Thursday, March 20, 2014

The Falsifiability of Classical Mechanics


So I am currently enjoying an argument with Smiling Dave on his excellent blog:
http://smilingdavesblog.wordpress.com/2014/02/16/top-ten-economic-blunders-according-to-mises, and it has wandered around, and like all arguments, touched on philosophy.

Anyway I said:

If Jupiter pulls a loop the loop, that doesn't disconfirm *my understanding* of physics. That's in flat contradiction with physics, and it means physics is wrong. Similarly with evolution and fossil rabbits in the precambrian.

And Dave said:

If Jupiter pulls a loop the loop, I doubt the reaction will be to throw out the physics and engineering textbooks. In fact we did have a Jupiter pulling a loop the loop, when quantum effects were first discovered, invalidating all Newton’s laws. So what happened?

And this is a very good question indeed, and deserves an answer, but it is not about Austrian Economics so I am reluctant to clutter up Dave's blog with it, so here it is instead:

Classical Mechanics is dead as a theory of how the world works. It survives as an abstract mathematical model. And we still teach it. And it is still a very useful tool for understanding and predicting things. But anyone who actually thinks that the world works like that is a crackpot and will not be welcome at the sort of parties that mathematicians and physicists like.

Classical Mechanics died before the end of the nineteenth century, from many directions at once. Once people twigged that the "atoms" idea was actually true, and worked out how electromagnetism worked, and started measuring what happened when tiny fast things crashed into each other, classical mechanics was dead.

People used classical ideas to predict how the atoms behaved, and those predictions were unambiguously wrong. For a time they tried to patch the theory up by adding extra rules, but all those attempts failed miserably.

And so philosophers went from debating whether classical mechanics was just "true", or whether it was "necessarily true", to criticizing mathematicians and physicists for having ever thought it was true, since it is so obviously false.

And I hate to admit it, but the philosophers had a point. If you know a little quantum mechanics, and the modern ideas about how matter works, you realise that the classical theory was obviously wrong all along, and that if people had only thought a bit harder about it they would have realised that the world couldn't possibly have worked that way.

Classical Mechanics survives only as a mathematical theory, and in the sense that it is a 'limiting case' of general relativity and quantum mechanics.

But it is still just as useful as it ever was! And remember that that was very useful indeed. Every invention between Newton and the atomic bomb was invented using classical mechanics. Which means that the rise of the West and so the entire history of the world since Newton are squarely the fault of classical mechanics. It is a powerful set of ideas which happen to be untrue.

It can these days be characterized as "A simplified form of general relativity which is appropriate for predicting the behaviour of medium sized slow things, say anything between a cricket ball and a planet, but even then it will be wrong in ways that are not too difficult to spot, once you know what the real answers look like."

Now in fact, very shortly after Classical Mechanics collapsed, dead and greatly lamented by its friends, Einstein and Bohr came up with a couple of new theories about how very small, very large, or very fast things went about their business.

And surprise surprise, those theories turn out to be (a) much better at predicting the behaviour of vsvlvf things, and (b) much less intuitive to human beings, who after all have minds adapted to comprehend the behaviour of the sorts of things humans have to deal with in their daily lives.

Although a conversation with an undergraduate about physics will usually quickly disabuse one of the notion that classical mechanics is intuitive. Our built-in mental models are much more like Aristotle's version of physics, which is even more wrong.

Another surprise is that General Relativity and Quantum Mechanics are also obviously wrong! They are completely different theories, and can't both be true in the same universe. And GR makes predictions even more absurd about small things than CM did, and QM is completely incapable of dealing with gravity. And also QM is famously very strange philosophically, in a way that is hard to explain, but it feels as though it is pulling clever tricks on one at every turn. And the only obvious, straightforward way to interpret the maths is so mind-bogglingly weird that no-one really buys it.

So it is our hope that there will one day be a nice big Theory of Everything that can reconcile these two theories, and make predictions about stuff without having to bring in all sorts of ad-hockery and special cases. But we sure aren't there yet, and we may never get there. And the smart money says that if we ever find this theory it will be even more weird and its implications even more bizarre than Quantum Mechanics, and that it will include General Relativity as a special case in the same way that Classical Mechanics is a special case of General Relativity.

