I didn't know that Newtonian space and time have been disproven as not overarching (time) and containing the universe (space). I am not espousing any position. Just looking for more information
Last question: accepting Newtonian space and time as real implies a change in understanding Einstein's space-time continuum? Would the latter be simply contained in the former? (I don't see how it would work because of relativity's doing away with objective location and size)
The parable of the surveyor is very enlightening! I always get confused by what exactly Leibniz thought time was, but Aristotelian writers (Edward Fesser is one) almost always say time is something human's make up in their minds. But they say this for philosophical reasons. Philosophers are...
Well you can't touch a wave, only particles. But can't they change into particles and thus be considered material in principle? This discussion can get really philosophical, but all I am looking for is the basic science facts that we know are true. Various interpretations are interesting but...
Hey!
I wanted to ask and learn more about what time is, and whether it even exists. Can relativity be understood solely in terms of rates of motion and subjective experiences, or do we really need to say this 4th dimension is a real thing. And if it is real, is it material?
Thank you
I am an avid student of philosophy, not mathematics. I was more interested in these topics for there philosophical implications. It seems to me that Zeno showed the uncountable infinity of space long before Cantor, and that that infinity alone leads directly to Banach-Tarski. I don't know why...
When we say 1/2 plus 1/4 plus 1/8 ect equals 1, are we doing more than making a set? When those fractions represent space, how can the spaceship approaching a limit even consider the limit to be a limit without a final term? It seems we see the limit from the outside dimension. I started this...
This might be a more geometrical question (which itself might be confusing things), but if you had the odd and whole numbers lined up like I said (each being like a little box), if you pulled all odd numbers back so that the "three" on the odd line lined up with the number two on the whole...
Its easiest for me to think the odd numbers are not less them all the whole numbers because of Hilbert's principle that you can add something less than an uncountable infinity to any infinity and have the same cardinality. I am definitely geometrizing the image of odd and whole numbers in two...
I've imagined Thompson's lamp in physical representation: half an object followed by it's quarter, ect. In arithmetic it would equal one, but in physical space the line of ever smaller objects can't go on forever, for then when put together the object wouldn't be perfectly finite anymore. An...
Finding where exactly something becomes that zero tangles me into knots, probably because I struggle with infinity. Aristotle said something can potentially be divided into an infinity, but not actually. I think that the object has the same measure whether divided or not. Math then seems to be...
Is a non-measurable part the same as a "simple substance", to use an old scholastic way to say it? This solution seemed to me to be saying that 0 and 0 can equal 1 (or a size). It seems the more I look, the more counter-intuitive is truth
My understanding of B/T was that it worked through the uncountable infinity of points within the original object. This is reconcilable with the object being discrete?
Hi! Does anyone think Banach-Tarski's paradox needs reworking? I first came across it in a video by Vsauce. I've been told that things might be reworked as to avoid the paradox, just as set theory was fixed so as to avoid Russell's paradox. How to make sense of a smallest unit of space is what...
I don't know what a set has to define it besides cardinality. But thanks to everyone for trying to help to understand a bit more. These are probably questions a lot of people wrestle with