Those two statements are diametrically opposed, if it bounces without end (infinite number of bounces) it never stops. If it stopped, it could not have bounced without end.
An infinite number of events does not necessarily mean an infinite amount of time. Figure the 1st bounce takes 1s, then the second 1/2s, then 1/4th, and so on... You get an infinite number of bounces in a finite amount of time.
Of course a ball bouncing infinitely is still impossible in real life, so let's look at something imminently possible: Your hand, waved through the air, passes through an infinite number of points, and yet arrives at the destination in a finite amount of time. How is it possible? The number of points your hand moves through is without end, so how can it ever finish? Well the answer is that there are an infinite amount of points, but only an infinitesimal amount of time is spent at each one.
This is, of course, ignoring the open question of whether the physical universe is continuous or discreet. I'm just saying, there's no mathematical issue with it being continuous, and the universe dealing with this infinity issue every time you move.
The primary reason being that back then, C++ compilers were not good enough to produce sufficiently fast code when using any of the things that make C++ worth using over C (heck and a lot of the things that really make it useful like templates weren't even present). Not with the kind of constraints Doom was operating under (getting those graphics on a 386 was something of a miracle, even with all the clever tricks used).
Except what? It means g++ is essentially doing the same thing as Visual C++ -- fixing problems with the standard in logical ways. The subset of C++ where you can't have a non-void function not explicitly return anything is a good subset of C++.
Obviously I'm taking it as given that the C++ standard has flaws.:)
Infinity of time, because in the abstract universe the ball is bouncing in, distance is meaningless, and you could say that each subsequent bounce takes exactly the same amount of time as before, and to the limits of the problem, redefine each bounce as same height as before (this part may be tricky to you, but dealing with infinity can not be done in your standard your euclidean space, you need some trivial modifications).
Meh. Yes it takes infinite time, in this coordinate space where you've defined the time and distance to be the same for each successively smaller bounce. You're basically just saying that it takes an infinite number of seconds to come to a stop if the length of a second is also asymptotically approaching zero.
In normal space-time (which works just fine, thanks), what happens is that each successive bounce is shorter in both distance and duration. The series consisting of the time length of each bounce converges, i.e. its sum is not infinite. It does not take infinite time.
Also, it's really not true that "the sum of an infinite series" equals anything. It's a loose way of describing something in English that oversimplifies to the point of being wrong. It's a fine shorthand between two people who really know what's meant, but if you don't have that frame of reference the normal English meaning isn't right.
That's actually kinda backwards. The normal English meaning doesn't seem right if you don't have the right mathematical frame of reference, and it seems as if we're talking loosely and informally about a different kind of equals. But if you have the correct mathematical background, then you realize we are using the term "equal" precisely, logically, and completely correctly, as is required for mathematical proofs.
"Converges on" doesn't mean the same as "equals".
But it does in cases where the series is absolutely convergent. That the sum of such an infinite series is equal to the number the sum converges on in the limit is a mathematical truth. That's the basis for the Fundamental Theorem of Calculus. It's the most important step in the proof of Euler's Formula that e^(i*x) = cos(x) + i sin(x). That the e, sin and cos can each be replaced with their equivalent Taylor Series and maintain the equivalence of the Formula is precisely what mathematicians mean by "equal".
The sum of the Taylor Series for cos(x) equals cos(x). 0.999... equals 1. These are both formally, precisely, and absolutely true statements.
The skeptic says "I agree that it converges on 1, but that's not the same as equals 1", so to reply with a proof that it converges on 1 is a bit silly.
A skeptic could incorrectly take issue with any step of any proof. I fully agree(d) that there are better proofs for explaining the concept to said skeptic, but it still remains true that the proof given is perfectly correct.
The right argument is: in the system of numbers we usually work with, 0.999... is just another way of writing 1 by definition.
No, not by definition. Our number system is not so sloppy that we have to rely on definition for such things.
You must be using some other form of logic that I am not aware of. You are talking about a bouncing ball, that is a physical object. If it is going to bounce an infinite number of times, it will take an infinite amount of time because it will never stop, ever. Hence, infinite amount of bounces.
Yeah, correct logic.;) But don't feel bad, it is confusing, especially when there are multiple infinities at work.
