0994: "Advent Calendar"

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Wnderer
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Re: 0994: "Advent Calendar"

Postby Wnderer » Fri Dec 23, 2011 6:55 pm UTC

The question that this comic brings to my mind is whether infinitesimal quantities are possible at all. Let say you were chopping the chocolate into smaller and smaller quantities as you chop the time into smaller and smaller quantities. At some point you are down to a molecule of chocolate, then atoms, subatomic particles and maybe super strings. There is a limit. Maybe there is a limit to how small a unit of time you can have or how small a distance of space can exist. There is a finite limit to speed. There is a finite limit to going backwards in time. There may be a finite limit to going forward in time. There maybe a finite limit to the size of the universe. Mathematics can conceive of infinities, but physically I'm not sure they exist.

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Re: 0994: "Advent Calendar"

Postby PolakoVoador » Fri Dec 23, 2011 7:25 pm UTC

Wnderer, I can think of an infinity: your mom's weight.

Ba dum tss!

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Re: 0994: "Advent Calendar"

Postby ysth » Fri Dec 23, 2011 8:07 pm UTC

11:58:35.62!

(Round half to even++)

Also: http://www.youtube.com/watch?v=8NPzLBSBzPI
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Re: 0994: "Advent Calendar"

Postby bmonk » Fri Dec 23, 2011 10:09 pm UTC

pbnjstowell wrote:Does it have to be chocolate?

The liquify-and-drink problem would be easy to solve if it was eggnog.

But there would be a slightly later problem with drinking it fast enough.
Having become a Wizard on n.p. 2183, the Yellow Piggy retroactively appointed his honorable self a Temporal Wizardly Piggy on n.p.1488, not to be effective until n.p. 2183, thereby avoiding a partial temporal paradox. Since he couldn't afford two philosophical PhDs to rule on the title.

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Re: 0994: "Advent Calendar"

Postby phonon266737 » Fri Dec 23, 2011 10:12 pm UTC

The Zeno thing is as stupid as the "go halfway to point A. do it again and again, but you'll never get there" thing.

The paradox might as well be called "The runner goes half of the way to the tortise, repeatedly. Why won't he ever pass it?"

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Re: 0994: "Advent Calendar"

Postby WizenedEE » Fri Dec 23, 2011 10:16 pm UTC

There would be 162 events. source

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Re: 0994: "Advent Calendar"

Postby Pfhorrest » Fri Dec 23, 2011 10:22 pm UTC

WizenedEE wrote:There would be 162 events. source

No fair bringing discrete time into a continuous function.
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Re: 0994: "Advent Calendar"

Postby bmonk » Fri Dec 23, 2011 10:25 pm UTC

dmm wrote:
Gye wrote:I had to Google "Advent Calendar". I've never seen one here in Canada.

That's strange, because advent calendars are stereotypically Anglican. Aren't there any Anglicans left in Canada?

Catholics had them too. And not the new kind with all square doors in order, but the old kind, with all sorts of objects as doors, and behind the door the new picture fit the old one.
Having become a Wizard on n.p. 2183, the Yellow Piggy retroactively appointed his honorable self a Temporal Wizardly Piggy on n.p.1488, not to be effective until n.p. 2183, thereby avoiding a partial temporal paradox. Since he couldn't afford two philosophical PhDs to rule on the title.

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Re: 0994: "Advent Calendar"

Postby CanadianNomad » Fri Dec 23, 2011 11:03 pm UTC

Gye wrote:I had to Google "Advent Calendar". I've never seen one here in Canada.

I grew up in Canada, moving between Ottawa and Vancouver. I'm not religious in any way, nor was I raised in a religious household. They have always been a part of christmas, no matter where I was, for me and my friends.
Don't you see them in every single pharmacy and grocery store you ever enter? I sure do.

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Re: 0994: "Advent Calendar"

Postby larvacea » Sat Dec 24, 2011 3:43 am UTC

Zeno wins this one thanks to material science; as illustrated, the calendar (no matter what its contents might be) has constant width, and it has constant length per row of little doors. Advent calendars (including Zeno's, of course) hang vertically. Therefore one would be able to use a finite section of this calendar as a space elevator. All attempts to do so have failed (viz., I see no chocolate-themed space elevators from Cadbury's, and believe you me, I am looking for them). Therefore Zeno was right, and you can never get to the end of his calendar.

Pre-Socratic philosophy, the ideal guide to space transport systems. Next week, Parmenides explains why preloaded tapered roller bearings will never catch on.

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Re: 0994: "Advent Calendar"

Postby pbnjstowell » Sat Dec 24, 2011 4:53 am UTC

larvacea wrote: ...chocolate-themed space elevators...


Didn't Willy Wonka have a space elevator?
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Re: 0994: "Advent Calendar"

Postby beason4251 » Sat Dec 24, 2011 7:05 am UTC

What if we summed them using p-adic numbers?