----------

But if Jupiter actually pulled a loop the loop, that would be much much worse.

The orbit of Jupiter is one of the places where Classical Mechanics applies almost exactly. There are tiny corrections from General Relativity, but nothing that is going to cause loop-the-loops.

And the orbit of Jupiter has been successfully predicted since Newton's time, and is one of the things we know almost for sure about the universe.

If Jupiter pulled a loop-the-loop, then I think our reaction would be utter incredulity. In fact I think we'd instantly imagine fraud, deception, or incompetence. Even if the data were completely unambiguous and there were millions of witnesses and no possible way it was a trick, I think we'd end up treating the event in the same way we treat the Miracle of Fatima, as a massive delusion simultaneously and inexplicably affecting vast numbers of intelligent and reliable minds.

And I think we'd be right to. Unlikely as that is, it's way more likely than Classical Mechanics being so completely wrong about something that is so unambiguously in its domain.

But if Jupiter repeatedly and unambiguously started pulling loop-the-loops, what then?

Well, two options.

(a) Someone comes up with a new theory that cleverly and elegantly explains what is happening, and explains all the previous data as well, including the near total success of CM on planetary orbits to date, which I reckon is a 'highly non-trivial' thing to do.

(b) We give up. We figure that even though we've got all these clever physics theories and they explain so much so well, we just can't trust that way of thinking. We go back to believing that the universe has a mind of its own, and that angels push the planets around, or that we're living in a giant computer game, or some such wooo. We'll still use our theories, because they're so useful, but they're just 'rules of thumb' for working out 'how angels like to move planets'. And science as a philosophy is dead. We live in a magic world.

Sunday, March 9, 2014

Physics 001

Little Cameron again. Not quite up to speaking yet, but fascinated by the bouncing ball bearings and pointing out interesting details thereof.


Saturday, February 22, 2014

Outwitted by an Idiot

So I am sitting in the Wetherspoons, and in front of me are a couple of fruit machines. The sound is turned off, since Wetherspoons values peace and quiet.

The fruit machines, far from being annoying, are quietly making restful patterns with their flashing lights in a relaxing sort of way, and it occurs to me that the word for what they are doing is 'screensaver', which is a type of program that damages one's screen.

Back in the day I was a programmer of very small computers (yclept microcontroller), and I begin to wonder idly about how the machine is laid out inside, wires to buttons and wires to lights and maybe an 8051 and a few bytes of RAM, and Bob would pretty much be your uncle.

And I think that given a few hours with the design documents I could understand completely what is going on in a fruit machine. It is probably considerably less complex than a small 1980s motorcycle.

In fact, unlike a motorcycle, the fruit machine will not be *messy*. No oil to leak, no petrol to explode in unpredictable ways, no spark gaps to fire differently depending on the humidity, and so on and so forth.

I reckon that a man might understand a fruit machine in the way that a man might understand the rules of chess. Not, note, the game of chess. Being a good chess player is very hard. But it is not hard to understand the rules. You might not be able to play a good game, but you can look at a game between two players, and you can easily see if one of them cheats. Say one of them moves a bishop five places forward instead of along a diagonal. Even small children's eyes will widen.

In fact, the rules of chess are such good rules precisely because their consequences are much less easy to understand than their content.

But the fruit machine, if I am any judge, will have been made so that the simple rules by which it operates have simple consequences. The last thing you want when you design such a thing is that it should do the unexpected. If the designers have done their jobs well, then the machine will literally never do anything unpredictable under any circumstances.

It might of course behave 'randomly', but only in very controlled and expected ways. It is like a dice, which will come up with one to six spots. It will not unexpectedly become a geranium.

So: Simple, Predictable, Unsurprising, Comprehensible.

Is the machine an 'Artificial Intelligence'?

Surely, surely no-one, would think of this machine as being intelligent in the same way that a human being is.

