Sunday, March 9, 2014

Anti-Paradox


I have become accustomed to using the word "anti-paradox" to describe a particular kind of time travel oddity.  I first encountered this word either on Wikipedia or TVTropes (sometimes it's hard to tell).  Now, despite my constant searching, not only can I not find the original article, but I cannot find any article anywhere on the internet using the word in the way I remembered seeing it.  The definition, as near as I can remember it, is as a follows:

An anti-paradox is a self-supporting, self-validating, tautological statement or situation.

It is a statement that is true precisely because it is true.

One of the examples that the article gave was the Robert A Heinlein book, "All You Zombies".   But that plotline is convoluted, and gross, so let me give a simpler example of a time travel anti-paradox.

A man is sitting in his room.  Suddenly, in a whir of sound and light, a metallic box appears in the room with him, and out steps an elderly gentleman.  The elderly fellow explains that this box is a time machine.  The elder has finished with time travel and wants to end his days as he remembers them before he left; and so, he is giving the machine to the younger man.  The younger man takes the machine and travels up and down the timeline, meeting famous people from history and exploring the technology of the future.  After decades of time travel adventures, saving the world from evil robot kings and stopping the Eiffel Tower from collapsing (he succeeds), the man becomes tired.  All this moving.  He wants to stop, and find some time, and just stay there.  But the only time he really remembers having any attachment to is the time before he left.  And so he returns to that day when he first got in the machine, and hands it off to his younger self, and stays there in his own time until such runs out.

This situation is an anti-paradox.  The man gets the time machine because he has the time machine because he gets the time machine because he has the time machine.  The attainment of the time machine is the cause of its own attainment.

This isn't contradictory, nor does it even offer an apparent contradiction.  It might be more correct to say that it makes too much sense.  The "problem" with it is that it doesn't have any exterior input.  No one builds the time machine.  The man has a time machine because he has a time machine.

I distinctly remember reading this situation as being called an anti-paradox.  Can anyone corroborate this?

If not, then let me propose the word for general use.  Anti-paradox: a self-supporting, self-validating tautology.

Friday, March 7, 2014

"Why Don't They Just Use the Time Turners to..."


The following video about sums up the way most people think of the Time Turners.

Why don't you just use them to travel back and kill Voldemort?  Or even Hitler?  As Snape says, you'd save countless innocent lives in the future.

I have never held back from criticizing Harry Potter.  Actually, I have kind of a hate-crush on the series.  Despite my sometimes overzealous criticism of everything about Harry Potter, the function of Time Turners as seen in Prisoner of Azkaban is the best depiction of time travel that I have yet encountered in any fictional medium.  It is one of the primary things in the series that I have to say, Rowling did perfectly.

Which is weird, because it's the most obvious point of criticism from everyone else.

Whenever you want to ask yourself the question, "Why don't they just go back in time and ...", stop, and ask yourself instead:

"Why don't they just not go back in time and rescue Buckbeak?"

Maybe that's too abstract at the moment.  Let me try something else.

You can go back and try to kill Voldemort.  Just get a Time Turner and spin it back a billion times.  Go ahead.

Most wizards are terrified of time travel.  The effects are supposed to make you go mad.  Wizards are cool with literal ghosts living in their rooms, and with dragons in their banks, and with actual fortune telling, and with lifting objects off the ground with magic, but they are absolutely superstitious about time travel.

Why are they superstitious about it?  Because weird, looping oddities occur that cause all of the wizards to experiment with time travel to go crazy.

from SMBC
Point is, most wizards avoid time travel.  Those that experiment with it are eccentric, even by wizard standards.  So it's possible that someone has actually used a Time Turner to kill Voldemort.

It just didn't work.

It's possible every time wizard to ever exist has gone back to kill Voldemort.  But it never works.

It will never work.

You can go back in time to kill Voldemort.  But you won't.

I know you won't, despite all your effort, because Voldemort doesn't die until the time of the story.