The important thing to note in this case is that yes the number of bounces is infinite, but the time each bounce takes becomes infinitely small. At the limit, the ball will be bouncing infinitely small bounces infinitely fast. You can accomplish an infinite number of things that take an infinitely small amount of time in no time at all.:)
Basically, your statement is equivalent to saying that the sum of any infinite series (in this case, the series is of the time it takes for each bounce, and you sum them up to get the total amount of time it takes) must be infinite. But this is not the case; there are many infinite series which sum to finite numbers. 1 + 1/2 + 1/4 + 1/8 + 1/16 +... is such an example. It sums to exactly 2, because yes you're adding infinite things, but at each step they get closer and closer (infinitely so) to 0.
Another fun example of infinities working oddly together is Gabriel's Horn. Take the curve 1/x for x > 0, and rotate it around the x-axis to create a 3D "horn" shape. The mouth of the horn is infinitely wide, and the tail of the horn is infinitely long. The surface area of this horn is infinite. However, because the mouth becomes infinitely flat, and the tail approaches infinitely narrow, it turns out that the Horn actually has finite volume. Thus the tongue-in-cheek observation that the only way to paint Gabriel's Horn is to fill it with paint.:)
Obviously in reality -- as if you could even have a Gabriel's Horn in reality -- it would take an infinite amount of time for the paint you pour into the horn to reach the bottom. By the same token, in reality a ball would not bounce infinitely because it would not be a perfectly inelastic collision and energy would be lost
No, because in both cases they are discreet balls, and both have the same ordinality. You can create a 1:1 mapping from the unordered set to the ordered set, so they are the same degree of infinity. So, doesn't make any sense to me. If it's right, I don't know why.
10^(-infinity) is 0. It may seem like it could be 0.0...1, but what you really get is 0.0... and you never reach the 1 because there are infinite zeroes. Or think of it this way: 10^(-infinity) is 1/(10^infinity). 10^infinity is infinity. 1/infinity = 0.
Look, call me prejudiced if you want, but to me Supermassive Black Hole just sounds more threatening than White Dwarf. Or any kind of dwarf for that matter.
There most certainly are things "after infinity", the infinity you know about is actually the smallest infinity.
Yes, yes, but you can't get from one to the other additively. "Infinity plus one" is not any bigger than infinity regardless of what kind of infinity you're talking about. The set of Positive Integers is the same size of infinity as the Non-Negative Integers. The first is infinite, you add the element 0, the result is the same kind of infinite.
He means your syntax is meaningless. "..." means infinitely repeating. You can't say 0.0...1 because you've already specified infinitely repeating 0s. You could use some alternative syntax to specify some finite number of 0s followed by a 1, or a finite number of 0s followed by an infinite number of 1s, but you can't say "infinity... plus 1!" The concept is meaningless.
Yes, but doing arithmetic with numbers that contain infinite number of decimal places is not the same as doing arithmetic on infinity. 9.99... - 0.99... = 9, that's basic arithmetic, and not on infinity.
How can you multiply.999... by anything at all? If the sequence is infinity, then any application of task or step can never be completed as it would take infinite time to perform the calculation.
Well you don't do it by long multiplication, because yeah you'd never get done. Instead you have to use other known and proven properties of multiplication to get the right answer. In this case the answer is especially easy to arrive at because multiplying by 10 in base 10 simply means you move the decimal place over one, and since there were infinite digits after the decimal, that doesn't change.
So 10 * 0.999... = 9.999... and you can do it in one step.:)
Well, that proof abuses the loosly defined meaning of "equals". You cannot "sum an infinite series", though you can use that expression as shorthand for what's really going on. The sum converges on 1 as the number of terms approaches infinity, but that's not really the same kind of equality as 1 + 1 = 2. Other proofs are better.
They're better in that they don't resort to limits, which some people haven't learned or have conceptual problems with.
But it's a perfectly fine proof. It uses the extremely well defined meaning of equals and the mathematically proven formula for calculating the sum of an infinite series, which it is just as possible to do as to say 9.99... which is infinite, or for that matter to say that the area under the curve x^2 from 0 to a is equal to (1/3)a^3. It's a very precise form of equals, not loose in the slightest.
I get that, however, once you multiply it by 10, the resulting number has (infinity-1) decimal places, not infinity.
No, it doesn't. There's an infinite number of 9s, and thus moving any finite number in front of the decimal place still leaves an infinite number after the decimal place. You never run out of 9s after the decimal place in either case.
I know the theories of math say that infinity - 1 = infinity but I don't buy it as infinity will always be greater than infinity - 1.