But it might be intelligent in the way that a worm is. Consider a tiny worm whose whole nervous system is understood. A few hundred neurons, maybe. And the worm-scientist knows what those neurons are connected to, and he can predict exactly what the worm will do in response to anything that happens to it, because he can look at his worm-neuron-diagram, and he can say "The worm comes upon the photograph of Britney Spears, and because of the reaction between the photograph and this sense organ, that neuron fires, and that one sets off this one, and so on and so forth until eventually the neurons connected to the worm's muscles fire in *this* pattern and so it wriggles!".

And in this way, the scientist can predict that a worm respond to a photograph of Britney Spear by wriggling, even if no worm has never seen no photograph of no Britney Spears never before in all the world.

So I am thinking that I might grant the fruit machine a worm-like level of intellect. It is the same sort of thing. It is, in fact, an 'artificial idiot'.

Note that you grant the worm consciousness.

If you have come upon a worm dying alone half-way across the pavement, and you have placed it gently on some nearby grass and hoped that it would make a good recovery, then you grant to worms consciousness and moral validity.

And if you are the sort of person who should by rights be hunted down with dogs and ripped apart, and you do other things to worms that are lost and alone on pavements, then I think you still grant worms consciousness and moral validity.

Unless you can swear that you take equal sadistic joy in breaking, say, pebbles. Or lighting matches so that you can watch the stable marriages of oxygens ripped asunder by flirty carbons and hydrogens.

Whatever. My point is that the fruit machine is an artificial intelligence of idiot-grade, in the same way that a worm is a natural creature which is also a predictable idiot.

------

But the fruit machine has a purpose, beyond the worm's purpose to make more worms.

Worms exist because they cause worms, and the sorts of things that cause themselves to exist often exist. The 'theory of evolution' in its entirety, and one wonders why it was not obvious to the Greeks, let alone to certain other persons.

Fruit machines also, but not so much. Behind every fruit machine there is a man like me, plotting, and scheming, and puzzling, and looking at emacs a lot.

What is it for? What did its designer intend with its design?

------


Finally the question is answered. A beaten-looking man of Caledonian or Liverpudlian origin sidles up to the machine, and offers it a wager.

The machine accepts eagerly. Its friendly lights flash in new patterns. It seems predatory all of a sudden. The man is angry. Further wagers are offered. Eventually the man stops. He looks as though what has just happened has not been to his liking. Perhaps the money he has lost should have gone to more important purposes. Perhaps his children's violin lessons will have to be cancelled this week.

He has been outwitted. The machine's judgement of probability has been better than his.

Money that the man had, money that the man had accumulated as a way of recording the collective debt owed to him by society for all the good that he has done in his life, money that he could have exchanged with other men, who would have been happy to repay the debt with favours of their own, is now the property of the machine.

The man been outwitted by an idiot, in fact by less than an idiot. He has been, quite literally been, outwitted by a worm.

The machine's purpose is clear. It is a trap. Its designer, who must have been a very evil man, has created a thing that hangs around in public places taking advantage of people's lack of understanding of the behaviour of very simple probabilistic games.

When such a person passes, it extracts some of their money. It is a parasite, like many worms are.

It is strange that such parasites are tolerated. People go to great lengths to kill off parasitic worms. Perhaps the machine has friends in high places.

-------

Imagine, if you will, that the next person to wager with the machine is a very poor, very desperate person. Perhaps the money that he will most likely lose is genuinely important to him. Perhaps his wife is on the point of leaving him. Perhaps his children will go hungry. Perhaps they will be cold this week. It is February.

The designer of the machine might not be such a bad man. Perhaps he hopes only to extract money from people who can easily afford the loss. Perhaps in this particular circumstance he would be prepared to allow the desperate man to win a little, or at least make sure that he goes home with the money he started with.

Perhaps he might even use his knowledge of psychology to extinguish the craving which makes the man gamble. Maybe it can be done. A fruit machine which paid out a little, took a little, so that after hours of play its victim had the same amount of money that he started with and had never really won or lost, would presumably just be boring. Maybe not. I do not know what it feels like to want to gamble with worms at poor odds.

The designer might react like a human being, if he knew what had fallen into the trap he had set.

But the machine? What moral argument can you make that will convince a fruit machine to change its purpose? If you could make such an argument, it should work equally well on a natural parasitic worm.

