What-if 0104: "Global Snow"

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dalcde
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What-if 0104: "Global Snow"

Postby dalcde » Wed Jul 09, 2014 9:24 pm UTC

Jed Scott wrote:From my seven-year-old son: How many snowflakes would it take to cover the entire world in six feet of snow? (I don't know why six feet...but that's what he asked.)

http://what-if.xkcd.com/104/

No citations at all?

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Re: What-if 0104: "Global Snow"

Postby Earthling on Mars » Wed Jul 09, 2014 10:04 pm UTC

dalcde wrote:No citations at all?

Maybe he decided citations were getting two ridiculous after last week's footnote within a footnote (which seems to be gone now).

He never explained how he calculated the actual number of snowflakes. Of course, it's easy enough to Google 'snowflakes per square foot', but it seems like a rather important detail left out...

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Re: What-if 0104: "Global Snow"

Postby HES » Wed Jul 09, 2014 10:06 pm UTC

Surely even a duck would sink through fluffy snow?
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Re: What-if 0104: "Global Snow"

Postby Mikeski » Wed Jul 09, 2014 10:34 pm UTC

HES wrote:Surely even a duck would sink through fluffy snow?

That duck is also a witch, so it's extra-floaty.

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Re: What-if 0104: "Global Snow"

Postby Pfhorrest » Wed Jul 09, 2014 10:44 pm UTC

Duck witch? Woo-ooo…

(Alternately: "Duckwich? Mmmmm.")
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Re: What-if 0104: "Global Snow"

Postby Eternal Density » Wed Jul 09, 2014 11:57 pm UTC

Image
For some reason this made me think of River Tam.
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Re: What-if 0104: "Global Snow"

Postby BlueCrab » Thu Jul 10, 2014 1:51 am UTC

“They use a special snow-measuring board, which is probably just a regular piece of wood”

Yep, pretty much.

noaa wrote:To make your own SMB, first acquire a 24 inch x 24 inch piece of plywood. A thickness of 3/8 inch to 1⁄2 inch is recommended to reduce the likelihood of having it blow away. For greater durability it is best to use exterior or marine grade plywood. Paint the plywood on both sides and all edges with a flat, white paint.

For a while the standard SMB was a piece of 1/2" styrofoam covered in aluminium foil. I was told that was relatively expensive though, especially for classes and clubs doing citizen science projects; I guess they decided wood was fine.
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Re: What-if 0104: "Global Snow"

Postby cellocgw » Thu Jul 10, 2014 11:35 am UTC

The final alt-text made the entire page extra-special :D

I am one of those grumps who thinks the official snow-depth measuring system is wacked. For one thing, after you brush off yr measuring spot, like as not it'll fill in faster than the surrounding region because of wind-blown snow.

I think I'll file a patent, followed closely by a Kickstarter campaign, for a better method of measuring total snowfall. It's going to involve a 1-meter diameter, 20-meter tall tube which is mounted vertically w/ a few cameras looking inwards. The cameras will be connected to a computer w/ HighlySophisticated(TM) software that counts each snowflake as it falls by, calculates the volume of said snowflake, and so on.
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Re: What-if 0104: "Global Snow"

Postby senor_cardgage » Thu Jul 10, 2014 3:37 pm UTC

dalcde wrote:No citations at all?



How about this?

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Re: What-if 0104: "Global Snow"

Postby HES » Thu Jul 10, 2014 4:02 pm UTC

Image
This only applies if the pile of snow is located in a (semi)impermeable recess. If it's on a tarmac carpark, on the other hand, it will soon be in a nice storm drain.
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Re: What-if 0104: "Global Snow"

Postby jgh » Thu Jul 10, 2014 11:09 pm UTC

I leave my fridge open when it's hot, and while people converge on my house from miles around to explain that I'm actually making my house WARMER, I slip out the back, sneak to their houses, and run their a/c units at full blast.

I have a vent in the wall behind my fridge, so the warmth extracted from inside the fridge gets expelled to the outside.

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Re: What-if 0104: "Global Snow"

Postby rmsgrey » Thu Jul 10, 2014 11:13 pm UTC

jgh wrote:
I leave my fridge open when it's hot, and while people converge on my house from miles around to explain that I'm actually making my house WARMER, I slip out the back, sneak to their houses, and run their a/c units at full blast.

I have a vent in the wall behind my fridge, so the warmth extracted from inside the fridge gets expelled to the outside.


So what you're saying is that if you leave the fridge door open, it's just an inefficient a/c unit?

