PulseFusion

 

Back in the day, we all had a device in our homes that operated at a temperature of 300 million degrees Kelvin. It was our cathode-ray-tube TV, and that was the temperature of the electrons accelerated by the tube's anode hitting the back of the screen. The inventor of electronic TV, Philo Farnsworth, also invented a fusion reactor that relied on a similar principle: hydrogen isotope ions are accelerated by an electric field until they collide and fuse. Lots of people have made these, including amateurs, and they are an established technique for use as a neutron source in hospitals and the like.

Unfortunately, no one has yet made one that generates more fusion energy than the electrical energy you need to put in to make it work.

The picture above from the Wikipedia article on fusors shows one working. The fusor consists of two concentric spherical wire cages: an anode on the outside and a cathode near the middle. Positive ions are attracted to the inner cathode and fall down the voltage drop. The ions collide in the center and fuse.

My purpose here is to propose a variation on this principle that may produce higher collision energies and temperatures, leading to more efficient fusion.  (This may have been thought of before, in which case please let me know in the comments, though a brief search online has not revealed it.)

This diagram is very similar to the device I described above, except that a conventional fusor operates in a steady state with the ions continually flowing towards the centre. My proposal is for a cycle:

1. Cage A and the containment vessel are both positively charged and hydrogen isotope ions are fed into the input. They are repelled by the two positive charges and their own charge and so form a thin spherical shell between Cage A and the containment vessel. It should be possible to hold a large number of ions in this pattern.
2. Cage A is switched off, and Cage B is set to a large negative voltage.
3. The ions accelerate through the now-neutral Cage A towards Cage B, forming an imploding spherical shell.
4. As soon as that shell has passed Cage A it is set to a large positive voltage to accelerate the ions faster.
5. When the shell collapses to the radius of Cage B that is switched off to allow the ions to pass through under their own inertia.
6. When they are through, Cage B is set to a large positive voltage to repel them towards the centre.
7. They then fuse in the middle (we hope...).
8. Go to 1.

If this works at all, it is immediately obvious that the idea can be extended: a series of concentric cages of reducing diameter could be placed between the containment vessel and the centre. As the sphere of ions implodes a positive-negative voltage wave would be applied sequentially at increasing speed to the cages to match the moving ions and accelerate them faster. In this way the device would act rather like an electrostatic particle accelerator, but in the form of a sphere rather than a straight line.

It may be possible to apply a small positive voltage to each cage as the ion sphere implodes through it to reduce collisions with that cage.  It may also be possible to make the device in the form of a series of concentric cylinders, rather than spheres, to generate a line of fusing atoms along its axis rather than a fusion volume at the middle of a sphere.

WorkMakesPoverty

Imagine a world in which people earn money by pouring coffee for each other while robots make the people's cars, the people's furniture, and the people's coffee machines.

You don't have to imagine that world; you're living in it.

Economics

The famous graph of productivity and wages above from the Economic Policy Institute (with the red arrow added by me) shows what's happened.  As I've pointed out before, the engine of history is engines.  Automation is the reason for the decoupling of productivity and wages, and automation really took off with the introduction of the microprocessor in the mid 1970s.  As more wealth is created without any human effort, the value of - and hence the wage for - human effort falls.

Suppose someone has a one-person business idea that causes a few of the coffee pourers voluntarily to pay them $1 for the useful product of the business.  Then suppose the microprocessor communications network that spans the World allows that business to expand without requiring the business to employ many people, or - in the extreme - not to employ anybody beyond its originator.  Now two billion coffee pourers are paying in their $1, and suddenly we have a billionaire who has achieved that status without exploiting anyone: they haven't employed anyone, and all their customers are volunteers.

That is a caricature of a Silicon Valley billionaire.  It is a caricature because some of them have exploited people to become very rich.  But they exploited hardly any people, because they employ hardly any people.

