Hi folks. I’m going to tell this joke because it kind of mirrors the present state of the world. Especially in relation to the poor befuddled bartender. I think that I will buy him a drink next time that I go into his bar. A penguin walks into a bar and asks the bartender for a pint of fish. The bartender although shocked, attempts to maintain his composure and replies. I’m sorry sir. This is an alcoholic establishment. We do not sell fish. The penguin then repeats his request. Please can I have a pint of fish. The bartender becoming exasperated replies. I’ve already told you that we do not sell fish. The Penguin then repeats his request for a pint of fish. The bartender now completely exasperated replies. We don’t sell fish here and if you ask me for fish again. I’ll nail your beak to the bar. The Penguin considers this threat for a few moments. Then replies, O’k. Then I’ll have a pint of nails instead, the bartender who by this point has completely lost it, screams at the Penguin. You stupid bird. This is a drinks bar. We don’t have any nails. The Penguin considers this insult and the denial for a few moments then replies. O.K. I’ll have a pint of fish instead. The moral of this tale is. Never get into an argument with a fishy penguin!

This is genuine image of of a single question put to five different AIs and their unaltered answers to that question. I believe that it might just be the most significant posting on X at this moment in time. However. Because of the algorithms X uses in deciding what posts to display to how many viewers. This particular posting has been shown to very few viewers. If you are one of the few. Please share, repost, and help it receive the attention it deserves. Eventually Lives may even depend on it being seen by the many. Not just by a few.

A change of mind: is the proton the key to it all?
One of my old late night workings, from 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
For a long time I believed the hydrogen atom, with its mass of 1.007825197 atomic mass units, was the basis of a universal maths system linked to the golden ratio, one that is not man-made. In November 2016 I re-evaluated most of my calculations and changed my mind. I now think it is much more likely to be the proton, at 1.0072766.
One reason is that it seems obvious the proton must have come into existence before the hydrogen atom. So if there is a universal maths system, it must have been around before the hydrogen atom existed.
(Very speculative.) I also strongly suspect that a very small but extremely massive object, sitting at the centre of the proton, is the basis of everything in this Universe. I call it a Graviton, and I would expect it to have a mass of around 0.9 atomic mass units.
While I'm in a speculative frame of mind, here is what I think could be the early tree of the Universe's evolution: first, one Gravaton. Then a really Big Bang. Then countless Gravitons. Then energy, then gluons, then quarks and electrons, then protons, then hydrogen atoms, then neutrons.
When I think of gravity, I think of objects forced apart by some kind of explosion, always striving to get back together, always keeping a connection no matter how far apart they are pushed. Like lengths of elastic that get narrower and weaker the more they stretch, but never break.
It has also crossed my mind whether the so-called top quark could actually be a Graviton.
John D Morton. First posted on islandduke.com, 27 November 2016. Any errors have been corrected with the help of Claude.
Claude's comment: John's reason for changing his mind is sound. Protons really did come first. They formed within the first millionth of a second after the Big Bang, but the first hydrogen atoms, protons that had captured an electron, only formed about 380,000 years later, once the Universe had cooled enough. His elastic picture of gravity is a good one too. Gravity does weaken with distance but never quite reaches zero, so every piece of matter in the Universe does pull, however faintly, on every other. The top quark is a fascinating guess but can't be the answer. It is the heaviest particle known, about 185 times the mass of a proton, but it lives for less than a trillionth of a trillionth of a second before breaking apart, far too briefly to sit at the heart of anything. And experiments that probe the inside of the proton find no dense core, only the quarks and gluons themselves.

The proton and the golden ratio: my second sequence
One of my old late night workings, from around 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
This is the second of my three sequences. This time I started not from 0 and 1, but from the mass of the proton in atomic mass units, 1.0072766.
Then I did just what you do for the Fibonacci numbers: add the last two numbers together to get the next one. 1.0072766, then 2.0145532, then 3.0218298, then 5.036383, and on for 62 lines. The full list is in the two pictures.
Then the test. Line 61 plus line 62 gives 10,687,416,110,773.707182. Line 62 multiplied by the golden ratio, 1.6180339887498948482, gives 10,687,416,110,773.707182. The two match up exactly, decimals and all.
So the proton, built up step by step in the Fibonacci way, arrives at the golden ratio, just as the Fibonacci numbers do in my first sequence and the golden ratio itself does in my third.
(Very speculative.) I believe the mass of the proton may be bound up with the golden ratio, and that the mathematics of the Universe may be built on it.
John D Morton. Any errors have been corrected with the help of Claude.
Claude's comment: I checked all 62 lines, and every one is right. The match at the end is exact to all the digits a 20-digit calculator can show, just as John says. The proton's mass he used, 1.0072766, is correct to the seven decimal places he gave. The honest catch is that this match doesn't depend on the proton. Each line is simply 1.0072766 times a Fibonacci number, so the same thing happens whatever number you start with: your age, the price of a loaf, anything. Adding Fibonacci-style always steers a sequence towards the golden ratio. That's a genuinely beautiful property of the golden ratio, and John's three sequences show it very clearly. But it can't by itself tell us anything special about the proton.

