Page 1 of 4

### What-If 0108: "Expensive Shoebox"

Posted: Wed Aug 13, 2014 10:03 pm UTC
Expensive Shoebox

Obviously antimatter would be off the scale, but suffers from the same issue as plutonium.

So how about filling the shoebox with nothing. The purest vacuum you can get. Just lofting it into LEO won't be too pricey, but getting it out into intergalactic space, I imagine that's going to cost a number with a lot of zeroes. Then again, if you try and bring it back outgassing would ruin your vacuum, unless you have a shoebox made of something other than the usual cardboard.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Wed Aug 13, 2014 10:22 pm UTC
cantab314 wrote:Expensive Shoebox

Obviously antimatter would be off the scale, but suffers from the same issue as plutonium.

So how about filling the shoebox with nothing. The purest vacuum you can get. Just lofting it into LEO won't be too pricey, but getting it out into intergalactic space, I imagine that's going to cost a number with a lot of zeroes. Then again, if you try and bring it back outgassing would ruin your vacuum, unless you have a shoebox made of something other than the usual cardboard.

That's a pretty good thought. The question asks what is the most expensive way to fill a shoebox, without specifying that the filling must be expensive or retain its value. I think filling it with some gas from Jupiter would work, since you have to escape from Jupiter's gravity to get it back.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Wed Aug 13, 2014 10:30 pm UTC
Assuming you could find a few \$1m postage stamps at auction, I think this is in the \$100 billion to \$1 trillion range - \$1M/stamp x 10-100 stamps/ML x 1000 ML/L x 10 L?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Wed Aug 13, 2014 10:35 pm UTC
If you want to actually fill it with something, then Cerium136 is a good candidate.
Rough cost estimate is 80\$ per mg for an enrichment of 20%. Cerium has a density of about 6.77g/cm^3, so our 15 liter shoebox would be slightly above 8 billion. I would assume that an increased enrichment leads to a drastic increase in price, so I wouldnt be surprised if you can get above 100 billion with it.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 12:15 am UTC
Is the large number including the Knuth (I just love saying "canoeth"!) notation something specific, or just a general "this is a funny-looking big thing"?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 12:25 am UTC
I am prety sure that that check/cheque is more expensive than the number of plank lengths in the universe. That assumes that any bank would accept that check/cheque.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 12:44 am UTC
tagno25 wrote:I am prety sure that that check/cheque is more expensive than the number of plank lengths in the universe. That assumes that any bank would accept that check/cheque.

That's actually not as useful an estimate as it seems, given that 10^200 is trillions and trillions of times larger than the number of Planck volumes in the visible universe. That check becomes ridiculous once it hits the seventh digit.

I'm still blanking on Su and it's driving me crazy because I should know that notation. Update: can't find it on Wolfram. Help me guys don't make me ask on SE like an idiot.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 1:15 am UTC
I think it might actually be Sn? There's mention of that in the Wikipedia article on the Busy Beaver problem - http://en.wikipedia.org/wiki/Busy_beaver

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 1:35 am UTC
Although, if you were to fill the shoebox with plutonium, it would not in fact cause a gigantic nuclear explosion, but rather only a small one, just enough to eject the plutonium ingots out and away from each other, ready for the next person to try it.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 2:09 am UTC
I have a question. Where can we find out the budgets for the folks who manufacture transuranic elements? Just one atom would cost thousands of dollars! But would Element 114 necessarily be more expensive to manufacture than Elements 113, 112, 111, etc.? In calculating the cost of one atom, should we include the wages and salaries of everybody who works in the lab? So how much would a shoebox full of Element 114 cost? I know, it's unstable, but still...

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 2:24 am UTC
How densely can antihydrogen currently be stored? It electrically neutral so it should suffer from the repulsion problem that antiproton storage suffers, but then I'm not sure how it can actually be trapped in the first place either. Assuming we have sufficient density the question is how long we can store it and how quickly we can produce it. I've read that the record for storage duration is 16 minutes. Assuming we can fit the trap into a shoebox, and it takes a minute to move the trap into the shoebox (or to place the shoebox over the trap), the question is becomes "how much does it cost to run CERN to produce antihydrogen for 15 minutes?" I'm guessing that's pretty spendy.

