The Standing Invitation

Archive for August 2011

A Bit of News

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Information is news. But what is information? A note, written in pencil on a page, contains information; but information is not made out of graphite deposited on cellulose. A TV broadcast is information; but information is not made out of radio waves, and it is not the vibration in the air molecules between the radio and your ear.

It is formless, shapeless, intangible. Nevertheless, it can be measured, quantified, treated mathematically.

Information reduces uncertainty. Toss two coins in the air – a penny and a pound coin, say ­– and catch them in your hand without looking at them. You are uncertain about whether they are heads or tails. This uncertainty is measurable: if you had to guess the outcome of the toss, you’d have a 25% chance of getting it right.

But you peek at your hand. You see that the pound coin has come up tails, but you can’t see the penny. With this new knowledge of the state of one of your coins, you have a 50% chance of guessing right. The information has doubled your chances; the uncertainty has dropped by half.

Information is measured in bits. One bit, short for binary digit, lowers your uncertainty about the world by one half. It reduces the number of yes/no questions you have to ask in life by one.

Note that the information content of a fact, measured in bits, depends on how uncertain you were to begin with. If I tossed a double-headed coin and told you it came out heads, that statement contains no information. It was always going to happen; no uncertainty reduced. Conversely, if I tell you I rolled a die and it came out six, that fact is worth 2.6 bits ­– more than one bit, because one yes/no question would not have been enough to remove the uncertainty. Identifying a card pulled from a pack of 52 cards is worth 5.7 bits.

How much information is contained in the expression “It will rain in the UK tomorrow”? Not much ­– the answer isn’t surprising. You could have guessed anyway.

After a week trapped in a mineshaft, a woman is rescued. The news report quotes her as saying “She is glad to be out.” Not much information. You would be surprised to hear her say, “Actually I preferred it down there.” That would be information.

But if that was what she’d said, would the journalist report it? Information-rich or not, does it make a good story? Or would the journalist have quietly turned off the camera, choosing not to show those bits?

The tanks of liberation roll into a bombed-out city. A flak-jacketed war correspondent films crowds of people welcoming the brave soldiers who have freed them, cheering them on. Surely very surprising, very information-rich. But how photogenic would the opposite case have been? A crowd of angry shopkeepers whose lives have been wrecked ­– would that footage be aired? Perhaps not. Regardless of what happened, it is likely that any images shown will be positive. Positive, and unsurprising. Information content low.

Information is news – but not all news is information.

REFERENCES

Information theory stuff from Richard Dawkins’s essay “The Information Challenge” as found in The Devil’s Chaplain; definitely worth a read.

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Written by The S I

August 19, 2011 at 11:59 pm

Organic Chemistry for Marxists

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In chemistry, a substance is defined by its molecular structure. One substance, one structure: if you alter the structure, it is by definition a different molecule. But often things are not that simple.

When considering how some molecules react, it is often necessary to draw them as though they existed as two or more resonance forms. The thiocyanate ion drawn above has two resonance forms, one with the negative charge on the sulphur atom, one with it on the nitrogen. Some reactions occur at the S end, some at the N end. Resonance forms allow us to see  why: they occur wherever the negative charge is located.

When we draw resonance forms, it is important to understand what we are not saying. Neither of these forms really exists; what really exists is something like an average, with the negative charge existing partially over the S, partly over the N.

Resonance forms are convenient fictions that exist only in the minds of chemists, but they are good at allowing us to predict the outcomes of chemical reactions, so we still freely use them despite knowing they are not true representations of the real world.

Which is fine, apparently, unless you’re a Marxist.

In the Soviet Union in the late 1940s, some Soviet chemists declared that resonance forms were incompatible with Marxist theory and should not be used. Marx taught that only the material world was important, making these imaginary structures at best a seductive illusion that would retard progress in the field, and at worst a threat to the very fabric of society.

Whether these scientists truly failed to recognise the models’ utility or were simply trying to gain personal advancement through a display their patriotic Marxier-than-thou attitude is debatable; nevertheless, it grew into a major controversy, probably much to the embarrassment of more practical people who just wanted their reactions to work. A conference was held in 1951 to lay down the law once and for all. The result was a report that stated that the theory of resonance, together with certain unwelcome theories from physics and biology “present a united front in the fight of reactionary bourgeois idealism against materialism.”

