

If I asked you to give me a Real number that is not computable, then you would simply be unable to describe it. "Most" Real numbers, therefore, are literally impossible to describe. There is a countable subset of computable numbers, which can be described with a finite amount of information. The Real number system is, however, mathematically tricky. It is not required by experimental data and it not known to be even theoretically consistent with observation. So the idea of a physical continuum or physical infinitesimals is definitely plausible and the idea of the converse is very questionable. There are no models that I am aware of that both explain the data and don’t involve a continuum or infinitesimals. To me, the salient point is the converse. To my knowledge we don’t have any valid physical models that lack this made a very broad original claim, and then brought in the EMR spectrum, but I was still responding to the broader context. So all of our physical models presume that infinitesimals are physically meaningful. All of our scientific models are based on calculus, and all of calculus is based on infinitesimals. To clarify, I was talking about calculus. That is why I said “These models underly all of physics”. I was responding with a very general statement about all of modern physics, not limiting my comments to EM at all. You shouldn’t have added the to my quote. I guess "would have more energy than the universe" is a boundary. I think, including - but not limited to - having being an infinite amount of energy. I guess "an EM wave that is too long to oscillate" is a boundary.Īn infinitely short wavelength would have other problems. Not only would it never oscillate it would never even start it first oscillate. You get the image, I suppose.Īre those atoms not real and physical, just because the distance is too great to observe them?Īs I said above: Using math as a convenient tool to explain / extra- / interpolate stuff doesn't mean that that stuff isn't real or not physical.Ī physically infinite EM emission would have an infinitely long wavelength. I won't bother to look up the appropriate prefix right now. Those atoms' apparent width would then be in the.

But they're composed of individual stars, some of which will be observed when they go supernova, eventually.which opens up the micro- and nano-arcsecond scale. You can always nudge your observing tool a bit to the right or left.Īll those faraway galaxies in the recently published JWST image.their apparent width is in the milliarcsecond range. And don't tell me that that only exists in math.Īlso, there definitely are infinite angles. Slanting the measuring scale yields another set of subdivisions, thanks to trigonometry. I guess "the Planck length" is a boundary. The physical world (as far we we understand) has real constraints on infinite subdivision. Likewise - while there are an infinite number of "real numbers" - this can only occur in the abstract world of math. Each step is a new one - even though you've been there before. The number of steps you can take in any direction - that is infinite: After each step, you add one to the count, yet you still can take another, uncounted step.ad infinitum. You start somewhere.and eventually you run out of unpainted places. You can "count" the area by painting it with exactly one layer of paint.

The distance you can travel, however, is infinite. The surface per se is boundless, but finite - it has a finite area, that can be determined. But that's all based on Axioms and some of the results don't necessarily 'make sense' to our intuition. Interestingly, the heroic and nerdy Mathematicians sorted out a lot about what infinity can mean, hundreds of years ago. That's just a mathematical idea and doesn't prove anything ' physical' about the Universe.
INFINITY AND INFINITESIMALS PLUS
I remember, when I was a lad, this (the surface of a sphere plus others) was brought up as an 'infinity' example.