It may seems intuitive that "infinity - 1 < infinity", but that's based on the understanding that infinity has some "value" and that you can subtract one from it. But infinity is not a number, and "infinity - 1" is not meaningful in the theory of math. Think about it: What number can you add 1 to and get infinity? There is no such number. So you have to think of infinity in a little different way, because it is not a value, but rather the concept of "without end". And if something is endless, taking some finite amount out of it still leaves it endless.
Try this: If you have an infinite conveyor belt that provides a never-ending sequence of beer bottles, does plucking one beer off the belt cause the sequence to end? No, it's still never-ending, which is what infinity means. After any finite amount of time, it's true that the number of beers that have gone past you on the belt is one less than it would have been otherwise, but after an infinite amount of time, the number of beers that have passed you is still infinite.
But you can never reach that result by just counting the number of beers at any given moment, and waiting until the numbers are equal. Because that would take infinite amount of time, and then you're no longer dealing with a number of beers, but rather infinite beers. That's the difficulty of thinking about infinity -- you can't think about it in terms of doing a finite amount of steps and waiting for it to tick over and become "infinity".
By the way, there are in fact different "sizes" of infinity, countable and uncountable but I don't want to go into that.:)
But it does reach 1, that's the whole point of the proof that 0.99... with infinite 9s is exactly equal to 1, and 1 - 1/infinity can also be expressed as 1 - 0.:)
But you use terms made for finite concepts : "one thing minus the same thing is zero". For example, if you subtract an infinite number of elements to set with infinite elements , how much elements are there ? Zero ? No; there are an infinite number of elements
Not true, the concept is not limited to the finite at all. Example: The set of integers is infinite. The set of integers minus the set of integers is the empty set.
If a = a, then a - a = 0, and the value of a is irrelevant. This is true regardless of whether a is a number with a repeating decimal. It doesn't matter if it's irrational and has an infinite number of seemingly random digits. Pi - Pi = 0. 3 + Pi - Pi = 3. 9 + 0.99... = 9.99... and therefore 9.99... - 9 = 0.99...
Because you're subtracting everything after the decimal point. 9.32 - 0.32 = 9, similarly 9.9-repeating minus 0.9-repeating is 9.
Limits aren't necessary for this step (or in fact for this proof). You don't need to actually perform each digit of the subtraction to know what the result is. It doesn't matter that there's an infinite number of 9s after the decimal, because what's after the decimal is equal in both cases.
it takes place during Newton's lifetime and Newton himself is one of the more major characters, along with Leibnitz and other less famous "natural philosophers."
Does it feature the infamous Newton vs Leibnitz Calculus Slap Fight?
Infix means you can't do the multiplication because you don't know what to multiply with at that point.
Yep, and as I learned many many years ago when I wrote an algebraic formula parser (cus parsers were an interesting problem I hadn't seen before), you basically have to create a binary tree that represents the dependency chain and evaluate them from the leaf nodes on up.
Which is what you get implicitly with RPN.
I'm not an RPN user, but I think it's advantages are clear. It was just one of those things I never bothered learning, because in school I only had access to TI calculators, and since then I haven't really had much need, and when I do the normal way is "good enough". But I can see that it is cool.
Just never design an ISA that way unless space savings is a major concern.:)
Um, the description of "squarish", much like the description "spiral", is referring to the 2D face-on structure. Most people would be comfortable describing something 50 times larger in two dimensions than in the 3rd as flat, and it doesn't matter which way is "up" (though the galactic axis does give a valid reference for "north" and "south). A flat disk is a flat disk regardless of its orientation. Also if you require everything to line up exactly then essentially nothing is flat -- not Kansas and not your table top. On the scale of the galaxy, and in a context where we're calling the 2D shape "square", "flat" is an apt enough description.
"Cube", however, is just plain fucking wrong. Pointless pedantry is just a way for a weak-minded person to try to sound smart by being literal when they can't sound smart by knowing what they're talking about. And you still failed at that.
Sure but the analogies were deliberately and amusingly bad, which can't be said for most bad analogies or for that matter the just plain bad posts like the OP. I can understand getting tired of doing the shtick, that's fine, I'm just saying the transition to being just yourself hasn't been a positive one from my point of view.
Slashdot Mirror
This new type of software is defined by its novel purposes: the improvement or fabrication of reality based on its users' ideas and imaginations.
I'm pretty sure Zombo.com has prior art on that.
You can do anything at Zombo.com. Anything at all. The only limit is your imagination.
