My brother is wrong

Just in case this is the post where I pick up a reader outside of my circle of family and close friends: My brother’s name is Patrick, he’s five years younger than me, he used to have a LiveJournal but I presume he isn’t using it any more because he posted this as a Note on Facebook instead. It’s set to “public”, so you can read it here as long as you have a Facebook login, but you needn’t worry if you haven’t because I’m going to quote the whole thing in sequence through this response. (Although, as you’ll see, he does take after me to a certain extent in the general area of philosophical wibbling, he doesn’t write to quite the kind of length that I do.)
Patrick’s Note is uninformatively titled “A few ideas” and begins as follows:

In the beginning, the universe was created.
There are two things that together convince me of this:

1. The physical law of entropy; and
2. The philosophical ‘First Cause’ argument.

Well, I have thrown some ideas in this general direction before. So a lot of this is going to be rehashing that. Let’s start with entropy.

The law of entropy, simply put, says that everything will stop. High school science teaches that every reaction in the universe reaches a state of equilibrium: so a bouncing ball will eventually come to rest, a candle will burn out, a battery will go flat, you and I will die, the sun will collapse, and so on.

But we needn’t stop here. You can “get behind” the law of entropy (so to speak) and see why things work that way. Here’s what I said last time. (To avoid confusion, any time in this post I block-quote something that isn’t from Patrick’s Note, I’ll put in italics.)

Think of a pool game, just before it starts; the balls are all ready, arranged in a triangle, and the first player is about to “break” them – an apt metaphor. How often would you expect the balls, rolling about the table, to coalesce back together in a neat triangle? Never, that’s how often, even though it wouldn’t break any laws of physics operating at the single-ball level. There’s a little leeway in the triangle; you can swap balls around, you can turn them over, and it still counts as the triangle. But however many arrangements of balls count as “being in the triangle”, there are a phenomenally vaster number of arrangements that don’t count as being in the triangle. That’s why the probability of them returning spontaneously to the triangle is so tiny that it can safely be ignored.

Particles and energy readily go from an improbable, non-random state (the triangle) to a probable, non-random one (scattered over the table), but not vice versa, because that’s what “improbable” means. Randomized energy is called “heat”. On a real pool table, some energy is lost (as heat) every time balls crash into each other or the sides, and also as they roll over the cloth, so eventually everything will come to rest. However, this is due to the interactions of large numbers of particles on the balls’ surfaces. If we were to shrink the table down so that each ball was a single particle, they would lose energy only when they met each other. Imagine watching a 2-second video clip of two balls meeting at high speed and bouncing off each other; could you tell whether the clip was being played forwards or backwards? If the cloth was smooth, and the balls didn’t lose too much speed, probably not. With single-particle interactions it’s not just a matter of not being able to tell. The very laws of physics operate exactly the same, whether we’re going backwards or forwards in time.
Entropy is one of only two physics concepts where the direction of time makes a difference; the other, which I gather works on much the same logic, is quantum decoherence. This might not be instantly obvious. You might think gravity was time-dependent – things fall down when you play the video forwards, up when you play it backwards. You’d be wrong. Think of someone tossing a ball up and catching it. As it goes up, it slows down; as it comes down, it speeds up. Exactly the same happens if you reverse the video. In either time direction, there’s a downward acceleration. The difference is that, to make it go up, you need to put work (non-randomized energy) in. When it comes down, that energy comes out again. A ball could spontaneously jump up from the ground, if only a whole bunch of energy were to suddenly converge on the spot right underneath it. That this doesn’t happen is due to entropy.
Anyway. Moving on.

The First Cause argument recognises that every effect (i.e. ‘thing that happens’) in the universe is caused by an earlier effect, and asks: what caused the first effect? It is a question that can be resolved in two ways:

• Option 1: There was no first effect. The universe stretches infinitely far back in time.

This theory collides irreconcilably with the law of entropy: after an infinite length of time, everything would have stopped, but this has quite clearly not happened yet. Even if the universe does go in cycles, as some supporters of this theory suggest, each cycle would have to be smaller each time (much like the aforementioned bouncing ball), or this would also contravene the law of entropy.

