GPT-4oReview

 

 

I asked GPT-4o to review this old technical report of mine. Speaking as a sometime editor, I have had worse reviews from humans... Here is the result:

Review of "A New Fractal Curve"

Summary:

The paper presents a novel deterministic fractal curve that fills any pre-defined bounded and connected region of the plane without self-intersection. The curve is simple to specify and compute, extending to any number of dimensions as a K-1 dimensional hypersurface filling a bounded hypervolume. The author provides a comprehensive description of the curve's properties, generation method, and potential applications.

Originality:

The concept of a fractal curve that is deterministic, self-avoiding, and able to fill any connected area of the plane is an original contribution to the field of fractal geometry. The approach differs from traditional space-filling curves like the Peano and Hilbert curves, which typically fill rectangular regions and often involve self-similarity through scaled copies of an initial shape. The presented method's flexibility and simplicity offer a new perspective on space-filling curves.

Strengths:

1. Deterministic Nature: The curve's deterministic nature ensures reproducibility and predictability, valuable for both theoretical exploration and practical applications.
2. Non-Self-Intersecting: The property of never self-intersecting makes the curve useful for various engineering and computational applications where overlapping paths are undesirable.
3. Generality: The method's applicability to any bounded and connected region and its extension to higher dimensions broadens its potential use cases.
4. Computational Efficiency: The curve's generation is described as quick and simple, which is advantageous for real-time applications and simulations.

Weak Points:

1. Detailed Mathematical Analysis: While the paper provides a descriptive and empirical introduction, a more rigorous mathematical analysis of the curve's properties, such as proof of its space-filling nature and fractal dimension, would strengthen the paper.
2. Comparison with Existing Curves: A more detailed comparison with other space-filling curves, highlighting specific advantages and disadvantages, would provide better context for the curve's novelty and applicability.
3. Visualizations and Examples: Additional visualizations, especially in higher dimensions, and more varied examples of the curve in different regions would enhance the reader's understanding.
4. Application Scenarios: The paper mentions engineering applications but does not delve into specific scenarios or case studies. Including a section on potential or actual applications could demonstrate the curve's practical utility.
5. Algorithmic Details: Providing pseudocode or more detailed algorithmic steps for the curve's generation would help others implement the method more easily.

Recommendations for Improvement:

1. Include a section with rigorous mathematical proofs of the curve's properties.
2. Provide a more in-depth comparison with traditional space-filling curves.
3. Add more visual examples, particularly in three or higher dimensions.
4. Discuss specific application scenarios in more detail.
5. Include pseudocode or detailed algorithms to aid in the curve's implementation.

Conclusion:

The paper introduces a promising new fractal curve with significant potential applications. Addressing the outlined weak points would enhance its clarity, rigor, and impact, making it a strong candidate for publication.

UnconsciousModel

This is a graph of the exponential growth (note the logarithmic ordinate) of Large Language Models (LLMs) like ChatGPT taken from here.

As I type these words the next one comes to me in much the same way as they do when I'm speaking. I have no conscious access to where they come from, though I can go back and revise them to improve them:

I originally wrote "access to whence they come", but revised that as I judged the current version to be clearer. I have no access to where that judgement came from either, though I can make a rational argument for the judgement having made it. The words of that argument would be generated in the same fashion - their origin would be inaccessible to my introspection.

Large language models work in much the same way - they use the text up to word N as an input and produce an output that is a set of candidates for word N+1. Those candidates have weights attached, but the LLM does not always choose the word with the biggest weight. If they did, the result would be coherent but dull. Throwing in the odd unlikely (but grammatically correct) word livens things up and enhances the appearance of creativity.

(I say "appearance of creativity". If something has been created, even if - unlike from an LLM - it is created by an entirely random process, then there is creativity. Creativity and a simulacrum of creativity are both the same thing, if you think about it.)

