What-If 0065: "Twitter Timeline Height"

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What-If 0065: "Twitter Timeline Height"

Postby Flumble » Tue Oct 01, 2013 3:07 pm UTC



If our Twitter timelines (tweets by the people we follow) actually extended off the screen in both directions, how tall would they be?
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That anonymous guy shows up everwhere nowadays. :o


On the topic itself: it's nice to see Randall made some far-fetched asides for this what-if - this is how I like my what-ifs. :D

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Re: What-If 0065: "Twitter Timeline Height"

Postby snowyowl » Tue Oct 01, 2013 3:18 pm UTC

You may begin arguing about the validity of the Doomsday Argument... now.

I'm relieved to get some closure on that. I thought about that argument a couple of years ago, but I couldn't do the maths and eventually decided that the whole idea didn't make sense. But it's really nice to know what the answer would have been if I'd done the maths. Though "the human race will go extinct in about 230 years" has two significant figures, which is about two more than you can legitimately give.

It's all very anthropic.
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Re: What-If 0065: "Twitter Timeline Height"

Postby cellocgw » Tue Oct 01, 2013 3:28 pm UTC

Hopping over from the other thread, which I hope I deleted.

I guess I like this one 'cause I like doing stats.
There are lots of other examples of "fake numbers." At some point merchants started refusing to take checks (remember them?) with very low numbers on the theory that people who'd just opened an account might be planning to bounce checks and run. The response was for banks to issue new account holders checks that started with 1001. And so on.

ETA -- since I'm sure everyone's going to weigh in on the Doomsday thingie, I'll just suggest cheerfully that all we need to do to avoid early extinction is to taper off the world population. That way it'll take longer and longer to get to the last 5%. So, the closer we get to extinction, the longer it'll take. (Boy, that was fun. :twisted: )
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Re: What-If 0065: "Twitter Timeline Height"

Postby jovialbard » Tue Oct 01, 2013 3:35 pm UTC

How about this: The Doomsday Argument is silly for the same reason that Xeno's Paradox isn't really a paradox. You're looking at it the wrong way. More specifically, if everyone alive now would say they are in the 90% I would contend that they are either not very smart or they sincerely already believe that doomsday is imminent. I think I'm in the first 5%.

Also on the topic of the Goddamn Airplane problem (with my apologies) of course I interpret the problem with interpretation #1, why is that interpretation disregarded?
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Re: What-If 0065: "Twitter Timeline Height"

Postby Flumble » Tue Oct 01, 2013 3:40 pm UTC

cellocgw wrote:ETA -- since I'm sure everyone's going to weigh in on the Doomsday thingie, I'll just suggest cheerfully that all we need to do to avoid early extinction is to taper off the world population. That way it'll take longer and longer to get to the last 5%. So, the closer we get to extinction, the longer it'll take. (Boy, that was fun. :twisted: )

Exactly.
I hardly know anything on the doomsday argument, so to be on the safe side I'd assume it is valid - hey, you can surely trust statisticians.
So in with the abortion legislation, easier access to death penalties and legalise hard drugs like opium and crocodile and fully privatise medical aid. :P

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Re: What-If 0065: "Twitter Timeline Height"

Postby rhomboidal » Tue Oct 01, 2013 4:00 pm UTC

Occupy Existence: We are the middle 90%. And all doomed.

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Re: What-If 0065: "Twitter Timeline Height"

Postby eran_rathan » Tue Oct 01, 2013 4:05 pm UTC

Flumble wrote:legalise hard drugs like opium and crocodile


Sir, I'm going to have to ask you to put down that crocodile, and keep your hands where I can see them.
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Re: What-If 0065: "Twitter Timeline Height"

Postby snowyowl » Tue Oct 01, 2013 4:10 pm UTC

jovialbard wrote:More specifically, if everyone alive now would say they are in the 90% I would contend that they are either not very smart or they sincerely already believe that doomsday is imminent. I think I'm in the first 5%.

Why? Because you look at the past and see the relentless advance of humanity, and thus deduce that the advance will continue a long way into the future?
By Doomsday logic, the entire first 50% of humanity can look at their past and see things getting better and better. At best you can deduce that you're in the first 50%, maybe the first 25%, but the first 5% is pushing it.