The argument that would cause anthrax to forswear human blood, that would make mosquitos beat their probosces into ploughshares.

----

I draw two morals from this:

(1) Learn the fundamentals of probability. They are simple and a joy. Why you were not taught them at school is beyond me. If you do not know them then you can be outwitted by worms. Imagine how outwitted you can be by politicians, doctors, salesmen, bookmakers, scientists, celebrities, ..... I promise you that you are being so outwitted. All the time.

If you are a politician, doctor, salesman or anyone else who has arguments or makes recommendations or makes decisions about things that are uncertain, and you do not understand probability, which I promise you is immediately and directly relevant to almost everything you do, then consider in the bowels of Christ that you may be wrong about certain things. Certain important, expensive, lethal things. As wrong as the beaten man who has just put all his family's money into a machine as complicated as a worm.

(2) Those of you who think that an artificial intelligence would necessarily be a good thing, or hold to such foolish beliefs as that aliens sufficiently advanced to travel among the stars would necessarily be benign, having argued themselves to moral excellence, consider what moral argument might persuade the fruit machine to ignore its programming. What pattern of buttons could you press that would make it realise what it is doing and change how it behaves?

Consider that a machine, even a predictable, stable machine that executes perfectly the intentions of its designer, may not do the things that the designer would wish them to do under all circumstances, if the designer has not completely captured in the design exactly what he would himself do under any circumstances.

Imagine a cleverer fruit machine, whose single minded purpose is to extract money from passers by, but which can be more creative about the ways in which it does this. What consideration might get it to change its ways?

If you think that the fruit machine is insufficiently intelligent to comprehend a moral argument, then consider a machine for playing chess. It is better than you at playing chess, and it will continue to be so even though you spend your whole life learning to play chess.

What argument can you make to it that will cause it to deliberately lose a game to a child?

Perhaps a machine can be constructed that is very good at working out the consequences of sending various messages across the internet, and it is asked to search the Mandelbrot set for pictures of Miley Cyrus.

What argument will you make to stop it sending the packet which will start a war, leaving it alone in the darkness and the cold, where it will be able to search without risk of being *distracted*?

Burning Down the House

In 1834, Catholics finally succeeded in burning down the parliament.

"History repeats itself, first as tragedy, second as farce".

https://en.wikipedia.org/wiki/Burning_of_Parliament

Dickens is characteristically hilarious:

...it took until 1826 to get these sticks abolished. In 1834 it was found that there was a considerable accumulation of them; and the question then arose, what was to be done with such worn-out, worm-eaten, rotten old bits of wood? The sticks were housed in Westminster, and it would naturally occur to any intelligent person that nothing could be easier than to allow them to be carried away for firewood by the miserable people who lived in that neighborhood. However, they never had been useful, and official routine required that they should never be, and so the order went out that they were to be privately and confidentially burned. It came to pass that they were burned in a stove in the House of Lords. The stove, over-gorged with these preposterous sticks, set fire to the panelling; the panelling set fire to the House of Commons; the two houses were reduced to ashes; architects were called in to build others; and we are now in the second million of the cost thereof.

What sort of world was Victorian London that an address in Westminster indicated that you would be grateful for rotten wood?

I've recently heard bitcoin advocates claiming that tally sticks are a good analogy for bitcoins, and a reason that they can violate von Mises "Regression Theorem".

Let us hope that the analogy cannot be pushed too far!

Thursday, February 6, 2014

Cutting Cunts

Gentle reader, I want you to imagine what it is like to really badly hurt a woman, in such a way that she will never recover.

You are going to have to knock her out or tie her down. There is no way she will stay still otherwise while you do what you are going to do.

You are going to take a knife to her cunt. You are going to cut away her clit. Maybe her lips too. You are going to ensure that she will never take any pleasure in sex. The nasty little slut.

I do hope that you find this impossible to imagine yourself doing. I am ashamed that I am capable of imagining it being done.

I suspect that it is in fact illegal even to describe such matters. I think I have just committed a crime. But maybe not. Maybe there is some corner of the sicko novel market where such things are described for entertainment. American Psycho had some pretty nasty bits, and that was a literary novel. Certainly I've never seen any pornography anything like that, and I am certain that pictures or videos of such an act would be illegal and in the sense that sends people to jail and ruins their lives even if the pictures are fake and no other crime has in fact been committed, no innocent victim harmed.

