0969: "Delta-P"

[Retsam]

The fact that so many people are trying to do math based on the time dilation between Narnia and the real world probably has C.S. Lewis rolling in his grave right about now.

[Zassounotsukushi]

I'm usually a big fan of the underlying physics & maths on XKCD, but for some reason the equation in this one struck me as being a little odd...
why does the depth of the ocean factor in the initial flow rate?
Surely the water would start as a trickle and flow in faster as the wardrobe sunk and the water pressure around it increased?

I also have doubts about the equation that was used and that's the reason I registered here.

Honestly I don't understand the pop culture reference at all. I mostly don't care either. I just know that it's talking about some portal where there is an area opened up in the ocean.

Basically all this accounts for is fluid acceleration. No viscous forces, but we really don't care. The pressure at the depth in question is rho*g*h and it exits into a pressure of atmosphere, or basically nothing for our purposes. All of the static pressure is converted into dynamic pressure, being 1/2 rho*v^2.

rho*g*h = rho v^2 / 2

Q = rho*v*A

rho*g*h = rho (Q/(rho*A))^2 / 2

Q = A * rho * sqrt(2 g h)

So really? What the heck? Why is this different from the equation in the comic?

[Soralin]

The fact that so many people are trying to do math based on the time dilation between Narnia and the real world probably has C.S. Lewis rolling in his grave right about now.

Hmm, perhaps we should calculate how much energy would be produced by such rolling? http://dresdencodak.com/2010/06/03/dark-science-01/

[JoeZ]

The fact that so many people are trying to do math based on the time dilation between Narnia and the real world probably has C.S. Lewis rolling in his grave right about now.

I found it pretty amusing as well. Especially with so many people doing the math, as if nobody else had already done it, without bothering to read the whole *two pages* of this thread, which has already visited the topic at least five times.

Time dilation doesn't really work, anyway, because they are returned to child form while retaining memories. Impossible to explain without invoking the supernatural, unless you assume some absurd thing, like that the wardrobe can suspend their brains, relaunch their consciousness in separate duplicate bodies in Narnia, and then, back on Earth, release them from suspension shortly later while reprogramming their brains to include all the new memories at an impossible rate. That's practically supernatural, anyway.

And anyway, if Narnia is a whole, separate, universe, why does it need to have time parallel to our own? Shouldn't it have its own temporal dimension? Shouldn't a portal like the wardrobe be able to bridge any points in space-time between the two worlds?

Also, as long as we're overanalyzing fantasy fiction, assuming that the surface gravity on Narnia is the same as that of Earth (Which it appears to be, at least judging from the movies), wouldn't it take work to push the water from low potential energy at the bottom of the ocean to the higher potential energy at the level of the lamppost? That would also slow down the flow of water.

[galibert]

Anyone familiar with the effects of severe time effects know how forces like pressure work in boundaries?

Well, if you have a flow it's somewhat obvious. Let's use a 1e6:1 ratio which is somewhere in the middle of all proposals here. If you have a flow of one particle per second in Narnia, you see flowing in 1e6 particles per second in here. And since PV=nRT and V doesn't change, T doesn't change (no change in kinetic energy), and n goes up by 1e6, then P goes up by 1e6. Oops. The wardrobe has a 1megabar internal pressure. And more, since it's also heated by the 100MW/m2 of sunlight (photons flow too). Perhaps that's why it's in the dark, but even the body IR radiation of somebody passing through would melt the house, and probably the town around it.

There was a sf universe where time control was the basis of ftl travel and weaponry amplification, but I just can't remember which one.

OG.

[CatCube]

This was good for a chuckle. Leaving aside the time differentials (which I think have been beaten to death), the equation leaves out the effects of head loss. Normally, for a relatively large, short pipe, you could probably get away with that, but since frictional losses are proportional to the square of the velocity, it'll still be a very significant term for this particular situation.

[Tiberius]

Velocity isn't conserved across different inertial reference frames. Four-momentum is. So the time dilation problem is really nonexistent. Also why would you need to move the wardrobe around to get all of the oceans? You do realize that they are all sort of connected right?

