Recent content by rmberwin

But if the statement is true, then it is probably (90%) false. That is the paradox.

A variation of the Liar's Paradox occurred to me: "Statistics are wrong 90% of the time". This statement seems to refute itself, but does so in a less straightforward way. I would appreciate any insights! And what about, "Statistics are wrong 50% of the time"? (Even odds.)

I came across the following argument that attempts to show that the notion of infinite decimal numbers is incoherent. Try adding these two numbers:05.4123482100439884... 16.3482518100560115... ___________________ 21.760600020?999999...By the Axiom of Choice, "There exist arbitrary infinite...

Ah, I see your point. But the Cantor set also has zero measure, which (I assume) means that all the points are disconnected. So I don't see how taking the limit at countable infinity would get to the final result. Probably a failure of imagination on my part.

I am puzzled by the derivation of the Cantor set. If the iteration of removing the middle-thirds leaves an uncountable set of points, it seems the iteration had to be performed an uncountably infinite number of times. Is this the case? If so, that seems paradoxical to me.

If the liquid in a soda straw moves up because the outside air pressure is greater than the pressure in the lungs, it seems that a straw wouldn't work in a vacuum. Is this the case?

When EM waves interfere, what happens to the energy?

So accelerating positive charges produce EM waves? Textbooks I've read mention only electrons.

I understand that sinusoidal EM waves result from charged particles in harmonic motion, e.g., up and down an antenna. But what if the charge is undergoing some more complicated periodic motion? Wouldn't the EM waves be non-sinusoidal? I saw in a textbook a hypothetical EM wave with infinite wave...

I saw it in one of the standard texts. I agree that technically there is no wave. But it is an electromagnetic disturbance, traveling at the speed of light. But if there's no wavelength, what is the color of the light?

I saw an example of a hypothetical EM wave that had constant E and B fields. Is that possible? How would it be produced? And wouldn't such a wave have an infinite wavelength?

Let's say we randomly select integers to construct a potentially infinite number, for example 3588945... There is a non-zero chance that eventually we will obtain any possible finite series of numbers, say a billion 3's in a row. It is known that pi is indistinguishable from a random series of...

I'm trying to teach myself some basic physics, and so maybe this question is stupid! But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon...