EPTAsk and answer stupid questions here! - Page 638
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JimmiC
Canada22817 Posts
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farvacola
United States18866 Posts
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GreenHorizons
United States24134 Posts
On July 03 2017 00:05 Uldridge wrote: It's like light. Shooting light at the speed of light (or close to it) will show that light, from your reference point, go at the speed of light. Maybe there are hard limits on what is possible in this universe and we should just put c at infinity instead of ~300000 km/s Or just put 300000 km/s = infinity. Can you do that in maths? Put a number = to infinity? Or is that just dumb?  This made me wonder, what would it take to be able to actually see light race past you? I'm imagining the image of a train passing on the horizon in the distance. Something like that visually (presumably it would be in space though) Like how far away, how bright, etc...? | ||
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IgnE
United States7681 Posts
On July 03 2017 10:13 GreenHorizons wrote: This made me wonder, what would it take to be able to actually see light race past you? I'm imagining the image of a train passing on the horizon in the distance. Something like that visually (presumably it would be in space though) Like how far away, how bright, etc...? | ||
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radscorpion9
Canada2252 Posts
Like if you travel between points A and B, you can always find a halfway point by dividing that length in half, something like A + (B - A)/2 on an axis collinear with A and B. You can find another halfway point between A and A + (B-A)/2; this is just (B-A)/4. You can in theory continue going on for infinity, creating an infinite set of points. The question is how can you travel an infinite number of points in a finite distance? The notion of travelling through an infinite set is nonsensical, as infinity never ends, so you can't complete the journey of travelling through that many points. This kind of implies the discretization of space, almost as if it were composed of tiny pixels as your computer monitor is. But then, I really get confused. Because lets say there are two pixels, denoted as zeros (0) here. In theory space would look something like this (extended to the edges of the universe): 00000 00000 00000 The space between each pixel is smaller than a pixel; so it seems to be implying a distance that is smaller than the smallest possible distance. But there has to be some demarcation between each pixel, i.e. the edge width would have to be a minimum size, i.e. a pixel's width. But that would be nonsensical because you would have a pixel with edges that are at least a pixel thick; and then the edges of those edge pixels would also have to have a minimum thickness. Of course in QM, they say that there is considerable uncertainty on position for particles. But for spacetime itself I haven't heard of any type of uncertainty. I don't even know what it would mean to say spacetime has uncertainty; its almost as if it doesn't exist until it is "probed" somehow. Maybe this is more a question for a high energy theorist, but anyway. Also I'm not sure any of these questions are really stupid...but whatever | ||
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Cascade
Australia5405 Posts
On July 03 2017 10:48 radscorpion9 wrote: Another weird thing about infinity that I never understood, is that you can in theory apply it to space. Like if you travel between points A and B, you can always find a halfway point by dividing that length in half, something like A + (B - A)/2 on an axis collinear with A and B. You can find another halfway point between A and A + (B-A)/2; this is just (B-A)/4. You can in theory continue going on for infinity, creating an infinite set of points. The question is how can you travel an infinite number of points in a finite distance? The notion of travelling through an infinite set is nonsensical, as infinity never ends, so you can't complete the journey of travelling through that many points. This kind of implies the discretization of space, almost as if it were composed of tiny pixels as your computer monitor is. But then, I really get confused. Because lets say there are two pixels, denoted as zeros (0) here. In theory space would look something like this (extended to the edges of the universe): 00000 00000 00000 The space between each pixel is smaller than a pixel; so it seems to be implying a distance that is smaller than the smallest possible distance. But there has to be some demarcation between each pixel, i.e. the edge width would have to be a minimum size, i.e. a pixel's width. But that would be nonsensical because you would have a pixel with edges that are at least a pixel thick; and then the edges of those edge pixels would also have to have a minimum thickness. Of course in QM, they say that there is considerable uncertainty on position for particles. But for spacetime itself I haven't heard of any type of uncertainty. I don't even know what it would mean to say spacetime has uncertainty; its almost as if it doesn't exist until it is "probed" somehow. Maybe this is more a question for a high energy theorist, but anyway. Also I'm not sure any of these questions are really stupid...but whatever This is Zeno's paradox. The flawed assumption is that you can't traverse infinitely many infinitely short distances in a finite time. Of course you can don't be silly. | ||
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radscorpion9
Canada2252 Posts