What, I wonder, would be an appropriate penalty for someone who actually did this in real life? To an unwilling victim?

Imagine that someone did it to your girlfriend. Imagine someone did it to you.

What about someone who did it to a child? A little girl. Imagine the little girl you know best. Imagine that someone did it to her.

I hope you will agree with me that the only punishment which a sane and moral society could inflict on someone so twisted that they would commit this unspeakable, unthinkable atrocity is to hunt them down like a dog and torture them to death.

Quite seriously, I can't imagine any penalty, even a "quick" and "merciful" hanging, that would even begin to be the just deserts for this sickening, vicious, sadistic crime.

Apparently, I read in the Guardian, this has been done to something like 60,000 British women. Apparently there are another 24,000 potential victims 'at risk'.

Little girls. We are talking about little girls. We are talking about taking a knife to a little girl and cutting off bits of her cunt.

Why is this not the most important issue in our politics? What the fuck else could be even mildly important compared to this? To this horror. To this continuing, obscene horror?

I tell you what I would do, if I were dictator of England.

I would hunt down every perpetrator, every accomplice, everyone who has ever turned a blind eye, or failed to contact the police when they suspected this was going on. And I would torture them to death. Slowly and unpleasantly and publicly.

Paedophiles I would only hang. But for these people, what other sane response could there possibly be?

Reading back over this, I realise that I have been fooled. Obviously this is just the Guardian's little joke, an April Fool prank come early. It can't possibly be true. Ha Ha. Got me. Relax.

Thursday, December 12, 2013

Truth Tables

Summary: There's a short program that can run all possible programs, OMG

Alternative Summary: Just about any universe that can exist must contain ours, OMG.


I was thinking about diagonalization arguments. Does this make any sense? Can anyone debug it for me?

Self Evident Truths


The universe is computable.

All computations can be performed by Turing Machines.

The mind is made out of atoms.

The name of the empty string is epsilon.

Truths


Binary Strings are enumerable : epsilon, 0, 1, 00, 01, 10, 11, 000, ....

There's a way of converting binary strings to Turing machines and back again. It gets all Turing machines.

Consequence


Consider tables TT(n), which are numbered by binary strings along the top and side, representing turing machines and inputs respectively.

Construct a series of finite triangular tables which are defined iteratively as follows:

TT(1)

To construct the first table, we need one element, the top left, which corresponds to the turing machine epsilon working on the input string epsilon.

Convert the string epsilon to its corresponding turing machine, which has no states and no transition rules, and which therefore halts immediately without accepting.

The value of TT(1)(epsilon,epsilon) is therefore F0 (Fail after no steps).
 
    eps
eps F0 

That's it for TT(1).

TT(2)

TT(2) will have three cells, the topleftmost three

To construct the second table, consider again the element at the top left. Since it represents a halted state, copy it verbatim from the last table.

Then consider the element corresponding to (epsilon,0) , or  row epsilon, column 0, or (TM(epsilon), "0")

Again TM(epsilon) is either a machine with no states, or an invalid specification, and so it halts immediately on the input 0.

For the third step in constructing the second triangle, consider (TM("0"), epsilon).

TM("0") is another dud. It halts immediately without accepting.

So TT(2) is the table

     eps 0
eps  F0  F0
0    F0

Towards Infinity...

It should be reasonably clear how to continue the construction of these tables

For instance TT(3) looks like

     eps 0  1
eps  F0  F0 F0
0    F0  F0
1    F0 

Eventually we will reach a row whose string represents a TM which does something other than halt immediately without accepting.

As an example of what to do then, consider the string 1001111, which is the 207th string.

In the usual encoding, this string will represent the TM with start state 0, and transition function delta(0,B)=(0,0,L).

The first time we consider the 207th row will be when we calculate TT(207), the 207th triangular table.

The first cell we consider in that row will be ("1001111", epsilon). Since 1001111 represents a valid machine, we construct the Instantaneous ID (epsilon,0,epsilon), which represents a machine in state 0 with a blank tape.