And, of course, for much of this the coffee pourers don't even need to pay $1.  The business gives them what they want free, and sells the pourers' personal details to advertisers.  As the cliché has it: if you get it for free YOU are the product. The implication here is that somehow this too is exploitation, but I think that stretches the idea beyond breaking point: I am hardly being sweated as indentured labour if that labour merely consists of scrolling down my search screen to the first link that doesn't have "Ad-" in front of it...

Another aspect of the graph above that is not often discussed is that it is one of the main reasons for very low inflation in recent decades (see "Disruptive Technology" here).  After the crash of 2008, developed nations' governments started printing cash like there was no tomorrow to rescue the banks - the euphemism was, and is, quantitative easing.  Setting aside whether this was right or wrong, or sensible or stupid, in previous ages it would have led to rampant inflation.  But this time it didn't.  And the reason it didn't is that our machines carried right on up the top curve making more and more wealth with fewer and fewer people, keeping wages flat.

Politics

Some say that the recent phenomenon of wages lagging behind productivity is caused by neoliberal economic policy. But neoliberalism didn't cause the microprocessor revolution, it didn't cause the resulting growth in wealth, and it didn't cause the resulting loss in the value of work; it merely didn't force the redistribution of that wealth.  In this regard it is simply a word for inaction; doing nothing under a different political label would have led to the same result.  Neoliberalism didn't make the wealth or the problem; it merely did nothing to correct it.  And if neoliberalism claims the growth in productivity, it is the fly on the chariot axle saying, "See what a dust I raise!" 

Forming a union to protect employees' rights, which is what led the curves in the graph to match up until the 1970s, only works if the business the union is negotiating with needs a lot of employees to function. If the business employs few people, collective bargaining simply doesn't work. And if it employs none, the whole idea is obviously completely inapplicable - you can't have a collective of zero people.

The hundred-and-fifty year-old Marxist idea that the labouring proletariat make wealth for capitalists, but can't benefit from that wealth themselves unless they unite to form a cartel to drive up wages or to force themselves into a controlling position has no application if the capitalists don't need a labouring proletariat to make money.  You can't have a strike of people who are already sitting on a sofa watching Netflix in the daytime.  And if they're pouring coffee for other coffee pourers, then any strike is necessarily misdirected.  Their exploiter isn't really Starbucks, nor is it Ford, who take a chunk of their coffee-pouring wages for a car that needed virtually nobody to work at its manufacture.  They don't have an exploiter; they are just not worth very much economically at all.  If someone finds that their circumstances are impoverished it doesn't necessarily follow that someone else is being actively unfair towards them.

Transitions

Here are a series of steps. But in reality all of the following transitions took time to happen; the changes have been a smooth exponential that started in prehistory and is continuing to rise up ... well, exponentially.  Remember that wherever you are on an exponential curve there is a plain behind you and a cliff ahead.

12,000 years ago the invention of agriculture meant that the economic value of hunter-gathering dropped, so hunter-gatherers started to labour on the land. In absolute terms they became better off. But in relative terms they were worse off than the owners of the land.

250 years ago the Industrial Revolution mechanised both agriculture and production, which meant that the value of working the land dropped, so agricultural workers started to labour in factories. In absolute terms they became better off. But in relative terms they were worse off than the owners of the factories.

50 years ago the microprocessor revolution automated factory production much further, which meant that the value of labouring in factories dropped, so factory workers started to labour in the service industries. In absolute terms they became better off. But in relative terms they were worse off than the owners of the service industries.

20 years ago microprocessors expanded into into the communications and service industries.  AI started to do work that previously only people could do like answering phones, writing legal documents, or diagnosing diseases.  This meant that the value of working in service industries dropped.

And now the workers have no economic sector that values their work to migrate to.

Alphabet (Google's parent company) is the fifth biggest company in the World.  It has 135,000 employees...

Human activities

We haven't evolved to work.  Most people don't like working.  Work is not needed for social interaction.  People in wealthy societies spend nearly half their lives not working because they're in education, then in retirement.  There is nothing inevitable about work.

And increasingly there is nothing necessary about work either - see the productivity graph above.