Here is where the problems begin.
First of all, the bouncing ball bounces lower each time because it is losing energy; mostly as heat, also as pressure waves (sound). The energy goes into the ground and into the atmosphere, and ultimately heads out into space. But energy can’t leave the universe. Otherwise, we wouldn’t call it the universe. So no, the cycle wouldn’t have to be smaller each time.
Second, remember the pool table? It is tremendously unlikely that the balls will ever spontaneously re-form the triangle, but not – in the unfeasibly-long term – impossible. You’d have to wait an incalculable length of time before it was likely to happen. But if the universe exists forever, then you have an incalculable length of time. Of course, to a time-traveller of unlimited scope, time will consist of unimaginably vast stretches of cold blankness punctuated by occasional tiny points of light. So, pretty much like space, then. In both cases, living creatures that happen to exist should not be surprised to find themselves close to one of the specks of light; they couldn’t have arisen anywhere else.
There’s a third possibility to consider, which I also looked at last time. On most maps, “south” is a single direction, but on a map of Antarctica, “south” means towards one particular point that doesn’t look particularly special in any way, except for the mapmakers having printed a dot and the words “South Pole” there. What if something similar was true of the direction we call “before”? Suppose you took the history of the universe as a big jumbled network of events, all linked by cause-effect links. Recall that the laws of physics are the same going either direction, except for entropy; and entropy simply means going from improbable to probable. Now, logically, some node somewhere in the jumble of cause-effect links must be the most improbable point in the network. Then perhaps what makes one part of spacetime “earlier” than another is how close it is to that point of maximum improbability. (So the Heart of Gold would have rebooted the universe every time they fired up the Infinite Improbability Drive.) In which case we have an earliest point for the universe, without having to be caused by anything, and without having to violate the rule that each cause-effect link must have the same amount of energy at both ends.
Oh, go on, then, say it. The universe is a ball of wibbly-wobbly timey-wimey stuff.
Time being reversible probably still sounds pretty implausible. It’s not. Since we’ve already quoted Doctor Who – once, in the classic show, the Doctor had to meet himself, and this caused a huge explosion. That was not very good science, but it was a garbled version of a real thing that is constantly happening on the subatomic scale: antimatter annihilation. An anti-particle is simply a particle going backwards in time. When it meets a particle and they both disappear, another way to look at it is that the particle has reversed its time-direction. This was something I meant to put in the previous post, but ended up leaving out. Let me talk about it now.
The TARDIS conveniently dematerializes before it goes anywhen, and so does Marty McFly’s DeLorean, and I think the same is true of every other science fiction time-machine. What if they didn’t? Imagine a car driving down the street, a perfectly ordinary car, except that when it gets to the middle of the block it (from the driver’s point of view) smoothly starts going backwards in time. What does everyone else see? Let’s say that, to the driver, it takes 10 seconds to get from one end to the other. It begins at time t=0, and it arrives at the far end at t=0. So at t=0, there are two cars, one at the beginning of the block driving forwards, and one at the end driving backwards. At t=5, the two cars meet in the middle and vanish.
To the driver, nothing at all untoward need happen. The people in the street are not so lucky. The mass of the car represents an incredible amount of energy, and the rule is that that can’t disappear. It all gets converted into photons. If the car weighs about 1000kg, then by E=mc² that becomes 180,000,000,000,000,000,000 (1.8 × 10²⁰) joules, which by my calculations is a 43-gigaton explosion. (You have to count the mass of both the car and the anti-car.) That’s very roughly nine times the world’s current total nuclear arsenal.

The point is, at the particle level this happens all the time. An electron or positron (anti-electron) will change direction and throw off a photon. Spontaneously, unpredictably, for no cause. Or it’ll absorb an incoming photon and change direction. Or an electron will meet a positron and they’ll vanish, yielding a photon. Or a photon will spontaneously split into an electron and a positron. These are all the same event, viewed at different angles to spacetime. That’s how wibbly-wobbly spacetime is. And did you notice the bit where two of those four situations happen spontaneously? You got that, right? So the main premise of the First Cause argument is false – it is not the case that everything that happens has a cause.

• Option 2: The first cause (effect number 0, if you like) was not part of this universe.

The main problem with this is that it stretches the definition of ‘universe’, traditionally used to mean ‘absolutely everything’. ‘Universe’ must therefore be redefined.

