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# story Story, Wednesday, Oct 23, 2019

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21 minutes ago, The Old Hack said:
3 hours ago, hkmaly said:

The number is actually rather small - astronomers think it's about 250 billion ± 150 billion. There are more of them in Andromeda Galaxy.

I still think that from one to four hundred billion may nonetheless be stretched far enough to include 'a lot.' All is relative, of course. When compared to the number of atoms in the galaxy, that number becomes vanishingly small.

Well, yes. Everything is relative, which means using "rather small" and "a lot" for same thing is not as contraindicating as it seems.

It's just that after talking about infinity, the "rather small" comes faster to me. Of course, ANY finite number is small compared to infinite, but the number of atoms in galaxy would be more logical example to say ... but maybe it's just me.

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2 minutes ago, hkmaly said:

Well, yes. Everything is relative, which means using "rather small" and "a lot" for same thing is not as contraindicating as it seems.

It's just that after talking about infinity, the "rather small" comes faster to me. Of course, ANY finite number is small compared to infinite, but the number of atoms in galaxy would be more logical example to say ... but maybe it's just me.

It's not just you, I don't think. The human brain kinda balks at dealing with certain kinds of numbers and sometimes individual brains adapt their own coping strategies. And may even employ different ones for the same number in different situations. I really respect good mathematicians because my own reaction is typically to shy off in terror.

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8 hours ago, The Old Hack said:

All is relative, of course. When compared to the number of atoms in the galaxy, that number becomes vanishingly small.

And if all else fails, try comparing the amount of nothing that exists against everything that does exist

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42 minutes ago, Pharaoh RutinTutin said:

And if all else fails, try comparing the amount of nothing that exists against everything that does exist

The tough part is expressing the amount of something and the amount of nothing in the same units so you can compare them.

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Okay, so I did some searching, and couldn't find a statement by Dan that the EGS multiverse was finite; in fact I found a couple of posts where he says the opposite. Either Dan changed his mind at some point and I didn't search hard enough, or I was remembering wrong.

That said, he did say that not all possible universes actually exist. (If I was remembering wrong, this is probably the post I was mis-remembering.)

Quote

I will say that I don't buy into a unique dimension for every single possibility, and I don't for several reasons. One, there would be so many dimensions that it would be beyond human comprehension and would be unwieldy for interaction. There may be infinite universes for all intents and purposes in EGS, but a separate universe for EVERY possibility or choice opens up the possibility of infinite universes where the only difference is how much Tedd tilted the cereal box one morning (thus impacting which flakes wound up in the bowl and in what distribution). That's just getting ridiculously complicated, moreso than even I want to delve into, and that's not even taking alternate dimensions interacting into account.

Another reason is that every single choice and possibility opens up way too many depressing dimensions. Every worst case scenario imaginable would exist in some form or another, and there would be some absolutely horrific universes out there. That's way too depressing for EGS.

ANOTHER factor is that people make choices for reasons and aren't just random. For example, let's say there's a scenario where a man has acquired a gun and shoots someone with it, and that someone is the reason he bought the gun in the first place. Allowing for every possible choice, there would be universes where he shoots the same person (though possibly in different places), shoots other people, shoots himself, or shoots nothing. All those are possible choices, but are they all choices that same man who bought the gun would make? If he was a different person who would make the choice not to shoot, it's also more likely that he never would have bought the gun in the first place. It's also likely that with such a different outlook, he would've wound up with a life so different that the motive for shooting the other person in question would no longer apply to him.

Lots of arguments can be made against the exact scenario I tried to give in the last paragraph, but the point is simple. There may be infinite possible actions, but there are finite probable actions to the point where the probability will be zero in the majority of the cases, leaving significantly fewer true choices. Deviations that would bring the probability above zero would likely require such a fundamental shift in the person that the scenario in question no longer even applies, thus bringing the probability back down to zero. This would still result in infinite universes, but the differences would be much more fundamental between every universe.

So I guess the question regarding the Lord Tedd issue is: in an infinite multiverse that does not include extremely-low-probability universes or essentially identical universes, would there still be an infinite number of Tedds?

15 hours ago, hkmaly said:
23 hours ago, Don Edwards said:

Of course, a tiny fraction of infinity...