Utility won out in the end, and the resonance theory eventually came to be recognised for what it is: a useful tool to understand the behaviour of molecules, depending on and representing reality, but not even pretending to be a perfect depiction of it. But throughout the 1950s in the Soviet Union, textbooks rarely dared to mention resonance.

The Marxist scientist declared that resonance forms were a just a model. And they were absolutely right. Where they went wrong is thinking this was a bad thing.

 

REFERENCES

Drawn from “A Soviet Marxist View of Structural Chemisty: The Theory of Resonance Controversy” by Loren R Graham: http://www.jstor.org/pss/22775

Written by The S I

August 17, 2011 at 11:59 pm

The Set of Everyone

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A few years ago, the abdominal ticking timebomb that was my appendix started to rebel against the system, and I was rushed to hospital. The offending organ was removed, and my life was saved. When I left the hospital, I did not receive a bill; the doctors didn’t give me a receipt for my bursting bits. Thanks to my country’s healthcare being publically funded, I was spared the unpleasant knowledge of the exact monetary value of my life.

But in a very real sense, I did pay for the operation. The tens of thousands of pounds my surgery cost were taken from me, a bit at a time, through taxation. My kamikaze appendix represented a return on my investment, since from birth to the moment I walked into the doctor’s office, this was money lost.

If the illness justifies the money I lost, would I have considered myself cheated if I never once got sick?

The problem is that we never know in advance that we will get ill. The money deducted from my income was spent on a probability. How likely am I to fall ill in the next year? In the next ten years?

A hypothetical situation: you know for certain that there is a fifty percent chance of catching a fatal illness in the next ten years. The illness is treatable, but the payment is expensive ­– and you have to pay it in advance.

You have two choices: you don’t pay, and hope you get lucky; or you do pay, but risk having spent your money on nothing. You decide to pay, just to be on the safe side. But ten years later, you are still in perfect health. You were lucky. Do you feel cheated? If yes, it is only because you are unaware of the other you, the probabilistic ghost of you, that could have been you.

Your decision to pay for treatment could be seen as paying for a probability, but it can also be seen as paying for a certainty ­­– the certainty of health for the set of all possible yous.

In order to act self-interestedly in an uncertain world, you need to consider not just who you are now, but who you might be later – and, by extension, all the people you might have been. It’s impossible to know which of the set of possible yous you will be in ten years time; it is in your interest to have a healthcare system that will take you in, whoever you happen to be.

I have no children, but someday I would like to. I have no idea what they will be like: boys or girls, healthy or unhealthy. But I know that I would want them to be born into a world where they are taken care of regardless of what bodies they were born into. I consider it the mark of a functioning society that the set of all possible mes, the set of all possible people everywhere, is looked after. It’s looking after Number One; but it’s doing so recognising that Number One being bigger than you are.

REFERENCES

This is all very Rawlsian; google the Veil of Ignorance. The ideas of probability and certainty are derived from Taleb’s wonderful The Black Swan.

Written by The S I

August 15, 2011 at 11:59 pm

Cold Power

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I once attended a science demonstration involving a model steam train.

It was quite a neat little toy, with a simple but fully functional combustion engine. You fill the boiler with water, and add a pellet of fuel. The fuel burns, producing heat. The heat causes the water to turn to steam. The steam expands, which pushes against a piston. This motion turns the wheel and sends the train shooting off across the lecture hall.

What we have here is a clear display of energy changing from one form to another: the kinetic energy of the train comes from the kinetic energy of the expanding steam, which ultimately comes from the fuel.

The train doesn’t know or care what fuel goes into it. Under the boiler could be a lump of coal, or burning wood or oil, or a hunk of uranium. All that matters is that the fuel gives off heat. If it can get hot, then it can push the train, and that’s all that really matters… right?

Well, not exactly.

