pol.htm

 

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7 minutes ago, Strange said:

(Again, from the photon view, this is related to how the photons interact with the electrons in the asymmetrical crystal structure - but I doubt there is a simple explanation of that.)

why is that?

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7 minutes ago, swansont said:

Quantum mechanics is not intuitive when your experience is classical.

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?

45 minutes ago, Strange said:

There is another mechanism where crystals can polarise light: https://www.uwgb.edu/dutchs/Petrology/xls-pol.htm

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.

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1 hour ago, Dalo said:

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?

Waves are continuous, not discrete. And wave phenomena are usually fairly easy to visualise (because we encounter waves and other periodic behaviours quite often).

Quantum effects are less intuitive. I assume the explanations for why light with one polarisation is absorbed preferentially is because the crystal planes have more/strong bonds in one direction than the other. That causes a stronger absorption for some polarisations than others (just as described previously for the polarising filter).

1 hour ago, Dalo said:

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. 

That is not what happens. They are preferentially scattered in one direction (because they are polarised) this means the beam can only be seen from one direction.

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1 minute ago, Strange said:

Waves are continuous, not discrete

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.

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Just now, Strange said:

Er, no. A sine function is continuous. GR depends on space being continuous (and differentiable). The reals form a continuum. And so on.

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.

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2 minutes ago, Dalo said:

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.

You seem to have this the wrong way round: the mathematics is continuous but the application may, in some circumstances, have to be discrete. A sine function is continuous. If you want to calculate a sine function with a calculator, then you will be limited to the values that the calculator can represent. That isn't mathematics, it is engineering. 

But maybe this deserves a separate thread...

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5 minutes ago, Strange said:

You seem to have this the wrong way round: the mathematics is continuous but the application may, in some circumstances, have to be discrete. A sine function is continuous. If you want to calculate a sine function with a calculator, then you will be limited to the values that the calculator can represent. That isn't mathematics, it is engineering. 

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.

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21 minutes ago, Dalo said:

I would think it is pretty obvious that mathematics understood as independent from the human mind cannot render the continuous.

It is pretty obvious that most mathematicians and philosophers would think exactly the opposite.

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2 hours ago, Strange said:

It is pretty obvious that most mathematicians and philosophers would think exactly the opposite.

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.

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19 minutes ago, Dalo said:

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.

I agree. That is the exact opposite of what you said earlier.

19 minutes ago, Dalo said:

Please do not confuse the practice of mathematics with its philosophy.

Errr...

 

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24 minutes ago, Strange said:

I agree. That is the exact opposite of what you said earlier.

I don't think so. Anyway, I'm glad we agree on something

3 hours ago, Strange said:

But maybe this deserves a separate thread...

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.

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17 hours ago, Dalo said:

So, in the end, it is all a mystery?

No, it's physics. But you have to actually study physics to have an understanding of it. 

17 hours ago, Dalo said:

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.

I don't accept this. And since you have admitted to being neither a physicist nor a mathematician, I don't see where you can stake any claim to the contrary.

Photons are not points.

17 hours ago, Dalo said:

But when we are asked about the particles or points themselves, it becomes too complicated?

Nature is complicated. The math is part of our attempt to model what nature is doing.

 

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3 hours ago, swansont said:

I don't accept this. And since you have admitted to being neither a physicist nor a mathematician, I don't see where you can stake any claim to the contrary.

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.

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27 minutes ago, Dalo said:

It would destroy the idea that Man can understand the universe, even if he does not grasp all the details.

 

No one man can understand it all these days. I have read somewhere that one of the ancient greek philosophers was the last man on Earth who could understand all known knowledge.

That is why we need to talk to and equally important listen to each other.

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14 minutes ago, studiot said:

No one man can understand it all these days.

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.

 

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49 minutes ago, Dalo said:

This is a very extreme position. Only mathematicians and physicists can understand the principles on which Nature works?

That is not what he said. He was just pointing out that your lack of mathematical knowledge doesn't really equip you to tell other people about the nature of mathematical functions. 

But, while it may sound extreme, it is probably true that only people with a certain level of mathematical knowledge can fully understand the details. Most people are capable of understanding the general principles, though, if they are well explained.

9 minutes ago, Dalo said:

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.

Unless you think effects like superposition or entanglement are intuitive, then it is pretty obvious that it is not metaphysics or dogma that tells us this, but simply our observations of the world.

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Just now, Strange said:

That is not what he said. He was just pointing out that your lack of mathematical knowledge doesn't really equip you to tell other people about the nature of mathematical functions. 

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.

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1 minute ago, Dalo said:

Except that I already know what a sin function is, and what is meant with "continuous" and "discrete" in mathematics.

If so, why are you making statements that are clearly false? Maybe you think you know what these words mean but are mistaken about that.

 

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