[Soralin]

And anyway, if Narnia is a whole, separate, universe, why does it need to have time parallel to our own? Shouldn't it have its own temporal dimension? Shouldn't a portal like the wardrobe be able to bridge any points in space-time between the two worlds?

Well if they had two separate timelines, and you had control over where each portal connected to, then you could do something like go through the portal, and reorient it to point back to the past of the other world, and step back through it.

It would be less that time moves faster on one side or the other, and more just a relationship between when you entered on one side, and when you exited on the other. Say for example, entering at time x on one side, would always result in ending up at time y on the other side, and entering at time x+1, would have you exiting at y+10. In that case, it's not so much that time is moving faster or slower on one side, rather, it's a function of when a portal leads to, dependent on when you enter. And the portal on the other side could have the inverse. I mean, I suppose it doesn't have to have the inverse, but if it didn't, then you'd end up with the problem that moving through the portal one way, and immediately going back through the other way, could have you end up some time forward, or backward, of when you first entered.

Time dilation doesn't really work, anyway, because they are returned to child form while retaining memories. Impossible to explain without invoking the supernatural, unless you assume some absurd thing, like that the wardrobe can suspend their brains, relaunch their consciousness in separate duplicate bodies in Narnia, and then, back on Earth, release them from suspension shortly later while reprogramming their brains to include all the new memories at an impossible rate. That's practically supernatural, anyway.

Well, anti-aging and repair mechanisms are useful to have around, although the anti-aging section may be set a little over-zealously here, although I suppose it could just be set to identify you and revert you back to the age or physical state that you entered with from that side, or such. And who knows how invasive an inter-dimensional portal actually is? I mean, if this is something that can move objects between different timelines, then using a workspace timeline, it could literally have all the time in the world to disassemble, reassemble, repair, record, etc., whatever it sends through, and make it appear seamless. And no matter how long or short such a thing would take, whatever is passing through could end up at the same time on the other side, and in the same state.

Also, as long as we're overanalyzing fantasy fiction, assuming that the surface gravity on Narnia is the same as that of Earth (Which it appears to be, at least judging from the movies), wouldn't it take work to push the water from low potential energy at the bottom of the ocean to the higher potential energy at the level of the lamppost? That would also slow down the flow of water.

Depends on how it works, it would definitely have to get the energy from somewhere. If that had to come entirely from the kinetic energy of what's entering, then it would be really hard to get most objects through. The two sides would have to be at practically equal elevation. I mean, if the gravity is the same, and if there's even 10m difference in elevation, an object would have to be moving through it at at least the same speed as it would take to launch something 10m skyward here on Earth. If that's the case, then no water at all would flow through if the opening on the other side was above sea level(assuming gravity is the same, and sea level in the same, and the radius of the other planet is the same, etc.). It would also mean that could could effectively disable the connection, or make it rather deadly, by moving one end up a couple stories in a building, or any other change in elevation, or from minor differences in local gravity.

On the other hand, if it's drawing power from some other source that shouldn't be a problem, and if you have a device that can connect universes, you have a lot of power options available to you, like setting up a connection to the inside of a star.

Hmm.. I wonder if you could double the flow rate by removing the back of the wardrobe. Or is that a required component?

[Headshrinker]

Well the wardrobe decides what passes through, the children couldn't always get through, but if thats not the case victory in narnia would be to tell the britts about it, they send 1,000 troops and 5,000 colinisers for 10 days they come back with a million strong army of 300th centry tech. WW2 is won and narnia is defended.

science wise,,,
Could gravity pass through the wardrobe. What happens if you push it over.
Lauching the wardrobe into space would destroy narnia with a vortex.
Or as 1 second-earth is 1 year-narnia a shot traveling at 1 light-second per year will travel at 1 light second per second. You could fire a catapult at the lamppost to create a sigularity missile on earth.

Interesting weapons if we can get wormholes to work. link target with space/link target to object near black hole/link target to blackhole.

[cephron]

I agree with the people saying you can't establish some sort of time-flow-rate difference between Earth and Narnia. It seems to me that it is only when people are observing/passing through the portal that the time is synchronized in any way at all, and that when people are not observing/passing through the portal, it's anyone's guess how much time has passed on either side relative to the other. The portal seems to be under the control of Aslan or the Emperor-over-the-sea (essentially "God" in that universe) and thus acts not according to repeatable/derivable principles but according to the decisions of an intelligent entity.