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Re: What-if 0104: "Global Snow"

Postby Zinho » Fri Jul 11, 2014 4:15 pm UTC

rmsgrey wrote:
jgh wrote:
I leave my fridge open when it's hot, and while people converge on my house from miles around to explain that I'm actually making my house WARMER, I slip out the back, sneak to their houses, and run their a/c units at full blast.

I have a vent in the wall behind my fridge, so the warmth extracted from inside the fridge gets expelled to the outside.


So what you're saying is that if you leave the fridge door open, it's just an inefficient a/c unit?


Yep, that's what he's saying. That would be an interesting setup to see, and I think it would take a bit more than a vent to make it work. You'd have to make sure that the heat exchanger for the fridge is exposed only to outside air, and that the outside air is prevented from mixing with the inside air. It would end up looking like an oversized window AC unit, and (as you suggested) be horribly inefficient since it's designed to operate at ~70 degrees instead of whatever your outside temp is at the moment (we're hovering at around 100 F here in North Texas). It wouldn't work with my fridge, either - the condenser in mine is distributed around four of the six surfaces (everything but the door and floor interface radiates heat).

As a side note, I'd like to put a plug in for using open refrigerators as heaters. If you insist on using electricity for heating, then opening your fridge produces less entropy per joule of heat produced than a resistance element would. I'm in favor of delaying the inevitable heat death of the universe for as long as possible. So remember: if you're cold at your desk, opening up your mini fridge and snuggling with the condenser is more environmentally sound than running an electric space heater! Do your part, keep the Universe alive for a bit longer.*

*I need to work on that slogan, it's not catchy enough.
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Re: What-if 0104: "Global Snow"

Postby Patrik3 » Fri Jul 11, 2014 5:13 pm UTC

Surely the best way to measure snow would be to wait until the storm is over, and then take a pipe to make a cross section, and apply lots of pressure to the top of the pipe until the snow inside is almost perfectly compact, and then take that reading instead?

I'd imagine even with the 6 hour rules, there's gonna be loads of other environmental factors (temperature, air pressure etc.) that affect how compact the snow is when it falls, as so distort the readings?

Also, did I misunderstand that fact at the end - if 6ft of snow fell across the world, then each kid in the US would only be able to roll 3 snowballs each from it?

That seems really off - I must have misunderstood - out of all the snow across the world?

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Re: What-if 0104: "Global Snow"

Postby speising » Fri Jul 11, 2014 5:23 pm UTC

you misunderstood.
they'd have enough to hit every other child three times. 210*70 million snowballs if i'm not mistaken.
Last edited by speising on Fri Jul 11, 2014 5:25 pm UTC, edited 1 time in total.

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Re: What-if 0104: "Global Snow"

Postby squall_line » Fri Jul 11, 2014 5:24 pm UTC

Patrik3 wrote:Also, did I misunderstand that fact at the end - if 6ft of snow fell across the world, then each kid in the US would only be able to roll 3 snowballs each from it?

That seems really off - I must have misunderstood - out of all the snow across the world?


Yes, I think you misunderstood.

The actual statistic is "every one of the 70 million kids in the United States would be able to make enough snowballs to hit every other kid with a snowball three times over." (bold added, italics in original)

So, 70,000,000 kids in the US would be able to hit the other 69,999,999 kids three times each. Or, each kid would be able to roll 69,999,999 * 3 ~= 210 Million snowballs each, not just 3 each.

Which would take a little bit of time to roll and throw...

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Re: What-if 0104: "Global Snow"

Postby Mikeski » Sat Jul 12, 2014 3:11 am UTC

squall_line wrote:each kid would be able to roll [...] 210 Million snowballs [...] Which would take a little bit of time to roll and throw...

If they could effectively roll and throw a snowball at the age of 2, and if we go with the Obama-care definition of "kid" that extends until age 26, they've got 24 years of snowball-throwing childhood.

If they sleep/eat/etc for 8 hours a day and throw snow the rest of the time, they've each got 24 years x 365.25 days/year x 16 waking hours/day x 3600 seconds/hour ~= 505 million seconds of potential-snowball-throwing childhood. They'd have to roll and throw a snowball every 2.4 seconds to use up all the snow before they became adults. And they'd all have to do it while constantly on the run to get close to every other kid during those 24 years.

