What-If 0106: "Ink Molecules"

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What-If 0106: "Ink Molecules"

Postby willpellmn » Thu Jul 24, 2014 2:40 am UTC

http://what-if.xkcd.com/106

Who exactly are these people who don't like the word "moist"? I think it's a great word; sounds almost exactly like what it describes. C'mon, baby, gimme a big moist kiss.

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Re: What-If 106: "Ink Molecules"

Postby rhomboidal » Thu Jul 24, 2014 3:01 am UTC

It wouldn't surprise me if HP started secretly depleting global cephalopod populations to keep ink prices artificially high.

Everyone should stop printing in protest. Or rather, start printing, and then stop.

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Re: What-If 106: "Ink Molecules"

Postby helo darqness » Thu Jul 24, 2014 3:21 am UTC

rhomboidal wrote:It wouldn't surprise me if HP started secretly depleting global cephalopod populations to keep ink prices artificially high.

Everyone should stop printing in protest. Or rather, start printing, and then stop.


Xerox has patented inkless printing. I'm not sure how far along in development and usage it is, but I remember reading about it a while ago. Talking about sticking it to the man, while being the man you're sticking it to.

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Re: What-If 106: "Ink Molecules"

Postby jimbo1qaz » Thu Jul 24, 2014 3:58 am UTC

Another reason I use refillable cartridges. Far, far cheaper and work just as well.
Only problem is hand stains, and slight chance of clogging the printer, possibly eventually putting it out of service.
Still far FAR cheaper than buying overpriced cartridges.

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Re: What-If 106: "Ink Molecules"

Postby npd » Thu Jul 24, 2014 4:04 am UTC

Jenny, Jonathan Larson/Rent, Jean Valjean, Manhattan -- is there some connection?

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Re: What-If 106: "Ink Molecules"

Postby HES » Thu Jul 24, 2014 5:16 am UTC

This is why I buy unbranded ink. It used to be ~£30 for 3 full sets, now it's closer to £12. I expected the price to go up as the printer got older and therefore rarer, but apparently not.

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Re: What-If 106: "Ink Molecules"

Postby Eternal Density » Thu Jul 24, 2014 5:56 am UTC

I love the squid pic at the end!
willpellmn wrote:http://what-if.xkcd.com/106

Who exactly are these people who don't like the word "moist"? I think it's a great word; sounds almost exactly like what it describes. C'mon, baby, gimme a big moist kiss.

I avoid it when writing fiction. Though I had to settle for "damp", which isn't much better.
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Re: What-If 106: "Ink Molecules"

Postby eviloatmeal » Thu Jul 24, 2014 6:24 am UTC

Image
This is my new favorite Randall thing. I think I might have to print it out and hang it above the printer.
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Re: What-If 106: "Ink Molecules"

Postby bachaddict » Thu Jul 24, 2014 6:40 am UTC

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Shouldn't that be 'this really cool dinosaur'?
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figure 3 seems to be wrong

Postby mrob27 » Thu Jul 24, 2014 7:06 am UTC

Randall wrote: So our answer, according to Fermi estimation, is in the neighborhood of a high 18-digit number.

... but the illustration clearly shows a 21-digit number:
Image
7 groups of 3 is 21 digits

... with the title text "'Plus or minus half a digit' is a weird concept.", referring to the error bars which are centered at the end of the last digit.

I think this is an error, and the example number should have 18 digits...
Spoiler:
what-if 106 21-digit number.png
Figure 3 from What-if 106
what-if 106 21-digit number.png (4.24 KiB) Viewed 8325 times
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Re: What-If 106: "Ink Molecules"

Postby CharlieP » Thu Jul 24, 2014 9:56 am UTC

It would have been cooler had Randall ended with a more self-descriptive statement, as a nod to http://xkcd.com/688/.

e.g.

"This sentence contains 1,714,726,842,976,215,214,897 molecules of ink".
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Re: What-If 106: "Ink Molecules"

Postby HES » Thu Jul 24, 2014 10:02 am UTC

CharlieP wrote:It would have been cooler had Randall ended with a more self-descriptive statement

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Re: What-If 106: "Ink Molecules"

Postby mojacardave » Thu Jul 24, 2014 10:28 am UTC

Hooray for a What-If that doesn't result in the inevitable demise of humanity (via squicky squirrelly horror).

rhomboidal wrote:It wouldn't surprise me if HP started secretly depleting global cephalopod populations to keep ink prices artificially high.

Everyone should stop printing in protest. Or rather, start printing, and then stop.


An ink price protest would be confusing - you'd have to wield blank signs.

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Re: What-If 106: "Ink Molecules"

Postby NoMouse » Thu Jul 24, 2014 10:51 am UTC

I guess I'm not the only one who asked this question: Can the squid ink really be used for printing?