Sure. Go ahead and redefine. But don’t expect me to be impressed. If I were to insist that I travel daily through a different universe, and in support of my argument redefined “this universe” to exclude the South Dunedin shopping centre, you would look at me funny, and quite rightly. This dodge is still a dodge when it’s not so obvious, like when C. S. Lewis proves (in Miracles) that there is something beyond “Nature” by first defining “Nature” to exclude human reason.

Our universe is contained inside another universe.
(‘Our universe’ can be defined as ‘everything our bodies are logically capable of interacting with’.)

Now define “interacting”.
Seriously. I can think of a couple of sensible applications, but one of them yields a very weird definition of “universe” and the other doesn’t help Patrick’s case. If “interacting” means directly interacting, then you’ve just excluded the sun (and all other stars) from “the universe”, because a human body that went there would almost instantly cease to be a human body or any kind of body. If, on the other hand, it means “affecting or being affected by, directly or indirectly”, well, by definition we are affected by whatever caused the universe, aren’t we?

It’s not as silly as it sounds; the idea is even gaining credibility in scientific circles. There are plenty of examples of universes nested inside our own one. Some well-known examples would be

• The Discworld (Terry Pratchett’s series of fictional books)
• The Matrix (from the Wachowski brothers’ movie of the same name)
• Azeroth, Second Life, and SimNation (all from computer games)
• Dreams.

At least two of these universes have other universes nested inside them: on the Discworld, an experimental project is run, called Roundworld, which is a very close copy of our universe; and the Matrix proper is contained within the so-called Real World, which is a copy of our universe projected forward in time. (There’s an Internet inside the Matrix, as well; Neo is running a web search for Morpheus when Trinity hacks his computer.)

“The idea is gaining credibility in scientific circles.”
I’m embarrassed to say that I have probably written some variant on this sentence myself, elsewhere. I’m not going to do it again, now. Not after seeing this.
What I think Patrick is referring to is the idea that our universe is a gargantuan computer simulation. Back when people were still looking forward eagerly to the first Matrix sequel, some scientist pointed out that, if you assume any civilization will one day have the technology to build a Matrix, and if civilization can be simulated inside a Matrix, then logically there will end up being Matrices inside Matrices inside Matrices, in which case the chance of our universe being the actual universe instead of a Matrix is pretty small.
What this does not mean, and where my dear brother is going off the deep end, is that any fictional universe counts as a Matrix.
There’s a King Arthur story of a knight who stopped for shelter one evening at a castle, and was entertained by a maiden (beautiful, naturally, this being King Arthur) who would never turn her back to him. It wasn’t until she stood for a moment between him and the fire, and the firelight came through her eyes, that he realized why not. She was a backless maiden, and this, I take it, was a bad thing for some reason. The Complete Idiot’s Guide to Publishing Science Fiction opens one chapter with that story to make a point: all stories are backless maidens, and all authors have to take great care not to turn their backs on the reader. Few can manage it with consistency. None can make their worlds anything like complete. If they could, then there would be a single correct answer to all the following questions and many thousands of similar ones:

• What was the last thing cooked in the Achings’ frying-pan before Tiffany hit Jenny Greenteeth over the head with it?
• Neo’s name in the Matrix is Thomas Anderson. What is Trinity’s?
• What colour were Clannia Foxton’s eyes?
• Did the top stop spinning?

It’s not just a matter of us not knowing the answer. The point is that there is no answer. Different fanfiction writers could answer each of these questions differently, without any of them violating canon. As the last one highlights, sometimes there’s no canonical answer on purpose. Yet if we imagine that this is also the case “within-world” – that the Achings bought themselves a frying-pan for the sole purpose of attacking fairy-tale monsters, which is the only thing it gets used for in the book – then we do violence to the very stories we are reading.
I think Patrick really does get this, deep down. Roundworld and the Matrix would be genuine nested universes, if they weren’t themselves fictional. Patrick’s choice of them rather than, say, the within-world fiction book Mr Bunnsy Has An Adventure, signals that, at some level, he knows fictional is not the same as simulated.

It is important to know that the term ‘real’ is neither binary nor absolute; it is a sliding scale, and a measure of how far something is from your own universe.