... is usually more or less just as big. In fact, you would need a VERY exotic definition of "fraction" to make it smaller. Normal "fraction" will end up just a variation of Hilbert's paradox of the Grand Hotel.

Nonsense! It's just a smaller infinity! ...Which would still be infinitely large, so I suppose you have a point...

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According to some versions of the infinite-worlds hypothesis, every time anything could go either of two ways the universe splits and it goes both ways... but there is also a continuous process of merging universes that are insufficiently different.

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That raises the question of what constitutes “sufficiently different”.

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13 hours ago, Pharaoh RutinTutin said:
21 hours ago, The Old Hack said:

All is relative, of course. When compared to the number of atoms in the galaxy, that number becomes vanishingly small.

And if all else fails, try comparing the amount of nothing that exists against everything that does exist

But just comparing. Do not try to make everything that is not be like some villains.

8 hours ago, ChronosCat said:

Okay, so I did some searching, and couldn't find a statement by Dan that the EGS multiverse was finite; in fact I found a couple of posts where he says the opposite. Either Dan changed his mind at some point and I didn't search hard enough, or I was remembering wrong.

That said, he did say that not all possible universes actually exist. (If I was remembering wrong, this is probably the post I was mis-remembering.)

My answer is that not all universes are "equal". That there is universe for every possibility, but the less likely the possibility is, the harder it is to reach that universe.

8 hours ago, ChronosCat said:

So I guess the question regarding the Lord Tedd issue is: in an infinite multiverse that does not include extremely-low-probability universes or essentially identical universes, would there still be an infinite number of Tedds?

On 4/10/2004 at 2:10 PM, Dan said:

Lord Tedd would have to be truly nuts to try to off all the other Tedds, as regardless of what nonsense "The One" tried to feed you, there are infinite dimensions to deal with (at least for all intents and purposes).

8 hours ago, ChronosCat said:
On 10/28/2019 at 1:29 AM, hkmaly said:

... is usually more or less just as big. In fact, you would need a VERY exotic definition of "fraction" to make it smaller. Normal "fraction" will end up just a variation of Hilbert's paradox of the Grand Hotel.

Nonsense! It's just a smaller infinity! ...Which would still be infinitely large, so I suppose you have a point...

No. Infinity, half of infinity and millionth of infinity have EXACTLY SAME SIZE. Seriously read that Hilbert's paradox article, and maybe something about cardinal numbers. There is even quite popular hypothesis that the next higher cardinal (next bigger size) after |X| is 2|X| .... so far, no success in proving or disproving that.

(Note that yes, there are smaller and bigger infinities. For example, the size of natural numbers is smaller infinity than size of real numbers.)

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1 hour ago, Don Edwards said:

there is also a continuous process of merging universes that are insufficiently different.

1 hour ago, ijuin said:

That raises the question of what constitutes “sufficiently different”.

In one reality you casually dropped your keys on the table and in another you carefully laid them on the dresser
This is annoying when they merge

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11 minutes ago, Pharaoh RutinTutin said:
1 hour ago, Don Edwards said:

there is also a continuous process of merging universes that are insufficiently different.

1 hour ago, ijuin said:

That raises the question of what constitutes “sufficiently different”.

In one reality you casually dropped your keys on the table and in another you carefully laid them on the dresser
This is annoying when they merge

It's more like this: In one reality, you casually dropped your keys on the table, then later found them and picked them. In other reality, you carefully laid them on the dresser, then later found them and picked them. Few days later, you are unlikely to remember what you did ... and unless one of those location made you late somewhere, there is no real differences between those universes and they can merge.

(Technically, picking the keys from different location is likely to take different amount of time, but that can be compensated by something else taking different amount of time, or not really matter because you will just wait little different time at bus station later.)

The idea behind the merge is that noone can observe that any merging took place. Sure, some proponents of merging claim that the merging is CAUSE of us not remembering past clearly, but seriously, you don't need any merging for that, human memory is simply not designed to be so reliable (mostly because it's not designed at all ; evolution is sloppy in lot of things where any committee would insist on proper logging so blame can be assigned).

By making notes of what exactly you did, you prevent lots of universes from merging ... until those notes will end up burned in incineration plant and therefore their contents stops to matter.