If we used the 2-adic metric and group the chocolates by powers of 2 starting from 2^0, we can write the following:

1=10-1
11=10^2-1
111=10^3-1
...

...1111=-1
This is because the distance between -1 and the successive terms in the sequence approaches zero using the p-adic metric for measuring distance. Since the distance between ....1111 and -1 is zero, we can say the two are equivalent. (This is in the same way we can say .99999.... and 1 are equivalent using normal metrics for measuring distance.)

Which means we can safely say we have consumed the equivalent of every chocolate if we consume negative one chocolates.

References:
http://web.williams.edu/go/math/eburger/BurgerMathHorizons.pdf
http://en.wikipedia.org/wiki/P-adic_number

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Re: 0994: "Advent Calendar"

Postby Proginoskes » Sat Dec 24, 2011 8:39 am UTC

Plasma Man wrote:Very clever, I like it. It's not just the time it takes to eat the chocolate that would slow you down, though - there's also the time needed to open the fiddly little doors.


And you'd better hope that the total amount of chocolate is NOT finite; you'll need an infinite amount of energy to open all of those doors, and the rest of the food in the world won't help you. (The doors are all the same size, you know.)

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Re: 0994: "Advent Calendar"

Postby Suncho » Sat Dec 24, 2011 10:40 am UTC

*liquefy

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Re: 0994: "Advent Calendar"

Postby RebeccaRGB » Sat Dec 24, 2011 11:08 am UTC

Suncho wrote:*liquefy

http://www.dangermouse.net/esoteric/chef.html wrote:(Note: The original specification used the word "Liquify", which is a spelling error. "Liquify" is deprecated. Use "Liquefy" in all new code.)
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Re: 0994: "Advent Calendar"

Postby sxiz » Sat Dec 24, 2011 3:32 pm UTC

Red Hal wrote:
JustDoug wrote:I'll see your Zeno...

All I wanna know is: how can you be certain that there's chocolate behind every little door until you look?
Because there's a goat behind the other one ...


solobutterfly wrote:because I am not familiar with this Zeno fellow, I choose to see this as some kind of reference to 24 (the television show) and heard the familiar ticking and dramatic music. Jack Bauer has to save Santa from the terrorists, or else Christmas will be blown up!


i love this thread.
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It's okay, the comic was a bit quixotic.

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Re: 0994: "Advent Calendar"

Postby Zylon » Sat Dec 24, 2011 6:24 pm UTC

phonon266737 wrote:The Zeno thing is as stupid as the "go halfway to point A. do it again and again, but you'll never get there" thing.

The Zeno thing IS that, genius. He's the one who came up with it in the first place.

And if only it were true, so many adventurer knees would still be intact.

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Re: 0994: "Advent Calendar"

Postby Gunslinger » Sat Dec 24, 2011 7:27 pm UTC

Wouldn't it be a Ross-Littlewood advent calendar?

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Re: 0994: "Advent Calendar"

Postby bigjeff5 » Sat Dec 24, 2011 10:08 pm UTC

Right, just so everyone who didn't know about Zeno understands, he was a greek philosopher back before most of the mathematical ideas relating to infinity were worked out. Also, in this time period the validity of a logical argument tended to be considered more important than the correctness of the argument. Experiments were discouraged, while pure reasoning was encouraged.

The paradox says that in order to get from A to B, you must first go halfway between A and B. In order to get from halfway between A and B to B, you must first go halfway between halfway between A and B and B. In other words, you must always go half the distance to the goal first, which creates a new half distance you must travel, over and over and you will never reach your destination. I believe the original thought problem had a turtle outrunning Achilles, but movement of the target is not strictly necessary - it's a problem with the conceptualization of convergent and divergent sets. The inverse of the problem, called Dichotomy, has Achilles never starting to chase after the turtle since for each half distance he must travel he must first travel halfway there, and halfway to the half way, etc. In essence, he didn't think it was possible to do an infinite number of things (i.e. pass through continuous halfway points) in a finite period of time. He had a real problem with time in general, essentially arguing that movement doesn't exist even though it obviously does.

Honestly, it's probably the most embarrassing thought problem to ever come out of ancient Greece, since it was so obviously false you wouldn't even need to conduct a demonstration to prove it. The simple fact of walking from one place to the next proves it false, so the fact that Zeno used it to argue the idea of "The One" is just a sad missed opportunity to figure out why the world doesn't work the way he expected it to.

It was ultimately useful though, since demonstrating it was false was a whole lot easier than coming up with a logical argument for why it was false, and it was the argument that philosophers cared about, not reality. So it forced philosophers to describe convergent sets and the like in order to refute it in a proper logical counter argument, and in that regard may have been influential in the development of calculus. According to Wikipedia it is also possibly the first example of the reductio ad absurdum argument form. Conceptualizing infinity is still notoriously difficult, and a great many people who think they do understand it actually don't, so you can't be too hard on the guy.