Really? Well, if it’s important to know, then I’m glad I know it now. Thank you.
What if I disagree? Did you feel like giving a reason why I should believe you on this?
I have, as it happens, said something rather similar myself. But there’s nothing non-binary or sliding about my definition. What I say is that what distinguishes the “real” universe from merely “possible” universes is that the “real” one is defined as the one we’re actually in. Which, if you think about it, rules out the Matrix hypothesis – or at least the usual corollary that the Simulators are somehow “real” in a way that other beings not found in our universe are not. In the set of all possible universes, there are of course many civilizations busy simulating our universe. For that matter, since the set of all possible universes also contains all possible ways our future could go, it must contain an instance of every one of those universes being simulated by our descendants. Including the ones that are simulating us.
Recursive simulation? Why not? If fiction counts as simulation, then this has already happened. “Roundworld” appears not in the Discworld novels proper, but in the Science of Discworld subseries, which alternates a Discworld story (the wizards create a simulated universe where there is no magic) with explanations of scientific concepts. Roundworld is not a “very close copy” of our universe, it is our universe. In the non-fiction chapters, the authors quite happily refer to Roundworld as “us”.
Also, if you do accept my speculations from back then, “the (real) universe” consists of the entire network of events which led to, and will lead from, our existence. You can’t cut off the beginning bit of that and call it “another universe” unless you’re being essentialistic about what counts as “our universe”, and, well, you can be essentialistic if you like, but then you don’t get to wax all sophisticated about reality being non-binary, because essentialism is pretty binary.

It is clear that these universes exist. If one were to talk about any fantasy world (Narnia or Hogwarts might be better known examples than the ones above), others would know what they were talking about. Applying the principle of Occam’s Razor – “do not needlessly multiply entities” – they are not mere constructs of one’s imagination, but have a separate existence. To borrow from a Discworld inhabitant, “[Santa Claus] must exist. How else could you so readily recognise his picture?” ‘Not real’ may mean ‘not in our universe’, but it does not mean ‘non-existent’. (The character in question is actually called the ‘Hogfather’, not Santa Claus, but they are equivalent.)

What passed through my head when I read this was an alternation of laughter, and the word “What?”, both in such a tone that, had I given voice to either one, passersby would have wondered (as they summoned library security) why I was doing chicken impressions.
Rather than impugn my own heredity, I will try and see if I can figure out where Patrick is coming from. I think the idea is that if fictional worlds were constructs of the imagination, then there would be a separate copy of them in everyone’s head, whereas if they are real then there only needs to be one of them. The mistake here is that people also carry copies of real things in their heads. No, not copies, models; simplified, object-oriented working simulacra. The set of physical entities encoding my knowledge about President Obama aren’t themselves part of President Obama, they’re part of me.
In case you don’t get it yet, try this. You know what your mother’s face looks like, right? Go on then – draw a photorealistic portrait of her from memory.
No?
Then knowing something doesn’t mean direct mental contact with it, it means mentally constructing a model (which can be pretty short of reality).
Therefore, even if fictional worlds actually exist, we still construct mental models of them when we watch or read about them.
Therefore, there is no breach of Occam’s Razor in supposing that fictional worlds are just mentally constructed models.

We can tell that these are different universes from ours, because if they were the same as ours, it would logically possible for our bodies to visit them, however practically infeasible. However, no one will ever go to Hogwarts and meet Harry Potter; he does not exist here.
(It is possible that someone will build a copy of Hogwarts and pay someone to act out his part, but that would only be a copy, not the ‘real thing’.)

But it is not logically impossible that he should. Hogwarts magic is physically impossible, but there is no direct contradiction involved. You’ll see, shortly, why I’m making this point.

