What-if 0094: "Billion-Story Building"

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What-if 0094: "Billion-Story Building"

Postby suso » Tue Apr 29, 2014 8:58 pm UTC

http://what-if.xkcd.com/94/

My daughter—age 4.5—maintains she wants a billion-story building. It turns out not only is that hard to help her appreciate this size, I am not at all able to explain all of the other difficulties you'd have to overcome.

Keira, via Steve Brodovicz, Media, PA


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The awesome thing about this one is that now this little girl has a theoretical building named after her. I hope she grows up, makes us eat crow and shows us what is "impossible".
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Re: What-if #0094: Billion-Story Building

Postby Mikeski » Tue Apr 29, 2014 9:12 pm UTC

You're thinking big when simplifying your problem might result in building a Dyson sphere or a ringworld, or at least terraforming the whole planet. (Laying out that much living space in one layer, rather than vertically.)

I like the Jetsons rings on the mega-mega-mega-skyscraper.

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Re: What-if #0094: Billion-Story Building

Postby fred84 » Tue Apr 29, 2014 9:13 pm UTC

could someone tell Randall to fix the "Keira-skyscraper" pic? It should read *10* not 100 Mega-Mega-Mega-Skyscrapers :P

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Re: What-if #0094: Billion-Story Building

Postby HES » Tue Apr 29, 2014 9:16 pm UTC

Do we even have the materials to do this? We certainly won't be making it out of wood:

(Spoilered for size)
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Re: What-if #0094: Billion-Story Building

Postby brenok » Tue Apr 29, 2014 9:20 pm UTC

I don't know why he's calling them "mega-skyscrapers", when they're obviously hecto-skyscrapers.

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Re: What-if #0094: Billion-Story Building

Postby Earthling on Mars » Tue Apr 29, 2014 9:20 pm UTC

I wish my parents had sent my questions to xkcd what-if when I was 4! :mrgreen:

(Oh wait, xkcd didn't exist when I was four.)

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Re: What-if #0094: Billion-Story Building

Postby ucim » Tue Apr 29, 2014 9:25 pm UTC

Skyscraper doesn't sound like a real word any more.

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Re: What-if #0094: Billion-Story Building

Postby HES » Tue Apr 29, 2014 9:30 pm UTC

It's more of a skypiercer, anyway.
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Re: What-if #0094: Billion-Story Building

Postby threap » Tue Apr 29, 2014 10:02 pm UTC

Good job Keira is not British. In traditional British usage, a Billion is a million million, 1012 - the term "milliard" was used to denote 1000 million / 109.

Fortunately for the solar system, the US meaning of the term "billion" now dominates...

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Re: What-if #0094: Billion-Story Building

Postby sonar1313 » Tue Apr 29, 2014 10:49 pm UTC

HES wrote:Do we even have the materials to do this? We certainly won't be making it out of wood:

(Spoilered for size)
Spoiler:
Image


This was the first question I had. If the footprint of the building was the same as that of the Empire State Building, it would have about half the volume of the Earth. We'd probably have to mine the earth's core to get enough iron. The second question I had: if this building got built at the equator, wouldn't the force of the earth's spin dislodge it from its foundation? And if you had a foundation strong enough to hold it in place, well, I've forgotten all I ever knew about angular velocity, but I would hazard a guess that the top floors of the building would be moving fast enough that if it hit anything, it would create a cataclysmic event beyond what's described in the one-second-day what-if.

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Re: What-if #0094: Billion-Story Building

Postby speising » Tue Apr 29, 2014 11:11 pm UTC

for a starter, anything above geosync orbit would have negative gravity, and since that includes most of it, it would be torn off it's foundations.
and i don't even want to think of the forces involved if it wasn't built at the equator. (well, a pole would maybe be the most benign place in this regard.)

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Re: What-if #0094: Billion-Story Building

Postby mcdigman » Tue Apr 29, 2014 11:26 pm UTC

for a starter, anything above geosync orbit would have negative gravity, and since that includes most of it, it would be torn off it's foundations.
and i don't even want to think of the forces involved if it wasn't built at the equator. (well, a pole would maybe be the most benign place in this regard.)


Well, that would have been true before, but the presence of this building would change what 'geosynchronous orbit' means -

A quick moment of inertia calculation, assuming the tower is a straight rod, suggests that if the tower only weighed as much as the moon, it would slow down one earth day to about 10 earth years. If more realistically (from the picture) it had the mass of jupiter, it would slow down a day to 264000 years. Except that now the skyscraper's gravitational influence on the earth is now similar in magnitude to the sun's, so we'd actually have to start factoring in the system's self gravity in our requirement's for the system's structural integrity...