It's not like your free will is impeded.  You can try all you want and do whatever you want to kill Voldemort.  No mystic force is going to tug at your insides and prevent you from pulling the trigger.  If you think about it, there is nothing impeding my free will when it comes to wining the Olympics.  But I'm never going to.  And you're never going to kill Voldemort.

Its physically possible to kill him.  Your bullets won't bounce harmlessly off of his chest, or stop in mid-air right in front of him, or whatever.  Not like you'll get far enough to find out, though; if your bullets were about to hit Voldemort, then they would hit Voldemort, and he would die.  And Voldemort doesn't die at that time.  So your bullets won't get close enough to prove they could hit him.

You're not going to kill Voldemort, because you're just not going to.  There's no better explanation.  You just don't.

If you did, he wouldn't be the antagonist of the book series.  And yet there he is, Avada Kedavra-ing people all over the place.  So whatever plans you make to kill him in the past, they just aren't going to work (and may just exacerbate the problem), and you should move on and try something else.

Please note how the causality works here.  I am not saying
Voldemort is alive in 1994 ----> You can't kill him in the past.
I am instead saying
You don't kill Voldemort in the past ----> Voldemort is alive in 1994.

So back to the original question:
"Why don't they just not go back in time to save Buckbeack?"

Think of what it entails that they do go back to save Buckbeak.  During most of the events leading up to the Shrieking Shack, there are two copies of Harry and Hermione.  One copy follows the other, and the two interact to a substantial extent.  We don't see the second copy because they stay hidden, but we do observe their actions as unexplained anomalies that occur to the primary copy.

By the time the group gets to the hospital room and Dumbledore advises them to use the Time Turner to save Buckbeak and Sirius, those events have already happened.

This is important.  The copy of Harry and Hermione seen by the protagonists when they travel back in time is not some fictional, hypothetical alternate timeline Harry and Hermione.  They are seeing Harry and Hermione.  That is, they are seeing themselves.  Just a few hours ago.  We just read about these parts.  These are the Harry and Hermione.  There are no Timeline A and Timeline B versions of the two; there's just Harry and Hermione, and the things that they cause to occur have already, in fact, occurred.

We saw these events forward, then reversed, then saw them again from a different perspective.  We did not switch tapes.

And here we have a situation that speaks to the reverse of the usual time-travel paradoxes.  The most famous, namely the grandfather paradox, asks what would happen if you went back in time and killed your grandfather (or yourself), thus ending your existence before you can go back in time to end your existence.  Another, related paradox asks what happens if you go back in time to kill Hitler, or save the Titanic, or whatever; if you succeed, then you erase your motivation for time traveling in the first place, so you would never time travel, which means you would never make the change, which means you would time travel.

This time we ask a weirder question, sometimes called an anti-paradox: what if Harry doesn't travel back in time, and therefore doesn't save himself from the Dementors?

Clearly, by the time we get to the part where Dumbledore recommends time travel, Harry doesn't have a lot of options.  If he decides not to, then he must already be dead.  But Harry isn't dead.  So Harry is going to decide to travel back in time.

However, it isn't just limited to Harry.  If Harry decides not to travel back in time, then Buckbeak must be already dead.  But Buckbeak isn't dead.  So Harry is going to decide to travel back in time.

And it isn't limited to who's alive and who isn't.  If Harry decides not to travel back in time, then those rocks in Hagrid's garden don't get thrown.  But the rocks in Hagrid's garden do get thrown.  If Harry doesn't, the blades of grass he stepped on won't get pushed down in quite the same way, but they do get pushed down in quite that way.  If Harry doesn't, the molecules of water in the lake won't get stirred up like they do, but they do get stirred up like they do.  The oxygen molecules he breathed wouldn't have been turned in to carbon dioxide, but they were turned in to carbon dioxide.  The entropy of Scotland wouldn't have seen any contribution from Harry's metabolism, but entropy did increase from Harry's metabolism.  On and on.

