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phantom-inker โ Day Two: 'FAQ #9'
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Published: 2023-02-26 17:00:05 +0000 UTC; Views: 16655; Favourites: 49; Downloads: 24
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...I mean, would you rather have her explain the ugly Christmas sweater again? ๐
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What a nice surprise checking your updates and diving into infinity (and beyond, sorry for that citation, but brushing up my dust memories about the Aleph function and related large cardinals I had to add this.)
And of course the Day Two update, thank you.
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I really like Ziaโs first answer where sheโs actually quite precise about how much she really does and doesnโt know about it. Itโs gibberish, but itโs really *precise* gibberish ๐
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Out of curiosity, just where was Chloe & Lynne the moment "The Event" happened, and what were they doing just before they transformed? I'll assume Chloe will say it was awkward and quite uncomfortable to gain so much mass rapidly, even moreso if she was somewhere public like grocery shopping or at the DMV.
I didn't ask Zia because it would be safe to assume she was at the university lab at the time. She could prove me wrong though. Zia will do Zia things.
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Chapter 10: "Day One." ย We're not there yet.
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Things got philosophical pretty quickly... xP
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So.... the correct answer is "all of them", right?
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lol, sure, why not? ๐
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Am I a nerd for understanding at least 3/4 of the terms used in the second panel? ๐
Also, I thought that Aleph-null was related to ordinality, rather than cardinality... I might be wrong though.
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The aleph numbers represent the cardinality of various classes of infinite orderable sets. Aleph-null is the zeroth class, proportional to the countable whole numbers.
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Ah, I was confusing it with omega and epsilon-naught, which are ordinal related.
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Even if the factors are very small, as long as they're more than infinitesimal, there should still be an infinite amount of habitable universes. That doesn't mean they actually have life, just that they could, but is that really what Zia meant? In any case, being in the 0% of universes with life is very interesting, something must have caused that.
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Infinities donโt often play by intuitive rules. Consider the diagram below. Two parabolas intersect on the plane. The area above f(x) is infinite. The area below g(x) is infinite. The area of their intersection, however, is not only finite, itโs actually tiny.
Science often encounters stuff like that, where infinite things *could* exist but the way the properties intersect practically means they *donโt*, like the โislands of stabilityโ within the atomic elements.
Zia is pointing out something pretty ย fundamental here, which is that the infinite universes have relatively few โ countable, even! โ forms that were conducive to life, likely because of the way their properties intersected with each other. Itโs hard to say if itโs true in the universe we live in, but she makes a good argument.
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Integrals don't care about the part above a function, they care about the part between a function and y=0, which may be negative. And it doesn't go against my point at all: The Drake equation is only multiplication. Any infinity multiplied by a positive finite number gives you infinity, the same type even.
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My point is that in math and science, infinite equations *often* combine together to produce finite results. It happens all the time in a zillion different contexts. I gave a simple easily-understood example; Iโd suggest you reread it and think hard about it until it makes sense to you.
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That can totally happen in mathematics, yes, but not by just multiplying infinity with a finite number. The Drake equation only has multiplication.
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I'm gonna just sit here and 
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That is related to the Copernican principle. The fact that we exist proves that there is a set of parameters and initial conditions that will cause a universe to contain humans. If that weren't the case, we humans could have never even considered that notion in the first place, because we wouldn't exist.
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Hey, I do understand some of these words! :P
(No kidding, as an astronomy enthusiast, the Drake Equation and the Fermi Paradox are quite familiar to me)
Just some personal perspective on this:
I imagine that parallel universes are actually located "sideways" in multi-dimensional time, where the one time dimension we observe is the one that's constantly going forward. The other dimensions in time would represent different outcomes in quantum-fluctuations, so if you'd travel sideways in time, you get to different parallel universes, where the further you get from your origin point, the more different these universes become. This would leave with an infinite number of habitable universes (since you would have a lot of them "close" to use that are nearly identical), but the chance of hitting one at random would be very small. There would be habitable "islands" within a vast ocean of uninhabitable universes multi-dimensional time.
TL;DR infinite universes, but only a small share is actually inhabitable despite their seemingly large number.
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This argument however doesn't take into account chaos theory, like the fact that very similar initial conditions can lead to a very different state in only a very short amount of time.
It also doesn't take into account entropy, which in this context make it more likely for universes to diverge than to converge.
Those two together will make it very unlikely that there is a universe so similar from a society standpoint, but so different from a biological one. Only a very recent multiverse split with a very radical biological shift could make that at least somewhat feasible.
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But apparently not in this canon, which is really weird. Almost seems to imply some higher being causing this.