On July 03 2017 11:02 Cascade wrote: This is Zeno's paradox. The flawed assumption is that you can't traverse infinitely many infinitely short distances in a finite time. Of course you can don't be silly. Yes, and Zeno's paradox has bothered me for at least a decade now. Infinity by its very definition is a quantity which has no end. We all agree you can not count infinitely high, you can not travel infinitely far. By definition, it is impossible to ever reach the end. If you have an infinite number of points to travel through, it doesn't matter how "short" the distances are. If you imagine assigning a number to each point you travel through, this would be equivalent to saying you can count infinitely high which is nonsense. No one can count to infinity, it never ends. That is what you are effectively saying when you say space is infinitely divisible. Also please don't say calculus does it all the time . Its a bit of a philosophical pet peeve. Calculus takes the limit of the summation of increasingly thin rectangles under a curve; it never actually adds infinitely thin slices infinitely many times. It just says, look what happens as we make the rectangles smaller, they seem to be bounded by this upper or lower limit. And those upper and lower limits seem to converge to the same number. Aha, this is the area under the curve. Finding a limit is not the same as actually going through an infinite number of steps. | ||
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Cascade
Australia5405 Posts
On July 03 2017 11:48 radscorpion9 wrote: Yes, and Zeno's paradox has bothered me for at least a decade now. Infinity by its very definition is a quantity which has no end. We all agree you can not count infinitely high, you can not travel infinitely far. By definition, it is impossible to ever reach the end. If you have an infinite number of points to travel through, it doesn't matter how "short" the distances are. If you imagine assigning a number to each point you travel through, this would be equivalent to saying you can count infinitely high which is nonsense. No one can count to infinity, it never ends. That is what you are effectively saying when you say space is infinitely divisible. Also please don't say calculus does it all the time . Its a bit of a philosophical pet peeve. Calculus takes the limit of the summation of increasingly thin rectangles under a curve; it never actually adds infinitely thin slices infinitely many times. It just says, look what happens as we make the rectangles smaller, they seem to be bounded by this upper or lower limit. And those upper and lower limits seem to converge to the same number. Aha, this is the area under the curve. Finding a limit is not the same as actually going through an infinite number of steps.Yes it matters how short the distance are. And not sure why you quoted "short" as if it's not a well defined concept. You can't count to infinity because each count takes at least a certain time t. These distances are infinitely small so you can pass through infinitely many of them. There is no time t that is smaller than all the travel time of your distances. The problem is that you accept the concept of infinitely small distances, but don't accept the concept that you can pass through infinitely many of them in a finite time. And it's silly to first use a limit formulation to set up the problem and then not allow limit formulations in the answer... "Prove that 2+2 is 4, but don't give me that natural number integer bullshit." | ||
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Buckyman
1364 Posts
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Cascade
Australia5405 Posts
On July 03 2017 13:35 Buckyman wrote: Distances smaller than a Planck length might not be well defined. We have multiple, mutually inconsistent theories of what happens at that scale and some of them can't distinguish pairs of points that are less than a Planck length apart. Sure. Not trying to argue that the universe is certainly continuous down to all scales. We'll most likely not find out in our lifetime. I'm arguing that Zeno's paradox doesn't conflict with it. | ||
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Uldridge
Belgium5186 Posts
Let's say you move from place A to place B. You need to traverse an n amount of smallest spaces in t time. How are you allowed to move into space from place A to place B? How is time (change from absolute positions) allowing you to do this? There must be a smallest space and a smallest time to traverse every smallest space. If there is something as a smallest time and smallest space, wouldn't nature be inherently discrete? You'd have these infinitesimal small "jumps" in space for every timeframe starting from A until you finally reach B. I think a severe lack of knowledge of what space actually entails is a big issue here when talking about thinks like this. Space is just thought of the thing where mass is in and moves through. It has no apparent properties, but allows everything in it have its properties. I think it might have properties we just don't know/understand/have studied yet. It might not be possible to even study it, ever, because it's such an esoteric natural phenomenon. What if space is just a bunch of planes spaced from each other in Planck's length giving rise to things like the uncertainty principle and collapse of wave function and all of the stochastic issues we have in QM? Edit: I mean, my text probably doesn't make a lot of sense (because I'm not a physicist) but it's more of philosophical pondering of how lacking our understanding of the most fundamental properties of nature actually are. | ||
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Simberto
Germany11922 Posts
