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### Re: Miscellaneous Science Questions

Posted: Fri Dec 28, 2018 6:58 pm UTC
tomandlu wrote:The universe cannot be infinitely old, since if it was, it could never have reached the present moment - true or false?

I really don't see how B follows from A, and people taking guesses seem to be thinking very differently from you.

I think the keyword is "old". With no starting point, could we have ever reached the present?

### Re: Miscellaneous Science Questions

Posted: Fri Dec 28, 2018 7:25 pm UTC
We reached the present from the previous moment, which we reached from the one before that. Each moment is the start of everything after, and has it's start in the moments before. There're plenty of starts, just not a start to all of the infinite starts (although, there are starts to all finite sets of starts).

### Re: Miscellaneous Science Questions

Posted: Fri Dec 28, 2018 7:26 pm UTC
tomandlu wrote:
doogly wrote:What you are proposing is that because there is an infinite extent in one direction, there cannot exist points at some finite distance from the origin. This makes no sense.

I was more thinking of infinite in both directions - it started an infinite amount of time ago being the significant point.

Ok, if it helps:
What you are proposing is that because there is an infinite extent in at least one direction, there cannot exist points at some finite distance from the origin. This makes no sense.

### Re: Miscellaneous Science Questions

Posted: Fri Dec 28, 2018 9:58 pm UTC
I think tomandlu is imagining starting at some particular point and then reaching an infinite future, which does seem impossible, since infinity is unreachable. It's certainly true that the universe cannot have started "infinity years ago," because if the universe is infinitely old, it had no start. But there is no reason we can't exist in a universe with no beginning.

### Re: Miscellaneous Science Questions

Posted: Fri Dec 28, 2018 11:48 pm UTC
I think actual, observed physics rules this out, but nothing logically prevents this from being the year "omega + 6000", where omega is the first transfinite ordinal.

For the other view, I once had my freshman philosophy professor make the claim that tomandlu asked about.

### Re: Miscellaneous Science Questions

Posted: Sat Dec 29, 2018 3:42 am UTC
To expand on why doogly is saying this is nonsense:

The argument rests on "every moment follows another", and then noting that an infinite past implies an infinite number of applications of the first rule to reach the present day.

But if every moment follows another, then every moment *precedes* another too (every effect has a cause, after all). The same line of reasoning would imply that the universe can't exist for an infinite amount of time, as an infinite future would imply an infinite number of applications of the rule to reach the present day. Thus, some day the universe will simply un-create itself for some reason.

That's ridiculous, thus the premise must be false, and thus the identically-premised argument about the *start* of the universe must be false. There was no start, the universe is an eternal thing.

### Re: Miscellaneous Science Questions

Posted: Sun Dec 30, 2018 7:58 pm UTC
Xanthir wrote:That's ridiculous, thus the premise must be false, and thus the identically-premised argument about the *start* of the universe must be false. There was no start, the universe is an eternal thing.

This is starting to remind me of Bolztmann's Brain...

I'd agree (I think) - since the conclusion to the premise is absurd/false, the premise must also be false. The trouble is, like Boltzmann, it doesn't really tell us what's true. My own preference is that the universe is eternal, but with an odd boundary between its dimensionless origin and end that gives the "bigger than a point" period of the universe a genuine temporal duration iyswim. I mean, when the universe had zero-length in any dimension, how can we talk about durations any more than we can talk about distances?

### Re: Miscellaneous Science Questions

Posted: Sun Dec 30, 2018 9:07 pm UTC
Sure, then you get an eternal universe and a finite duration observable big-banging universe. Lots of models like that.

I think, if we were to take this as seriously as a philosophy professor might, the salient observation is that time is not a clock. This supposed philosopher might believe that it is, but that is probably not very well supported, and certainly not *necessarily* the case. For it is true that you cannot have a clock that has been ticking for an infinite amount of time. I can say the universe's time extends infinitely into the past, but not that something has been ticking for the entire time. But the fact that a clock couldn't do that doesn't mean that time can't, because time isn't a clock.

### Re: Miscellaneous Science Questions

Posted: Mon Dec 31, 2018 9:18 am UTC
DavidSh wrote:I think actual, observed physics rules this out, but nothing logically prevents this from being the year "omega + 6000", where omega is the first transfinite ordinal.

For the other view, I once had my freshman philosophy professor make the claim that tomandlu asked about.

No, I do not think that is consistent. How old would such a universe be? And what special event happened on "year omega" to distinguish it from all other moments?