Those two statements are diametrically opposed, if it bounces without end (infinite number of bounces) it never stops. If it stopped, it could not have bounced without end.
An infinite number of events does not necessarily mean an infinite amount of time. Figure the 1st bounce takes 1s, then the second 1/2s, then 1/4th, and so on... You get an infinite number of bounces in a finite amount of time.
Of course a ball bouncing infinitely is still impossible in real life, so let's look at something imminently possible: Your hand, waved through the air, passes through an infinite number of points, and yet arrives at the destination in a finite amount of time. How is it possible? The number of points your hand moves through is without end, so how can it ever finish? Well the answer is that there are an infinite amount of points, but only an infinitesimal amount of time is spent at each one.
This is, of course, ignoring the open question of whether the physical universe is continuous or discreet. I'm just saying, there's no mathematical issue with it being continuous, and the universe dealing with this infinity issue every time you move.
Doom was written in C, not C++.
The primary reason being that back then, C++ compilers were not good enough to produce sufficiently fast code when using any of the things that make C++ worth using over C (heck and a lot of the things that really make it useful like templates weren't even present). Not with the kind of constraints Doom was operating under (getting those graphics on a 386 was something of a miracle, even with all the clever tricks used).
Except what? It means g++ is essentially doing the same thing as Visual C++ -- fixing problems with the standard in logical ways. The subset of C++ where you can't have a non-void function not explicitly return anything is a good subset of C++.
Obviously I'm taking it as given that the C++ standard has flaws. :)
C++ is as awful as it is useful: Extremely.
Ha! That's a pretty great quote there yourself Mr. AC.
Uh g++ catches that error for me. Though on the other hand, I consider -Wall -Werror to be basically non-optional arguments.
How long until it comes to absolute STOP ?
Infinity of time, because in the abstract universe the ball is bouncing in, distance is meaningless, and you could say that each subsequent bounce takes exactly the same amount of time as before, and to the limits of the problem, redefine each bounce as same height as before (this part may be tricky to you, but dealing with infinity can not be done in your standard your euclidean space, you need some trivial modifications).
Meh. Yes it takes infinite time, in this coordinate space where you've defined the time and distance to be the same for each successively smaller bounce. You're basically just saying that it takes an infinite number of seconds to come to a stop if the length of a second is also asymptotically approaching zero.
In normal space-time (which works just fine, thanks), what happens is that each successive bounce is shorter in both distance and duration. The series consisting of the time length of each bounce converges, i.e. its sum is not infinite. It does not take infinite time.
Also, it's really not true that "the sum of an infinite series" equals anything. It's a loose way of describing something in English that oversimplifies to the point of being wrong. It's a fine shorthand between two people who really know what's meant, but if you don't have that frame of reference the normal English meaning isn't right.
That's actually kinda backwards. The normal English meaning doesn't seem right if you don't have the right mathematical frame of reference, and it seems as if we're talking loosely and informally about a different kind of equals. But if you have the correct mathematical background, then you realize we are using the term "equal" precisely, logically, and completely correctly, as is required for mathematical proofs.
"Converges on" doesn't mean the same as "equals".
But it does in cases where the series is absolutely convergent. That the sum of such an infinite series is equal to the number the sum converges on in the limit is a mathematical truth. That's the basis for the Fundamental Theorem of Calculus. It's the most important step in the proof of Euler's Formula that e^(i*x) = cos(x) + i sin(x). That the e, sin and cos can each be replaced with their equivalent Taylor Series and maintain the equivalence of the Formula is precisely what mathematicians mean by "equal".
The sum of the Taylor Series for cos(x) equals cos(x). 0.999... equals 1. These are both formally, precisely, and absolutely true statements.
The skeptic says "I agree that it converges on 1, but that's not the same as equals 1", so to reply with a proof that it converges on 1 is a bit silly.
A skeptic could incorrectly take issue with any step of any proof. I fully agree(d) that there are better proofs for explaining the concept to said skeptic, but it still remains true that the proof given is perfectly correct.
The right argument is: in the system of numbers we usually work with, 0.999... is just another way of writing 1 by definition.
No, not by definition. Our number system is not so sloppy that we have to rely on definition for such things.
You must be using some other form of logic that I am not aware of. You are talking about a bouncing ball, that is a physical object. If it is going to bounce an infinite number of times, it will take an infinite amount of time because it will never stop, ever. Hence, infinite amount of bounces.
Yeah, correct logic. ;) But don't feel bad, it is confusing, especially when there are multiple infinities at work.