Every single infinitesimal impact Harry had on the universe would not have occurred, and they all did occur.  Maybe humans didn't notice each little thing like entropy and O2 --> C02 reactions, but physics is notoriously unconcerned with human cognizance.  Those things did happen, and in fact we "saw" them happen on screen the first time through, before Harry and Hermione decide to go back in time.

So that's why they don't use the time turner to stop Voldemort.  Because everyone to use a time turner to stop him fails, has failed, and will fail.  It's a plan that never works and will never work.  There isn't even any reason to try, and anyone who has tried to do anything with time travel has gone insane or worse.

As to why our heros don't at least attempt it, maybe it's because if they did, then the story would be about their colossal failure and collapse into madness, which isn't the sort of thing that tends to make it in to books.  At least not children's books.

So, despite everything else I've said on the subject, when it comes to time travel, I really have to tip my hat to Rowling.  She did it very well.

Of course, the real question is why wizards would take literally the most dangerous item they know of -- so terrifying that people accustomed to conversing with ghosts leave them locked in a special, secret vault deep underground where no one can find them -- and lend it to a 13-year-old girl so she can get to her classes on time.  But that's another post.

Thursday, February 20, 2014

Opposed Checks in D&D are the Same as Coin Flips

This is a lesson in statistics and probability, as applied to the popular Dungeons and Dragons role playing game.  I'm having trouble lately with the LaTeX embedder: if you see a lot of dollar signs and slashes, then check your plugins and permissions on your browser and allow MathJax to work, so you can see the equations better.

At least since version 3.0, the Dungeons and Dragons rule book has featured a rule of opposed checks.  These are supposed to represent, using dice, the opposition of two separate skills: so, your ability to Hide versus the orc's ability to Spot; your ability to tie a rope versus the orc's ability to escape from bonds.  You roll your skill, the orc rolls his skill, you apply modifiers, and the higher outcome wins.

Even before this, rolling dice was a common way to set the difficulty of something in old versions and in other non-d20 games.  How hard is the door to force?  You didn't think of it, now you're on the spot, so you roll a die to figure out how hard it is.  Then you tell the PCs to beat that number on their own roll.  Makes sense.

Doing checks this way is, from a probabilistic point of view, about as good as flipping a coin. The probability of the PC winning is slightly more than 50-50.  In terms of DCs, an opposed check (before modifiers) is equivalent to a DC of 10.5.

I'll prove it.

When you roll a die, a number comes up.  A random number, hopefully.  If the dice has $n$ sides, then this number is between $1$ and $n$.  It is customary to denote a random number with a capital letter: in this case, I'm going to call $X$ the result of rolling the die; $X=1, 2, 3,\ldots, n$, depending on what we roll.

If we consider some number between $1$ and $n$, say 6, then the probability that $X=6$ is, as we all know, $1/n.$  It is common to write this as $\Pr(X=6) = \frac{1}{n}.$  And, of course, it isn't just for $X=6$ that this is the case, but for any number $x$ between $1$ and $n$.  More generally, for any such $x$, we write $\Pr(X=x) = \frac{1}{n}.$

In our case, we are going to roll the same die twice.  This gives us two random numbers (the results of the two dice), which we will call $X_1$ and $X_2.$  For concreteness, suppose this is an opposed strength check between the PC and an Orc.  We'll say that $X_1$ is the die we (the GM) roll for the Orc, and $X_2$ is the die that the PC rolls.  We want to know $\Pr(X_2 \geq X_1)$, that is, the probability that the second result is higher than the first or in game terms, the probability that the PC wins his contest against the Orc.

This could go a number of ways.  The GM might roll a 1, in which case the PC is guaranteed to win, or the GM might roll a $n$, in which case the PC has to also roll $n$ or lose, with other possibilities in between.  But we don't want to consider the probability of the PC winning given some particular roll from the GM, because that's trivial.  So what we want to do instead is consider all of these possibilities.

We look at
$$\Pr(X_2\geq X_1) = \sum_{x=1}^n \Pr(X_2 \geq x) \cdot \Pr(X_1=x),$$
which means that we consider the probability of the GM rolling some number $X_1=x$, then multiply by the probability of the PC winning given this roll, then consider this for all the possible $x$ the GM might roll and add these together.  That gives us the probability of the PC winning his roll, regardless of what the GM rolls.