Apparently, it can.

But I'm afraid it wouldn't work well in an ink-jet printer. And even if it would, it would start to smell, unless you store your printer in the fridge.

You can also eat it.
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Re: What-If 106: "Ink Molecules"

Postby cellocgw » Thu Jul 24, 2014 11:36 am UTC

FWIW, the concept of "half a digit" is actually used here and there. Start with an "order of magnitude" estimate, which basically says pick the "x" in 10x , then shift by "half a digit" in the log sense: either multiply by 5 or divide by 2 (or the other way around :mrgreen: ).



Meanwhile, I heartily encourage all primary school math classes to include estimation in the curriculum. It's a great skill and avoids the infamous "but that's the answer my calculator gave" response to an answer that's clearlly off by a factor of 100.
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Re: figure 3 seems to be wrong

Postby BrianK » Thu Jul 24, 2014 12:51 pm UTC

mrob27 wrote:
Randall wrote: So our answer, according to Fermi estimation, is in the neighborhood of a high 18-digit number.

... but the illustration clearly shows a 21-digit number:
Image
7 groups of 3 is 21 digits

... with the title text "'Plus or minus half a digit' is a weird concept.", referring to the error bars which are centered at the end of the last digit.

I think this is an error, and the example number should have 18 digits...
Spoiler:
what-if 106 21-digit number.png


I get the 8675309 reference ("Jenny, I got your number"). But none of the other digits are triggering anything. Does anyone see any other number references in there?

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Re: What-If 106: "Ink Molecules"

Postby richP » Thu Jul 24, 2014 1:46 pm UTC

eviloatmeal wrote:Image
This is my new favorite Randall thing. I think I might have to print it out and hang it above the printer.

Pshaw. ne ful no: you need separate squids for each color.
On the plus side, cleaning the cartridges is a really simple process, you just bring a sperm whale close to the printer.

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Re: figure 3 seems to be wrong

Postby cellocgw » Thu Jul 24, 2014 2:07 pm UTC

BrianK wrote:
mrob27 wrote:
Randall wrote: So our answer, according to Fermi estimation, is in the neighborhood of a high 18-digit number.

... but the illustration clearly shows a 21-digit number:
Image
7 groups of 3 is 21 digits



I get the 8675309 reference ("Jenny, I got your number"). But none of the other digits are triggering anything. Does anyone see any other number references in there?


Well, try dialing 525.6002 and 460.1212 :twisted: (no, I haven't)
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Re: What-If 106: "Ink Molecules"

Postby m1el » Thu Jul 24, 2014 2:35 pm UTC

I counted black pixels on this image:
Image
And indeed there are 161 black pixels.

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Re: What-If 106: "Ink Molecules"

Postby Flumble » Thu Jul 24, 2014 2:40 pm UTC

cellocgw wrote:FWIW, the concept of "half a digit" is actually used here and there. Start with an "order of magnitude" estimate, which basically says pick the "x" in 10x , then shift by "half a digit" in the log sense: either multiply by 5 or divide by 2 (or the other way around :mrgreen: ).

101/2 is approximately 19/6 (or 3.2 or π or 2(π/e)^π or 3.16 or √10), not 5 or 2.

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Re: What-If 106: "Ink Molecules"

Postby mrob27 » Thu Jul 24, 2014 3:07 pm UTC

CharlieP wrote: "This sentence contains 1,714,726,842,976,215,214 molecules of ink".

FTFY

BrianK wrote: I get the 8675309 reference ("Jenny, I got your number"). But none of the other digits are triggering anything. Does anyone see any other number references in there?


Yes, the next 6 digits are 525,600, a Rent reference (also mentioned in xkcd 1047, and in another what-if though I forget which one). I searched around in my numbers page for the 24601212 digits, but found nothing. Maybe they're just gratuitous references to the number of hours in a day, minutes in an hour, and nucleons in a Carbon atom :P

Flumble wrote: 101/2 is approximately 19/6 (or 3.2 or π or 2(π/e)^π or 3.16 or √10), not 5 or 2.

5 and 2 are close enough for Fermi estimation, which I think was @cellocgw's point, though if you want to be a bit closer to √10 you could use 4 and 5/2.
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Re: What-If 106: "Ink Molecules"

Postby rmsgrey » Thu Jul 24, 2014 4:18 pm UTC

mrob27 wrote:
Flumble wrote: 101/2 is approximately 19/6 (or 3.2 or π or 2(π/e)^π or 3.16 or √10), not 5 or 2.

5 and 2 are close enough for Fermi estimation, which I think was @cellocgw's point, though if you want to be a bit closer to √10 you could use 4 and 5/2.