The important thing to note in this case is that yes the number of bounces is infinite, but the time each bounce takes becomes infinitely small. At the limit, the ball will be bouncing infinitely small bounces infinitely fast. You can accomplish an infinite number of things that take an infinitely small amount of time in no time at all. :)
Basically, your statement is equivalent to saying that the sum of any infinite series (in this case, the series is of the time it takes for each bounce, and you sum them up to get the total amount of time it takes) must be infinite. But this is not the case; there are many infinite series which sum to finite numbers. 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... is such an example. It sums to exactly 2, because yes you're adding infinite things, but at each step they get closer and closer (infinitely so) to 0.
Another fun example of infinities working oddly together is Gabriel's Horn. Take the curve 1/x for x > 0, and rotate it around the x-axis to create a 3D "horn" shape. The mouth of the horn is infinitely wide, and the tail of the horn is infinitely long. The surface area of this horn is infinite. However, because the mouth becomes infinitely flat, and the tail approaches infinitely narrow, it turns out that the Horn actually has finite volume. Thus the tongue-in-cheek observation that the only way to paint Gabriel's Horn is to fill it with paint. :)
Obviously in reality -- as if you could even have a Gabriel's Horn in reality -- it would take an infinite amount of time for the paint you pour into the horn to reach the bottom. By the same token, in reality a ball would not bounce infinitely because it would not be a perfectly inelastic collision and energy would be lost
No, because in both cases they are discreet balls, and both have the same ordinality. You can create a 1:1 mapping from the unordered set to the ordered set, so they are the same degree of infinity. So, doesn't make any sense to me. If it's right, I don't know why.
10^(-infinity) is 0. It may seem like it could be 0.0...1, but what you really get is 0.0... and you never reach the 1 because there are infinite zeroes. Or think of it this way: 10^(-infinity) is 1/(10^infinity). 10^infinity is infinity. 1/infinity = 0.
Look, call me prejudiced if you want, but to me Supermassive Black Hole just sounds more threatening than White Dwarf. Or any kind of dwarf for that matter.
There most certainly are things "after infinity", the infinity you know about is actually the smallest infinity.
Yes, yes, but you can't get from one to the other additively. "Infinity plus one" is not any bigger than infinity regardless of what kind of infinity you're talking about. The set of Positive Integers is the same size of infinity as the Non-Negative Integers. The first is infinite, you add the element 0, the result is the same kind of infinite.
What do you mean it's not a "real" number.
He means your syntax is meaningless. "..." means infinitely repeating. You can't say 0.0...1 because you've already specified infinitely repeating 0s. You could use some alternative syntax to specify some finite number of 0s followed by a 1, or a finite number of 0s followed by an infinite number of 1s, but you can't say "infinity... plus 1!" The concept is meaningless.
Yes, but doing arithmetic with numbers that contain infinite number of decimal places is not the same as doing arithmetic on infinity. 9.99... - 0.99... = 9, that's basic arithmetic, and not on infinity.
How can you multiply .999... by anything at all? If the sequence is infinity, then any application of task or step can never be completed as it would take infinite time to perform the calculation.
Well you don't do it by long multiplication, because yeah you'd never get done. Instead you have to use other known and proven properties of multiplication to get the right answer. In this case the answer is especially easy to arrive at because multiplying by 10 in base 10 simply means you move the decimal place over one, and since there were infinite digits after the decimal, that doesn't change.
So 10 * 0.999... = 9.999... and you can do it in one step. :)
Well, that proof abuses the loosly defined meaning of "equals". You cannot "sum an infinite series", though you can use that expression as shorthand for what's really going on. The sum converges on 1 as the number of terms approaches infinity, but that's not really the same kind of equality as 1 + 1 = 2. Other proofs are better.
They're better in that they don't resort to limits, which some people haven't learned or have conceptual problems with.
But it's a perfectly fine proof. It uses the extremely well defined meaning of equals and the mathematically proven formula for calculating the sum of an infinite series, which it is just as possible to do as to say 9.99... which is infinite, or for that matter to say that the area under the curve x^2 from 0 to a is equal to (1/3)a^3. It's a very precise form of equals, not loose in the slightest.
I get that, however, once you multiply it by 10, the resulting number has (infinity-1) decimal places, not infinity.
No, it doesn't. There's an infinite number of 9s, and thus moving any finite number in front of the decimal place still leaves an infinite number after the decimal place. You never run out of 9s after the decimal place in either case.