Our imaginations can visit them, though; many people when reading books feel they can ‘see’ the stories happening, and stop noticing that all they can physically see are ink marks on paper.
In some cases our wills can visit them as well; players visit Azeroth via an avatar (in computing terms, a player’s character: to put it more broadly, an inhabitant of a universe controlled from outside). Avatars can affect their universes much as we do ours, but the extent of their effect is dictated by the rules of the universe: for example, Azeroth’s inhabitants can interact with each other, but do not have a lasting effect on their surroundings, while visitors to Second Life can control the environment directly, without having to get their avatars to do it.
Of course, the words ‘inside’ and ‘outside’ are physical directions, so it’s difficult to apply them properly to metaphysical concepts. ‘Inside’, as I use it, refers to the where the ‘data store’ of each universe is: the Discworld is stored in books, Azeroth in computers, the Matrix on DVDs, and dreams in neurons, each of which are objects in our universe – so these universes are all ‘inside’ ours.

Most of that is unobjectionable, beyond the objections already raised. I’m just including it because I said I’d reproduce the whole thing. The really serious problem is coming up.

If universes can exist within our universe without their inhabitants being aware of ours,our universe could be inside another without us being aware of it. For that matter, it must be; as has already been demonstrated, it was started from outside.
There is a very important thing to note about that:

Here it comes...

Logic may not apply to other universes.

My brother does not know what logic is.
Here is some logic, courtesy of Lewis Carroll:

(1) No one takes in the Times, unless he is well-educated;
(2) No hedge-hogs can read;
(3) Those who cannot read are not well-educated.
Therefore, no hedge-hog takes in the Times.

Here is some more:

(1) No kitten, that loves fish, is unteachable;
(2) No kitten without a tail will play with a gorilla;
(3) Kittens with whiskers always love fish;
(4) No teachable kitten has green eyes;
(5) No kittens have tails unless they have whiskers.
Therefore, no kitten with green eyes will play with a gorilla.

If you work through that one, it turns out that no kitten with green eyes likes fish or has whiskers or a tail. Those statements are factually false, and Premise (2) is also doubtful; but that doesn’t make a difference to the logical validity of the conclusion.
For all logic boils down to one very simple rule—

• If P, not not-P.

—where P is any proposition whatsoever.
The consequences, should this be false, are more than inconvenient; they’re more than alarming. They are existence-breaking.
If it is not true that

• If P, not not-P.

that means that it is true, of some proposition P, that

• Both P and not-P.

There’s a couple of things to be careful of here. Often, in our daily lives, we come across sentences that are in a sense both true and false. Am I in a dentistry class? Yes and no. Are most books bestsellers? Yes and no. But a logical proposition is not just a sentence, it is one meaning of a sentence. In each of these cases, we have a true proposition

• I take notes in a dentistry class.
• Most copies of books (counting four copies of The Wee Free Men as four books) are copies of bestsellers.

and a false proposition

• I am enrolled in a dentistry class.
• Most distinct books (counting four copies of The Wee Free Men as one book) are bestsellers.

wrapped up in a single sentence. Ambiguous sentences are both true and false if they can be used to express both true propositions and false propositions. The propositions themselves can only be true or false.
Also, it might seem that there is a third possibility: “no fact of the matter”. We’ve already seen some examples.

• The last thing cooked in the Achings’ frying-pan before Tiffany hit Jenny Greenteeth with it was bacon and eggs.
• The last thing cooked in the Achings’ frying-pan before Tiffany hit Jenny Greenteeth with it was not bacon and eggs.

Neither of those is true or false; there is no fact of the matter. Right? Wrong. The second one is true. The last thing cooked in that frying-pan was nothing, because the frying-pan in question does not exist. It is fictional. What about these?

• If the Achings and their frying-pan had existed, the last thing cooked in it before Tiffany hit Jenny Greenteeth with it would have been bacon and eggs.
• If the Achings and their frying-pan had existed, the last thing cooked in it before Tiffany hit Jenny Greenteeth with it would not have been bacon and eggs.

Neither true nor false? Wrong again – both false. Given the set of possible universes, the subset of that set in which Tiffany and her family are real contains some possible universes where the meal was bacon and eggs, and other possible universes where the meal was not bacon and eggs. Therefore, excluding either one makes for a false “if” statement.
No-fact-of-the-matter sentences are not always about fictional stories. There are other kinds, such as

• The electron went through the left slit (and not the right).
• The electron went through the right slit (and not the left).

Again, both false. Here the false proposition which both depend on is

• An electron which passes through a two-slit barrier must go through one slit or the other.

Which sounds like common sense, given how objects behave at the scales we’re used to, but common sense is not the same thing as logic.
What about this?