Edit: although, just to have fun with the idea, tweaking fiction with a bit more fiction doesn't hurt

[Retsam]

To the people correlating Narnia with modern American politics: C.S. Lewis was a British author writing around the time of WWII. Lewis wasn't advocating anything to do with textbooks; in fact Lewis seemed to lean towards being a theistic evolutionist. (Though he mostly left the subject alone, which may perhaps be the wisest answer) Nor was Lewis trying to advocate serious law reform. It's silly to say "I won't read Narnia because there are Christians who support [those things]". If anything, that seems like a rather glaring inability to differentiate between individuals of a group, similar to opposing all Muslims because a few of them are terrorists.

If the Christianity mucked up the plot, or if they were in general simply badly written books that were only popular due the controversy that they incited (which is my impression of Phillip Pullman's work, especially the movie), but they're not. In the time that they were written, Christian children's novels were not controversial or uncommon. The only reason we talk about them is because they're exceptionally well written. It's just as much of a shame to me when I hear people say "I won't let my children read Narnia because it's Christian" as it is when I hear Christians say "I won't let my children read Harry Potter".


On a lighter note: I just remembered this comic, which some of this analysis reminded me of.

[Eternal Density]

If you like Narnia (or pro-Copernian planetary mythology, a topic which greatly interested C.S. Lewis) then you'll love this book, as I did: http://narniacode.com/ All the seemingly random details in each book now make so much more sense to me! Especially why the jovial Father Christmas shows up, which was always puzzling without any context.

Also, For SPAAAAAAAAAAAAAAAAACE! And for Aslan!!

[fr00t]

I am strongly pleased by this comic.

I remember narnia so fondly; I'm afraid to go back lest the religiosity ruin good memories. Though, even as a child the ending was incredibly bad. In my interpretation the whole thing casts faith in a negative light, as the metaphor of lion-jesus pushing the win button makes for an absolutely terrible work of fiction.

[dysprog]

Is it worth reading or watching?

Myself being a Christian, I can say that it was very worth reading. The recent movies also do a decent job. I can see how a non-Christian may not like it due to the Christian nature, but imagine that it is still quite entertaining.

As an atheist, I can tell you that I have absolutely no problem at all with the Chronicles of Narnia. In the early books especially, the christian allegory is light enough to be ignored.

[Zassounotsukushi]

I was wrong!

I had been solving for the mass flow rate. The comic is about the volumetric flow rate.

The area is 1m x 2m by the way. You probably would have guessed that anyway. But some idiots were talking about water leaking through the holes punched to attach the anchor. I don't really know anything about Narnia. I just know it gets flooded in the comic.

[Solandri]

Calculating this out, Earth time is about 5.433 X 10^-8 times Narnia time. So factoring this into the equation the actual flow rate is 0.0217 L/sec. This would be the equivalent of a bad leak in our garden. So no doubt the evil white witch will be inconvenienced by this. Now here is a more interesting question... what happens if the white witch, in order to save her Rudabegas, decided to solve the flooding issue by plugging the hole? Anyone familiar with the effects of severe time effects know how forces like pressure work in boundaries?

Pressure is just force divided by area. Assume the area is the same on both sides and the problem simplifies to a force balance between two different time flows, which you can probably equate to the water's mass increasing by a large amount as it crosses the threshold.

The bigger problem is that nearly all forms of teleportation violate conservation of energy. Normally when a pressure vessel underwater implodes, the energy released is just the pressure times the volume. By adding teleportation to the mix, you've turned that into the mass of the entire ocean accelerated to 200 m/s, which needless to say is much, much larger. Stick a hydroelectric turbine generator on it, and after the wardrobe has flooded Narnia you lift it above the ocean's surface to let the water drain back out of Narnia. And there's your perpetual motion machine.