Breaking this down, we find
$$\Pr(X_2\geq X_1) = \sum_{x=1}^n \sum_{y=x}^n \frac{1}{n} \frac{1}{n} = \frac{1}{n^2}\sum_{x=1}^n\sum_{y=x}^n 1 = \frac{1}{n^2}\sum_{x=1}^n (n-x+1).$$
Stopping for a second, for people less familiar with this stuff, the $\sum_{y=x}^n$ term means that we add up every value of $X_2$, starting at $x$, and ending at $n$.  Concretely, if we're rolling a d20, and the Orc's roll is $X_1=15$, then we add up contributions from $y=15,16,17,18,19,20,$; that's $6 = 20-15+1$ terms we consider.  More generally, it is $n-x+1$ terms, which is why we wrote $(n-x+1)$ there.  Moving on,
$$\Pr(X_2\geq X_1) = \frac{1}{n^2} \left(\sum_{x=1}^n n - \sum_{x=1}^n x + \sum_{x=1}^n 1\right) = \frac{1}{n^2}\left(n^2 - \sum_{x=1}^n x + n\right).$$
The term $\sum_{x=1}^n x$ means the sum of the first $n$ numbers.  So,
$$\sum_{x=1}^n = 1 + 2 + 3 + 4 + 5 + \cdots + n.$$
Those who've had Calculus will be familiar with this, but other people maybe no so much.  There's a beautiful formula due to Gauss, arguably the first person to discover it, whose proof is even more beautiful.  Consider the following image:

This shows a bunch of stacks of squares, increasing from 1 to 2 to 3, on up to $n$.  The area of these squares is $\sum_{x=1}^n x.$  Now consider a second one of exactly the same size: the two interlock, forming a rectangle:

The width of the rectangle is $n$ and the height is $n+1$, so its areas is $n(n+1)$.  But the area of the rectangle is equal to twice the area of the stacked squares!  Therefore,
$$\sum_{x=1}^n x = \frac{n(n+1)}{2}.$$

So then, carrying on with our equation, we now have
$$\Pr(X_2 \geq X_1)  = \frac{1}{n^2}\left(n^2 - \frac{n(n+1)}{2} + n\right) = 1 - \frac{n+1}{2n} + \frac{1}{n} = \frac{2n - n - 1 + 2}{2n} = \frac{n+1}{2n},$$
which, as I said, is slightly better than 50% probability.

For a 6-sided die, it is $\frac{7}{12}.$  For a 20-sided die, it is $\frac{21}{40}$, which is a 52.5% chance of success, which corresponds to a DC of 10.5.  A flat DC 10 is a 55% chance of success.  So rolling an opposed roll for the Orc is the same as considering the Orc's passive check.

That is without modifiers.  To include modifiers, start at flat DC 10, and modify as
$$DC = 10 + (\text{Orc's mod}) - (\text{PC's mod}).$$
For an Orc with +3 and a PC with -1, the check would be at
$$DC = 10 + 3 - (-1) = 14.$$
This will be (mostly) statistically equivalent to a modified opposed check ($\pm$ a 2.5% sliver of probability)

I did this all for dice, which are what is relevant to RPG players.  For dice, the result is not quite $1/2$ because the rolls can only equal certain specific results (like 1, or 7) and a tie goes to the player, but in a general case, it is actually true that the probability of a second random number being larger than the first random number is exactly $1/2$: that is, $\Pr(X_2>X_1) = \frac{1}{2}.$  I'll prove it.