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Re: What-if #0094: Billion-Story Building

Postby donbock » Tue Apr 29, 2014 11:28 pm UTC

Isostatic subsidence would convert the few floors (less than 1%) of the Keira-skyscraper into basement levels. Even if it sank all the way to the Earth's core, the overall height of the Keira-skyscraper wouldn't be diminished by much.

Seems like the mass of a Keira-skyscraper would be large enough for its gravity to pull it into a spherical shape. Maybe if you built it out of balsa wood...

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Re: What-if #0094: Billion-Story Building

Postby asdf28 » Tue Apr 29, 2014 11:47 pm UTC

Another problem, if there aren't enough already, is time. I don't really see the point of requesting floors to be built, that I'll never see. If I spend 1 minute visiting floor, and change floors once a minute for 10 hours a day; I can only visit about 220,000 stories in a year, and 15,000,000 stories in a lifetime.

So . . . I'll be modest. Now I want a 15,000,000 story skyscraper.

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Re: What-if #0094: Billion-Story Building

Postby CrunchyFrog » Wed Apr 30, 2014 12:00 am UTC

I loved this one enough to create an account about it. Bonus to whoever can rewrite this to pass the Up-Goer 5 test.

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Re: What-if #0094: Billion-Story Building

Postby poxic » Wed Apr 30, 2014 12:00 am UTC

If you got a hotrod elevator to travel at ten floors per second, it would take about three years to get to billionth floor.

To get there in 24 hours, the elevator would need to travel on the order of 35,000 meters per second. That's only Mach 64 or so.
Last edited by poxic on Wed Apr 30, 2014 12:04 am UTC, edited 1 time in total.
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Re: What-if #0094: Billion-Story Building

Postby imantodes » Wed Apr 30, 2014 12:02 am UTC

It seems like it would be simpler to change your target audience. Build a skyscraper for springtails. Each floor can probably be a millimeter or less. You don't need to worry about elevators, because springtails don't know how to press buttons. A billion millimeters is still rather tall, but... less unfeasible.

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Re: What-if #0094: Billion-Story Building

Postby Showsni » Wed Apr 30, 2014 12:20 am UTC

Good job Keira lives in America, or it would be a thousand times bigger than that!

(I refuse to use the short scale.)

If we just had a thousand million cube shaped rooms and had to stack them to make a building (with as much width and breadth at the base as we liked) how feasible would the resulting building be and what shape would be best for it?

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Re: What-if #0094: Billion-Story Building

Postby maxh » Wed Apr 30, 2014 12:25 am UTC

A (potential) solution to the problem of collapse is that there's no requirement that each floor be of equal size. A pyramidal building might be able to support its own weight. (Of course, the problem of materials then becomes greater.)

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Re: What-if #0094: Billion-Story Building

Postby Zee_Tee » Wed Apr 30, 2014 12:54 am UTC

Once she gets a little older, she might be interested in checking out Tsutomu Nihei's Blame! series.

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Re: What-if #0094: Billion-Story Building

Postby Djehutynakht » Wed Apr 30, 2014 1:03 am UTC

These are engineering (and physics) challenges that we can overcome.

Let's do it.

Maybe we can build it on Jupiter or such.

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Re: What-if #0094: Billion-Story Building

Postby rmsgrey » Wed Apr 30, 2014 1:14 am UTC

Djehutynakht wrote:These are engineering (and physics) challenges that we can overcome.

Let's do it.

Maybe we can build it on Jupiter or such.


I think you meant "build it out of Jupiter"...

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Re: What-if #0094: Billion-Story Building

Postby Djehutynakht » Wed Apr 30, 2014 3:11 am UTC

...we could try that.

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Re: What-if #0094: Billion-Story Building

Postby SuperSteve » Wed Apr 30, 2014 5:08 am UTC

speising wrote:for a starter, anything above geosync orbit would have negative gravity, and since that includes most of it, it would be torn off it's foundations.
and i don't even want to think of the forces involved if it wasn't built at the equator. (well, a pole would maybe be the most benign place in this regard.)


What if we build two of them on opposite sides of the world and connect them to each other? Equal and opposite forces sum to zero, so there's no net force on the foundation or the earth.

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Re: What-if #0094: Billion-Story Building

Postby willpellmn » Wed Apr 30, 2014 5:14 am UTC

I like the alternate elevator proposals, though I don't really get how the "roller coaster" would work.