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Of course. Their name is @phantom-inker. :-P
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Are we including subsets of infinity in this? (Like that of the Hilbertโs paradox of the Grand Hotel)
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That first answer was the more interesting of the two, even if only a handful of people get it.
Love the background equation theme going on there.
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The first answer is a really great answer. Zia's rarely wrong ๐
But, to Chloe's point, it's completely gibberish to almost everyone, herself included ๐
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And, of course, the reality is that she's probably underselling how extensive things could be.
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The correct answer to that question is 1
There is 1 universe, just one, no parallel ones.
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Bear in mind that there are serious physicists who believe that the quantum waveform function doesn't collapse at all. ย We don't know for certain how to empirically test it yet, but it might be an actual feature of our universe, and if it is, there's a lot of other universes out there.
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I know, it is highly speculative though, but in the ย context of thy story of course it is a fact. Sorry
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I didn't go far enough with higher mathematics to describe this rigorously, but in my fiction writing I'm using the conceit that there are a plethora of universes/dimensions out there, and they overlap. Individual personalities expand to fill the continuum of space/time which they are able to endure. So it's not that there is 'another you' out there, it is the SAME you living out >>a different set of circumstances<<. When the tension between realities grows so great that the limits of endurance are reached, the personality abandons one reality..."dying" in it from the POV of others still within that reality...and fully enters the other(s). You see this within your dreams, as the echoes of that other reality flash before your eyes before you awaken.
It makes for some interesting philosophical and storytelling fodder....
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What about paradoxes in dreams?
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My working theory is that some dreams are closer to a 'finished' reality than others. If the basic structure of that reality is unworkable long-term, or if it's somehow repugnant, the personality will 'bail' early and so the details will never be finished and are subject to change...well, like dreams.
But then again there are some dreams that are so realistic and lifelike that you don't even realize that they are dreams until the moment you wake up. I remember one dream where I was at work, taking readings on a chiller, when the power went out and the chiller started winding down...and I suddenly woke up. Did someone, in that reality, crash a jetliner into the building? Dunno....
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Are these genuine mathematical terms? 
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Fermi paradox is more of a biology thing (basically, "the universe is so big, so where is everyone?"), but several others are things I vaguely recognize as "this thing exists".
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If there are infinite universes, there would also be an infinite amount with people...
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Not really, your can have finite sets within infinite sets. Consider an infinite set of every number(including every fraction and irrational number) between of 1-10(Inclusive) how many of those numbers are whole numbers? The answer is 10. As a percentage that's 0% of the set, but still 10 total.
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I don't feel like repeating myself from other the rest of comments in this comment chain.
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Okay, but in the infinite set of all numbers from 1-10... how many whole numbers are there? For that matter, in the infinite set of all universes, how many are this one right here? Finite sets exist in infinity.
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If every universe has a non-zero chance of containing people, then you would be right in saying that there are an infinite amount of people in total, but if there is one universe with 1 person and all the other universes contain 0 people, then there are definitely a finite number of people (namely one person) in an infinite amount of universes. These 2 are the extreme cases on either end and the truth lies somewhere in the middle (if there are an infinite amount of universes that is).
Also, in math there are specific rules when limits (a tool to deal with zeros and infinities) lead to situations like 0/0, inf/inf, 0โฐ, etc. These rules can help determine whether the result is 0, infinity or a finite non-zero value.
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Like I said in another reply, part of the infinite amounts of universes of the infinite multiverse has people in them.
But it's still part of infinite, so it's still infinite amount of universes with people in them.
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It is possible to take a finite part of an infinite group. The set of positive integers is infinite, but it is still possible to take a finite subset of the first 100 integers. These 100 integers are still a part of the whole infinite set.
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Yes, you can grab a finite part, but since it's infinity, you will never be able to grab all of any sub section of infinite.
There is always more of a sub section to grab.
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That's not necessarily true if there are an infinite amount of finite subsections, rather than a finit amount of infinite subsections.
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Not necessarily. E.g. if chances for people go the lower the further we get from the universe with optimum conditions (which may or may not be ours).
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You could say half (or any other portion) of infinity doesn't have people in it.
But it's still part of infinity, thus STILL infinite.
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Lots of things in mathematics have situations where infinities effectively cancel each other out, or where something that seemingly would be infinite actually is finite under the right circumstances. ย With enough study of limit theory and calculus and set theory, this is perfectly normal, and you can grow pretty comfortable with equations that have infinities in them. ย But without that study, it can seem ridiculous, and the notion of even having different kinds of infinity seems preposterous โ despite that being a critical component of modern mathematics.
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I have to disagree.
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Oh? Then pray tell, what happens when you divide infinity by infinity?
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