Here is another graph.  It's of happiness against age from a study of about 1.2 million people by the economist Danny Blanchflower.  The Y axis is a measure of happiness.

What it shows is that work contributes to making people miserable and retirement (look at the steepest up gradient...) makes people happy.

Every retired person I know (and I am of that age, so I know a few) is busier and happier in retirement than they were when they were working.  The happiness is perhaps unsurprising, but why are we all so busy?  The answer is that we are all doing unpaid hobbies - things that we would have done for work when younger if only they had paid enough.  (To be fair, I was one of the tiny minority of incredibly fortunate people who had a paying job that was more or less my hobby - I was a university lecturer and researcher.)

Economics and politics again

My pension, and the pensions of pretty much everyone who has one, is paid for out of company dividends from shares owned by pension funds.  Having bought shares in the companies that are following the top curve in the graph at the head of this essay, pensioners have detached themselves from the bottom curve.

Clearly what is needed is a mechanism to extend the idea of a pension to everyone from the start of their adult life onward, as their work is increasingly unneeded and so increasingly can't produce wages to support them.  In other words, we need a UBI, a Universal Basic Income.

The economic and political solution to this that is usually proposed is a reasonable one: tax the profits of the companies on the top curve and use the money to pay a UBI of - let's say - $25,000 a year to the people on the bottom one.

But I would like to propose an alternative that might work better: allow companies to pay some of their tax bill in shares.  The dividends from those shares would then be used to pay the UBI, just like a pension.  Governments would have to appoint independent pension fund managers to look after the scheme, just as pensions are now administered.  And there would have to be some strict rules in place to prevent skulduggery like governments selling shares when they needed a bit of cash, or like companies paying shares as tax that they knew for some reason were going to give poor dividends relative to the company's performance.

Conclusions

Work used to give most people a reasonable standard of living.

Now work makes people poor.

The only way to correct this is with a Universal Basic Income funded by companies' increased profitability from automation.

Postscript

The late Iain M. Banks used to say, "Money is a sign of poverty."  He meant that a society with a fully automated supply of goods and services would not need money to regulate their distribution.  He may well have been right; we are already approaching a society where WORK is a sign of poverty.

I wrote this without being paid for it; it is one of my hobbies.

But this could have been written by the GPT3 AI...

CarbonHedge

How can we remove carbon dioxide from the air by doing nothing?  Read on...

This, as you can see, is a hedge.  Hedges are made of trees that are forced to be mere bushes by repeated pruning.  This one, near my house, is in late Summer, just before the pruning is done.

And here it is a little further along, just after the tractor and flail has passed over it.

But opposite it is another hedge that hasn't been, and now therefore can't be, pruned:

It has grown into a row of trees, though it is still a reasonably effective hedge.  It does, admittedly, have a few holes that the pruned hedge does not have.  I'll return to these below.

People have suggested coppicing hedges as biofuel to replace fossil fuels. But burning biofuel is neither very clean, nor is it very effective as a means of carbon reduction because it doesn't actually reduce atmospheric carbon, it is merely carbon neutral.  And coppicing would be quite a laborious activity, even with machinery.

So the obvious thing to do is to allow the vertical shoots in the first picture to become the trees in the third by not trimming the tops of hedges as in the second.  The bottom couple of metres of the sides could still be trimmed to stop branches growing across roads or into crops at low levels.  And the time saved by not trimming the tops could be spent wandering along with a dibber, collecting blackberries.  Don't eat them!  But, when you get to a gap forming in the hedge, plant a few brambles with the dibber to block it.  (You can eat the rest of the blackberries for lunch...)

What effect would this have on the UK's CO₂ reduction strategy?

The UK has about 700,000 kilometres of hedges.  If they are about two metres thick on average, that's 140,000 hectares of potential trees.  The UK plans to plant 30,000 hectares of forest per year over the next 30 years to absorb CO₂, so simply leaving the nation's hedges to grow vertically would achieve just under five years worth of the total (that is 15%) by doing nothing except a day's pleasant blackberrying once a year...