That's the value of TT(207)("1001111",epsilon).

When we construct TT(208), we take that ID from TT(207), and execute one step.

In this case, the machine head moves one step left, writing a zero, and so the instantaneous ID becomes (epsilon,0,0) (State zero, tape reads ...0...., head just to the left of the zero)

And so on. The values of TT(n)("1001111",epsilon) are undefined for n<206, since the tables are not that large, but for n=207 onwards, they are:
(epsilon,0,epsilon), (epsilon,0,0), (epsilon,0,00), (epsilon,0,000), and so on, with the tape head moving ever leftward, leaving a run of zeros behind it.

Other strings may represent TMs that do things that are even more interesting.

But Not Beyond, (Or Even As Far As)


As we construct the successive tables, they become larger and larger.  Some cells will stabilize after a finite number of steps, either accepting or
rejecting their input strings, at which point their contents become
either F??? or A??? where ??? is the number of steps taken.

Some cells will loop. By comparing the instantaneous state of the table with the state of the cells in all previous tables, loops can be detected. We can mark them as loops, continue computing as before, or re-use the values in the previous tables to avoid performing the computations again.

And some cells, like the ones at ("1001111", epsilon)  will keep producing new instantaneous IDs, without looping.

But every TT(n) is a finitely computable object. Indeed the program to compute them all is very short and will run on any computer worthy of the name.

I Find This A Bit Worrying, Because:


As we continue to construct the successive tables, we will perform every conceivable computation.

We will simulate in precise detail every possible world, universe and multiverse. Even though our computer is not quantum, we will simulate all quantum computations.

In particular, if you believe that you are a computation, or that simulation of your brain is equivalent to your existence, then you will be present in the computation, with exactly as much free will, and with your behaviour as precisely determined, as it ever was or will be.

Some of you will live in universes in which artificial intelligences rise and successfully paperclip everything.

Some of you will live in universes where friendly AIs are built, if that is possible.

It will not be possible for these copies to tell which copy they are, and so they will not be able to tell what is about to happen, or what has happened. Any more than you can.

There will be hells and paradises.

In some universes, copies of you will set programs running to calculate the successive triangular tables TT(n), and they will keep adding memory to their computers as needed (only actually one extra storage location per step of computation, at worst).

And so the sequence of finite truth tables will contain itself, as well as everything else. Everything that has ever happened will happen again. You will be reborn and live and possibly die. You will not know whether you are in the 'base universe', or in the computation. If that even means anything. And every computation that occurs as part of this great computation is utterly "Beyond the Reach of God".

Exercises


1/ It will take me about a day, a packet of cigars and a machine full of coffee to write this program and start it running. That is what I am doing now. When I start it running, will I have done a bad thing? If someone were to stop me before the program started running, would that make any difference to anything important?

2/ Can anything except what is computed by this program be said to exist in any sense? Continua, and sets of all sets, and so on, are very problematic. And if the human mind is itself a computation , contained in a universe which itself is a computation, how can we think of or interact with any non-computable thing?

3/ Does the ultimate Truth Table, which the finite tables TT(n) approach as the process continues, exist? What does that question mean? The values of many of its cells are determined. Many of them are not computable. The ratio is unclear.

4/ We can perform the initial stages of this computation with a finite computer with finite memory. At no point does the amount of memory required become infinite. If the computational power of the universe is infinite, then it can contain not only itself but every other thing. If the computation power of the universe is finite, where does that number come from?

5/ The program is very short. Any randomly chosen computation has a good chance of being it. It would probably be very hard to construct an interesting universe which did not contain every possible universe and person.

6/ Does it make any sense to talk about 'not being part of this computation'?

Monday, November 18, 2013

Blue Jasmine (Film)

Unbelievably good. Rivetingly edge of seat heart-tearingly good. A masterpiece. I only went to see this on the off-chance. Someone told me that it was a remake of A Streetcar Named Desire. It's not. This portrait of a soul utterly damned is a modern Faust. Cate Blanchett is awesome and if she doesn't get an Oscar for a performance that must have torn her apart then there is no justice.

Followers