### Re: Miscellaneous Science Questions

Posted: Mon Dec 31, 2018 4:02 pm UTC
Eebster the Great wrote:
DavidSh wrote:I think actual, observed physics rules this out, but nothing logically prevents this from being the year "omega + 6000", where omega is the first transfinite ordinal.

...

No, I do not think that is consistent. How old would such a universe be? And what special event happened on "year omega" to distinguish it from all other moments?

Basically you would have two sets of years. The first set of years would start with year 0, and continue for a countably infinite number of years. The second set of years would start with year omega, and continue again for a countably infinite number of years. Normalish physics would progress within each set of years. We would declare that every year in the second set takes place after every year in the first set. So that this would be meaningful, we set the state of the beginning of year omega to depend on the entire set of states of the first set of years, possibly at the limit in some sense of those states.

I'm not sure "how old" would be a meaningful question here. In one sense it is infinitely old at year omega and beyond.

### Re: Miscellaneous Science Questions

Posted: Mon Dec 31, 2018 5:30 pm UTC
DavidSh wrote:Basically you would have two sets of years.
But there's only one universe. How would you meaningfully connect the universe that existed in the first set of years with the universe that existed in the second set of years? And sure, by symmetry, it looks like the same question as a universe that (maybe) had a starting point, but lasts forever, except that in the second case, there isn't a "thing" that happens at "forever", but in the first case, there is such a thing (the creation of the universe) that happened "forever ago", unless you go with the idea that things don't have to have starting points.

Which I suppose is possible, but should be made explicit.

Jose

### Re: Miscellaneous Science Questions

Posted: Mon Dec 31, 2018 5:34 pm UTC
If things don't have starting points, the ordinals aren't the way to model them.

### Re: Miscellaneous Science Questions

Posted: Mon Dec 31, 2018 7:09 pm UTC
I'm not sure there is any consistent way to have a universe with a definite start in the infinite past. But if there is, its age would still just be "countably infinite" and the current year could not be consistently assigned any ordinal. If it were, either it would be a limit ordinal, in which case the previous year would have no date, or it would be a successor ordinal, in which case a finite number of years ago there was a year without a date. Instead, you would assign calendar dates the usual way, picking an arbitrary zero such that all years before are given a negative integer and all days after a positive integer. Except that almost all years are somehow "infinitely long ago" and therefore cannot be assigned integer dates. By the above argument, they cannot be assigned ordinal dates either, and there is no way to trace a causal history from the past to the present.

It just seems like nonsense in my head.

### Re: Miscellaneous Science Questions

Posted: Mon Dec 31, 2018 8:56 pm UTC
Eebster the Great wrote:I'm not sure there is any consistent way to have a universe with a definite start in the infinite past.

Yeah I am pretty good at imagining and I cannot imagine that.

### Re: Miscellaneous Science Questions

Posted: Tue Jan 08, 2019 9:28 am UTC
Please don't accidentally disprove all of existence guys, I just started looking for a house.

### Re: Miscellaneous Science Questions

Posted: Tue Jan 08, 2019 4:57 pm UTC
I know disproving the universe now seems bad, but imagine if it happened after you closed?

### Re: Miscellaneous Science Questions

Posted: Fri Jan 11, 2019 11:34 am UTC
p1t1o wrote:Please don't accidentally disprove all of existence guys, I just started looking for a house.

As long as it's not in Orqwith, you should be fine...

### Re: Miscellaneous Science Questions

Posted: Fri Jan 11, 2019 12:49 pm UTC
Maybe don't buy one in Isendale either. Rough neighbourhood, high crime rate, history of flooding, ...

### Re: Miscellaneous Science Questions

Posted: Fri Jan 11, 2019 7:17 pm UTC
I'm gonna try for an infinite past universe.

For analogy, think of negative tempurature. It is hotter than *all positive tempurature*. So there is an infinite amount of tempurature that is "colder" than it.

We place an order on events. There are events before, and events after. If we can make a consistent ordering of events such that an infinite number of events happen "before", then we have this model.

Now, all of the events *before* where causally connected to the now, things get bad. But why do they have to be?

Imagine a causal disconnection of a chain of events past a certain point. (For example, something falling into a black hole; what happens within the black hole is causally disconnected from what happens outside). If you can causally disconnect one chain of events from another, and label it *before*, and have that causally disconnected sequence of events be unbounded, you can have a date of omega+400 or whatever.

Now, justifying that those events are *before* is more than a bit tricky.

In the black hole case (where only a finite sequence of events occur in the causally disconnected "in black hole" event sequence), the events within it all happen "before" the black hole evaporates. And the events outside can be "after" the black hole evaporates. So despite being disconntected, we can reasonably argue they are *ordered*.