In general, while the idea is pretty ludicrous from a science-fiction perspective, I could totally see it being used for fantasy. Maybe when she reaches her angsty teen years, Keira can write a story about Hell being some insane extradimensional superworld that's the size of the entire Milky Way Galaxy, with every inhabited planet having a single gigantic tower that houses the souls of everyone that ever died on that planet in the entirety of the species's lifespan (gravity and such would obviously be different in such a metareality). It could become the "Twilight" of its generation and Keira could retire at the age of 16. Better be nice to her now just in case, Dad....

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Re: What-if #0094: Billion-Story Building

Postby asdf28 » Wed Apr 30, 2014 5:30 am UTC

Showsni wrote:If we just had a thousand million cube shaped rooms and had to stack them to make a building (with as much width and breadth at the base as we liked) how feasible would the resulting building be and what shape would be best for it?


With somewhat arbitrary parameters (minimize cost of foundation, minimize cost of not having the building collapse,
minimize exterior perimeter; almost specified in http://ohcamacj.dyndns.org:8088/~jonath ... meters.txt), I get a 14-story disk-like building with a radius of 4925 rooms.

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Re: What-if #0094: Billion-Story Building

Postby NotAllThere » Wed Apr 30, 2014 6:04 am UTC

Let's say an average book has a volume of .001m3. Then a billion books will have a volume of about 1 km3. The largest building in the world is the Boeing Everett factory, at (over) 0.01 km3. So to hold a billion stories, you'd need around 100 Boeing Everett factories. Not entirely unfeasible. But it would take a while to fill it, since there's currently only about 300'000'000 books in the world, and not all of them are stories.

But I suppose you could invoke L-space.
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Re: What-if #0094: Billion-Story Building

Postby keithl » Wed Apr 30, 2014 7:34 am UTC

Perhaps Keira's daddy did not understand her request. Postulate that she actually wants "story" as in "tale". The 1948 film noir "The Naked CIty" ends with the line "There are eight million stories in the naked city. This has been one of them." Perhaps she merely wants a building that will hold a billion people with one story each. At 200m2 per person (with passageways), 100 stories high, that is a 45 by 45 kilometer building.

Or perhaps she just wants the stories, sans people, as movies on DVD. One DVD disk in a standard case is about 400cm3. A billion cases could be jammed into 400,000 cubic meters, about 40% of the volume Empire State Building. For Keira to access to her vast DVD collection, we will need aisles and shelves low enough for her to reach, and ceilings tall enough for Daddy. So, assume aisles on 1.5 meter centers, 5 shelves high, and 3 meters between floors. At 1.5 cm per DVD width, that is about 7,000,000 cubic meters, half the volume of the Boeing 787 assembly hangar at Everett, Washington, the largest building in the world.

If we store the movies on hard disk, 1000 movies in 6TB in 400 cm3, Daddy can pack the drives pretty dense because only one needs to be powered at a time. At 2.5 million movies per cubic meter, that is only 400 cubic meters, about 200 square meters of floor space stacked two meters high. They would fit in my house - though their weight would collapse the floor.

By the time Keira reaches adulthood, we will routinely store information in DNA. George Church's book "Regenesis" has been coded in DNA, and he duplicated 70 billion copies, three times as many copies as the 100 most popular books of all time. At 2E21 bits per gram, and a DNA density of 1.7, the 48E18 bits of all those movies would fit in about 15 cubic millimeters, Barbie's teacup.

Maybe Keira will want a building containing a quintillion stories by that time - a long trillion for you ancient Brits.

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Re: What-if #0094: Billion-Story Building

Postby NotAllThere » Wed Apr 30, 2014 7:49 am UTC

Movies are too wasteful of space. Let's do it via epub. According to this http://blog.safaribooksonline.com/2009/11/16/how-big-is-the-average-epub-book/ the median size is 3MB. So a billion stories is 3'000'000'000MB ~ 3PB. Even using a bunch of current paltry 3TB hard drive, that's only 1000 harddrives I could fit that in my cellar.
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Re: What-if #0094: Billion-Story Building

Postby keithl » Wed Apr 30, 2014 7:50 am UTC

BTW, if Keira wants a billion story structure, all she needs is some Upsidaisium.

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Re: What-if #0094: Billion-Story Building

Postby speising » Wed Apr 30, 2014 8:13 am UTC

NotAllThere wrote:Movies are too wasteful of space. Let's do it via epub. According to this http://blog.safaribooksonline.com/2009/11/16/how-big-is-the-average-epub-book/ the median size is 3MB. So a billion stories is 3'000'000'000MB ~ 3PB. Even using a bunch of current paltry 3TB hard drive, that's only 1000 harddrives I could fit that in my cellar.

that's strange. i think i don't have a lot of ebooks above 1MB. i just looked at a folder of 773 epubs with 219MB total.