[InfinityLink0]

Another problem we need to consider when looking at this situation is whether gravity is conserved through the portals. In the game Portal it wasn't, but seeing as light is conserved (as evidenced by the 4 children being able to see each other as they were going through the wardrobe one at a time) I see no reason why it wouldn't be in this situation, as the force behaves (at least according to the standard model) similarly. If the wardrobe settled on the ocean floor face down -- and as the open doors would shift the center of mass forward, this seems probable -- than the gravitons of the Earth would travel through the wardrobe and pull on things horizontally in Narnia. A beam of gravitons traveling in a straight line from the wardrobe would travel across Narnia accelerating anything it encountered towards the lamppost. This effect would change the behavior of the water two different ways. If you think the temporal shift to Narnia is not abrupt, more of a gradient as described previous posters, this effect would merely weaken the surge of water. But if the time shift reduces the surge of water to a trickle, than the gravitons would also slow. I'm not sure what effect this would have on the observed force of gravity.

[StClair]

i came for the religious battles, thus i am disappoint.

Stick around for a bit - someone just called global warming/climate change a "fairy tale" for the "tree huggers."

[InfinityLink0]

i came for the religious battles, thus i am disappoint.

Stick around for a bit - someone just called global warming/climate change a "fairy tale" for the "tree huggers."

Are you suggesting that the debate over Anthropogenic Global Warming is a religious one? While the disregard for evidence and myopic close-mindedness of the alarmists has given a belief in the issue a religious quality, it is certainly not religious.

Nothing against religion (I'm a Christian myself), but taking things on faith should stay in religion, and looking at facts and evidence needs to be used in the scientific method.

[ITD]

Is it worth reading or watching?

Myself being a Christian, I can say that it was very worth reading. The recent movies also do a decent job. I can see how a non-Christian may not like it due to the Christian nature, but imagine that it is still quite entertaining.

As an atheist, I can tell you that I have absolutely no problem at all with the Chronicles of Narnia. In the early books especially, the christian allegory is light enough to be ignored.

Also, as an atheist (and Jewish to boot), I found that enjoyed looking for the Christian references. It was almost like a treasure hunt, or an Easter Egg hunt ( ), trying to see if I could find them all. Dawn Treader was my absolute favorite.

[Harry Voyager]

Had to copy the image to another tab in my browser to read it.

And lest we forget, the wardrobe is selective about when it opens up. Sometimes it's just a wardrobe.

I hate that the "Chronicles of Narnia" movie series died just before my favorite story in that series, "The Silver Chair". But then, "Voyage of the Dawn Treader" is my second-favorite story and the movie hardly did it justice, so perhaps it's just as well.

I recall that the BBC version got through the Silver Chair, and did a pretty good job of it. THey even manage to get Tom Baker playing the Marshwiggle.

The mental image of Aslan with the Space Core is hilarious.

"Son of Adam"
"Space Adam?"

Just remember, omnipotent also includes omnipatient. It also includes onmi-nuke, but we'll get there in its due time.

Anyone else heard of the DnD campaign where one guy had a ring of transportation thrown into the sea, and the other half of the pair had an adamantium plate with a small hole welded to it?

I knew a guy who managed to work the rules of one campaign such that he was able to teleport antimatter into the Underdark. I'm told that ended the campaign, and promoted his character to a god.

[Airbuilder7]

The fact that so many people are trying to do math based on the time dilation between Narnia and the real world probably has C.S. Lewis rolling in his grave right about now.

Hmm, perhaps we should calculate how much energy would be produced by such rolling? http://dresdencodak.com/2010/06/03/dark-science-01/

Haha, I enjoyed the comic. Never seen it before; thanks for linking! It kinda reminds me of "Girl Genius," only more dystopian. (And, given the focus on cybernetics and prosthetics, is there any connection between Dr. Kusanagi and Maj. Motoko Kusanagi from "Ghost in the Shell"?)

[TiLt]

How big are those doors?
400000/(sqrt(2*10*2000))
= 2000m^2
which means that those doors are about 44.7m by 44.7m

[Piogre]

Am I the only one who thinks there was a basic mix up here?