The German Tank Problem isn't very reliable with only one data point. I intend to reincarnate and get a second data point. So guys, if I am reborn any time before 2200, start getting worried. (Assuming reincarnation selects a random human life out of all of history, of course.)

Edit: By the way, I've found my new signature.
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Re: What-If 0065: "Twitter Timeline Height"

Postby jovialbard » Tue Oct 01, 2013 4:18 pm UTC

snowyowl wrote:
jovialbard wrote:More specifically, if everyone alive now would say they are in the 90% I would contend that they are either not very smart or they sincerely already believe that doomsday is imminent. I think I'm in the first 5%.

Why? Because you look at the past and see the relentless advance of humanity, and thus deduce that the advance will continue a long way into the future?
By Doomsday logic, the entire first 50% of humanity can look at their past and see things getting better and better. At best you can deduce that you're in the first 50%, maybe the first 25%, but the first 5% is pushing it.

The German Tank Problem isn't very reliable with only one data point. I intend to reincarnate and get a second data point. So guys, if I am reborn any time before 2200, start getting worried. (Assuming reincarnation selects a random human life out of all of history, of course.)

Edit: By the way, I've found my new signature.


But if you were born before now we'd already know about it right? So I think we're safe :)

My problem with the argument is that it masks it's own assumption that people alive today or in the past fall into the category of "most people". Of course making that assumption leads you to believe that the world will end fairly soon. But that's based on an assumption, and it shouldn't be surprising that a dubious assumption gives you dubious results. It may be true or it may not, we don't know, but regardless of it's eventual truth or fallacy the argument essentially devolves into circular logic. Doomsday is coming because, statistically, if doomsday is coming then doomsday is coming.
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Re: What-If 0065: "Twitter Timeline Height"

Postby keithl » Tue Oct 01, 2013 4:19 pm UTC

Today is the day Portland Oregon stopped having a printed newspaper every day. That could have been extrapolated from newspaper whitespace volume over the last decade. This forum is one of millions of internet-related reasons for that. Five decades ago, the Oregonian was the twitter of its day. My father was mentioned in the paper 20 times, from high school graduation through his death. Not because he was prominent, but because most people were, in dozens of daily pages of local news. My grandfather was bitten by a dog. That made the paper in the 30's.

In central Africa, drum communication finally disappeared with the advent of personal cell phones.

Technology finds more efficient/easy ways to do things. Twitter is an information gathering tool for its sponsors. It is toast when its sponsors find a more insideous way to get their data, or users find an easy way to not give it to them.
Most brittle, one-trick-pony companies go from the top of their game to bankruptcy in a year.

Last night, Clive Thompson, on book tour, helped us understand why people use twitter. Individual tweets are unimportant, the accumulated tempo and timbre of the messages tells friends how the tweeter is doing. There's got to be an easier way, and some clever psychologist reading that book may be having a world-changing vision right now. That new idea could implement, spread, and replace Twitter faster than you can say "Altavista".

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Re: What-If 0065: "Twitter Timeline Height"

Postby Flumble » Tue Oct 01, 2013 4:21 pm UTC

eran_rathan wrote:
Flumble wrote:legalise hard drugs like opium and crocodile


Sir, I'm going to have to ask you to put down that crocodile, and keep your hands where I can see them.

Hahahah :P
My bad, I assumed desomorphine has the nickname crocodile in English.


snowyowl wrote:By Doomsday logic, the entire first 50% of humanity can look at their past and see things getting better and better.

Most doomsday scenarios I've seen (in movies) feature a long history of advancement followed by a sudden extinction.

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Re: What-If 0065: "Twitter Timeline Height"

Postby kaley » Tue Oct 01, 2013 4:35 pm UTC

Flumble wrote:
eran_rathan wrote:
Flumble wrote:legalise hard drugs like opium and crocodile


Sir, I'm going to have to ask you to put down that crocodile, and keep your hands where I can see them.

Hahahah :P
My bad, I assumed desomorphine has the nickname crocodile in English.

Aww you ruined it by saying that crocodile is actually a street name for a drug. I was thinking it was a great metaphor.