GapOfTheGods

 

I am aware of the God-of-the-gaps nature of definitions of intelligence, whereby something that a computer becomes able to do successfully, like chess, is removed from the canon of intelligent ability.  By this process intelligence becomes a melting iceberg, drifting towards the Equator, with a smaller and smaller area upon which we humans may stand.

Despite that, I would like to propose a new definition of intelligence:

Intelligence is the ability to moderate impulses by deliberation.

By impulses I mean, in human terms, emotions.  But also, at a lower level, I mean such phenomena as a single-celled organism swimming up a chemical gradient towards food.

Let me start by considering systems that are entirely emotional and that do not deliberate: computers.  Consider what happens when you run a Google search.  The Google machine is completely unable to resist its impulse to respond.  If you were to ask it, "What is the best way to subvert the Google search engine?" it would return you a list of websites that would be its very best effort to answer your query correctly.  All computer systems, including all current AI systems, are entirely driven by their irresistible emotional need to respond to input.

If you type something at Generative Pre-trained Transformer 3 it will respond with coherent and rational text that may well be indistinguishable from human composition.  In that regard it is on its way to passing the Turing Test for intelligence.  But it cannot resist its emotional need to respond; the one thing you can guarantee is that, whatever you type at it, you will never get silence back.

But now suppose someone asked you, "What would be the best way for me to murder you?"  You would hesitate before answering and - if free to do so - not answer at all.  And under compulsion you would frame a considered lie.

Everything that responds to input or circumstances, from a thermostat, through a computer, a single-celled organism, to a rat, then a person, has an impulse to respond in a certain way.  But the more intelligent the responder, the more the response is mediated by prior thought and mental modelling of outcomes.  The degree of modification of the response depends both on the intensity of the immediate emotion with which the response starts, and the intelligent ability of the responder to model the situation internally and to consider alternatives to what the emotion is prompting them to do.  If you picked up a hot poker, the emotional impulse to drop it would be well-nigh impossible to resist.  But if someone held a gun to your head you would be able to grit your teeth and to retain your grip.  However, the single-celled organism swimming towards food would not be able to resist, no matter what danger lay ahead.

Today's AI systems are far cleverer than people in almost every specialised area in which they operate in just the same way that a mechanical digger is better than a person with a shovel. Computers are better than people at translating languages, playing Go or poker, or - of course - looking up information and references.  But we know that such systems are not intelligent in the way that we are with complete certainty once we see how they work; even a near-Turing-Test-passing program like GPT-3 is not thinking in the same way that we do because it cannot resist its impulse to do what it does. 

We are not used to regarding the physics that drives computers to do exactly what they are programmed or taught to do as an emotion, but that is what it is.  If you see someone whom you find sexually attractive, you know it immediately, emotionally, and certainly; that is your computer-like response.  But what actions you take (if any) when prompted by that emotion are neither certain nor immutable. 

Note that I am not saying that computers are deterministic and we are not.  Nor am I saying that we have "free will" and they do not, because "free-will" is a meaningless concept.  There is no reason to suppose that an AI system such as the current ones that work by machine learning could not be taught to moderate impulses in the same way that we do.

But so far that has not been done at all.

Finally, let me say that this idea makes evolutionary sense.  If our emotions were perfect guides to behaviour in all circumstances we would not need intelligence, nor even consciousness, with the considerable energy consumption that both of those require.  But both (using my definition of intelligence) are needed if an immediate emotional response to a situation is not always optimal and can be improved upon by thinking about it.  

LightWorm

 

Nerve fibres conduct impulses at a speed of around 100 ms^-1, which - in this age of gigabit light fibres - is a bit sluggish.

But we can now genetically engineer neurons to emit light when they fire, and to fire when light strikes them.  In addition light fibres are simple structures, consisting of two transparent concentric cylinders with different refractive indices. That is a lot simpler than a nerve's dendrite or axon (the nerve fibres that conduct impulses between nerve cells). We know that living organisms can make transparent materials of differing refractive indices (think about your eyes), and they excel at making tubular and cylindrical structures. Indeed plants and animals consist of little else.