• This proposition is false.

If it’s true, then that makes it false, but if it’s false, then that makes it true. There you go – a proposition that is both true and false. Right? A tricky one, I’ll admit; I like my fellow New Zealander Arthur Prior’s solution best. Any proposition P is synonymous with

• This proposition is true, and P.

Therefore,

• This proposition is false.

is synonymous with

• This proposition is true, and this proposition is false.

—which is a “both-and” proposition. “Both-and” propositions are only true if both halves are true. Now, if that proposition is false, then the second half of it is true; but the first half is still false, and so the proposition as a whole comes out as false. Despite appearances, its being false does not make it true.
So are we clear now? Propositions are strictly Boolean, which is to say they can be either true or false, not both and not neither. That’s what a proposition is. Now, let’s have a look at some implications.
Consider a true proposition, such as

• It rained in Dunedin on 10 May 2013.

Since this is true, it is also true that

• Either it rained in Dunedin on 10 May 2013, or Japan won World War II.

This looks wrong, because we tend to read “either-or” propositions as “if” statements. In other words, we read this as if it meant

• If it had not rained in Dunedin on 10 May 2013, this would mean that Japan won World War II.

which is, of course, false. And it would follow, from our “either-or” proposition, if we weren’t sure that it did, in fact, rain in Dunedin on that day. But an “either-or” proposition is the opposite of a “both-and” proposition; as long as at least one half is true, the proposition as a whole is true. (For clarification: by “either-or” I mean “and/or”, one or both is true, not xor, one and only one is true.)
The same also applies to every single one of the following:

• Either it rained in Dunedin on 10 May 2013, or I am a ctenophore.
• Either it rained in Dunedin on 10 May 2013, or Doctor Who is a documentary series.
• Either it rained in Dunedin on 10 May 2013, or the Earth is a great icosidodecahedron.
• Either it rained in Dunedin on 10 May 2013, or J. R. R. Tolkien wrote Fifty Shades of Grey.
• Either it rained in Dunedin on 10 May 2013, or cannibalism is morally right.

We can generalize:

• If P, either P or Q.

—for any P and any Q.
Now put together what we’ve got:

• If P, either P or Q.
• Both P and not-P.
• P, therefore either P or Q.
• Either P or Q, and not-P, therefore Q.

...for any proposition Q, including the Japanese winning World War II, me being a jellyfish, and all the other ones. If anything at all is beyond the reach of logic, every single one of those is true. You needn’t take my word for it.
“But—” No. No, it doesn’t make a difference if our “either-or” statements are about things happening in different universes. Replace “it rained in Dunedin on 10 May 2013” with “Neo wears a black trench-coat and sunglasses” and all the above works just the same. So no, “Logic works in this universe, just not other ones” is not a way out.
“But—” No. No, you don’t get out of it by breaking logic again and declaring that the argument we’ve just seen doesn’t work because it’s a logical argument and we’re outside logic now. If you try, what you’re doing is simply making a new proposition, to the effect that

• Even if there is some proposition P of which it is true that both P and not-P, Daniel Copeland is not a comb jelly.

We can call this proposition R. And guess what? Not-R, the proposition that R is false, is also a proposition which can fill the role of Q. Both R and not-R are true. Since not-R is true, I am a comb jelly. It is also true that I am not a comb jelly, of course, because that too is a conceivable proposition, but that doesn’t mean that it is not true that I am a comb jelly. Did I just say “The fact that I am not a comb jelly does not mean that I am not a comb jelly”? Yes, I did. That’s what happens when you haven’t got logic. Facts no longer mean themselves.
“But—” No. No, non-Boolean truth-values don’t solve anything either. “Did Japan win World War II?” “A fish.” All that does is create yet another proposition,

• The correct answer to the question of whether Japan won World War II is a fish.

and, well, you know the drill by now. If all propositions are true, then yes, all propositions of this form—

• The truth-state of proposition P is entity X.

—are true (and false, and a fish, and pornographic, and morally obligatory, and a dollar, and 1.57 nautical miles, and the NZ Bill of Rights Act 1990, and...) There is one way out of this, and one way only, and it is this:

• If P, not not-P.