So, consider  $X_1, X_2$, which are still random numbers, but not necessarily from a die.  For instance, we might push blocks on ice, and $X_2$ and $X_1$ gives the distance the blocks travel before coming to rest.  Or throw darts at a wall and $X_2,X_1$ are the distances from a bullseye.  Or something.  It's also not necessarily that case that every possible value is equally likely.  For a fair die, every number has probability $1/n$ or coming up; for throwing darts at a bullseye, if we're any good, then we will be more likely to be near the bullseye.  Let $\Pr(X=x) = p(x)$, where $p(x)$ is just some function: give it a value $x$ and it gives you a probability $p$.  Here $p(x)$ is called the "probability distribution function".  For simplicity, we also consider $\Pr(X\leq x) = F(x)$, called the "cumulative density function".  This is the probability of $X$ being less than some value $x$; as we'll see, a separate symbol for this is really useful.

As before, we have
$$\Pr(X_2\geq X_1) = \int \Pr (X_2\geq x)\cdot\Pr(X_1=x)dx = \int (1-F(x))p(x) dx = \int p(x)dx - \int F(x)p(x)dx.$$
You may be wondering what the weird S is, the $\int$ thing.  That's an integral sign, and it basically just means "add up all the possible values of $x$."  It's different from the $\sum$ symbol in that $\sum$ considers only discrete values while $\int$ considers continuous spectra of values.  We have used here the fact that $1 = Pr(X\leq x) + Pr(X\geq x) = F(x) + \Pr(X\geq x)$ to express this in terms of $F$.

If we add up all the probabilities of things happening, we should get 100%; that is, $\int p(x)dx = 1.$  This makes sense; the probability that we roll a 1 or a 2 or a 3, etc, is 1.  So
$$\Pr(X_2\geq X_1) = 1 - \int F(x)p(x)dx.$$
To fully evaluate this, we can write it another way.  Think what happens if, instead of rolling for the orc first then making the PC roll higher than that, we have the PC roll, then roll for the orc and make sure the orc rolls lower.  It's the same thing in the end, but can be written as:
$$\Pr(X_2\geq X_1) = \int \Pr(X_2 = x) \Pr(X_1 \leq x) = \int p(x) F(x) dx.$$
Comparing these two,
$$\int p(x) F(x)dx = \Pr(X_2\geq X_1) = 1 - \int p(x) F(x)x,$$
which must mean $\Pr(X_2 \geq X_1)  = \int p(x)F(x)dx = 0.5.$

So, the long and short of it is, if we have two random numbers that we produce in the same way, one after the other, and we want to know the probability that the second is larger than the first, then this is 50%.  In terms of D&D, this means that if you generate the DC for a skill check by rolling a die, then have the PC roll to beat that die, then you may as well flip a coin to accomplish the same thing.  This also means you can fix the DC of the opposed rolls at 10, and just add the Orc's bonuses and subtract the PC's bonus to increase the DC; it achieves the exact same thing.

If this result is unsatisfying to you, consider using a different system of opposed rolls that changes the dice used by each party, for slightly swingier results.

Note: this was originally written on 2/20/2014, but was updated on 5/7/2018 to make the wording more clear.

Wednesday, January 29, 2014

Speculating on Blindsprings


I recently stumbled on to a web comic called Blindsprings, after seeing a banner ad for it.  Let me take this time to recommend it to you.

Blindsprings is a comic that just went online back in October.  If you go to the website, you can see that not much has happened yet.  As such, it's hard to gauge just what the story is or where it's going.  So far though, surmising from the information available, I think this has the potential to be something really, truly great.  What is also exciting is being able to see the story develop from the beginning.

Plus, the artwork is beautiful.

this was the ad for it
Here's a non-spoilery description blurb of it:

The main heroine is a young girl named Tamaura.  She lives alone in the forest, where she attends to animals and plants trees and performs many other tasks for a shady group known as "the spirits".  It's a simple, idyllic kind of life.  One day she meets a young man named Harris, who has heard a fable of her and came to investigate the truth of it.  The two become friends, and after spending time with her, Harris decides to go off to a place called Kirkhall to study what is called Academic Magic.

The setting is not the standard "medieval" fantasy kind of setting, but something more like early Enlightenment era.  Really, not much of it has been revealed yet, so that's mostly a surmisation.  We are not even finished with the prologue.