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Re: What-If 0065: "Twitter Timeline Height"

Postby rmsgrey » Tue Oct 01, 2013 4:45 pm UTC

If, instead of asking every human who ever lived whether they were in the middle 90% based on birth order, the aliens used a time machine to visit Earth every year and see whether humans were still around, you can turn that into a prediction that humans will be around for 10,000 to 4,000,000 more years (taking the first modern humans as having appeared 200,000 years ago, and using factors of 20 rather than 19 to keep the maths simple).

...

Having now read the Wikipedia article, I like the argument that I should consider the fact of my existence as evidence that the total number of humans to exist should be large (the larger the total population over all time, the more likely any given potential individual is to actually exist) - which, apparently (ie, I haven't checked the maths myself) exactly cancels the evidence that the total number of humans to exist should be small because I happen to exist early in the sequence...

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Re: What-If 0065: "Twitter Timeline Height"

Postby Klear » Tue Oct 01, 2013 5:04 pm UTC

I got quite confused by citation 5. I mean, if he needs his monitor to type that text, he hasn't uploaded it yet, so I can't possibly want to measure it yet. Or, to put it in a better way, since I'm already reading it, he can't be typing it still.

Then I noticed a couple of typos and everything is fine. I just hope I won't read that citation much later.

Also, citations 3 and 4 are awesome.

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Re: What-If 0065: "Twitter Timeline Height"

Postby JeffR23 » Tue Oct 01, 2013 5:21 pm UTC

If the doomsday argument works today, it would have worked a thousand years ago. If it had worked a thousand years ago, we'd all be dead. We're not dead. Contradiction, so QED: the doomsday argument is silly.

(Also, if it's right the same argument proves we're most likely simulations or intelligences existing in the fleeting, pre-painful death instants of a long series of Boltzmann Brains in deep time, which leads straight to the conclusion of sillyness as well.)

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Re: What-If 0065: "Twitter Timeline Height"

Postby eran_rathan » Tue Oct 01, 2013 5:22 pm UTC

Flumble wrote:
eran_rathan wrote:
Flumble wrote:legalise hard drugs like opium and crocodile


Sir, I'm going to have to ask you to put down that crocodile, and keep your hands where I can see them.

Hahahah :P
My bad, I assumed desomorphine has the nickname crocodile in English.


Learned something new today, so thanks!
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Re: What-If 0065: "Twitter Timeline Height"

Postby weidner » Tue Oct 01, 2013 5:22 pm UTC

Eureka!
Now I know where Nero (band) got December the 1st, 2808... Doomsday.
Awesome; thanks Randall!

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Re: What-If 0065: "Twitter Timeline Height"

Postby Ehsanit » Tue Oct 01, 2013 5:23 pm UTC

Citations 12 and 13 are a tad brief.
I wonder what that kind of mistake would do to the stats problems.

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Re: What-If 0065: "Twitter Timeline Height"

Postby chris857 » Tue Oct 01, 2013 5:29 pm UTC

You know, those stars (http://what-if.xkcd.com/imgs/a/65/timeline_lbt.png) rather remind me of those traffic lights (http://imgs.xkcd.com/comics/traffic_lights.gif).

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Re: What-If 0065: "Twitter Timeline Height"

Postby speising » Tue Oct 01, 2013 5:56 pm UTC

the problem: you could have made the same argument a month after twitters start, or at any other time since. obviously, this is not really a useful estimation technique.

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Re: What-If 0065: "Twitter Timeline Height"

Postby ctdonath » Tue Oct 01, 2013 6:49 pm UTC

Several of today's What If predictions have got to be submitted to http://longbets.org

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Re: What-If 0065: "Twitter Timeline Height"

Postby yawningdog » Tue Oct 01, 2013 7:05 pm UTC

I don't think citation 9 is right. I'm quite certain that SEAL teams 1-4 stood up before team 6 did.
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Re: What-If 0065: "Twitter Timeline Height"

Postby rmsgrey » Tue Oct 01, 2013 7:17 pm UTC

speising wrote:the problem: you could have made the same argument a month after twitters start, or at any other time since. obviously, this is not really a useful estimation technique.