It seems like the concept is water would appear flowing much faster in narnia, so the major water flow would become catastrophic, due to time dialation.

but if this is the case, there was a mistake, because one second here is a longer time there, so water flow would be minimal


seems like a better use would be to use it to break falls, by putting the wardrobe horizontal at the base of a building, then your velocity is slowed WAY down and you're fine

but now I'm just thinking about portal physics...

[CatCube]

How big are those doors?
400000/(sqrt(2*10*2000))
= 2000m^2
which means that those doors are about 44.7m by 44.7m

Watch your units. The comic says 400,000 liters per second. You have to divide by 1000 to get m^3/s, which matches the 2000 m and 9.81 m/s (≈10 m/s) that you've used elsewhere. It works out to about 2 m^2, which is about right for a standard door 36" wide and 80" tall. (Whether the wardrobe is about the same size is arguable--I'm not sure the book actually specified, and I don't know what the average size of a wardrobe in WWII-era British manor would be.)

[Wilhelm]

Narnia, math and Portal 2?

Good show, Randall!

[Pfhorrest]

No Christian I know (and, considering I'm a Christian myself, that's quite a few) believes there is any such impending Noah-esque flood; indeed, the Bible clearly states God's promise not to ever flood the entire Earth again after the Deluge.

Random thought: if the world were to flood in Noahide proportions, how many Christians would that dissuade from their faith? Probably just the literalists, I imagine. (On a related note, I'm curious what the non-literal interpretation of Noah's flood is; the "days" of creation are interpreted as cosmological epochs, what is the Flood [complete with Noah, etc] interpreted as?)

[Dinoguy1000]

No Christian I know (and, considering I'm a Christian myself, that's quite a few) believes there is any such impending Noah-esque flood; indeed, the Bible clearly states God's promise not to ever flood the entire Earth again after the Deluge.

Random thought: if the world were to flood in Noahide proportions, how many Christians would that dissuade from their faith? Probably just the literalists, I imagine. (On a related note, I'm curious what the non-literal interpretation of Noah's flood is; the "days" of creation are interpreted as cosmological epochs, what is the Flood [complete with Noah, etc] interpreted as?)

True, us literalists are wholly unprepared for the possibility of another global-scale flood.

The non-literal interpretation of Noah's flood was that it was unusually severe flooding around rivers (or a catastrophic rise in the water level of the Black Sea caused by the Mediterranean Sea breaching a sill in the Bosporus Strait, if you subscribe to the Black Sea deluge theory).

[Bugzaren]

I think the idea of dropping the cupboard into the ocean is looking in the wrong direction.

If you want to kill the white which (and the rest of Narnia as well) sent the cupboard into space. Eventually all the air would flow out of Narnia and everyone would suffocate.
This would also solve the problems of the doors of the cupboard eventually closing since the pressure would be on the inside instead of the outside.

Also it would become rather windy in Narnia.

[Grog]

Speaking of fairy tales: Global warming. (don't call it "climate change" if you still want so say the sea is rising) During the height of Roman power the sea level was a least 2 feet higher. Almost immediately after the Ice age ended the sea level was 3 yards or 9 feet higher than it was today. Really what we need to worry about is tree huggers keeping us from having fun. (note: not written in a condescending tone)

To act like I really care: Narnian world was flat or something like that so the water would just flood off the edges draining our oceans near completely rather than drop our ocean a comfortable few feet.

OT: Two recent studies show that:
a) Global warming is real (but this now accepted, because all along the centuries climate has changed)
http://www.sciencedaily.com/releases/2011/10/111021144716.htm
b) This is the first time in the last 20'000 years that temperature are rising in both emisphere, and not only one, without any major event involved (like volcano eruptions). The only possible explanation is the human impact on the carbon cycle:
http://www.sciencedaily.com/releases/2011/10/111021074532.htm

So much for the fairy tales.

In Topic: it took me minutes of blank staring to understand it, but then I couldn't stop smiling.

[mturyn]

I wanted to go live with the Scrubbs, whom I always assumed were being painted over-nastily.

And, for that matter, I should probably have enjoyed the company and opinions of Vita Sackville-Baggins, and her notional cousin Rebecca Baggins.