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On 10/27/2019 at 8:29 PM, hkmaly said:

If I remember correctly, in that movie the same would be true for EVERYONE, it's just that the mentioned villain actually tried that. Of course the science behind this idea is so bad I would be disappointed if it showed in EGS ... so I hope Dan revisited that or found some interesting way how to make it work for Tedd specifically.

I don't think at that point we would be able to figure how many times it changed, unless there will be some bonus speaking about it like it was after Painted Black, or it would be mentioned in commentary like with the Dewitchery Diamond ...

The problem is that if it's finite number, then WHY exactly that number? Say the number is 1234567. Why not 1234568? Physical laws just don't work that way. Sure, it doesn't need to be just 1 or infinity, but the explanation for specific number tends to get more complicated the higher number it is.

Meanwhile, there is no problem with having just finite number in reach. Especially if it's limit of device, not the theory behind it. In fact, any specific device is likely to only be capable of reaching finite number of universes, because either it can address them somehow (in finite way) or it's completely random but will eventually break.

Note that in last explanation, the number of universes was not specified, but the provided examples of "where lost socks go" and "steven universe" would suggest there is enough of them to cover even very nonsensical things.

... is usually more or less just as big. In fact, you would need a VERY exotic definition of "fraction" to make it smaller. Normal "fraction" will end up just a variation of Hilbert's paradox of the Grand Hotel.

The number is actually rather small - astronomers think it's about 250 billion ± 150 billion. There are more of them in Andromeda Galaxy.

Well if you "notate" in something as obsolete and primitive as arabic numerals ...

For big numbers, you need Knuth's up-arrow notation. And if you somehow happen to need even bigger finite numbers, you can find inspiration about how to write them in Graham's number. Of course, there are also functions you CANT compute growing asymptotically faster than any functions you CAN compute. Which I would say answers the question about how good handle mathematicians have on really big finite numbers.

Those handle much larger numbers than we deal with, or even can imagine, and there are several weaknesses; the first obvious one is no matter how many symbols you throw at it in any scheme you have yet imagined or may in the future possibly conceive of, there are far more integers higher than that expression than below it. Read that again. No matter what you do, this will always be true.

The next is, your expression in blah, blah, blah notation gives you one specific number. If there is any size to it, it is not computable, not in the age of the universe with a universe full of processors. But yet, it represents one specific number. So the notation yields a set of specific numbers from a vast pool that you basically can't express. You get a sampling of very fine points in a vast ocean. Sparse beyond all reason.

It is useful for exactly what Donald Knuth was active in, comparing orders of magnitude of processing required for various algorithms, not for numeric representation. Even if it's an exact answer to a specific problem, you can't grasp what the number means. It's big beyond belief, and way bigger beyond belief feels the same.

I read a similar article recently that pointed out that we can't see the haystack, only the needles. We see a lot of needles, specific numbers and fractions, in a vast haystack of real numbers that we can't really see. We can at best approximate them. A few particularly useful ones, like pi and e have names.

The set of all integers is countably infinite, aleph zero. The set of all fractions is still countably infinite. The set of all real numbers is not, it is a higher order of infinity, aleph one.

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9 hours ago, hkmaly said:

Yes.

From the forum post:

Quote

Nope--several goo cells/demon nuclei were sent out to other dimensions, but none actually succeeded in their supposed mission. In fact, as far as we know (myself included, given that I haven't planned for EVERY dimension affected yet), the "Omega Goo" that Ellen fought was the worst case of the goo.

Soo would that be because Beta Tedd was able to contact all the other Tedd's that the goo cells were sent after and warn them in time, or just that the goo cells were that inept in doing what that were made to do? "Omega Goo" being the worst case scenario is kinda both good and bad, good in that if a goo cell was sent after Terra, it's likely she was able to deal with it despite Magus being out of the picture.  Bad that if Grace hadn't been around, "Omega Goo" might have actually succeeded.

Quote

Tiffany, in my opinion, is a more useful character than I even anticipated, and is bound to show up in the main story somehow eventually (that doesn't necessarily mean she and Susan will meet).

Given that Dan made that post back in 2004, I get the feeling that he's hinting at introducing Diane?

Edit: double checked, yeah the post was made in April 2004, Diane was introduced in December 2004.