A: rocket ship outside black hole.
B: rocket ship crosses event horizon.
C0: pilot in rocket ship does a polka, inside event horizon.
C1: someone outside eats a donut
D: black hole evaporates due to hawking radiation.
E: the universe's greatest novel is written

Now C0 is causally disconnected from C1, D or E, but "obviously" it happens "before" D, and E happens "after" D.

All we now need is a way for a similar situation, but the events in C0 to be unbounded time-wise, yet still happen "before" D.

### Re: Miscellaneous Science Questions

Posted: Fri Jan 11, 2019 10:26 pm UTC
Yakk wrote:Now, all of the events *before* where causally connected to the now, things get bad. But why do they have to be?
Let's suppose that was exactly my definition of "before". So the distinction you're making is definitely not my definition of "before", but that doesn't necessarily mean it's a bad distinction, but I'd have to ask why we'd care about that distinction.

So if we go with the pragmatic definition of truth, believing that C0 is before D and E will enable me to act successfully where believing the opposite would not. Can you suggest a scenario where Alice believes that C0 is before E and Bob believes the C0 is after E and these beliefs matter?

### Re: Miscellaneous Science Questions

Posted: Sat Jan 12, 2019 12:14 am UTC
Quizatzhaderac wrote:So a "Hypercarnivore" is any species of animal whose natural diet is 70% or more meat. In order for this not to be a stupid name/categorization, I'd expect two things to be true: 1) this category is especially carnivorous 2) A large proportion of members of this category are in the 70-99% range.

These two assumptions would imply that a lot of the animals I think of as "Carnivores" have diets containing non-animal matter. So what specifically do these animals eat apart from meat? So it would depend on the animal, so using Wikipedia' examples of hypercarnivores, what do alligators, eagles, lions, wolf, dolphins, snakes, spiders, scorpions, and sharks eat aside from meat?

Most predators also eat the gut contents of their prey. I know that cats rely so much on this that they need taurine as a supplement in their food (in the wild, they get this from the bile of their prey). Incidentally, for this same reason, feeding only meat (i.e., muscle tissue) to your cat will slowly kill your cat.

I can't tell you the exact details of all of those hypercarnivores, but the idea that some animals survive from only eating muscle tissue is certainly incorrect.

### Re: Miscellaneous Science Questions

Posted: Sat Jan 12, 2019 6:14 am UTC
The Wikipedia article says "A hypercarnivore is an animal which has a diet that is more than 70% meat, with the balance consisting of non-animal foods [...]." So clearly it is using "meat" to refer to any animal matter, not just skeletal muscle. The term "hypercarnivore" suggests that most (or at least many) carnivores rely on animal tissue for less that 70% of their diet, which contrasts sharply with the common view of carnivores. It also makes me wonder what is the defining distinction between carnivores and omnivores if even a "hypercarnivore" can get nearly a third of its energy from plants.

By the way, I think black holes probably are the best analogy for an infinitely old universe with a beginning, but it's worth pointing out that Schwarzschild black holes have no beginning. Real astrophysical black holes do of course, but they also have an end and so probably aren't true black holes in the pure sense, and I would expect all the infinities to disappear in an adequate theory of quantum gravity.

### Re: Miscellaneous Science Questions

Posted: Mon Jan 14, 2019 9:35 am UTC
Eebster the Great wrote: It also makes me wonder what is the defining distinction between carnivores and omnivores if even a "hypercarnivore" can get nearly a third of its energy from plants.

At a guess, an omnivore can survive purely on a herbivore diet, but a carnivore must have meat.

### Re: Miscellaneous Science Questions

Posted: Mon Jan 14, 2019 10:18 am UTC
tomandlu wrote:
Eebster the Great wrote: It also makes me wonder what is the defining distinction between carnivores and omnivores if even a "hypercarnivore" can get nearly a third of its energy from plants.

At a guess, an omnivore can survive purely on a herbivore diet, but a carnivore must have meat.

I believe that is a facultative carnivore (as opposed to an obligate carnivore). I think it's similar to the distinction between facultative and obligate anaerobes. But you persuaded me to check, and Wikipedia says,

Animals that depend solely on animal flesh for their nutrient requirements are called obligate carnivores while those that also consume non-animal food are called facultative carnivores. Omnivores also consume both animal and non-animal food, and, apart from the more general definition, there is no clearly defined ratio of plant to animal material that would distinguish a facultative carnivore from an omnivore.