So I propose genetically engineering neurons (nerve cells) that communicate optically rather than chemically. The synapses where transmitted signals from axons are received by dendrites as inputs to other neurons are small enough to transmit light instead of the neurotransmitter molecules that perform this function in natural neurons.  And light is easy to modulate chemically, so inhibitory neurotransmitters would just need to be more opaque, and excitatory ones would need to enhance transparency.  And, of course, it would be straightforward to create both inputs to, and outputs from, such a system using conventional light fibres, which would allow easy interface to electronics.

Doing this in a human brain might present a few challenges initially, so it would be best to start with a slightly simpler organism. Caenorhabditis elegans (in the picture above) is a small worm that has been extensively studied. So extensively, in fact, that we know how all 302 of its neurons are connected (that's for the hermaphrodite C. elegans; the male has 383 neurons, and we know how they're connected too).  We also know a great deal about the genetics of how the animal's nerve structure constructs itself.

Let's build a C. elegans with a brain that works at the speed of light...

TuringComplete

This is an edited version of a piece by me that appeared in the Communications of the Association for Computing Machinery, Vol 37, No 9 in 1994.

I recall asking my six-year-old, "How do you know that you are?" She considered the matter in silence for several minutes, occasionally drawing breath to say something and then thinking the better of it, whilst I conducted an internal battle against the Demon of False Pedagogy that was prompting me to make helpful suggestions. Eventually she smiled and said, "Because I can ask myself the question." 

Even with the usual caveats about parental pride, I consider that this Cartesian answer was genuine evidence of intelligent thought. But she doesn't do that every day, or even every week. And no more do the rest of us. Intelligent thought is rare. That is why we value it. 

The most important aspect of Turing's proposed test was his suggestion that it should go on for a long time. Speaking, reading, and writing are very low-bandwidth means of communication, and it may take hours or even days for a bright and original idea to emerge from them. We should also remember that there are many people with whom one could talk for the whole of their lives without hearing very much that was interesting or profound. 

The distress caused to researchers from Joseph Weizenbaum himself onwards by the ease with which really dumb programs such as ELIZA can hold sensible (if short) conversations has always been rather amusing. The point is surely not that such programs are poor models of intelligence, but that most of us act like such programs most of the time — a relaxed conversation often consists of little more than a speaker's words firing off a couple of random associations in a listener's mind; the listener then transposes a few pronouns and other ideas about and speaks the result in turn. In speech we often don't bother to get our grammar right, either. ELIZA and her children mimic these processes rather well. 

The researchers' distress arises because — in the main — they take a masculine view of conversation, namely that it is for communicating facts and ideas. But the most successful conversation-mimicking programs take a feminine view of conversation, namely that it is for engendering friendship and sympathy between the conversationalists (see, for example, You Just Don't Understand—Women and Men in Conversation by Deborah Tannen). Of these two equal aspects of conversation, the latter happens to turn out to be the easier to code. Of course the resulting programs don't really "feel" friendship and sympathy. But then, perhaps neither do counselors or analysts. 

I suspect that a real Turing Test passing program will end up coloring moods by switching between lots of ELIZA and PARRY and RACTER processes in the foreground to keep the conversation afloat, while the deep-thought processes (which we haven't got a clue how to program yet) generate red-hot ideas at the rate of two per year in the background. What's more, I suspect that's more or less how most of us work too, and that if the deep bit is missing altogether in some people, the fact hardly registers in quotidian chatter. 

CostDisBenefit

Today, a poorly-researched and highly dodgy cost-benefit analysis of democracy.

First, let me say that, as a way of making decisions that affect large numbers of people's lives, cost benefit analyses are at best morally questionable and at worst actively bad.  That is opposed to, for example, one person making a cost benefit analysis of something that will only affect them (rather like Darwin's list on whether or not to marry; Emma Wedgwood, of course, was free to turn him down).  That seems to me to be an entirely legitimate way to make a decision, if a little cold.