Or just use 3 all the time.

2 is 0.3 digits; 5 is 0.7 digits; 3 is 0.5 digits

(to 3sf: 0.301; 0.699; 0.477 respectively)

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Re: What-If 106: "Ink Molecules"

Postby mathmannix » Thu Jul 24, 2014 5:19 pm UTC

mrob27 wrote:
BrianK wrote: I get the 8675309 reference ("Jenny, I got your number"). But none of the other digits are triggering anything. Does anyone see any other number references in there?


Yes, the next 6 digits are 525,600, a Rent reference (also mentioned in xkcd 1047, and in another what-if though I forget which one). I searched around in my numbers page for the 24601212 digits, but found nothing. Maybe they're just gratuitous references to the number of hours in a day, minutes in an hour, and nucleons in a Carbon atom :P


While we're on musicals, 24601 is Jean Valjean's number (and his asteroid.) That just leaves 212, which we might as well leave as being the (original) area code for New York City - including, of course, Broadway - where Rent once played (at the Nederlander (212-921-8000) from 1996-2008) and Les Mis currently plays (at the Imperial Theater (212-239-6200) beginning this year, and previously from 1990-2002.)
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Re: What-If 106: "Ink Molecules"

Postby mrob27 » Thu Jul 24, 2014 6:32 pm UTC

mathmannix wrote:While we're on musicals, 24601 is Jean Valjean's number (and his asteroid.) [...]

Oh yes, thanks for pointing that out. That's almost certainly where the 24601 comes from. And if it were up to me the 212 would be deleted to make it an actual 18-digit number :P so the illustration agrees with the text it's illustrating.

in an alternate timeline, Randall wrote:So our answer, according to Fermi estimation, is in the neighborhood of a high 18-digit number. We might be off by several orders of magnitude in either direction, but in either case, it's definitely a number you could print out on a single line.

Image

Now, let's do some actual research and find out how we did.


... there, that's better. :wink:
Spoiler:
what-if 106 fig3 fixed.png
How I would fix figure 3
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Re: What-If 106: "Ink Molecules"

Postby Gil-Galad » Thu Jul 24, 2014 7:35 pm UTC

I don’t understand the final answer. What is „161 pixels“ supposed to mean?

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Re: What-If 106: "Ink Molecules"

Postby rmsgrey » Thu Jul 24, 2014 8:14 pm UTC

Gil-Galad wrote:I don’t understand the final answer. What is „161 pixels“ supposed to mean?


It's the number of (black) pixels in the "161 pixels" image.

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Re: What-If 106: "Ink Molecules"

Postby Plasma_Wolf » Thu Jul 24, 2014 8:45 pm UTC

This article immediately reminded me of the QI comment on Graham's number. A number so large that all the universe's matter (I assume that this doesn't include dark matter), is not enough to write it down (Even if you needed one atom for each digit). It was once the largest (finite) number used in a mathematical theorem. Trying to work out how many digits it has is already an incredible task.

The QI bit is here.

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Re: What-If 106: "Ink Molecules"

Postby rmsgrey » Thu Jul 24, 2014 9:11 pm UTC

Plasma_Wolf wrote:This article immediately reminded me of the QI comment on Graham's number. A number so large that all the universe's matter (I assume that this doesn't include dark matter), is not enough to write it down (Even if you needed one atom for each digit). It was once the largest (finite) number used in a mathematical theorem. Trying to work out how many digits it has is already an incredible task.

The QI bit is here.


It's not just the matter in the universe - even if you wrote one digit in every planck volume in the universe, you wouldn't even come close to the number of digits in Graham's number...

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Re: What-If 106: "Ink Molecules"

Postby gmalivuk » Fri Jul 25, 2014 1:55 am UTC

I'm pretty sure you'd need to iterate the number of digits in the number of digits in ... in the number of digits something like g63 times before g64 enters the realm of things it's possible to write down in this universe.
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Re: What-If 106: "Ink Molecules"

Postby ps.02 » Sat Jul 26, 2014 5:45 am UTC

helo darqness wrote:Xerox has patented inkless printing. I'm not sure how far along in development and usage it is

Hmmm, well, the offices I've worked in have always had inkless laser printers. (As do I at home.) At one of these offices there was an old inkless plotter that printed with melted wax, a bit like crayons. At another, there was a 3D printer that used resins, which I presume are also inkless. And the stores and restaurants I visit tend to give me receipts printed using some kind of inkless thermal process.

None of the above applications of "inkless printing" are what'd you call cutting-edge technology.

(Come to that, back in the dot matrix / daisy wheel / Selectric type ball days, if your ink ribbon was shot, you could still print with carbon paper. Does that count as inkless printing?)