Go read it.

After you've read it, come back here and let's talk about it.  There's not much of it (so far), so should be easy.

There are SPOILERS below.

Sunday, January 26, 2014

What is Spin? A Concrete Explanation.

To say that a particle has "spin 1/2" is to say that it must be rotated through 720 degrees before it can return to its original configuration.  This is not something normally witnessed in the world of classical mechanics, and so this aspect of quantum mechanics is often piled up with unhelpful metaphors and mysticism.

I wrote a post previously trying to point out that quantum mechanical spin is just a degree of freedom.  Spin tells you the components of a particle in a combination of two wave states with the same energy.  You can make pseudospins and isospins with any two such states, no matter what they are.  When you rotate the system, the components get mixed up -- just like angular momentum states.  You have to rotate the system by 720 degrees before the components get mixed up enough to be un-mixed up (i.e. back to there they were).  That's all it is.

What gives spin states this weird property is that the space of rotation is three dimensional, but the spin "vector" is only two-dimensional.  Rotations of typical vectors with three components (even if one of those components is zero) work just the way you'd think they should.  But, it's not completely surprising that 2D objects in 3D space don't rotate like 3D objects in 3D space.

To illustrate where spin comes from, and how it contrasts to orbital angular momentum, consider the case of rotation in 2 dimensions.  The best way to talk about rotations is to start at the unit circle.

Thursday, January 23, 2014

Everything Cool is Impossible


Physics has known for a long time how to build a time machine.  The possibility in a real spacetime geometry was first noted by Van Stockum, but this possibility was only really first analyzed by Frank Tipler in the 70's.  All you need is a massive rotating cylinder.  And also it has to be infinitely long.

This illustrates how frame dragging
can lead to time travel 
Since then, at least a dozen other possibilities have been proposed for time travel to the past, and physicists have proven that these spacetime geometries result in what are called "Closed Timelike Curves" (CTCs), which are trajectories a massive object could follow to go back in to its own past.  We know that they would work within the theory of General Relativity.  But, they're all impossible.  They either require the universe to be rotating (it isn't), they require infinitely large systems (we can't make them), they require negative-mass matter (no such matter exists), or they require you perform your time travel within the interior event horizon of a Kerr black hole (which is fine, but then you can't leave).

This situation is worse than merely having a concept of physics that excludes time travel, or that merely says that time travel is impossible.  For if time travel was excluded by theory, then we could always say the theory was incomplete.  What we have instead is a system that fully allows time travel possibilities without prejudice, as long as we're able to break some other law of physics to get there.  It's not just the stubborn "no" of a parental figure; it's like having your parents describe step-by-step exactly what you can do to eat chocolate cake for breakfast, and one of those steps is "eat infinite broccoli".

Physics also knows how to effect FTL travel.  The speed of light puts a prohibitive barrier on
our ability to explore the stars, but a number of work-arounds have been proposed.  Technically, relativity only prohibits local FTL movement, but says nothing of global FTL travel.  So if you can distort space and time in just the right way, you can move however fast you want.  One of the more frequently explored proposals is wormhole travel.    Wormholes produce a kind of "short cut" in spacetime, and it is actually a Federal Law that when you want to discuss how wormholes work you must draw two dots on a sheet of paper, "A" and "B", draw the straight line connecting them, then fold your paper so "A" and "B" touch and jab a pencil through it.  While going along the line you draw may take billions of years, going through the wormhole may take minutes.
My lawyers also recommend I show you this diagram

Sadly, you can't make a wormhole.  And even if you made a wormhole, the throat collapses when you try to travel inside of it, so you can't even use the wormhole for travel anyway.

Another proposal is the Alcubierre warpdrive.  This contracts spacetime in the front and expands it in the back, producing what some call a "wave" of spacetime contraction that "tips over" the light cones inside the warp bubble.  Locally, you're moving slower than light, but globally you may be moving, in theory anyway, as fast as you want.