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Re: 0994: "Advent Calendar"

Postby phlip » Sat Dec 24, 2011 10:58 pm UTC

Gunslinger wrote:Wouldn't it be a Ross-Littlewood advent calendar?

That would be if the calendar started out empty, and every time you took out a chocolate, you added another 10 chocolates to the end... only to find that come Christmas day, and the infinigluttony is over, that the calendar is empty again.

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Re: 0994: "Advent Calendar"

Postby addams » Sun Dec 25, 2011 1:36 am UTC

tups wrote:Gave me a chuckle anyway .... google Zeno's paradoxes and Zeno of Elea if you have been momentarily distracted during your classics education and thus currently have no idea what this is about.


That is some fun reading. Of course, I have not finished it all.

Wiki I could be gone for hours.

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Re: 0994: "Advent Calendar"

Postby Tiw » Sun Dec 25, 2011 5:26 am UTC

Understanding of the continuum and rigorous treatment of infinitesimals are still developing. Zeno's treatment of the paradoxes of the continuous and the discrete were one step along this path. They were not "bad math". Even with the integral calculus, as some on this board seem to think, mathematicians did not have all it takes to deal rigorously with all the issues Zeno raised. Non-standard analysis was formulated by Robinson only in the 1960s. Smooth infinitesimal analysis started to be formulated even after that.

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Re: 0994: "Advent Calendar"

Postby Proginoskes » Sun Dec 25, 2011 5:50 am UTC

phlip wrote:
Gunslinger wrote:Wouldn't it be a Ross-Littlewood advent calendar?

That would be if the calendar started out empty, and every time you took out a chocolate, you added another 10 chocolates to the end... only to find that come Christmas day, and the infinigluttony is over, that the calendar is empty again.


For some reason, that reminded me of Goodstein's Theorem:
http://en.wikipedia.org/wiki/Goodstein%27s_theorem

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Re: 0994: "Advent Calendar"

Postby adho » Sun Dec 25, 2011 7:05 am UTC

bigjeff5 wrote:so you can't be too hard on the guy


But YOU can be. You seem to have missed the entire point of a paradox. A series of statements that are acknowledged as true leading to a contradiction or impossibility.
Zeno was undoubtedly of great intelligence.
Far from being the most embarrassing problem, it was perhaps one of the most thought provoking, encouraging contemplation of infinitude and limits.

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Re: 0994: "Advent Calendar"

Postby RabbitWho » Sun Dec 25, 2011 1:35 pm UTC

You can get Advent Calendar's with chocolate in them? When I was a kid it was just exciting to see what picture was behind the flap each day. On Christmas day it was always Jesus.

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Re: 0994: "Advent Calendar"

Postby chapel » Sun Dec 25, 2011 3:36 pm UTC

But if I use this, Christmas will never arrive. What is this, Narnia?

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Re: 0994: "Advent Calendar"

Postby skitch78 » Sun Dec 25, 2011 6:55 pm UTC

RabbitWho wrote:You can get Advent Calendar's with chocolate in them? When I was a kid it was just exciting to see what picture was behind the flap each day. On Christmas day it was always Jesus.


I shed a tear for your chocolate-less childhood.

chapel wrote:But if I use this, Christmas will never arrive. What is this, Narnia?


I wanted to put a new box-set of Narnia books (or a single bound compilation) on my Christmas list... but since all the recent publishings HAVE THE BOOKS OUT OF ORDER, I decided against it. Don't want to have that kind of blasphemy in the house for my kids to run across.

One of these days, when the last bookstore is finally going out of business, I will walk in with a Sharpie and properly number the series.

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Re: 0994: "Advent Calendar"

Postby lesmith11 » Sun Dec 25, 2011 11:30 pm UTC

skitch78 wrote:
I wanted to put a new box-set of Narnia books (or a single bound compilation) on my Christmas list... but since all the recent publishings HAVE THE BOOKS OUT OF ORDER, I decided against it.



I had the Chronicles of Narnia (single bound compilation) around 12 years ago and it was in the wrong order even back then. Hardly a recent thing...sorry.

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Re: 0994: "Advent Calendar"

Postby cjmcjmcjmcjm » Sun Dec 25, 2011 11:59 pm UTC

dan131m wrote:Surely I can't be the only one who thought the title text would be along the lines of, "But everyone knows that you'll somehow finish by December 8 anyway."

Either that, or you forget after the first week and finish the rest between Orgasm Day and Christmas Eve
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Re: 0994: "Advent Calendar"

Postby Gye » Mon Dec 26, 2011 10:57 am UTC

CanadianNomad wrote:
Gye wrote:I had to Google "Advent Calendar". I've never seen one here in Canada.