But what is cost-benefit analysis?

Suppose some project is proposed that will affect many people, some positively and some negatively.  The project might be building a new hospital that will require an ancient woodland to be felled.  A cost benefit analyst will go out and ask the people one or more of four questions:

1. "What would you be prepared to pay for your share of the new hospital?"
2. "What sum would you be prepared to accept to forgo the new hospital?"
3. "What would you be prepared to pay to preserve the woodland?"
4. "What sum would you be prepared to accept to see the woodland cut down?"

Questions 1 and 3 are known as willingness-to-pay questions, and Questions 2 and 4 are known as willingness-to-accept questions.  The analyst would add up people's answers and use the result to decide what it was that the people really wanted.  Note that the people aren't actually going to have to stump up the money they've offered, nor to get the money they've requested; cost-benefit analysis is just a way of getting a measure of how people think about something.  Of course both the wording and the order of the questions will almost always affect the results.

Why is all this morally questionable or outright bad?

Let's start with willingness-to-pay.  Suppose you are a rich environmentalist who can afford private health care.  In answer to Question 3 you may say, "I'll pay $1 million to keep the wood."  Your answer will shift the average a great deal, and will swamp the answers of the many poor people who answered $10 to Question 1 because they want the hospital built.  Willingness-to-pay is the exact equivalent of letting people buy votes, something that only the most swivel-eyed libertarian might propose.  It leads directly to gross inequality in influence, and indirectly to inequality in accumulated resources.

Is willingness-to-accept better?  Suppose you are a poor environmentalist who is passionate about the wood.  In answer to Question 4 you may say, "Pay me $1 trillion to cut the wood down."  Once again your answer gives you disproportionate influence.  Willingness-to-accept effectively gives everyone a veto over anything they don't like, as they all bid up the cash they demand to numbers requiring exponential notation just to write down.  It would mean that nothing with any opposition at all (no matter how irrational or ill-informed) would ever get done.

So, having established that it's rubbish, let's use cost-benefit analysis to decide if we should pay for democracy.

I set two surveys on Twitter (above). One asked what people would be willing to accept to forgo their vote, and the other asked what they'd be willing to pay to get one.

As you can see, the results are superficially completely irrational.  Most respondents wouldn't even be prepared to accept $1,000 to give up their vote.  Given that, you'd logically expect the same people, no matter how poor they were, to be prepared to pay at least $10 to get a vote.

But what's actually happening is more profound.  Offered both choices the majority are saying, "I'm not even going to play this game."  They presumably regard a vote as a right (as do I), and so they think its provision is outside the sordid realms of monetary transaction.  In short, they think the very questions are implicitly category errors.

However, I am quite intrigued by the one-in-five people who would be prepared to sell their right to vote for $1,000 and the one-in-five (possibly different) people who would pay up to $100 to get a vote.  So I suppose that I had better finish with how I would answer: I too wouldn't play the game; I'd campaign for monetary reward or cost for votes to be removed from the system.

But, to actually answer the questions, my willingness-to-pay for a vote is entirely dependent on geography.  I live in a safe parliamentary seat, so I know in advance that the probability of my vote either way altering the result is vanishingly small.  Thus the opportunity cost of my paying for a vote is such that I know that I could archive far more for others (and maybe myself) by giving the vote's cost to charity instead, which is what I would do.  If I lived in a marginal seat that could go either way with just 100 votes that argument would change completely, and I'd probably pay around $100 for a vote.  If I were asked for much more than that, the charity argument would still win.

My willingness to accept payment to give up my vote would work in the same way.  If I could do more for others and myself with the money I was payed than the expected good that would come from casting my vote, I'd take the money and do the good.

I am a lapsed utilitarian.

GeneEnvironment

Note: there may be some flaw in the logic of this argument.  Or, alternatively, it may be an established result in genetics that my (brief...) researches have failed to find.  If either, tell me in the comments and I will amend as necessary. But if neither, I present it as a possible explanation of an important phenomenon.