But you can't make the Alcubierre warp drive either.  If you took the mass of the universe and made it negative, the Alcubierre warp drive requires ten times that number in negative-mass matter to move a standard-sized spaceship.   To clarify, we haven't even found one single particle of negative-mass matter.

Science knows how to make a Bag of Holding, and can even make a Bag of Holding that slows down time (see chapter 3 here).  You can store a lifetime supply of hot pies and ice cream in the same box, and whenever you take them out the pie is still oven-fresh and the ice cream still ice cold, and so even twenty years later you can serve yourself delicious pie a la mode.  But, like so many awesome things, it requires either negative mass or impossible mater distributions and can't be made.

I just made a post about how the Bag of Holding (aka, Van den Broeck Bubble) can be exploited to, potentially, travel to parallel worlds (if any even exist).  This one is a lot more speculative, requiring ideas way beyond established science, but is at least partially based in what we already know about general relativity and curved-space geometry.  It isn't really scientific, but if we wanted to know if there were other universes, this has potential to actually find them.  But it also requires not only negative mass, but infinitely much of it.  So we won't ever be able to try.

Pictured: A guy wearing a green screen.
Not Pictured: An invisibility cloak 
Science has pretty recently discovered (less than ten years ago) how to make a literal cloak of invisibility.  It involves bending light in just the right way.  We know what that just-the-right-way way is, and we even know how to make materials that bend light in just that way.  Sadly, it only works for a single frequency (i.e. color) of light at a time.  There's no way to be completely invisible, because there don't exist materials with  the right optical properties naturally.  So you can be green-invisible, but you'll still be perfectly visible in red and blue.  I guess you'll just look slightly more purple?

I recently calculated (as part of my research) how to make a slightly different kind of cloak, namely a shadow cloak.  Also something you'd read about in fantasy books, the shadow cloak works on the same spacetime distortion principle as for a black hole, but now modified to work with optical materials (so not requiring it be made of actual black holes).  A perfect realization  would allow light to enter, but trap it there.  If you were wearing it, you would appear to be not just covered in a black garment, but actually swathed in shadows.  (Look at a black object, then look at an unlit hole; there's a big visual difference)  You'd also probably heat up a lot (since all the energy is trapped), which would make this kind of material perfect for solar panels, increasing their efficiency probably to near 100%.  But you can't make the shadow cloak, because it requires material parameters that are both infinite and negatively infinite.  Like with the invisibility cloak, you can only realize this (if at all) for a single color of light at a time.  Which vastly diminishes its coolness.

You can probably see where my knowledge tends to specialize, but physics knows a lot more cool things in the quantum domain, such as teleportation devices and solutions to the P=NP problem.  All of which, we know how it would work, and only minor technicalities render it impossible.  Things like wavefunction collapse, quantum decoherence, and the no-cloning theorem.

Any time there's something cool in physics, there's something else that renders it impossible.

Again, this isn't the situation of wanting to do something incredible and merely lacking a theoretical model to describe it.  Our formulations of physics account for it exactly.

It's just that all the cool stuff is impossible.

More and more, it just seems like the Universe comes equipped with fail-safes against our ever doing the cool things of science fiction.

Wednesday, January 22, 2014

What Do Wizards Even Do?


The Malfoys are very rich.  The Weasleys are very poor.  However, they are not nearly as poor as the inbred and horrible Gaunts.

Why?

This is again part of the same basic problem with the series: Rowling never bothered to figure out her universe from the perspective of the characters who live in it.

How do wizards generate wealth?

As revealed in the books, there are really only so many things a wizard or witch can do professionally.  You can make wands.  You can make magical pranks.  You can manufacture magical candy.  You can sell books or robes.  You can teach at Hogwarts (and there's only a dozen positions there).  You can work for a news publication.  Or you can work for the Ministry of Magic.  That is the entire wizarding economy.

For instance, when the students begin taking their OWLS and deciding their classes for future employment, almost every single job opportunity considered is at the Ministry of Magic.  Harry becomes an auror, but what else was he going to become?  An accountant?