But as bachaddict pointed out the question doesn't technically ask us to retain the value in the box. So how to we measure value then? One obvious way is to do something fantastically expensive to accomplish the filling of the box and take the expense of the operation. I think if we're being fair we have to say that only things that lead directly to filling the box count. So flying to Jupiter to fill it with Jupiter gas is legitimate. Buying all of the Earth's mining production for a year to select a random sample to place into the box is not. But if we're being particularly nefarious maybe we can measure the value of the box as the amount people would be willing to pay for us _not_ to fill the box. Shoebox blackmail or ransom, essentially. It might not be terribly expensive to fill the box with a smallpox culture, but you could probably extort a hefty ransom not to. But I think we can do even better. I propose to fill the box with brainstem. Specifically I propose to fill the box with tiny cross sections of human medulla oblongata. We can take cross sections about 30 nanometers wide, and an adult medulla oblongata is about 2cm x 1.25cm at its narrowest. Our 10 liter box can fit about a billion of these cross sections. What's the combined wealth of the top 1/7 of the world's population?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 2:29 am UTC
Along the lines of stamps and other valuable collectibles, are there any really valuable relics or artwork that fit in a shoebox? I imagine a (real and verifiable) Shroud of Turin might be worth a lot, and might fit in a shoebox. Most of the other "priceless" things I can think of off the top of my head are too big (Collector's Edition set of Dead Sea scrolls, Ark of the Covenant, etc.) or too cheap (the Hope Diamond is only about a quarter-billion).

The idea is at least as valid as the manmade element one; the Catholic church may not pay tens of billions for an artifact, but you won't find any scientists ponying up for a shoebox full of ununoctium or antihydrogen, either.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 2:34 am UTC
Wouldn't an SD card filled with RSA keys for all current bitcoins be like 7 billion dollars (and not even fill up the sd card)? and then you could put something else on top of it? I feel like there was a lot of opportunity to mix and match things that are small, and extremely valuable.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 2:44 am UTC
Trickster wrote:
tagno25 wrote:I am prety sure that that check/cheque is more expensive than the number of plank lengths in the universe. That assumes that any bank would accept that check/cheque.

That's actually not as useful an estimate as it seems, given that 10^200 is trillions and trillions of times larger than the number of Planck volumes in the visible universe. That check becomes ridiculous once it hits the seventh digit.

Given that, I'm wondering how he wrote out the number longhand in the small box on the che{ck,que}.

And since a bounced check is worth nothing and I doubt anyone's bank account contains (1000^1000^1000*etc) in any currency, I think you have to step back to the trillion-dollar commemorative coin. Or (1000^1000^1000*etc)-dollar commemorative coin, if you like that number better.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 5:05 am UTC
The labor theory of value suggests the most expensive way to fill a shoebox is to spend a lot of time doing so. As things stand, the shoebox is probably appreciating in value quite nicely.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 5:29 am UTC
Wouldn't a stack of \$500,000,000 bearer bonds be a bit more than \$2 billion? Even if they had to be folded a little to fit? But those are probably counterfeit.

How about art? According to Wikipedia http://en.wikipedia.org/wiki/List_of_most_expensive_paintings the most expensive painting is Cézanne's "The Card Players" http://en.wikipedia.org/wiki/The_Card_Players which was last sold for more than \$250 million in 2011. That's a canvas about 47.5 × 57 cm which if carefully rolled up could easily fit. Given inflation and the increase in value a few of those rolled up together could top the \$2 billion mark.

And that could be done in the real world without "What-If" style technology. According to Guiness (an indirect reference at http://www.guinnessworldrecords.com/news/2011/10/confirmed-brahim-takioullah-sets-world-record-for-largest-feet/) Robert Wadlow had feet 47 cm long, which would mean a shoe box that could easily contain the canvases without damaging them.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 5:33 am UTC
How big is a small house?

What is a small house build of? 251kg for such seems awfully little...

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 6:39 am UTC
AJMansfield wrote:Although, if you were to fill the shoebox with plutonium, it would not in fact cause a gigantic nuclear explosion, but rather only a small one, just enough to eject the plutonium ingots out and away from each other, ready for the next person to try it.

Exactly how small is the smallest possible nuclear explosion? Are we talking "oh shit my room is on fire" small or "oh shit my block is a crater" small?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 6:54 am UTC
Pfhorrest wrote:Exactly how small is the smallest possible nuclear explosion? Are we talking "oh shit my room is on fire" small or "oh shit my block is a crater" small?

It's "oh shit we all have radiation poisoning" small, see http://en.wikipedia.org/wiki/Demon_core for reference.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 8:10 am UTC
Mirkwood wrote:The labor theory of value suggests the most expensive way to fill a shoebox is to spend a lot of time doing so. As things stand, the shoebox is probably appreciating in value quite nicely.