Quote

Dark Sarah needs a little more CHARACTER development, but then again, so does normal Sarah. Regular Sarah already has a good personality in my mind, but she doesn't get enough opportunities to show it off, which is one reason NP exists in the first place (even though she won't star in the next one due to my previously neglecting three other characters in NP).

I think by now Sarah's had quite a bit of development character-wise, I wonder if Dan would consider doing more with Dark Sarah now?  I guess there is that patreon image that shows that if both were to meet, makeouts would ensue, but that's probably on the extreme end of things.

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12 hours ago, ijuin said:

That raises the question of what constitutes “sufficiently different”.

A change to the code base that isn't just white space.

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8 hours ago, Darth Fluffy said:

The set of all integers is countably infinite, aleph zero. The set of all fractions is still countably infinite. The set of all real numbers is not, it is a higher order of infinity, aleph one.

And the set of all unreal numbers are in Unreal Tournament?

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13 hours ago, hkmaly said:

I suppose I really should have included a link to that post as well... (I did come across it when I was doing my search, but it wasn't the post I was looking for so I ignored it.) Thanks for correcting my mistake.

At any rate, while apparently at the time of Painted Black Dan felt  there were infinite Tedds, I was also wondering if based on what Dan said in the post I quoted, whether it makes more sense for there to be an infinite or finite number of Tedds. It seems to me with those limitations (and with the limitation that a "Tedd" presumably has to be the child of the alternates of Edward and Noriko Verres and have similar genetics), finite makes more sense... but then, I'm not that good with math or numbers, so I don't entirely trust my own judgement on that.

14 hours ago, hkmaly said:

No. Infinity, half of infinity and millionth of infinity have EXACTLY SAME SIZE. Seriously read that Hilbert's paradox article, and maybe something about cardinal numbers. There is even quite popular hypothesis that the next higher cardinal (next bigger size) after |X| is 2|X| .... so far, no success in proving or disproving that.

(Note that yes, there are smaller and bigger infinities. For example, the size of natural numbers is smaller infinity than size of real numbers.)

*sigh* That's what I get for trying to make a joke about something I don't really understand...

I did read the Hilbert's Paradox article when you linked it, and thought I understood the basic concept, but I apparently was distracted by the narrative elements of the thought experiment and didn't even realize I had failed to grasp the concept it was trying to illustrate. (Most of the article went over my head.) I think I understand the concept now (but then I thought that before, too).

As for those other two articles you linked, I think I picked up a few bits and pieces here and there, but I'm afraid they were mostly unintelligible to me.

14 hours ago, ijuin said:

That raises the question of what constitutes “sufficiently different”.

I would expect that a scientific theory of merging timelines would say that for two timelines to merge they must be identical at all but the quantum level as of the time of the merge.

For a story, it depends on the author. If I was writing such a story, and was just trying to get rid of redundant worlds (not play around with the repercussions of mergings that aren't seamless) I'd go with something like what hkmaly said above; when the two world are so similar that neither any of the characters nor the reader would be able to tell the difference between the worlds, they become one.

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41 minutes ago, ChronosCat said:

I did read the Hilbert's Paradox article when you linked it, and thought I understood the basic concept, but I apparently was distracted by the narrative elements of the thought experiment and didn't even realize I had failed to grasp the concept it was trying to illustrate.

Hilbert's Hotel gets a lousy rating on ALL review sites, because the staff will wake you up an infinite number of times every night and force you to change rooms.

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8 hours ago, The Old Hack said:

And the set of all unreal numbers are in Unreal Tournament?

For the Complex numbers (Real plus Imaginary numbers), the cardinality would be Aleph-One squared, which is of the same order as Aleph-One.

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17 hours ago, Darth Fluffy said:

Those handle much larger numbers than we deal with, or even can imagine, and there are several weaknesses; the first obvious one is no matter how many symbols you throw at it in any scheme you have yet imagined or may in the future possibly conceive of, there are far more integers higher than that expression than below it. Read that again. No matter what you do, this will always be true.

${\displaystyle 2^{\aleph _{0}}}$

You are right if we talk about any expression representing finite number, however.

17 hours ago, Darth Fluffy said:

I read a similar article recently that pointed out that we can't see the haystack, only the needles. We see a lot of needles, specific numbers and fractions, in a vast haystack of real numbers that we can't really see. We can at best approximate them. A few particularly useful ones, like pi and e have names.