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Re: What-if 0104: "Global Snow"

Postby PayasYouDraw » Mon Jul 14, 2014 10:46 am UTC

Zinho wrote:
As a side note, I'd like to put a plug in for using open refrigerators as heaters. If you insist on using electricity for heating, then opening your fridge produces less entropy per joule of heat produced than a resistance element would. I'm in favor of delaying the inevitable heat death of the universe for as long as possible. So remember: if you're cold at your desk, opening up your mini fridge and snuggling with the condenser is more environmentally sound than running an electric space heater! Do your part, keep the Universe alive for a bit longer.*

*I need to work on that slogan, it's not catchy enough.
"Save the universe: leave your fridge open!"
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Still missing something. Any suggestions?


I like it, though I generally insist on using electricity for heating because there's no other option, but I guess other parts of the world don't have that problem. But at home we have a convection heater and an electric radiator (it's full of oil or something). I suspect the latter is more efficient as the heating element must be smaller, but I can't be sure.

It might get cold enough outside to keep the food from the fridge suitably cold, but we need to keep the freezer part as a freezer.
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Re: What-if 0104: "Global Snow"

Postby ps.02 » Mon Jul 14, 2014 5:12 pm UTC

PayasYouDraw wrote:But at home we have a convection heater and an electric radiator (it's full of oil or something). I suspect the latter is more efficient as the heating element must be smaller, but I can't be sure.

Heating based on electric resistance is basically 100% efficient. All the energy input has to go somewhere, right? Where will it go that isn't turned into heat? The only loss of efficiency is the negligible light or sound from the heater that reaches outside the home being heated.

An interesting corollary is that if you use resistance-based heating, the efficiency of all your other electric appliances doesn't matter either. Incandescent lights, phone chargers plugged in but not in use, monitors in sleep mode, spinning hard disks, pretty much all of your "wasted" energy isn't really wasted: it simply reduces the load on your heater, at the same 100% efficiency. Well, except for the excess light (including infrared) that escapes through your windows.

Of course, none of this is true during the parts of the year when you aren't heating the house. But in the winter, feel free to ignore all the typical household tips for power savings, like unplugging things and using CF light bulbs.

So if a resistance heater is 100% efficient, why do people think they're not the best choice? Because, while creating 1J of heat uses 1J of (electric) energy, moving 1J of heat from one place to another often requires less than 1J of energy. Thus it is that air conditioners and heat pumps are, by that measure, more than 100% efficient. Especially if the source / sink is sited somewhere without the temperature extremes of the atmosphere, i.e., underground or in a body of water.

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Re: What-if 0104: "Global Snow"

Postby jpvlsmv » Mon Jul 14, 2014 6:38 pm UTC

Mikeski wrote:
squall_line wrote:each kid would be able to roll [...] 210 Million snowballs [...] Which would take a little bit of time to roll and throw...

If they could effectively roll and throw a snowball at the age of 2, and if we go with the Obama-care definition of "kid" that extends until age 26, they've got 24 years of snowball-throwing childhood.

If they sleep/eat/etc for 8 hours a day and throw snow the rest of the time, they've each got 24 years x 365.25 days/year x 16 waking hours/day x 3600 seconds/hour ~= 505 million seconds of potential-snowball-throwing childhood. They'd have to roll and throw a snowball every 2.4 seconds to use up all the snow before they became adults. And they'd all have to do it while constantly on the run to get close to every other kid during those 24 years.


So they would have 7.2 seconds facing each other kid, which we could manage by having them all line up into two facing lines, and rotating them past each other (line A moves one person to the left every 7.2 seconds, the person at the end of line A becomes the first of line B, and the person at the end of line B becomes the first of line A. When a child returns to their original starting position in line, they have been opposite every other child once.)

Assuming they are standing shoulder to shoulder (2 feet apart) in the lines, they're going along at a very-slow .25 ft/s (.17 mph). Not even walking pace.

The line is 13000 miles long, or the length of a car trip from New York to Argentina.[cite]http://www.oregonlive.com/travel/index.ssf/2010/03/nothing_like_a_road_trip_but_1.html[/cite] At The Long Walk pace, it would only take 4.5 months of travel, or 30 times as long as that book's winning contestant.

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Re: What-if 0104: "Global Snow"

Postby mathmannix » Mon Jul 14, 2014 8:29 pm UTC

BlueCrab wrote:“They use a special snow-measuring board, which is probably just a regular piece of wood”

Yep, pretty much.

noaa wrote:Paint the plywood on both sides and all edges with a flat, white paint.


So not just any regular piece of wood, it has to be white. Although, I would think that would make the snow harder to see.
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Re: What-if 0104: "Global Snow"

Postby Mikeski » Tue Jul 15, 2014 2:26 am UTC

jpvlsmv wrote:
Mikeski wrote:
squall_line wrote:each kid would be able to roll [...] 210 Million snowballs [...] Which would take a little bit of time to roll and throw...