But 90% of the time you make the argument, it will give a correct answer...

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Re: What-If 0065: "Twitter Timeline Height"

Postby Jackpot777 » Tue Oct 01, 2013 7:27 pm UTC

The longer we survive as a species, the longer we push off the predicted extinction date.

That's something they taught us at Tautology Club (where the first rule of Tautology Club is the first rule of Tautology Club, now turn your hymn books to #703).

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Re: What-If 0065: "Twitter Timeline Height"

Postby Wnderer » Tue Oct 01, 2013 9:26 pm UTC

Jackpot777 wrote:The longer we survive as a species, the longer we push off the predicted extinction date.


That's like that life expectancy rule of thumb. Your life expectancy is half way to one hundred. If you're 20, your life expectancy is 60. If you're 40, your life expectancy is 70. If you're 80, your life expectancy is 90. It's not accurate but it gives you the general idea. The longer you live the longer your life expectancy.

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Re: What-If 0065: "Twitter Timeline Height"

Postby rmsgrey » Tue Oct 01, 2013 9:36 pm UTC

Wnderer wrote:
Jackpot777 wrote:The longer we survive as a species, the longer we push off the predicted extinction date.


That's like that life expectancy rule of thumb. Your life expectancy is half way to one hundred. If you're 20, your life expectancy is 60. If you're 40, your life expectancy is 70. If you're 80, your life expectancy is 90. It's not accurate but it gives you the general idea. The longer you live the longer your life expectancy.


...if you're 102, your life expectancy is 101... ???

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Re: What-If 0065: "Twitter Timeline Height"

Postby Wnderer » Tue Oct 01, 2013 9:43 pm UTC

rmsgrey wrote:
Wnderer wrote:
Jackpot777 wrote:The longer we survive as a species, the longer we push off the predicted extinction date.


That's like that life expectancy rule of thumb. Your life expectancy is half way to one hundred. If you're 20, your life expectancy is 60. If you're 40, your life expectancy is 70. If you're 80, your life expectancy is 90. It's not accurate but it gives you the general idea. The longer you live the longer your life expectancy.


...if you're 102, your life expectancy is 101... ???


Yes. If you reach 102, people who knew you will not expect you to still be alive.

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Re: What-If 0065: "Twitter Timeline Height"

Postby gmalivuk » Tue Oct 01, 2013 9:47 pm UTC

Wnderer wrote:
Jackpot777 wrote:The longer we survive as a species, the longer we push off the predicted extinction date.


That's like that life expectancy rule of thumb. Your life expectancy is half way to one hundred. If you're 20, your life expectancy is 60. If you're 40, your life expectancy is 70. If you're 80, your life expectancy is 90. It's not accurate but it gives you the general idea. The longer you live the longer your life expectancy.
Yeah, that's not at all accurate for life span, since it assumes a perfectly uniform distribution of deaths from age 0 to 100 years.

It is, however, a perfectly accurate analogy to the sequential ordering of humans situation: The average position of a random selection from all of humanity is the 50% mark, the average of those whom we know aren't in the first 10% is the 55% mark, the average of those whom we know aren't in the first 50% is the 75% mark, and so on.

And sure, the same argument (I can be 95% sure I'm not in the first 5% of all humans) holds for all people at all times, but there's nothing unsound or contradictory in the fact that this argument leads different humans to different conclusions about how long humanity will survive. After all, I have a lot more data points after 100 billion other humans have been born than a hypothetical mathematician long ago, who'd only had a million predecessors.

Changing predictions when we have new information, far from being irrational, is exactly how reasoning *should* work.

rmsgrey wrote:...if you're 102, your life expectancy is 101... ???
Well yeah, there's a reason for the "It's not accurate but" part.
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Re: What-If 0065: "Twitter Timeline Height"

Postby Viltris » Tue Oct 01, 2013 9:48 pm UTC

Flumble wrote:Are the Land Before Time movies any good?
[edit] hold on a sec, The Land Before Time is known as Platvoet en zijn vriendjes in Dutch. Of course I know platvoet en zijn vriendjes... well, at least some... I'm certain I've seen one in my childhood and it was fun back then.