The approximation can be useful sometimes. But yes, the set of numbers someone ever specifically cared about has measure zero in real numbers.

17 hours ago, Darth Fluffy said:

The set of all integers is countably infinite, aleph zero. The set of all fractions is still countably infinite. The set of all real numbers is not, it is a higher order of infinity, aleph one.

Actually, it's   is the continuum hypothesis I mentioned, which may or may not be true.

13 hours ago, Scotty said:
Quote

Nope--several goo cells/demon nuclei were sent out to other dimensions, but none actually succeeded in their supposed mission. In fact, as far as we know (myself included, given that I haven't planned for EVERY dimension affected yet), the "Omega Goo" that Ellen fought was the worst case of the goo.

Soo would that be because Beta Tedd was able to contact all the other Tedd's that the goo cells were sent after and warn them in time, or just that the goo cells were that inept in doing what that were made to do? "Omega Goo" being the worst case scenario is kinda both good and bad, good in that if a goo cell was sent after Terra, it's likely she was able to deal with it despite Magus being out of the picture.  Bad that if Grace hadn't been around, "Omega Goo" might have actually succeeded.

"Supposed" mission.

13 hours ago, Scotty said:
Quote

Tiffany, in my opinion, is a more useful character than I even anticipated, and is bound to show up in the main story somehow eventually (that doesn't necessarily mean she and Susan will meet).

Given that Dan made that post back in 2004, I get the feeling that he's hinting at introducing Diane?

Edit: double checked, yeah the post was made in April 2004, Diane was introduced in December 2004.

No, because Diane wasn't supposed to be the Diane we know now in December 2004. But it's possible that those useful elements of Tiffany were merged into Diane later ...

6 hours ago, ChronosCat said:
On 10/29/2019 at 0:43 AM, ijuin said:

That raises the question of what constitutes “sufficiently different”.

I would expect that a scientific theory of merging timelines would say that for two timelines to merge they must be identical at all but the quantum level as of the time of the merge.

For a story, it depends on the author. If I was writing such a story, and was just trying to get rid of redundant worlds (not play around with the repercussions of mergings that aren't seamless) I'd go with something like what hkmaly said above; when the two world are so similar that neither any of the characters nor the reader would be able to tell the difference between the worlds, they become one.

Those two explanations might be closer to each other than it seems. Quantum physics is weird like that. Like, for start, let's say "any observer" instead of "any of the characters nor the reader" ...

"Two worlds will merge if and only if no observer can make a measurement which would give different results in those universes" sounds like something which could be physically valid definition, just like "As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body."

5 hours ago, Don Edwards said:
6 hours ago, ChronosCat said:

I did read the Hilbert's Paradox article when you linked it, and thought I understood the basic concept, but I apparently was distracted by the narrative elements of the thought experiment and didn't even realize I had failed to grasp the concept it was trying to illustrate.

Hilbert's Hotel gets a lousy rating on ALL review sites, because the staff will wake you up an infinite number of times every night and force you to change rooms.

I'm pretty sure it's just finite number of times, BUT the rating will be lousy regardless. I'm not giving good rating to any hotel forcing me to change room even just four times per night.

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32 minutes ago, hkmaly said:

No, because Diane wasn't supposed to be the Diane we know now in December 2004. But it's possible that those useful elements of Tiffany were merged into Diane later ...

Dan still could have taken Tiffany as a template for Diane, remember Susan was originally supposed to be Grace, but when current Grace came to be, the original template morphed into Susan (though one could argue it came full circle when Adrian cast the Illusion spell to make Grace look like his "Niece", though Dan does link the Susan-Grace page in that page's commentary so I guess there wouldn't be much of an argument after all). Tiffany gave us a glimpse into who Susan might have been if certain things didn't happen, a bubbly cheerleader who was nonetheless intelligent and deductive. Diane wasn't all that bubbly but she was still shown as being intelligent and deductive and looked a lot like Susan, sure, Diane as we see her today is probably more close to Tiffany than when she was first introduced, but that doesn't mean Dan didn't use Tiffany as a starting point for Diane.