If they could effectively roll and throw a snowball at the age of 2, and if we go with the Obama-care definition of "kid" that extends until age 26, they've got 24 years of snowball-throwing childhood.

If they sleep/eat/etc for 8 hours a day and throw snow the rest of the time, they've each got 24 years x 365.25 days/year x 16 waking hours/day x 3600 seconds/hour ~= 505 million seconds of potential-snowball-throwing childhood. They'd have to roll and throw a snowball every 2.4 seconds to use up all the snow before they became adults. And they'd all have to do it while constantly on the run to get close to every other kid during those 24 years.


So they would have 7.2 seconds facing each other kid, which we could manage by having them all line up into two facing lines, and rotating them past each other (line A moves one person to the left every 7.2 seconds, the person at the end of line A becomes the first of line B, and the person at the end of line B becomes the first of line A. When a child returns to their original starting position in line, they have been opposite every other child once.)

Wherever you're from, you have the most well-behaved kids in the universe.

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Re: What-if 0104: "Global Snow"

Postby Pfhorrest » Tue Jul 15, 2014 3:13 am UTC

mathmannix wrote:So not just any regular piece of wood, it has to be white. Although, I would think that would make the snow harder to see.

It's probably for thermal regulation. White paint will absorb the least sunlight, heating the wood the least, and melting the snow the least, to provide the best simulation of snow landing on other snow.

Since you're measuring from the bottom of the wood to the top of the snow heap anyway, you wouldn't care that the snow is hard to see against the wood; it just matters how the snow looks against whatever backdrop is off to the side of the wood, and you can have an intern hold up a black cloth while you pull out the measuring tape if that's really necessary.
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Re: What-if 0104: "Global Snow"

Postby PayasYouDraw » Tue Jul 15, 2014 10:49 am UTC

ps.02 wrote:
PayasYouDraw wrote:But at home we have a convection heater and an electric radiator (it's full of oil or something). I suspect the latter is more efficient as the heating element must be smaller, but I can't be sure.

Heating based on electric resistance is basically 100% efficient. All the energy input has to go somewhere, right? Where will it go that isn't turned into heat? The only loss of efficiency is the negligible light or sound from the heater that reaches outside the home being heated.

An interesting corollary is that if you use resistance-based heating, the efficiency of all your other electric appliances doesn't matter either. Incandescent lights, phone chargers plugged in but not in use, monitors in sleep mode, spinning hard disks, pretty much all of your "wasted" energy isn't really wasted: it simply reduces the load on your heater, at the same 100% efficiency. Well, except for the excess light (including infrared) that escapes through your windows.

Of course, none of this is true during the parts of the year when you aren't heating the house. But in the winter, feel free to ignore all the typical household tips for power savings, like unplugging things and using CF light bulbs.

So if a resistance heater is 100% efficient, why do people think they're not the best choice? Because, while creating 1J of heat uses 1J of (electric) energy, moving 1J of heat from one place to another often requires less than 1J of energy. Thus it is that air conditioners and heat pumps are, by that measure, more than 100% efficient. Especially if the source / sink is sited somewhere without the temperature extremes of the atmosphere, i.e., underground or in a body of water.


Good point. Though our heaters have no way of knowing how hot the house is, so we just turn them on if we feel cold. Presumably we find we can turn them on for less time when we have loads of other stuff plugged in.

I'm thinking comparing the power draw of each heater would be an interesting experiment for next winter.
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Re: What-if 0104: "Global Snow"

Postby peregrine_crow » Tue Jul 15, 2014 11:54 am UTC

jpvlsmv wrote:So they would have 7.2 seconds facing each other kid, which we could manage by having them all line up into two facing lines, and rotating them past each other (line A moves one person to the left every 7.2 seconds, the person at the end of line A becomes the first of line B, and the person at the end of line B becomes the first of line A. When a child returns to their original starting position in line, they have been opposite every other child once.)