Perhaps, but it's wrong.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 9:04 am UTC
CraXy wrote:Wouldn't an SD card filled with RSA keys for all current bitcoins be like 7 billion dollars (and not even fill up the sd card)? and then you could put something else on top of it? I feel like there was a lot of opportunity to mix and match things that are small, and extremely valuable.

I like that idea! Buying all existing cryptocurrency would cost about 9 billion dollars. Of course the price would rise as it was bought, increasing the cost.
I wonder what zero-day exploits are worth by data size.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 11:02 am UTC
If we limit the question a bit, by saying we cannot create new things to put in the box (jupiter gas, cheques, minting new coins...) and can only use existing valuables (RSA keyes for BTC, etc...), then stuffing the box full of credit cards/cash cards belonging to the richest people on the planet might be a good idea...

...until they get recalled, that is.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 11:23 am UTC
Haha, checks. I find it amusing how most Americans have no clue how backwards their banking system is that so many people have to use checks. Here you can't even *get* checks. I mean, what a stupid concept, a non-verifiable piece of paper that the user can write for an arbitrary sum? Can you say "just asking for fraud"?

Checks? Come on, join the modern world. :Þ

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 12:38 pm UTC
Correct me if I'm wrong, but shouldn't the number of swords hit max at 2^31 - 1? Or is this some floating-point thing I just never really understood?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 1:16 pm UTC
I'm with bachaddict, I don't think Randal quite answered the question that was asked. He was focused on the value in the box and not the cost of getting it there.

If every human destroyed everything they owned (including themselves) and a tiny sample of each mess was added to the box, it would then cost everything humanity ever created along with everything we'd ever be capable of creating. The total worth of our species used to fill a shoe box.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 1:19 pm UTC
KarenRei wrote:Haha, checks. I find it amusing how most Americans have no clue how backwards their banking system is that so many people have to use checks. Here you can't even *get* checks. I mean, what a stupid concept, a non-verifiable piece of paper that the user can write for an arbitrary sum? Can you say "just asking for fraud"?

Checks? Come on, join the modern world. :Þ

I'm not saying you're wrong, but here in America there are a lot of people who trust checks (they're not that different from cash; they're physical and you have to mail them or deliver them in person, and they're more secure than cash - in theory, but I'm presenting an opinion here that I don't hold - because only the stated recipient can spend them), but don't trust online banking, or even the use of credit cards. Much less letting a cell phone know your financial information! You can't "hack" a check, but who knows what can happen when the computers and satellites know your information?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 2:03 pm UTC
mathmannix wrote: You can't "hack" a check, but who knows what can happen when the computers and satellites know your information?

Sadly, checks are rather easily hacked. Granted, for a significant fee, you can have your bank refuse a check (at least under some circumstances), but more than once a crook printed his own checks w/ someone else's account number in the mag-ink codes along the bottom. I recall one case where a fella printed "vanilla" deposit slips with his account number on them and stuffed them in a bank's lobby. Everyone who used one of these slips to deposit ended up crediting the crook's account.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 3:04 pm UTC
Alsadius wrote:I think it might actually be Sn? There's mention of that in the Wikipedia article on the Busy Beaver problem - http://en.wikipedia.org/wiki/Busy_beaver

Yeah, I was thinking busy beaver, but I haven't seen it written with the script n before... but it must be. It makes too much sense--er, as much as any of that check makes "sense", anyway.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 3:10 pm UTC
"And the box itself is probably worth something too."

Obligatory Futurama reference.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 3:34 pm UTC
KarenRei wrote:Haha, checks. I find it amusing how most Americans have no clue how backwards their banking system is that so many people have to use checks. Here you can't even *get* checks. I mean, what a stupid concept, a non-verifiable piece of paper that the user can write for an arbitrary sum? Can you say "just asking for fraud"?

Checks? Come on, join the modern world. :Þ
What country is this?

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 4:08 pm UTC
DavesNotHere wrote:And that could be done in the real world without "What-If" style technology. According to Guiness (an indirect reference at http://www.guinnessworldrecords.com/news/2011/10/confirmed-brahim-takioullah-sets-world-record-for-largest-feet/) Robert Wadlow had feet 47 cm long, which would mean a shoe box that could easily contain the canvases without damaging them.

Except the question explicitly stated that it was a "size 11 shoebox", not just some arbitrary shoebox.

So while your assertion may hold true, inasmuch as there may exist a box for shoes large enough to contain the painting, in the context of this What-If, it doesn't apply.