On July 03 2017 18:57 Uldridge wrote: See, that's what I'm not entirely convinced with. Let's say you move from place A to place B. You need to traverse an n amount of smallest spaces in t time. How are you allowed to move into space from place A to place B? How is time (change from absolute positions) allowing you to do this? There must be a smallest space and a smallest time to traverse every smallest space. If there is something as a smallest time and smallest space, wouldn't nature be inherently discrete? You'd have these infinitesimal small "jumps" in space for every timeframe starting from A until you finally reach B. I think a severe lack of knowledge of what space actually entails is a big issue here when talking about thinks like this. Space is just thought of the thing where mass is in and moves through. It has no apparent properties, but allows everything in it have its properties. I think it might have properties we just don't know/understand/have studied yet. It might not be possible to even study it, ever, because it's such an esoteric natural phenomenon. What if space is just a bunch of planes spaced from each other in Planck's length giving rise to things like the uncertainty principle and collapse of wave function and all of the stochastic issues we have in QM? Edit: I mean, my text probably doesn't make a lot of sense (because I'm not a physicist) but it's more of philosophical pondering of how lacking our understanding of the most fundamental properties of nature actually are. Afaik, we haven't really figured out if space is discrete or continuous. But on any scale we can observe, space is continuous. It might be discrete at a smaller scale, but we don't have any instruments to investigate that. The same is true for time. However, this is not fundamentally a problem. If both are continuous, everything works fine, as you can just describe your position in space as a real (Or R³) function of time. That means that for any point in continuous time, you have a position, and you visit any position on the way between A and B. No problem. If time is discrete, you jump between spots each fundamental time unit. If space is discrete, you jump between the discrete space positions (think chessboard or something.) Once again, we haven't observed any of that, so we can't really say anything about the mechanisms thereof. Your argument that there must be a "smallest" space or time unit is not valid. There is absolutely no problem in moving between two spaces in a continuous spacetime. | ||
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Uldridge
Belgium5186 Posts
On July 03 2017 11:48 radscorpion9 wrote: Also please don't say calculus does it all the time . Its a bit of a philosophical pet peeve. Calculus takes the limit of the summation of increasingly thin rectangles under a curve; it never actually adds infinitely thin slices infinitely many times. It just says, look what happens as we make the rectangles smaller, they seem to be bounded by this upper or lower limit. And those upper and lower limits seem to converge to the same number. Aha, this is the area under the curve. Finding a limit is not the same as actually going through an infinite number of steps.It doesn't? So what volume does every rectangle have? How many rectangles are there then? I've always thought about it like that, which is also my argument for a seemingly continuous reality, which could be represented, or actually is discrete, because you use the smallest space between the next point in space to eventually come to area or volume or whatever. This is also @Simberto btw | ||
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Dangermousecatdog
United Kingdom7084 Posts
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Acrofales
Spain18365 Posts
On July 03 2017 11:48 radscorpion9 wrote: Yes, and Zeno's paradox has bothered me for at least a decade now. Infinity by its very definition is a quantity which has no end. We all agree you can not count infinitely high, you can not travel infinitely far. By definition, it is impossible to ever reach the end. If you have an infinite number of points to travel through, it doesn't matter how "short" the distances are. If you imagine assigning a number to each point you travel through, this would be equivalent to saying you can count infinitely high which is nonsense. No one can count to infinity, it never ends. That is what you are effectively saying when you say space is infinitely divisible. Also please don't say calculus does it all the time . Its a bit of a philosophical pet peeve. Calculus takes the limit of the summation of increasingly thin rectangles under a curve; it never actually adds infinitely thin slices infinitely many times. It just says, look what happens as we make the rectangles smaller, they seem to be bounded by this upper or lower limit. And those upper and lower limits seem to converge to the same number. Aha, this is the area under the curve. Finding a limit is not the same as actually going through an infinite number of steps.This. Because unlike some people here, mathematicians know you cannot ever do anything infinitely many times. You can only show that as you do it more and more times, the value gets nearer and nearer to whatever you were trying to prove (if you want to know more, look at epsilon-delta definition of a limit)... and THAT you can prove. And that is, incidentally how calculus showed Zeno's paradox to be nonsense. The point of the paradox is that you're assuming the distance covered in an infinitesimal time to be non-infinitesimal, and there is absolutely no reason why that should be true. | ||
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DarkPlasmaBall
United States46209 Posts