Minor nitpick, but unless I misunderstood your method that doesn't actually work. Imagine it for the case of 4 children. If we number them 1 to 4 they will go through these states:

1 2 | 2 3 | 3 4 | 4 1 | 1 2
4 3 | 1 4 | 2 1 | 3 2 | 4 3

Child 1 faces both 2 and 4 twice and is never matched up with child 3.
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Re: What-if 0104: "Global Snow"

Postby HES » Tue Jul 15, 2014 1:55 pm UTC

You're moving both lines of kids, not just one.
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Re: What-if 0104: "Global Snow"

Postby jpvlsmv » Tue Jul 15, 2014 2:05 pm UTC

peregrine_crow wrote:
jpvlsmv wrote:So they would have 7.2 seconds facing each other kid, which we could manage by having them all line up into two facing lines, and rotating them past each other (line A moves one person to the left every 7.2 seconds, the person at the end of line A becomes the first of line B, and the person at the end of line B becomes the first of line A. When a child returns to their original starting position in line, they have been opposite every other child once.)


Minor nitpick, but unless I misunderstood your method that doesn't actually work. Imagine it for the case of 4 children. If we number them 1 to 4 they will go through these states:

1 2 | 2 3 | 3 4 | 4 1 | 1 2
4 3 | 1 4 | 2 1 | 3 2 | 4 3

Child 1 faces both 2 and 4 twice and is never matched up with child 3.


I agree with your counterexample. I don't know why it doesn't work... Ah, there's a double-move at each step-- the head and tail of the lines move past each other, which is why 1 and 3 never oppose.

But...
Just ensure that there are an odd number of children in a line, and it works:

Code: Select all

A: 1 2 3 | 2 3 4 | 3 4 5 | 4 5 1 | 5 1 2 | back to original posistion
B: 5 4   | 1 5   | 2 1   | 3 2   | 4 3   |


If there's an even number of total children, have one child (* in the diagram below) sit off to the side of the line and exchange snowballs with whoever's at the end of line A:

Code: Select all

A: 1 2 3 * | 2 3 4 * | 3 4 5 * | 4 5 1 * | 5 1 2 * | back to original posistion
B: 5 4     | 1 5     | 2 1     | 3 2     | 4 3     |


Of course, the * child will need a huge pile of snow to make the 210M snowballs from. The other kids would at least get some exercise from walking (I think about 5 extra calories/mile at this pace over BMR, which would be enough energy to convert about 1 m3 of snow into steam)
Mikeski wrote:Wherever you're from, you have the most well-behaved kids in the universe.

I'm from the same universe where 6 feet of snow fall all at once, and every kid makes snowballs from them.

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Re: What-if 0104: "Global Snow"

Postby mathmannix » Tue Jul 15, 2014 3:34 pm UTC

and do all the kids in this universe leave their houses at the exact same time and begin bouncing their rubber balls in unison when it's not winter?
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Re: What-if 0104: "Global Snow"

Postby Flumble » Tue Jul 15, 2014 4:06 pm UTC

jpvlsmv wrote:Of course, the * child will need a huge pile of snow to make the 210M snowballs from.

I liked you first solution better: just ensure there's an odd number of children. :)

Now, what's the optimal route (or path, if you hate kids) for everyone to walk, assuming Earth is not a uniform blob of land+snow with equidistant children? (if it is, you probably just get one large route through all the starting points; well, you'd still have to optimise for snow-gathering, but that probably doesn't lead to a significant change in the route over time. Well, thinking about it does give numerous of "probably"s, so maybe it isn't as straight-forward as I assume.)

[edit] This sounds like a nice pre-bachelor's research subject; optimisations for parts of this problem exist, but combining and optimising the combination might be a tough job.

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Re: What-if 0104: "Global Snow"

Postby Neil_Boekend » Thu Jul 17, 2014 12:55 pm UTC

mathmannix wrote:and do all the kids in this universe leave their houses at the exact same time and begin bouncing their rubber balls in unison when it's not winter?

Sounds really creepy.
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Re: What-if 0104: "Global Snow"

Postby moody7277 » Fri Jul 18, 2014 8:06 pm UTC

Neil_Boekend wrote:
mathmannix wrote:and do all the kids in this universe leave their houses at the exact same time and begin bouncing their rubber balls in unison when it's not winter?

Sounds really creepy.


Even more so when you know what IT is that makes them do that.
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Re: What-if 0104: "Global Snow"

Postby Eebster the Great » Tue Jul 22, 2014 5:38 am UTC

From what I can tell, in a six foot snowfall over the entire surface of the Earth with average snow density (which probably isn't reasonable, since six feet of snow will be much more packed than average), there will be around 50 moles of snowflakes.

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Re: What-if 0104: "Global Snow"

Postby Flumble » Tue Jul 22, 2014 8:40 am UTC

Eebster the Great wrote:From what I can tell, in a six foot snowfall over the entire surface of the Earth with average snow density (which probably isn't reasonable, since six feet of snow will be much more packed than average), there will be around 50 moles of snowflakes.

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