I believe that definition is not quite correct, as an obligate carnivore is merely an organism that must consume some animals to survive (but doesn't necessarily exclusively consume animals), while a facultative carnivore is one that sometimes eats animals but is capable of surviving with no animal matter at all. But maybe there is some slight inconsistency in the way the terms are applied between disciplines. In any case, it seems that the term "omnivore" is not very precisely defined.

### Re: Miscellaneous Science Questions

Posted: Mon Jan 14, 2019 4:28 pm UTC
I found a helpful sub-section of a Wikipedia article: Omnivore Classification, contradictions and difficulties. One of the definitions is that omnivores need to be able to derive both energy and nutrients from both plants and animals. For example felines apparently will eat grass as a laxative, but they can't really digest it.

### Re: Miscellaneous Science Questions

Posted: Fri Mar 15, 2019 7:00 pm UTC
Eebster the Great wrote:I'm not sure there is any consistent way to have a universe with a definite start in the infinite past.
...
It just seems like nonsense in my head.

Isn't that symmetrical with saying there will be an end at a definite but infinitely far date in the future?
Which sounds the same as saying there is a specific last number at infinity. (Or a first number at negative infinity)
Or asking where does the line X=Y start.

If the universe is seen as a (time)line plotted through phase space, and we explicitly assume it doesn't have endpoints, then all you're left with is relative distances along the line from features in the path like minimums and inflection points. T increases in one direction along the line when you parameterize it, but the only reason to pick a particular point for T=0 is if that simplifies the equations.

We're arbitrarily picking a spot to zoom in on and talk about because it is part of the line that passes close to a low entropy region and has observers in it to make things interesting. It seems convenient to measure time as distance along the line from that entropy minima, but not meaningful in absolute terms.

### Re: Miscellaneous Science Questions

Posted: Fri Mar 15, 2019 7:23 pm UTC
Yeah, I'm basically saying that, in either direction, the universe is either infinite or it isn't. If the universe has a beginning or end, that beginning or end must be some finite time in the past or future. So if the universe is infinitely old (has no finite age), then it has no beginning, and as you point out this works in reverse too.

None of this is to suggest there is anything inconsistent with a universe with a single endpoint at some finite timelike separation that is infinite in the other direction (a beginning but no end, or vice-versa).

### Re: Miscellaneous Science Questions

Posted: Fri Mar 15, 2019 7:54 pm UTC
Looking back on the earlier parts of this discussion about "year omega" raises a math question that I guess might belong here:

Can you not do subtraction on transfinite ordinals? "Omega minus one" seems like something that couldn't exist, because omega is by definition the first number after all the finite ordinals, so one less than that would be "the last finite ordinal", and there is no such thing.

### Re: Miscellaneous Science Questions

Posted: Fri Mar 15, 2019 8:16 pm UTC
Pfhorrest wrote:Looking back on the earlier parts of this discussion about "year omega" raises a math question that I guess might belong here:

Can you not do subtraction on transfinite ordinals? "Omega minus one" seems like something that couldn't exist, because omega is by definition the first number after all the finite ordinals, so one less than that would be "the last finite ordinal", and there is no such thing.

ω - 1 does not exist, 1 + ω = ω, and ω + 1 > ω. It's not completely intuitive. You can describe a partial function for subtraction, but it will never work if the implied result would be less than a limit ordinal. In other words "there exist ordinals α,β such that α≥β and that, for no ordinal γ, we have γ+β=α." Note that this implicitly allows 0 to be an ordinal; it's still true. However, "[for] every ordinals α,β such that α≥β, there exists a unique ordinal γ such that β+γ=α). That's why ordinals have unique representation in Cantor Normal Form.

In the example where the only ordinals in question are in [0, 2ω), we could say that ω + 10 happened 5 years before ω + 15, but not how long after year 20 it happened, which is the idea. That's why Tom was talking about disconnected timelines and stuff.

Source: https://math.stackexchange.com/a/1339986

### Re: Miscellaneous Science Questions

Posted: Tue Mar 19, 2019 7:21 pm UTC
Given the energy density/vacuum energy of space as some value, and the Bekenstein bound as an upper limit of the information content of a region of space with a finite amount of energy, is it meaningful to talk of a vacuum information content? Would it make sense to try and find some other way of measuring the information content of space so as to use that to derive something about the nature of vacuum energy?