Because then the lecturer filled the boiler not with water, but with liquid nitrogen. This was at about -196 ˚C, and so exposure to air at room temperature caused it to bubble and boil. Inside the train, it gave off huge amounts of expanding nitrogen gas. This, too, pushed against the piston, turned the wheel and sent the train moving again.

So liquid nitrogen is clearly a good fuel for the steam train. But liquid nitrogen is cold. It doesn’t generate heat in the same way that a burning lump of coal does, and when it’s in the train, the train becomes icy-cold even as it moves. Where does the heat that moves the engine come from?

It comes from outside. Energy flows through the walls of the boiler, heating the liquid nitrogen and causing it to boil. While the train moves, the world gets slightly colder.

A fuel can work by emitting heat, in the case of petrol, or by absorbing heat, in the case of liquid nitrogen, and it doesn’t matter in the slightest. What drives the engine is not energy generation, but energy flow. There is a difference in energy between starting state (fuel in the tank) and the end state (fuel consumed), and there is an allowed pathway that allows for the removal of this difference – consumption of the fuel in a way that happens to propel the engine. In thermodynamics, as in so many other things, it’s the differences that make things interesting.

But I’m afraid I can’t foresee a world of high-speed rail travel in trains powered by liquid nitrogen. The little model was only good for a few minutes before the ice caused its wheels to stick. It fell over, the liquid nitrogen spilled, and all the tiny passengers promptly asphyxiated.

Written by The S I

August 13, 2011 at 11:59 pm

Cultural Engineering

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Should Scotland be independent? It’s a complicated question, and I don’t intend to address it here. What I want to ask is the same question, but with a shift in emphasis: should Scotland be independent?

Let’s say you have a large number of people in the north of the UK who want independence from the south of it. Where should you draw the line on the map? Perhaps you might divide the country into squares, poll each square, and then declare as your new proposed border that line north of which fifty-one percent of the population wants independence. That’s certainly one way of doing it ­– and to me it makes much more sense that simply assuming that the most natural and parsimonious way of carving up the country happens to coincide exactly with the border between Scotland and England that was drawn up in the 13th century.

For me, independence for Scotland makes little sense when compared with, say, independence for that group of people who tend to vote differently from the rest of the country. The area this group occupies might correlate with the region we call Scotland, certainly ­– might even correlate with it because it’s Scotland, because that is a specifically Scottish way of thinking ­– but simply to assume it seems wrong.

Of course what I’m missing is that Scotland is a distinct cultural entity. People in Scotland might feel Scottish, as opposed to British.

The feeling of nationhood is a real phenomenon, and not something to be ignored. The people who would gain from Scottish independence ­– members of a devolved government of a region of a United Kingdom who might see themselves as one day being the all-powerful government of an independent Rebublic of Scotland – know this quite well. They know they have a vested interest in cultural distinctiveness from England.

Scottish Gaelic is spoken by about 60,000 people in Scotland, a tiny percentage of the population. And yet it is the words “Fàilte gu Alba” that greet new arrivals at Edinburgh Airport, and all the signs on the Scottish Parliament have equal priority for English and Gaelic. Is this a generous move to accommodate the few thousand people who feel more comfortable conversing in Gaelic? Hardly. It is an attempt to remind us that Scotland is different from the rest of the UK. It is part of a drive to reintroduce and promote a language for Scotland.

The expressed goal is to ‘preserve’ a uniquely Scottish culture, one that has suffered from centuries of English oppression. And perhaps this is a worthwhile enterprise. But bygone cultures are never revived; they are only ever recreated, with modifications, to suit the present-day needs of those recreating it. Treat with suspicion those who say they are preserving some past golden age while installing computers in their offices. They are picking and choosing from what is available to them, and they are doing it because they plan to profit from it.

Written by The S I

August 11, 2011 at 11:59 pm

Doing Maths Without Numbers

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Define ‘one’. Go on, try.

Well, ‘one’ is what you have when there’s only one of something. You have one duck. There – one. But that’s circular. You still need to define ‘one’ for you to have one duck.

All right, it’s one more than zero. ‘One’ more? Circular again, and what’s this ‘zero’ you’re talking about now?