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Re: What-If 106: "Ink Molecules"

Postby Wolfkeeper » Sat Jul 26, 2014 5:35 pm UTC

There's only one problem with this what if.

C isn't a molecule.

Graphene is (mostly) the molecule, and it's a huge molecule (of variable size, but huge.)

The carbon ink is made of graphene.

So the estimate is probably off by many orders of magnitude, and I want my money back!

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Re: What-If 106: "Ink Molecules"

Postby stianhat » Sun Jul 27, 2014 9:46 am UTC

Wolfkeeper wrote:There's only one problem with this what if.

C isn't a molecule.

Graphene is (mostly) the molecule, and it's a huge molecule (of variable size, but huge.)

The carbon ink is made of graphene.


The carbon in this ink is certainly what is called "carbon black" or "lamp black" in the litographic world. It is not graphene, it is simply amorphous carbon, carbon without any organized and repeating crystal structure. While on topic, graphene, graphite, diamond, wurtzite, etc are all structures, not molecules. Sometimes the repeating unit is the same unit, some times the repeating unit is a molecule. It never makes sense to call it a huge molecule in any case. It is an ordered assembly, where the ordering is of far greater importance (usually) than the number of atoms.

On topic again: The repeating unit in amorphus carbon is C and that means it is acceptable to ask how many atoms of C instead of how many molecules of ink-substance

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Re: What-If 106: "Ink Molecules"

Postby Wolfkeeper » Sun Jul 27, 2014 2:56 pm UTC

stianhat wrote:
Wolfkeeper wrote:There's only one problem with this what if.

C isn't a molecule.

Graphene is (mostly) the molecule, and it's a huge molecule (of variable size, but huge.)

The carbon ink is made of graphene.


The carbon in this ink is certainly what is called "carbon black" or "lamp black" in the litographic world. It is not graphene, it is simply amorphous carbon, carbon without any organized and repeating crystal structure. While on topic, graphene, graphite, diamond, wurtzite, etc are all structures, not molecules.


Wrong.

A molecule is defined to be atoms held together by atomic bonds. There's no definition that requires it to be organized in a repeating crystal structure; indeed most molecules aren't crystals. For example, nitrogen (N2) is not a crystal. Any such definition would be extremely problematic.

Amorphous carbon consists of (to a reasonable approximation) small flakes of graphene loosely pressed together.

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Re: What-If 106: "Ink Molecules"

Postby Heimhenge » Mon Jul 28, 2014 10:16 pm UTC

Isn't this "gray area" between molecular and empirical formulae clarified by the notation: (C)n ??? Or have I forgotten that much about chemistry?

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Re: What-If 106: "Ink Molecules"

Postby Copper Bezel » Mon Jul 28, 2014 10:38 pm UTC

Could have used the unit cell of graphite, which apparently has twelve atoms....
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Re: figure 3 seems to be wrong

Postby Bob Stein - VisiBone » Tue Jul 29, 2014 12:41 pm UTC

mrob27 wrote:... but the illustration clearly shows a 21-digit number:

...I think this is an error, and the example number should have 18 digits...


Agreed, @mrob27. I posit that Randall miscounted due to being enthralled with the first guesstimate being a multiple of 3. So he didn't have to figure out where to put the left comma. Or he's testing whether we are: "Wow that could be the actual number. It totally looks like six groups of three digits."

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Re: What-If 106: "Ink Molecules"

Postby cryptoengineer » Tue Jul 29, 2014 1:23 pm UTC

Does anyone else feel that this page feels unfinished? Randall gathers the data (ignoring that 'carbon black' isn't single Carbon atoms), then doesn't really do the math to answer the original question.

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Re: What-If 106: "Ink Molecules"

Postby gmalivuk » Tue Jul 29, 2014 1:33 pm UTC

He did answer the original question, though...
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Re: What-If 106: "Ink Molecules"

Postby brenok » Tue Jul 29, 2014 1:54 pm UTC

cryptoengineer wrote:Does anyone else feel that this page feels unfinished? Randall gathers the data (ignoring that 'carbon black' isn't single Carbon atoms), then doesn't really do the math to answer the original question.

He does answer the question, it's approximately a 18 digit number.

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Re: What-If 106: "Ink Molecules"

Postby Showsni » Tue Jul 29, 2014 9:32 pm UTC

cellocgw wrote:Meanwhile, I heartily encourage all primary school math classes to include estimation in the curriculum. It's a great skill and avoids the infamous "but that's the answer my calculator gave" response to an answer that's clearlly off by a factor of 100.


They do; or at least, it's on the GCSE syllabus. There's very often a question like "Estimate the solution to (63.2^0.5 + 4.02)/2.05^2" at the start of the non calculator paper.


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