I grew up in Canada, moving between Ottawa and Vancouver. I'm not religious in any way, nor was I raised in a religious household. They have always been a part of christmas, no matter where I was, for me and my friends.
Don't you see them in every single pharmacy and grocery store you ever enter? I sure do.

Edmonton, here. I spotted one in a Sobeys after reading the comic, so they're clearly around, but I have a hard time imagining them being at all common. It's literally never come up.

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Re: 0994: "Advent Calendar"

Postby AvatarIII » Mon Dec 26, 2011 11:21 am UTC

Gye wrote:
CanadianNomad wrote:
Gye wrote:I had to Google "Advent Calendar". I've never seen one here in Canada.

I grew up in Canada, moving between Ottawa and Vancouver. I'm not religious in any way, nor was I raised in a religious household. They have always been a part of christmas, no matter where I was, for me and my friends.
Don't you see them in every single pharmacy and grocery store you ever enter? I sure do.

Edmonton, here. I spotted one in a Sobeys after reading the comic, so they're clearly around, but I have a hard time imagining them being at all common. It's literally never come up.


odd that they are so rare in parts of Canada, but in the UK EVERYONE has one.

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Re: 0994: "Advent Calendar"

Postby bmonk » Mon Dec 26, 2011 4:41 pm UTC

bigjeff5 wrote:Right, just so everyone who didn't know about Zeno understands, he was a greek philosopher back before most of the mathematical ideas relating to infinity were worked out. Also, in this time period the validity of a logical argument tended to be considered more important than the correctness of the argument. Experiments were discouraged, while pure reasoning was encouraged.

. . .

Honestly, it's probably the most embarrassing thought problem to ever come out of ancient Greece, since it was so obviously false you wouldn't even need to conduct a demonstration to prove it. The simple fact of walking from one place to the next proves it false, so the fact that Zeno used it to argue the idea of "The One" is just a sad missed opportunity to figure out why the world doesn't work the way he expected it to. . . .


Furthermore, in the modern version, if you take a line of boys on one side of the gym, and an equal line of girls on the other side, and at the end of each minute blow a whistle that allows the kids to walk halfway to the center--in theory they will never reach the center, but after about 20 minutes they will be close enough "for all practical purposes".
Having become a Wizard on n.p. 2183, the Yellow Piggy retroactively appointed his honorable self a Temporal Wizardly Piggy on n.p.1488, not to be effective until n.p. 2183, thereby avoiding a partial temporal paradox. Since he couldn't afford two philosophical PhDs to rule on the title.

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Re: 0994: "Advent Calendar"

Postby keithl » Mon Dec 26, 2011 7:28 pm UTC

Space Elevators? Planck Time? Oh come now, you would be thwarted by special relativity before encountering either! If the squares are 3 centimeters apart, then when you are only 10 rows below the last full row shown, between 153.5 and 76.7 picoseconds before midnight, your hand will need to move at 1.3 times the speed of light. A few squares before that, the gravity waves from the extreme acceleration and deceleration of your hand would melt the chocolate. And given time zones and the international date line, some clown in New Zealand could destroy the planet (with an increasingly dense stream of mouthbound chocolate creating a black hole) before you finished the first row.

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Re: 0994: "Advent Calendar"

Postby bigjeff5 » Mon Dec 26, 2011 7:36 pm UTC

adho wrote:
bigjeff5 wrote:so you can't be too hard on the guy


But YOU can be. You seem to have missed the entire point of a paradox. A series of statements that are acknowledged as true leading to a contradiction or impossibility.
Zeno was undoubtedly of great intelligence.
Far from being the most embarrassing problem, it was perhaps one of the most thought provoking, encouraging contemplation of infinitude and limits.


You seemed to have missed where the embarrassment comes from, and I don't think I made it very clear, which I apologize for.

Instead of exploring the implications of the fact that his logic, which was valid, did not match reality, which proved his conclusions incorrect, Zeno used this and several other similar paradoxes to argue what amounts to a religious belief.

It was a serious missed opportunity, that was saved by the fact that other philosophers were forced to form logical refutations of the paradox due to the heavy emphasis on logical argument at the time.

Again, the embarrassment isn't the paradox, it's a great logical conundrum. The embarrassment is what he was using them to argue for, which had scant evidence to support it. It's somewhat understandable though, because at the time physical evidence was not highly regarded among philosophers.

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Re: 0994: "Advent Calendar"

Postby danicastone » Tue Dec 27, 2011 4:12 am UTC

You've all forgotten the most important thing... getting the nearly-infinite-chocolates advent calendar into the store as soon as possible!

Seriously though, I would buy the hell out of this, even if (especially if) it began on the 23rd and ended at the last point when it was feasible to eat chocolates without choking to death. Christmas Eve should definitely become Vaguely-Educational Chocolate Orgy Day.


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