Everywhere. In any conceivable universe. Logic is supreme. There is no escaping it.
What we can say, without contradiction, is

• It rained in Dunedin on 10 May 2013, but the set of possible universes includes one which is identical to the real one except that it did not rain in Dunedin on 10 May 2013.

But the people in that universe are no more free of logic than we are.

The rules that govern our universe make everything run on logic. (Even, for example, art: in order to exist, art requires intelligence; intelligence requires life; life requires biological reactions; biology requires chemistry; chemistry requires physics; physics requires maths; and maths requires logic. Okay, so maybe intelligence doesn’t require life as such if it’s vested in a computer, but the computer requires chemistry as well.)
The rules that govern the Discworld make everything run not exactly on logic, but dramatic necessity (known to the inhabitants as ‘narrativium’). Things happen mainly because the story requires them to happen, not necessarily because they make sense (though the logic they have there is similar to ours). Most other stories are the same; hence the concept of ‘happily-ever-after’, which only ever happens in stories.
By the same token, the rules governing our parent universe (i.e. the universe that contains ours) may not be the same as ours. We can logically deduce that it exists, but beyond that, we have no idea what happens there. The same is generally true of all super-universes: for example, Sims (from the game of the same name) do not see our universe, as the game does not use any physical sensors (e.g. camera or microphone) at all; they merely receive the commands that the player enters.
For that matter, Sims could not understand our universe even if they did see it, as it’s far too complicated. For example, they have no concept of mathematics, as they don’t need it; the only maths that applies within their universe is their finances, and their money is controlled by the player of the game, not the Sims themselves. The inhabitants of the Discworld could probably cope if they were transported here, as their reality is very similar to ours, but there are a lot of things they would need to learn: for example, that ‘down’ is a relative term, and that things on a ball will stick to it instead of falling off, if the ball is big enough.

There are, of course, things we don’t understand. There may be things it is impossible that we should ever understand (or there may not, but I won’t argue that point just here). But whichever of the set of possible-universes-in-which-some-civilization-is-simulating-our-universe we arbitrarily designate “our parent universe”, logic applies there too. Otherwise – well, you’ve seen what happens otherwise.
Occasionally, the If P, not not-P rule gets broken in fiction. What saves us from the no-logic catastrophe in these cases is merely the fact that it’s fiction. Since P is, in fact, false, Both P and not-P never arises (only not-P is actually true). And usually, charitable readers can wangle some kind of consistency out of the text by dropping some underlying assumption, albeit sometimes with seriously strange results. For instance, the propositions, both affirmed in the Narnia canon, that

• Reepicheep had a Dryad sing a prophetic lullaby to him when he was an infant in the cradle.
• The Dryads had all been asleep for hundreds of years until Aslan woke them for the war against the Telmarines, at which point Reepicheep was already an adult.

can be reconciled if we suppose that

• Reepicheep was hundreds of years old when he fought in Caspian’s army and sailed on the Dawn Treader.

which is probably not what C. S. Lewis intended. This is another good reason not to confuse “simulated universes” with mere fiction.
As you saw when I asked you to draw your mother from memory, we don’t actually hold super-accurate pictures of the world in our minds. That’s why I also don’t count dreams as simulated universes. It is quite common in dreams for something to change into another thing without any change ever taking place. In mine, often whatever’s going on is simultaneously a book or movie I’m enjoying, and actually happening to me. How can that logically be? It can’t. It isn’t. It’s a dream. Dreams aren’t real. When I’m dreaming, my mind isn’t doing logic.
It’s very hard, I know, to believe that your mind doesn’t hold a seamless, continuous, one-for-one model of the world. But it doesn’t, not by a long shot. Consider the “blind spot” we all have in each eye – the point where the optic nerve plunges through the retina. You don’t see it mainly because you keep both eyes open all the time. Shut your left eye, and look at the circle:

Moving backward or forward you should find a point where the cross disappears. Now, books and websites that mention this tend to say something misleading at this point: that “the brain fills in the background”, so you don’t notice the hole. The philosopher Daniel C. Dennett shows (in Consciousness Explained) that a better way of putting it would be that the brain doesn’t bother to inquire of the eye about what’s going on in that area. If your higher-level functions press the issue, then instead of sending a sharply-worded letter to the eye, your visual system returns an answer based on the area’s immediate surroundings.
I won’t go on about this much more because I’m going to write an Imponderable about it some day, but the reason I brought it up in the first place was to point out that it also pertains to logic. Dennett gives an instructive illustration in The Intentional Stance, beginning with the story of a lemonade-seller who inadvertently hands out the wrong change. As you’ll see the details depend on American currency, but we all know what quarters, dimes, and pennies are, right?