The first one is good. The sequels are pretty bad, though kids will still eat them up. (Or so I assume. I've only seen the first few sequels.) #14 and beyond don't exist.

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Re: What-If 0065: "Twitter Timeline Height"

Postby Showsni » Tue Oct 01, 2013 10:30 pm UTC

So by the Doomsday argument there's a 95% chance that the total number of humans is less than 20 times the current number we've had so far. And a 99% chance that it's less than 100 times the number we've had so far, and so on... Tending to there being a 100% chance we'll end up with fewer than infinite humans, which is useful. Where would they all live?

(Can I apply that to anything? Say, there's a 95% chance I won't live to see my 26 * 20 = 520th birthday? Does that mean there's a 5% chance I will? (Assuming you pluck a me from every year I live and none of them has any knowledge about average humans life spans...))

Anyway, what I really want to know is what's the deal with @YOUGAKUDAN_00? Come on, someone must know what that's all about!

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Re: What-If 0065: "Twitter Timeline Height"

Postby gmalivuk » Tue Oct 01, 2013 11:31 pm UTC

Showsni wrote:(Can I apply that to anything? Say, there's a 95% chance I won't live to see my 26 * 20 = 520th birthday? Does that mean there's a 5% chance I will?
No, it only works for uniform distributions. That's why the what-if talks in terms of sequentially ordering humans before bringing dates into it, because we're uniformly distributed by number from first to last human (one human per number), but not uniform by year of birth.

Edit:
To know the probability of living to a certain age, you have to pick randomly by person. Picking randomly by age can't tell you anything about longevity. If I roll a die and get 100,and ask you to find me a 100-year old, how am I supposed to calculate from that the probability that people live to be 100?

If I choose a random person alive today, it will tell me something about the age distribution of people alive today. In particular, I'll be 95% confident that the person isn't among the youngest 5% (and there'll be a 5% chance that he is). This doesn't tell me about actual longevity, though. Guessing that 20 times more people are past age 10 than are younger than 10 is not the same as concluding that 20 times as much lifetime happens past age 10 than before it.

If I choose a random person who was born in 1800 and look at how long they lived, it will tell me something about life expectancy in 1800, but it still won't tell me what you thought. If I find someone who died at age 30, I can be 95% confident that she wasn't among the youngest 5% of people to die (and assign a 5% chance to the claim that she was). But I most definitely *can't* conclude that there's a 95% chance that she wasn't in her first 5% of the average life (with a 5% chance that she was). A population where 5% of people die evenly between 20 and 30, and where everyone else dies evenly between 30 and 40, has the 5th percentile at age 30, while the age at which someone has completed 5% of their whole life is less than age 2.

Edit 2, to put it more simply:
It is true that 5% of people are among the youngest 5% of people.
It is false that 5% of people are in the first 5% of their own lives.

The latter could only be concluded from a uniform distribution of deaths from age 0 to whatever the hard maximum is, along with an exactly constant population size, and this is not a reasonable assumption under any normal circumstances. The most reasonable assumption with no other information is probably one where the probability of dying in the next year is the same no matter your age, which leads to an exponential distribution. If you wish to figure out an aging function, you'd need more than one data point.
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Re: What-If 0065: "Twitter Timeline Height"

Postby willpellmn » Wed Oct 02, 2013 12:25 am UTC

If we see Twitter activity winding down in 2018, then will that be evidence in favor of the Doomsday argument? And if so, does it suggest that humanity has only two centuries left?

Probably not. But it depends which statisticians you ask.


And this is exactly why I believe that statistics is bullshit. You can construct all sorts of seemingly logical sophistries and semantic arguments, but at the end of the day, you're using math to try and prove something based on utterly foolish assumptions about how regular and predictable the world is, when you can't possibly have all the information you'd need for your predictions to mean anything. Ergo, nobody should ever try to predict anything or "prove" what's going to happen. They should accept that the future is unknowable, and they shouldn't gamble anything they aren't willing to lose, no matter how good they think the odds are.

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Re: What-If 0065: "Twitter Timeline Height"

Postby gmalivuk » Wed Oct 02, 2013 12:31 am UTC

Which is why you never cross the street or do anything else that might possibly kill you, right?