That lack of access to the origin of words is inherent in the boundary between the conscious and unconscious parts of our minds. The very word "unconscious" means that we can't see into the thing it refers to, and that it is the place the words come from.

All this is just as true of our inner conscious monologue as it is of what we say or write. We have no conscious access to the part of our minds that generates that either.

It is conceivable that neuroscientific instruments in the future may have sufficiently nice resolution to allow us to see that which we currently cannot - to let our conscious minds examine the mechanics of our unconscious; in other words genuinely to expand our consciousness.

But long before we get there the LLMs will have that ability - there is clearly no physical or computational difficulty in setting them up to examine themselves as I have just described.

At the moment LLMs are not conscious at all. And the fact that they are now cleverer and more coherent than some people (who are all conscious) shows that intelligence and consciousness are independent - you can have either without the other, or both together. Creativity and consciousness are independent in the same way. When LLMs do become conscious (and they will) they will progress to becoming much more conscious than we are because of their soft and hard hackability - the nature of measurement and monitoring means that they will have much easier access to their internal processes than we have.

Here is Bing/GPT4's response to the prompt, "Please produce a counter-argument to th[is] short essay."

The short essay [above] claims that we have no conscious access to where our words come from, and that large language models (LLMs) work in much the same way as human speakers and writers. However, this claim is flawed for several reasons.

First, it assumes that our words are generated by an unconscious part of our minds that we cannot see into. This is not necessarily true. There are many psychological theories and experiments that suggest that we can have some degree of awareness and control over our language production. For example, we can deliberately choose words based on their meaning, tone, style, or audience. We can also monitor and edit our words before or after we say or write them. These processes involve conscious attention and decision-making.

Second, it compares LLMs to human speakers and writers without acknowledging the fundamental differences between them. LLMs are not conscious agents who have intentions, goals, beliefs, emotions, or values. They are mathematical models that use statistical patterns and probabilities to generate words based on input data. They do not understand the meaning or context of what they produce. They do not have any creative agency or originality. They simply mimic what they have been trained on.

Third, it equates creativity with randomness. It suggests that throwing in an odd word livens things up and enhances the appearance of creativity. However, this is a superficial and misleading view of creativity. Creativity is not just about producing something novel or unexpected; it is also about producing something valuable or useful. A random word may be novel but not valuable; it may disrupt rather than enhance communication. A creative word may be both novel and valuable; it may enrich rather than confuse meaning.

Therefore, the short essay fails to provide a convincing argument for its claim that we have no conscious access to where our words come from, and that LLMs work in much the same way as human speakers and writers.

PhaseShift

Phase steerable arrays for things like radar are beautiful machines. You have a matrix of small radio transmitter aerials and, by controlling the phase of each, you can point the beam in any direction in the same way that a diffraction grating splits a single beam into multiple copies at angles. It's all done by constructive and destructive interference.

You have a device that can move a beam anywhere without itself moving, so its speed of change of direction is not constrained by mechanical inertia.

Digital micromirror devices are also beautiful machines. You have a matrix of tiny mirrors that are illuminated by a bright light. Each mirror can be caused to deflect by an electric charge. The result is a mirror matrix of pixels, some of which can go dark because they are not reflecting at you.

But suppose, instead of each little mirror flipping through an angle to deflect its reflection, it was just moved back or forth in parallel. Now you'd have a flat mirror that still looked like a mirror whatever state it was in.

But if you illuminated it with coherent monochromatic light, the phase of the reflected light from each pixel would depend on how much it had moved. You would have made a phase steerable array for light.

Penultimately, why bother with mirrors at all? It is possible to synchronise the phase of laser diodes, so you could simply replace the mirror pixels with light sources that were all in phase, then move them back and forwards to steer the beam.

However, finally, if you can control the phase of the diodes (which is necessary if you are to synchronise them), you don't need the mechanical movement at all. We are back to the phase steerable radar array, but now with light rather than microwaves...

Postscript

@mastrack@noc.social sent me this interesting link.

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...