I know the theories of math say that infinity - 1 = infinity but I don't buy it as infinity will always be greater than infinity - 1.
It may seems intuitive that "infinity - 1 < infinity", but that's based on the understanding that infinity has some "value" and that you can subtract one from it. But infinity is not a number, and "infinity - 1" is not meaningful in the theory of math. Think about it: What number can you add 1 to and get infinity? There is no such number. So you have to think of infinity in a little different way, because it is not a value, but rather the concept of "without end". And if something is endless, taking some finite amount out of it still leaves it endless.
Try this: If you have an infinite conveyor belt that provides a never-ending sequence of beer bottles, does plucking one beer off the belt cause the sequence to end? No, it's still never-ending, which is what infinity means. After any finite amount of time, it's true that the number of beers that have gone past you on the belt is one less than it would have been otherwise, but after an infinite amount of time, the number of beers that have passed you is still infinite.
But you can never reach that result by just counting the number of beers at any given moment, and waiting until the numbers are equal. Because that would take infinite amount of time, and then you're no longer dealing with a number of beers, but rather infinite beers. That's the difficulty of thinking about infinity -- you can't think about it in terms of doing a finite amount of steps and waiting for it to tick over and become "infinity".
By the way, there are in fact different "sizes" of infinity, countable and uncountable but I don't want to go into that. :)
But it does reach 1, that's the whole point of the proof that 0.99... with infinite 9s is exactly equal to 1, and 1 - 1/infinity can also be expressed as 1 - 0. :)
But you use terms made for finite concepts : "one thing minus the same thing is zero". For example, if you subtract an infinite number of elements to set with infinite elements , how much elements are there ? Zero ? No; there are an infinite number of elements
Not true, the concept is not limited to the finite at all. Example: The set of integers is infinite. The set of integers minus the set of integers is the empty set.
If a = a, then a - a = 0, and the value of a is irrelevant. This is true regardless of whether a is a number with a repeating decimal. It doesn't matter if it's irrational and has an infinite number of seemingly random digits. Pi - Pi = 0. 3 + Pi - Pi = 3. 9 + 0.99... = 9.99... and therefore 9.99... - 9 = 0.99...
9.999... -- 0.999... = 9 ? why ?
Because you're subtracting everything after the decimal point. 9.32 - 0.32 = 9, similarly 9.9-repeating minus 0.9-repeating is 9.
Limits aren't necessary for this step (or in fact for this proof). You don't need to actually perform each digit of the subtraction to know what the result is. It doesn't matter that there's an infinite number of 9s after the decimal, because what's after the decimal is equal in both cases.
it takes place during Newton's lifetime and Newton himself is one of the more major characters, along with Leibnitz and other less famous "natural philosophers."
Does it feature the infamous Newton vs Leibnitz Calculus Slap Fight?
Infix means you can't do the multiplication because you don't know what to multiply with at that point.
Yep, and as I learned many many years ago when I wrote an algebraic formula parser (cus parsers were an interesting problem I hadn't seen before), you basically have to create a binary tree that represents the dependency chain and evaluate them from the leaf nodes on up.
Which is what you get implicitly with RPN.
I'm not an RPN user, but I think it's advantages are clear. It was just one of those things I never bothered learning, because in school I only had access to TI calculators, and since then I haven't really had much need, and when I do the normal way is "good enough". But I can see that it is cool.
Just never design an ISA that way unless space savings is a major concern. :)
Um, the description of "squarish", much like the description "spiral", is referring to the 2D face-on structure. Most people would be comfortable describing something 50 times larger in two dimensions than in the 3rd as flat, and it doesn't matter which way is "up" (though the galactic axis does give a valid reference for "north" and "south). A flat disk is a flat disk regardless of its orientation. Also if you require everything to line up exactly then essentially nothing is flat -- not Kansas and not your table top. On the scale of the galaxy, and in a context where we're calling the 2D shape "square", "flat" is an apt enough description.
"Cube", however, is just plain fucking wrong. Pointless pedantry is just a way for a weak-minded person to try to sound smart by being literal when they can't sound smart by knowing what they're talking about. And you still failed at that.
Sure but the analogies were deliberately and amusingly bad, which can't be said for most bad analogies or for that matter the just plain bad posts like the OP. I can understand getting tired of doing the shtick, that's fine, I'm just saying the transition to being just yourself hasn't been a positive one from my point of view.