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Re: What-if #0094: Billion-Story Building

Postby Ekaros » Wed Apr 30, 2014 8:32 am UTC

In the end the volume of it isn't that big... Also mass isn't that massive either. If thee footprint was to be on scale of old school skyscraper...

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Re: What-if #0094: Billion-Story Building

Postby PhilHibbs » Wed Apr 30, 2014 8:38 am UTC

donbock wrote:Isostatic subsidence would convert the few floors (less than 1%) of the Keira-skyscraper into basement levels.

It wouldn't sink into the Earth. The Earth would sink into it.

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Re: What-if #0094: Billion-Story Building

Postby CharlieP » Wed Apr 30, 2014 8:42 am UTC

threap wrote:Good job Keira is not British. In traditional British usage, a Billion is a million million, 1012 - the term "milliard" was used to denote 1000 million / 109.


No, things would be much, much easier if Keira were British, since she would simply be asking for a building that housed a billion tales. A structure with 10^9 or 10^12 floors would be a billion-storey building. :D
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Re: What-if #0094: Billion-Story Building

Postby CharlieP » Wed Apr 30, 2014 8:50 am UTC

American billions, trillions etc. bug me because the prefix doesn't really mean anything - at least in the long scale "bi" = two lots of 000,000, "tri" = three lots of 000,000 etc.

But this makes numbers stupidly large, so why not recalibrate the short scale so that billion = 10^6, trillion = 10^9 etc. You could either get rid of "million" entirely or use it as an acceptable alternative for "thousand" (which would make billions of people millionaires overnight).

I see no practical downsides to converting everything. :lol:
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Re: What-if #0094: Billion-Story Building

Postby dalcde » Wed Apr 30, 2014 9:57 am UTC

CharlieP wrote:American billions, trillions etc. bug me because the prefix doesn't really mean anything - at least in the long scale "bi" = two lots of 000,000, "tri" = three lots of 000,000 etc.

But this makes numbers stupidly large, so why not recalibrate the short scale so that billion = 10^6, trillion = 10^9 etc. You could either get rid of "million" entirely or use it as an acceptable alternative for "thousand" (which would make billions of people millionaires overnight).

I see no practical downsides to converting everything. :lol:

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Re: What-if #0094: Billion-Story Building

Postby Pfhorrest » Wed Apr 30, 2014 10:25 am UTC

If we're going to revise the number naming scale, let's make one that both gives us finer name resolution at the lower numbers of digits, and a much larger domain reaching into the higher numbers of digits, by naming only the square of the previously named number.

Ten
Hundred = ten squared
Ten hundred
Myriad = Hundred squared
Ten myriad
Hundred myriad
Ten hundred myriad
Byriad = Myriad squared
Ten byriad
Hundred byriad
Ten hundred byriad
Myriad byriad
Ten myriad byriad
Hundred myriad byriad
Ten hundred myriad byriad
Tyriad = Byriad squared
[fill in fifteen orders of magnitude with the obvious pattern]
Quadyriad = Tyriad squared
[fill in thirty-one orders of magnitude with the obvious pattern]
Quintyriad = Quadyriad squared
[fill in sixty-three orders of magnitude with the obvious pattern]
Sextyriad = Quintyriad squared
[and so on]

So an n-yriad is 10^((1+n)^2).

Then again, a short scale n-illion is 10^(3+3n), and a long-scale n-illion is 10^(6n), so they're all pretty simple patterns where the significance of the 'n' is pretty obvious.
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Re: What-if #0094: Billion-Story Building

Postby CharlieP » Wed Apr 30, 2014 10:51 am UTC

So, a tenth of a sextyriad is ten hundred myriad byriad tyriad quadyriad quintyriad? I like it.
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Re: What-if #0094: Billion-Story Building

Postby cellocgw » Wed Apr 30, 2014 11:21 am UTC

Mmmmmm... peanut butter! I hope it's the kind with crunchy bits -- I add whole flax seed to mine for even more crunchablemunchiness!

Wait, what were we talking about?
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Re: What-if #0094: Billion-Story Building

Postby xorsyst » Wed Apr 30, 2014 11:23 am UTC

I've travelled 36 years into the future to say one word:

Paternoster

Much more space-efficient than a standard lift [elevator]


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