Half of two? Okay, fine, but what’s two? Well, that’s twice one, isn’t it? Circular again. People trust mathematics with their lives, and yet all it seems to rest on is circular arguments. Can’t we do better than this?

Let’s start at the very beginning, with something really fundamental: “things are what they are.” A duck is a duck. A submarine is a submarine.  “It is what it is” is a property shared by all things. Let’s call this the property of identity, of being identical with itself – the property of being what it is.

Everything is identical to itself. If you grouped together everything that is identical to itself, the set would have everything in it. And the set of everything not identical to itself would be empty.

We have defined an empty set – a group with no members. The set of four-sided triangles is empty, because nothing is both a triangle and four-sided. So is the set of things that are not identical to themselves, because nothing is.

Now we’re used to the idea of sets, consider this: what does the set of three ducks have in common with the set of three triangles? Call it the cardinality of the set ­– a measurement of how much is in it.

Imagine the set of all empty sets. What do all these empty sets have in common? Let’s call it zero ­– the cardinality of an empty set. We have now defined zero. If something is the same as zero, then it has the same cardinality as the set of all things not identical to themselves.

Now that we know what zero is, how many things are identical to zero? There’s just one thing that’s identical to zero: zero. If you filled a set with things identical to zero, there would only be one thing in it. The cardinality of the set of all things that are identical to zero, is one.

And the cardinality of the set of all things that are identical to ‘one’ or ‘zero’ is two. And the cardinality of the set of all things that are identical to ‘zero’ or ‘one’ or ‘two’ is three, and so on and so on and so on.

To break the circularity of mathematics, Bertrand Russell defined ‘I have two hands’ as:

“There is such an a such that there is a b such that a and b are not identical and whatever x may be, ‘x is a hand of mine’ is true when, and only when, x is a or x is b.”

And this is how you do maths without numbers.

 

REFERENCES

The BR quote was from A History of Western Philosophy (1945); also see My Philosophical Development (1959).

The layout of the above argument was from a YouTube video on mathematical logic, but I can’t remember where it is; I’ll update this if I find it.

Written by The S I

August 9, 2011 at 10:00 pm

Posted in Science

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The Mechanical Soul

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(And now for some wild speculation.)

If we accept that evolution is true, we must also come to terms with humans being a blurred region on a continuum that we share with animals, fungi, plants, and bacteria. And this is why some people don’t accept it.

Nobody likes to be told he is not special, and that is precisely what evolution tells us. There is nothing inherently special about being human. We are not the Chosen Ones. And some people cannot take this ­– can’t take the idea, not just that we are related to apes, but that we are apes. These people would rather ignore evidence and lie to themselves (and, by banning its teaching, effectively lie to their children) than accept the knock to human dignity.

My prediction is that, just as evolution has shown us that there is nothing special about being human, advances in artificial intelligence will tell us that there is nothing special about being alive.

People cling to the idea of an immaterial soul, and strongly resist the notion that it might have a biological origin. If all we are is bits of brain tissue, mechanical and deterministic, what’s the point of being alive at all?

But when AI really takes off, we will be forced to re-examine these beliefs. Not only will we someday build machines that are as able to think and feel and care as we are; we will also, on the way, build all the machines that come between. We will show, again, that we are on a continuum, with our minds differing only by complexity and computational power from Babbage’s difference engines.

How will people react to this?

Many will simply not care. The discovery of natural selection will have prepared the ground; the appearance of AI will only serve to confirm a hypothesis already believed my many. And anyway, what does it matter? We still need to pay the bills.

There will be others who will react with the flat hostility of present-day Creationists. Deny it all! Refuse to believe! Ban this immoral research! Computers are only a theory!

But many – one hopes – will find their own lives improved by the knowledge. It is good for the soul to know one’s place in the world, and understanding the ways in which we are not special will highlight and even enhance our awareness of the ways in which we are. They who already peer into the night sky and marvel at its cold beauty will turn their gazes inward, and will be just as awed by what they see there.

 

 

REFERENCES

All I’ll say is that Douglas Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid is a wondrous, wonderful book.

Written by The S I

August 7, 2011 at 9:00 pm