Note: I liked the first book until the leo[?---please decline] ex machina at the end, didn't care for the rest until "The Magician's Nephew"---a demned fine buke---and loathed the last for as long as it took to slog through it---which same doggedness got me through the last of the Pullman trilogy. I can't hear plot or characterisation or music in the language over the noise of axe-grinding.

[yurell]

Q = A * rho * sqrt(2 g h)

So really? What the heck? Why is this different from the equation in the comic?

They're the same. His Q is your Q/rho — you've done it in mass per unit time (hence why you have density there), while the comic is in volume per unit time.



That said, with the time dilation thing ... what if the Witch does it the other way? Water coming from Narnia would flow incredibly quickly.

[Eebster the Great]

The fact that so many people are trying to do math based on the time dilation between Narnia and the real world probably has C.S. Lewis rolling in his grave right about now.

Hmm, perhaps we should calculate how much energy would be produced by such rolling? http://dresdencodak.com/2010/06/03/dark-science-01/

I loled when I saw "Man and Superman."

That said, with the time dilation thing ... what if the Witch does it the other way? Water coming from Narnia would flow incredibly quickly.

She would first have to find Spare Oom.

[eatadonut]

I always assumed that Narnia was a dream-world, and that the children never actually went there as much as entered stasis in the forest of coats, and controlled avatars of themselves. This solves time problems neatly.

And, since you no longer have to deal with conservation, I think it's safe to assume that water would flow into Narnia at the same explosive rate it entered the wardrobe. At least, it would in Hollywood.

[rhhardin]

Dimensional analysis always gives the same answer for water and gravity.

[Pike]

Anyone familiar with the effects of severe time effects know how forces like pressure work in boundaries?

Well, pressure is force over area. Force is mass times acceleration, and acceleration is distance over time squared.
So perhaps pressure could have a relationship to the inverse square of time.

Say the 'rate of time' is ten times slower in Narnia than on earth - that would imply that the pressure exerted by the ocean on the wardrobe opening (on Narnia side) is a 100th of the pressure on the Earth side of the wardrobe.

Thinking about the energy of the actual particles as the move from earth to Narnia makes a nonsense of that logic though.

Basically the answer is; if you don't think about it too much, it all makes sense.

[Fire Brns]

Problem: Raising ocean levels due to climate change...

Speaking of fairy tales: Global warming. (don't call it "climate change"... During the height of Roman power the sea level was a least 2 feet higher. ... after the Ice age ... sea level was 3 yards or 9 feet higher ... Really what we need to worry about is tree huggers ...

You are being dismissive lol. Extreme sacasm BTW and you were taking a subpar comic and making it less funny.

[Fire Brns]

OT: Two recent studies show that:
a) Global warming is real (but this now accepted, because all along the centuries climate has changed)
http://www.sciencedaily.com/releases/20 ... 144716.htm
b) This is the first time in the last 20'000 years that temperature are rising in both emisphere, and not only one, without any major event involved (like volcano eruptions). The only possible explanation is the human impact on the carbon cycle:
http://www.sciencedaily.com/releases/20 ... 074532.htm

Whenever I see a study like this the temperatures are taken from different location over time. Once cited in antartic study as "recording site too cold to return to" You won't convince me and I won't convince you because simple data "interpretation" is proof enough for you the way the existence of scriptures is proof enough for a hard core Christian. Stop bringing this up, My reason for original posting that is in my previous posting.

Edit: grammer

[danix]

seems like a better use would be to use it to break falls, by putting the wardrobe horizontal at the base of a building, then your velocity is slowed WAY down and you're fine

but now I'm just thinking about portal physics...

You'd land in the snow, though your vertical speed would turn into horizontal speed.

Now you're thinking with portals!

[Spectrum]

Two important points that have been overlooked:

1) It would take a while for the wardrobe to sink 2 km, and the flow rate through the portal would increase relatively gradually. So the White Witch would probably have plenty of time to get away, but in any case, she definitely would know what hit her.

2) Following the dictum:

Only on Xkcd can you start a topic involving Hitler and people spend the better part of half a dozen pages arguing about the quality of Operating Systems.

I observe that C. S. Lewis' concept of parallel universes can be applied to the comparison of the Linux and BSD kernels.