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2 hours ago, Scotty said:
3 hours ago, hkmaly said:

No, because Diane wasn't supposed to be the Diane we know now in December 2004. But it's possible that those useful elements of Tiffany were merged into Diane later ...

Dan still could have taken Tiffany as a template for Diane, remember Susan was originally supposed to be Grace, but when current Grace came to be, the original template morphed into Susan (though one could argue it came full circle when Adrian cast the Illusion spell to make Grace look like his "Niece", though Dan does link the Susan-Grace page in that page's commentary so I guess there wouldn't be much of an argument after all). Tiffany gave us a glimpse into who Susan might have been if certain things didn't happen, a bubbly cheerleader who was nonetheless intelligent and deductive. Diane wasn't all that bubbly but she was still shown as being intelligent and deductive and looked a lot like Susan, sure, Diane as we see her today is probably more close to Tiffany than when she was first introduced, but that doesn't mean Dan didn't use Tiffany as a starting point for Diane.

I would say that, just as in case of Susan-Grace, he didn't do it deliberately.

In her first appearance, she's neither bubbly nor deductive. And, frankly, doesn't look SO much like Susan. Now, her more-or-less second appearance in 2007? There she might already started to merge with Tiffany ...

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3 hours ago, hkmaly said:

Actually, it's   is the continuum hypothesis I mentioned, which may or may not be true.

Even if it is not true, both are greater than Aleph 0.

And I stand by the "any scheme" statement; 2^Aleph 0 is still on the small side of the vastness. That should be obvious, just keep increasing the base integer.

This is worth a read. I don't buy the notion that reals are a fiction; a very few of them are far too useful, even if we only use the approximation.

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13 hours ago, The Old Hack said:

And the set of all unreal numbers are in Unreal Tournament?

Maybe? Quaternions get used to render 3D on a 2D screen.

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3 hours ago, Darth Fluffy said:
7 hours ago, hkmaly said:

Actually, it's   is the continuum hypothesis I mentioned, which may or may not be true.

Even if it is not true, both are greater than Aleph 0.

That's true. However, ${\displaystyle \aleph _{1}}$might be smaller than the size of set of all real numbers.

3 hours ago, Darth Fluffy said:

And I stand by the "any scheme" statement; 2^Aleph 0 is still on the small side of the vastness. That should be obvious, just keep increasing the base integer.

While it's on the small size of the vasteness, it's obviously bigger than any integer. There are bigger Von Neumann ordinals, probably (as in "sounds like true, but not sure if it can be proved without axiom of choice").

3 hours ago, Darth Fluffy said:

Maybe but too long for today.

2 hours ago, Darth Fluffy said:
16 hours ago, The Old Hack said:

And the set of all unreal numbers are in Unreal Tournament?

Maybe? Quaternions get used to render 3D on a 2D screen.

All? Definitely not. Some of them, yes.

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2 hours ago, hkmaly said:

That's true. However, ${\displaystyle \aleph _{1}}$might be smaller than the size of set of all real numbers.

While it's on the small size of the vasteness, it's obviously bigger than any integer. There are bigger Von Neumann ordinals, probably (as in "sounds like true, but not sure if it can be proved without axiom of choice").

Maybe but too long for today.

All? Definitely not. Some of them, yes.

I have done 3D to 2D, not for a game, not even real time, ages ago, and I did not use quaternions; did not even know what they were. It's said to be more efficient, and I can believe that. Just a guess, but to stay competitive, most popular immersive 3D environments probably use them for rendering. Guessing almost certainly for VR.

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13 hours ago, Darth Fluffy said:

I have done 3D to 2D, not for a game, not even real time, ages ago, and I did not use quaternions; did not even know what they were. It's said to be more efficient, and I can believe that. Just a guess, but to stay competitive, most popular immersive 3D environments probably use them for rendering. Guessing almost certainly for VR.

Not personally done this but touched it in school: There are basically three methods of computing graphics: "manually", with specific equations for each thing you want to do, with matrixes and with quaternions.

Manual methods gets hard to write, debug and modify. Might be in some cases most efficient to compute, but with graphics cards specifically optimizing the general methods, not so often.

Compared to matrixes, quaternions are smaller (4 numbers instead of 9), allow smooth rotations more easily and are more resistant to rounding errors.