On July 03 2017 20:29 Uldridge wrote: It doesn't? So what volume does every rectangle have? How many rectangles are there then? I've always thought about it like that, which is also my argument for a seemingly continuous reality, which could be represented, or actually is discrete, because you use the smallest space between the next point in space to eventually come to area or volume or whatever. This is also @Simberto btw Doing things like extrapolating/ using induction/ finding limits/ integrating an area allows for conclusions to be drawn based on a set of mathematical knowledge that may have an infinite number of steps (which makes it impossible to actually proceed through from a step-by-step procedural perspective). It's the virtue of being able to conceptualize what you're doing in math, rather than just trying to grind out computations. You recognize patterns that are justified mathematically, and use them to circumvent the task of needing to mechanically do something infinite times. When radscorpion9 said that we don't actually add infinite things, I think he meant that it's literally impossible to perform the calculations infinitely many times (as it would never end) so we do things like putting in ellipses (e.g., the series "1 + 1/4 + 1/9 + 1/16 + 1/25 + ..." converges, and we can find that sum, and it's not by actually doing infinitely many additional problems). No one could possibly say, "Hey everyone, I actually took the time to add up all the numbers in that series and here's my answer!" because there are an infinite number of numbers in that series (each fraction's denominator is generated by the next perfect square, and there are infinitely many perfect squares). | ||
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DarkPlasmaBall
United States46209 Posts
On July 03 2017 01:34 Simberto wrote: Infinity is really weird. I would suggest going to an introductory analysis class to get a better understanding about how weird infinity is. A fun example is the "infinite hotel". A hotel has infinite amounts of rooms, all of which are full. Another guest arrives. What does the guy at the counter do? + Show Spoiler + He has everyone move to the room which has the next number. So the guy in room one goes to room two, the guy in room two goes to room three, etc... The new guy then moves into room number one, which is empty. Ok, ok, but what if an infinite amount of people appear on the doorstep? + Show Spoiler + Still no problem. Just have everyone move to the room with double their number. One goes to two, two goes to four, etc... everyone still has a room, and all the rooms with uneven numbers are free, so you can fit infinite people in there easily. But wait, there is more. Because infinity isn't equal to infinity. Sometimes it is, but there are infinities that are larger than others. Namely, there are infinities where you can count all of the thing in them, and there are those that you can't count. If you are interested in this, take a look at cantors diagonal arguments, they are really fun, and not that hard. This is the difference between the amount of rational numbers and the amount of reals. There are countably infinite amounts of rational numbers, but there are uncountably infinite reals. So, one could say that there are infinitely more reals than there are rationals. This reminds me of set theory, bijections, and Day9's video on it  | ||
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Uldridge
Belgium5186 Posts
On July 03 2017 21:56 DarkPlasmaBall wrote: Doing things like extrapolating/ using induction/ finding limits/ integrating an area allows for conclusions to be drawn based ...on a set of mathematical knowledge that may have an infinite number of steps (which makes it impossible to actually proceed through from a step-by-step procedural perspective). It's the virtue of being able to conceptualize what you're doing in math, rather than just trying to grind out computations.+ Show Spoiler + You recognize patterns that are justified mathematically, and use them to circumvent the task of needing to mechanically do something infinite times. When radscorpion9 said that we don't actually add infinite things, I think he meant that it's literally impossible to perform the calculations infinitely many times (as it would never end) so we do things like putting in ellipses (e.g., the series "1 + 1/4 + 1/9 + 1/16 + 1/25 + ..." converges, and we can find that sum, and it's not by actually doing infinitely many additional problems). No one could possibly say, "Hey everyone, I actually took the time to add up all the numbers in that series and here's my answer!" because there are an infinite number of numbers in that series (each fraction's denominator is generated by the next perfect square, and there are infinitely many perfect squares). No, I get that, and I understand that maths just uses these methods as shortcuts to get to useful results, but that still doesn't change the fact that it's conceptually the case for integration. And so it can be the case for reality as well. But in reality it wouldn't be an infinite number of infinitesimal spaces or planes, it'd be just a very large amount of very small spaces or planes. | ||
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Thieving Magpie
United States6752 Posts
Great job with this discussion guys--I'm learning a lot about how you guys think about/ignore aspects of this problem, it's great really. | ||
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Cascade
Australia5405 Posts
philosopher: First, divide up one meter first in half, then that half in half again, then in half again, and so on for infinity. mathematician: ok, sure. philosopher: then, to traverse this meter, you need to traverse infinitely many distances. mathematician: yes. philosopher: but you cant do infinitely many things in a finite time! mathematician: You can. Traveling at 1m/s, I will travel the first piece in half second, the second in a quarter second, third in eights of a second, and so on for infinity. philosopher: HANG ON DONT GIVE ME THAT RECURSIVE CRAP!!! I mean... If you can't accept that the infinite number pieces can be traveled in a finite time, then how can you split up the finite length into infinitely many pieces to start with? The solution is exactly the same thing as you do when you formulate the problem... It's just... Philosophers I guess. | ||
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