That, and Mr. Wadlow likely had all of his shoes custom-made, and with shoes that large a cordwainer may not even bother with also creating a custom box in which to place the shoe for transport; it's not going to be on a store shelf, after all. Shoe bags are much more convenient, cheaper to make for such things, and take up less space when used to store shoes in a closet (although they don't stack as nicely).

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 4:13 pm UTC
Zowayix wrote:
KarenRei wrote:Haha, checks. I find it amusing how most Americans have no clue how backwards their banking system is that so many people have to use checks. Here you can't even *get* checks. I mean, what a stupid concept, a non-verifiable piece of paper that the user can write for an arbitrary sum? Can you say "just asking for fraud"?

Checks? Come on, join the modern world. :Þ

What country is this?

Imma guess Kenya. Someone over there is about to wire me a ton of money, yes yep.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 4:15 pm UTC
KarenRei wrote:Haha, checks. I find it amusing how most Americans have no clue how backwards their banking system is that so many people have to use checks. Here you can't even *get* checks. I mean, what a stupid concept, a non-verifiable piece of paper that the user can write for an arbitrary sum? Can you say "just asking for fraud"?

Checks? Come on, join the modern world. :Þ

What can I say.

We use the Imperial system.
Some people still pay \$0.25 for a text message.
This: https://arkencounter.com/

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 4:18 pm UTC
Elite racehorse semen vials also put you in the billion dollar range.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 4:53 pm UTC
Mikeski wrote:The idea is at least as valid as the manmade element one; the Catholic church may not pay tens of billions for an artifact, but you won't find any scientists ponying up for a shoebox full of ununoctium or antihydrogen, either.

I dunno - if you have a shoebox sized stable storage device that let you keep the exotic matter intact long enough to conclude a sale and delivery, I imagine a lot of scientists would be willing to pay for it. And if not, the world's military would definitely be interested in something capable of delivering blocks of antimatter to a target...

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 5:30 pm UTC
Zowayix wrote:
KarenRei wrote:Haha, checks. I find it amusing how most Americans have no clue how backwards their banking system is that so many people have to use checks. Here you can't even *get* checks. I mean, what a stupid concept, a non-verifiable piece of paper that the user can write for an arbitrary sum? Can you say "just asking for fraud"?

Checks? Come on, join the modern world. :Þ
What country is this?

Iceland, but my understanding is that there's lots of other countries in Europe that are like this as well, not just us.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 5:56 pm UTC
rmsgrey wrote:
Mikeski wrote:The idea is at least as valid as the manmade element one; the Catholic church may not pay tens of billions for an artifact, but you won't find any scientists ponying up for a shoebox full of ununoctium or antihydrogen, either.

I dunno - if you have a shoebox sized stable storage device that let you keep the exotic matter intact long enough to conclude a sale and delivery, I imagine a lot of scientists would be willing to pay for it. And if not, the world's military would definitely be interested in something capable of delivering blocks of antimatter to a target...

Now you're filling the box with technology that doesn't exist (yet), so you might as well fill it with the cures for cancer or aging or AIDS, or a warp drive or a time machine, or some other super-sci-fi gear instead. Or the formulas/designs for hundreds of such things, stored on microSD cards.

Even if you are personally nonreligious (or of another religion), there are a few billion religious people who would find an item owned by their deity/chief prophet/etc. to be of immense value.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 6:00 pm UTC
I'm surprised DNA has not been mentioned yet - it is the densest store of information in current use, and information in a form that can make protein machines that make stuff. DNA for viral vectors that can cure all diseases, DNA for bacteria that poop transistors, DNA for photosynthetic golems that turn landfills into starships. Probably all that DNA would fit in a cubic millimeter. We could devote another cubic millimeter to the DNA for the computation system that figures out what to fill the rest of the shoebox with, along with DNA to embed the user manuals in our primitive brains.

Since it would take vast resources to design all this superduper DNA, the expense of the DNA would be incomprehensibly huge, but "the most expensive way to fill" the box with this DNA would be to do the research and development very, very inefficiently. I can suggest a few of my former co-workers and managers to staff this team. We will need some very smart physicists to develop access to the myriad of alternate universes necessary to provide enough resources for this team to waste in their development process.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 6:04 pm UTC
I'm wondering if that is Randall's actual signature on that check?

I'm off to my bank now to find out.

### Re: What-If 0108: "Expensive Shoebox"

Posted: Thu Aug 14, 2014 6:13 pm UTC
I'm only certain of how to calculate the number of digits of the first third of that monstrosity in the check. It's something like 10^4500 digits, plus whatever the Knuth and that third bit add.