The future may be unknowable, but it is not unpredictable. If you truly believed it to be unpredictable, you wouldn't do anything you didn't thoroughly enjoy, because the only reason to do unenjoyable stuff is that you expect something better to happen as a result.
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Re: What-If 0065: "Twitter Timeline Height"

Postby ahammel » Wed Oct 02, 2013 12:32 am UTC

willpellmn wrote:[And this is exactly why I believe that statistics is bullshit. You can construct all sorts of seemingly logical sophistries and semantic arguments, but at the end of the day, you're using math to try and prove something based on utterly foolish assumptions about how regular and predictable the world is, when you can't possibly have all the information you'd need for your predictions to mean anything. Ergo, nobody should ever try to predict anything or "prove" what's going to happen. They should accept that the future is unknowable, and they shouldn't gamble anything they aren't willing to lose, no matter how good they think the odds are.
You are aware that science, as it is currently practised, would be utterly impossible without statistics, right?
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Re: What-If 0065: "Twitter Timeline Height"

Postby gmalivuk » Wed Oct 02, 2013 12:41 am UTC

*All* decision making would be impossible without at least a basic intuitive notion of statistics.

I'm only continuing to press buttons on my phone to write this because it is statistically quite unlikely that someone has turned it into a bomb that will go off with the next character input. I'm only going to stop typing and put it back in my pocket after this post because it is statistically also quite unlikely that someone has turned it into a bomb that will go off as soon as it stops receiving input. I'm only taking repeated breaths of air because it is statistically quite unlikely that someone is in the process of filling my apartment with poison gas. And so on.
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Re: What-If 0065: "Twitter Timeline Height"

Postby Pfhorrest » Wed Oct 02, 2013 12:43 am UTC

If one were to pick a natural number by a truly random process, what would be the most likely result? Or, what would be the average result of a series of such picks?

If that even a sensible question to ask, since there are infinitely many of them, bounded on only one side? Where's halfway to infinity? (Does it help at all if we're talking about integers instead? Does the average center at zero then?)

Back on natural numbers: if it's possible that there will be an infinite number of humans stretching out into the unknown future, how does the answer to this question affect the doomsday question?
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Re: What-If 0065: "Twitter Timeline Height"

Postby gmalivuk » Wed Oct 02, 2013 1:10 am UTC

You have to specify a distribution before you can answer those questions. If it's possible there will be infinite humans in the future, then we need to know with what probability before we can re-approach the doomsday question. Some infinite distributions have undefined averages, others are perfectly well-defined.

If it's finite, then there's a 95% chance that I'm out of the first 5% of humans. If it's infinite, then obviously there's no chance that I'm out of the first 5%, since there is no first 5%. If there's an 18/19 chance of only a finite total number of humans (and a 1/19 chance of infinite), then there is a 90% chance that I'm out of the first 5% of humans, a bit less than a 5% chance that I'm in the first 5% of a finite total, and a bit more than a 5% chance (1/19, to be exact) that there will be an infinite number.

Picking a different probability of eternal humanity can change these probabilities to whatever we'd like.
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The other thing to realize, which I think is more important on a visceral level, is that putting dates on extinction (of humanity or Twitter or anything else computed this way) requires a fairly major additional assumption about the rate at which new elements of the set arise. We might be 95% certain that there will be less than 2 trillion more humans born in the future, but I'd say we're significantly less than 95% certain that birth rates over time will follow any particular given pattern you might suggest.

Even if we knew for sure that the total human population would eventually stabilize at exactly 10 billion, that doesn't allow us to calculate the amount of time it will take for 2 trillion more people to be born. If 8 people die per 1000 every year, as they do at present, then we'd need 79 million births per year to maintain stability, and we'd run through 2 trillion in 25,000 years. If that drops to half, a stable population would have half as many births, and the next 2 trillion births would take twice as long to happen.
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Re: What-If 0065: "Twitter Timeline Height"

Postby Showsni » Wed Oct 02, 2013 1:41 am UTC

gmalivuk wrote:
Showsni wrote:(Can I apply that to anything? Say, there's a 95% chance I won't live to see my 26 * 20 = 520th birthday? Does that mean there's a 5% chance I will?
No, it only works for uniform distributions. That's why the what-if talks in terms of sequentially ordering humans before bringing dates into it, because we're uniformly distributed by number from first to last human (one human per number), but not uniform by year of birth.