### Re: Miscellaneous Science Questions

Posted: Tue Mar 19, 2019 8:17 pm UTC
The Bekenstein bound is an upper bound, not a lower bound. To reach the bound you need to form a black hole. For constant energy density (E ∝ V ∝ R3), it gives Smax ∝ R4, which is not particularly intuitive. Given a vacuum energy of 10-9 J/m3, the formula is approximately Smax = 1018 m-4 R4.

### Re: Miscellaneous Science Questions

Posted: Tue Mar 26, 2019 12:40 am UTC
What are the main reasons that the atmosphere/ground/anything doesn't get so cold at night and doesn't get so hot during the day? (Also consider that the coldest moment of the day is usually just before dawn whereas the hottest moment is usually just after solar noon.)

### Re: Miscellaneous Science Questions

Posted: Tue Mar 26, 2019 1:50 am UTC
The main reason is the comparatively thick atmosphere of the Earth, which absorbs infrared radiation at night and circulates air. Mars has a thin atmosphere and much more dramatic temperature changes, from about -125 C to 25 C. On the Moon, with no atmosphere, it's even worse (-173 to 127 C). On Mercury, it varies between -173 C and an incredible 427 C. And on the surface of Venus, with its extremely thick atmosphere, the temperature hardly varies at all between day and night, hanging around 462 C (probably; we can't measure it directly).

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 7:28 pm UTC
Yup, directly observable by just observing the temperature changes on a clear night vs a cloudy night; cloudy nights stay much warmer than clear nights, because more of the earth's absorbed heat is reflected back by the clouds (and probably just generally by the wetter atmosphere) rather than beaming straight out into space.

The coldest/hottest moments are easy to explain: just before dawn is when the earth has been leaking stored solar heat the longest without getting a recharge; a little after solar noon is when the balance of stored heat leaking out + solar heat coming in reaches a max. (It takes a bit for the atmosphere + ground to reach max temp, which is why it lags solar noon.)

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 7:53 pm UTC
There doesn't seem to be a miscellaneous math questions thread, or else I'm blind, so I'm putting this here.

Can the complex numbers be put in 1:1 correspondence with the reals? It seems like two-dimensional numbers built out of integers could be put into correspondence with the naturals (start with 0,0, 1,0, 1,1, 0,1, -1,1, -1,0, -1,-1, 0,-1, 1,-1, then 2,-1, 2,0, 2,1, and so on round and round forever) which can trivially be put in 1:1 correspondence with the integers, so it seems plausible that the complex numbers, being basically two-dimensional reals, might be put in 1:1 correspondence with the reals, but I don't know if the density of the real numbers throws some kind of wrench in that. Something something space-filling curves maybe?

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 8:09 pm UTC
A space-filling curve maps R to R2 or R3 or larger and can be constructed for any finite dimension n using existing techniques. The complex numbers are trivially identified with R2 by z ↦ (Re[z],Im[z]), or vice-versa: (x,y) ↦ x + yi. So if you just compose that with any curve that fills the plane, you are done. For instance, take any real number, put it through a Hilbert curve, then convert its coordinates to a complex number. That gives you a 1-1 correspondence.

Another way of intuitively seeing why complex numbers must have the same cardinality as real numbers is that every complex number is just an ordered pair of real numbers. Any set of countable-length tuples of real numbers has the same cardinality as the real numbers.

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 8:41 pm UTC
Eebster the Great wrote:Any set of countable-length tuples of real numbers has the same cardinality as the real numbers.

I'd say that part is far less intuitive than complex numbers mapping to R².
I like the idea of interleaving digits, like (AAA.aaaaa...,BBB.bbbbb...)→ABABAB.abababababab..., trusting that any real number is an infinite string of digits and that by interleaving the digits you keep a just as infinite string of digits.

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 8:51 pm UTC
Yeah, interleaving digits works well, as you can always answer the question "what's the Nth digit before/after the decimal point" in finite time, and it's a bijection (I think), so you don't have to establish a different injection the other way.

My favorite 2d-to-1d injection, tho, is proving the rationals are the same cardinality as the integers by just writing out the rational on one line with a slash, like "42/5", then interpreting it as a base-11 number where the "/" is the digit with value 10. Boom, each rational is immediately injected to unique integers. ^_^

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 8:53 pm UTC
Yeah, the mapping of complex numbers to R2 was taken as obvious in my post; the mapping of R to R2 is what I was unsure about.

### Re: Miscellaneous Science Questions

Posted: Fri Mar 29, 2019 9:21 pm UTC
Pfhorrest wrote:Yeah, the mapping of complex numbers to R2 was taken as obvious in my post; the mapping of R to R2 is what I was unsure about.

That would be the space-filling curve you mentioned.