---

There is a meta-analysis in Nature Genetics on 14,558,903 (!) partly dependent twin pairs that shows that the heritibility of a wide range of traits is 49%.  That is to say differences in those phenotypical traits is 49% determined by a person's genes, and 51% by their environment.

This seemed rather close to 50% to me, and set me wondering if there is an evolutionarily stable strategy (ESS) at play that is forcing the figure to 50%.  The first such ESS that was discovered (by R.A. Fisher) is the one that gives a 50/50 sex ratio in a wide range of species.  An ESS doesn't have to settle at 50%; for example the ESS between hawks and doves in the human population (and many others) is heavily weighted towards the doves.

So.  The question to ask is, if you are a gene, in order to maximise your fitness how much of the phenotype you develop should you control, and how much influence should you hand over to the environment?  (Note importantly that "the environment" here includes all the other genes in the organism and any influence that they might have over that phenotype; and that those genes will be subject to the forces I am about to describe as well.)

Let's look at a simple specific made-up example.

Suppose you are a gene that controls everything about a fur-colour phenotype and you are a gene for green fur.  There is another, rival, genetic allele for brown fur.  In a verdant forest you, green-gene, will leave more offspring, and brown-gene will diminish in the population.  In contrast, in a brown-coloured savanah your brown-gene competitor will come to dominate.

Now suppose a mutation arises capable of causing either green or brown, and that switches the phenotype fur to green or brown depending on the colour of its surroundings when the organism of which it is a part is developing.  Clearly individuals posessing that new mutation will be able to colonise both the forest and the savanah, and the new gene will come to dominate (assuming the cost of its working is not greater than that of the other two).  This new gene has handed over some of the determination of its phenotype to the environment, and has thereby gained an advantage over its more dictatorial predecessors.

But a gene that has no influence at all over any phenotype, and which leaves the determination of the phenotypes to the environment (which includes the other genes, remember), has no fitness because it cannot influence its reproductive success.  It may get carried along for the reproductive ride as non-coding DNA, or it may just be eliminated altogether.

In our example, suppose the developing organism adopts the colour of the nearest object during its development, as opposed to switching between just green and brown.  And suppose it grows up in a nest surrounded by bright orange flowers.  Clearly, in this case, the gene will have given up too much control to the environment.

So in general we can see that it makes sense for a gene to allow some environmental influence over its phenotype to allow a versatile response to different conditions.  But it must not allow too much environmental influence lest it loses control and hence loses fitness.  We can show this graphically:

The X axis and the blue line are the proportion of the influence of the gene on the phenotype, which allows the gene to control things. The red line is one minus this - the proportion of the influence of the environment on the phenotype, which allows the phenotype to adapt to its surroundings in some way.  If we multiply those together, we get the yellow curve, which is the benefit the gene gets for a given proportion.  That is, the gene "wants" control, and it "wants" adaptability, but these are in opposition, so it can't have all of both; when one increases that increase necessarily drives the other one down. Unsurprisingly, given the symmetry of this example, the maximum - the most beneficial point for the gene - is at 50%, which is the figure we set out to explain.  But the symmetry seems a bit of a cheat.

So suppose we change the form of the blue line (and consequently the red one) so it is merely some (in general non-symmetrical) function, f, of the genetic proportion (call that g) along the horizontal axis.  As in the graph above for the simple case f(g) = g, the new general f(g) generates values in the interval [0, 1].  The yellow curve, the benefit the gene sees, B, is now:

B = f(g) . [1 - f(g)] = f(g) - f(g)²

(all other things being equal, the gene's fitness, ω, will be proportional to B).  The maximum value of B will be where dB/dg = 0:

dB/dg = f'(g) - 2f'(g)f(g) = 0

which gives:

f(g) = 1/2 .

So the watershed value of 50% for the maximum benefit to the gene doesn't change, regardless of the form of f(g).

There must, of course, be exceptions to this simple analysis.  But it does show how, for phenotypes that must adapt to their environment, the genes that control them would be expected to hand exactly 50% of their influence over the phenotype to that environment.