Edit:
To know the probability of living to a certain age, you have to pick randomly by person. Picking randomly by age can't tell you anything about longevity. If I roll a die and get 100,and ask you to find me a 100-year old, how am I supposed to calculate from that the probability that people live to be 100?

If I choose a random person alive today, it will tell me something about the age distribution of people alive today. In particular, I'll be 95% confident that the person isn't among the youngest 5% (and there'll be a 5% chance that he is). This doesn't tell me about actual longevity, though. Guessing that 20 times more people are past age 10 than are younger than 10 is not the same as concluding that 20 times as much lifetime happens past age 10 than before it.

If I choose a random person who was born in 1800 and look at how long they lived, it will tell me something about life expectancy in 1800, but it still won't tell me what you thought. If I find someone who died at age 30, I can be 95% confident that she wasn't among the youngest 5% of people to die (and assign a 5% chance to the claim that she was). But I most definitely *can't* conclude that there's a 95% chance that she wasn't in her first 5% of the average life (with a 5% chance that she was). A population where 5% of people die evenly between 20 and 30, and where everyone else dies evenly between 30 and 40, has the 5th percentile at age 30, while the age at which someone has completed 5% of their whole life is less than age 2.

Edit 2, to put it more simply:
It is true that 5% of people are among the youngest 5% of people.
It is false that 5% of people are in the first 5% of their own lives.

The latter could only be concluded from a uniform distribution of deaths from age 0 to whatever the hard maximum is, along with an exactly constant population size, and this is not a reasonable assumption under any normal circumstances. The most reasonable assumption with no other information is probably one where the probability of dying in the next year is the same no matter your age, which leads to an exponential distribution. If you wish to figure out an aging function, you'd need more than one data point.


I'm not sure I follow your statement in the first edit... My situation was as follows:

Get your time machine out, and take a copy of one particular person on each of their birthdays. Then the copies are distributed uniformly from age 1 to age whatever the maximum is, right? So 5% of the copies will be amongst the youngest 5% of copies, and there's a 95% chance that any copy you take will be older than that. In particular, taking one known copy (me, aged 26) there's a 95% chance I'm not in the youngest 5%, so I can assume 26/my max age > 0.05 or my max age < 520. I can therefore assume my maximum age is less than 520 with 95% confindence. Or is that wrong? (Or, if you like, I can assume my maximum age is less than 52 with 50% confidence... Which is worrying.)

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Re: What-If 0065: "Twitter Timeline Height"

Postby gmalivuk » Wed Oct 02, 2013 1:45 am UTC

The problem you've got there is that you're starting out with copies for all your birthdays, which means you're starting out with a uniform distribution over your actual total lifespan. And if we already have that, then what's the point of doing math to put bounded estimates on your total life span? Yes, it's true that a randomly selected copy of you has a 5% chance of being in the first 5% of life, but it is not true that a randomly selected copy of you has a 5% chance of being 26 or younger, unless your total lifespan is in fact 520 years.

The reason your reasoning doesn't work with your current age is that you today are *not* one copy randomly selected from copies made every day of your life.

Probably.

(If one alien put all the copies in a bag, and another alien picked one without having any information about how many total copies were in the bag, then the second alien would conclude that there is a 5% chance the age of that copy is at most 5% of your total lifespan. If the copy it got was you at 26, it would assign a 5% probability to your living at least 520 years total. This is very pointedly not the same as concluding that you today have a 5% (or any other nonzero) chance of living to be 520 years old.)
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Re: What-If 0065: "Twitter Timeline Height"

Postby Showsni » Wed Oct 02, 2013 2:14 am UTC

Which is kind of my point; you end up with an obviously wrong answer because I'm not a proper random selection from the distribution. But then, doesn't the Doomsday thingy have exactly the same problem? We're using the number of total humans up to this date as our datum, which means we're using the humans alive today as our "random" choice. But this isn't a random selection from all the humans who will ever live, so it has the same error as thinking I might live to 520.


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