The boy’s sign says “LEMONADE – 12 cents a glass.” I hand him a quarter, he gives me a glass of lemonade and then a dime and a penny change. He’s made a mistake. Now what can we expect from him when we point out his error to him? That he will exhibit surprise, blush, smite his forehead, apologize, and give me two cents. Why do we expect him to exhibit surprise? Because we attribute to him the belief that he’s given me the right change – he’ll be surprised to learn that he hasn’t. Why do we expect him to blush? Because we attribute to him the desire not to cheat (or be seen to cheat) his customers. Why do we expect him to smite his forehead or give some other acknowledgement of his lapse? Because we attribute to him not only the belief that 25 – 12 = 13, but also the belief that that’s obvious, and the belief that no one his age should make any mistakes about it...
But now look yet more closely. The boy has made a mistake all right, but exactly which mistake? This all depends, of course, on how we tell the tale – there are many different possibilities. But no matter which story we tell, we will uncover a problem. For instance, we might plausibly suppose that so far as all our evidence to date goes, the boy believes:
 (1) that he has given me the right change
 (2) that I gave him a quarter
 (3) that his lemonade costs 12 cents
 (4) that a quarter is 25 cents
 (5) that a dime is 10 cents
 (6) that a penny is 1 cent
 (7) that he gave me a dime and a penny change
 (8) that 25 – 12 = 13
 (9) that 10 + 1 = 11
(10) that 11 != 13
Only (1) is a false belief, but how can he be said to believe that if he believes all the others? It surely is not plausible to claim that he has mis-inferred (1) from any of the others, directly or indirectly...
The boy is basically on top of the situation, and is no mere change-giving robot; nevertheless, we must descend from the level of beliefs and desires to some other level of theory to describe his mistake, since no account in terms of his beliefs and desires will make sense completely. At some point our account will have to cope with the sheer senselessness of the transition in any error.

“Sheer senselessness” on our part, not some shift in the nature of logic, is why you get irrationalities in dreams and stories. Our minds do their best, but they fall a long way short of full, seamless, logically consistent representations of reality; as with the blind spot, we don’t notice the holes not because the brain is “filling them in” but because it isn’t asking about them. We can be mindful, but we can’t be constantly and unrelentingly mindful. Most of the time, we rely on our ability to turn reasoned responses first into habits and then instincts, so we only have to do the reasoning once.

The question is: how different is our parent universe from our own? Are we as similar to them as the Discworld is to us, or as different as the Sims? Without being able to see it, we can have no way of knowing. The more different it is, the less we will be able to understand; and without knowing for sure what rules govern its operation, we can argue nothing about it – apart from its existence.

Those gaps in consciousness which allow us to short-change people by accident are where the Sims spend their whole lives. They wouldn’t understand our world, but they don’t understand their own, either. They have no minds; there is no workspace in the program dedicated to modelling the world from each character’s point of view to enable them to make their own decisions. They find the routes to things they want, such as the fridge or the TV, because those things emanate signals (not displayed to the player) which are muffled by the walls. The Sims have no more grasp of their environment, or freedom to respond intelligently to it, than a bacterium following a chemical gradient. Sure, they look like people, but so do clockwork dolls. We have nothing to learn from them about logic in other universes. Logical contradictions boggle our minds not because we are Sims but because logical contradictions cannot be true.

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I do love my brother, really. I don’t intend the ribbing in this essay to be taken any more seriously than the stories I told in my speech at his wedding, a year or two ago, about his childhood. (He took a bar out of a bite of soap once, and even with toddler teeth somehow managed to go all the way through before he figured out it wasn’t food...)
But one thing I like about my family is that we can tell each other we’re wrong without getting cross. And here, my brother is wrong. Your move, Patrick.