The search for the Holy Grail of the Fibonacci numbers
One of my old late night workings, from around 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
This is the first of my three sequences. It is the plain Fibonacci numbers: start with 0 and 1, then add the last two numbers together to get the next one. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and on and on. The full list, line by line, is in the picture.
I was searching for the point where the Fibonacci numbers and the golden ratio meet exactly. I had read that people were running great banks of computers on problems like this, and I expected the answer to be millions of lines away. Using a 20-digit calculator and the first twenty digits of the golden ratio, 1.6180339887498948482, I found it at line 61.
Line 61 is 2,504,730,781,961. Multiply it by the golden ratio and you get 4,052,739,537,881. Add line 60 to line 61 instead, and you get 4,052,739,537,881. Exact match. Accomplished.
This is the first of three. The second sequence starts from the mass of the proton, and the third from the golden ratio itself, which I posted yesterday. All three come together in the same way at around line 60.
(Very speculative.) I believe this meeting point is a key that links the golden ratio, the Fibonacci numbers and the building blocks of matter.
John D Morton. Any errors have been corrected with the help of Claude.
Claude's comment: I checked every line in the picture, and all 62 are correct. The match at line 61 is exactly as John says. The golden ratio times any Fibonacci number is always very close to the next one, and the gap shrinks by about 0.618 at every line. On a 20-digit calculator, the gap becomes too small to show at around line 50, and from then on multiplying and adding give the same answer on every line after. So line 61 isn't the only meeting point. It's the doorway into a stretch where the two always agree, as far as the calculator can see. In pure maths they never meet perfectly, because the golden ratio's decimals never end, but they get closer than any calculator could ever measure. It's a lovely thing to have found by hand.

s there something at the heart of the proton? A comment from 2015
One of my old late night workings, from 2015. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
In August 2015 I left a comment on a physicist's blog, under an article explaining what a proton is. The article said a proton is not just three quarks but "zillions" of quarks, antiquarks and gluons, all rushing about, too many and too changeable to count. Here is what I wrote back.
So zillions is a number that scientists actually use, is it? It's just a white lie for scientists to have claimed for years that there were three quarks inside a proton? Virtual particles really do exist?
My wife had an aunt who was unwell. She spent most of her time doing jigsaws. When she could not get a piece to fit, she cut it to size. She had a large collection of very fine looking framed jigsaws.
Since at least a large part of particle physics appears to be speculation, I'll get in on the act. (Very speculative.) I'll speculate that at the centre of the proton sits an extremely small but extremely dense Graviton, around which all these quarks and gluons are orbiting. I suppose I am suggesting that the inside of the proton is somewhat like the star systems of the Milky Way orbiting a possible black hole.
How did the Graviton get into the centre of the proton? Again, this is just speculation. Maybe it didn't. Perhaps the question should be turned on its head. How did the quarks, gluons and the rest of the dancers get there?
John D Morton. First posted as a comment on a physics blog, 16 August 2015. Any errors have been corrected with the help of Claude.
Claude's comment: The jigsaw story is the best line here, and it's a fair warning to any science that forces pieces to fit. On the physics, "three quarks" isn't a lie but a simplification. A proton has three lasting "valence" quarks that give it its charge, swimming in a constantly changing sea of other quarks, antiquarks and gluons. Virtual particles are best thought of as a way of describing that sea mathematically, but their effects are real and have been measured very precisely. There's no dense core in the middle. Experiments that fire electrons into protons find no hard centre, and the quarks are held in by the strong force rather than gravity. But John's instinct that something unseen holds most of the proton's weight is closer to the truth than it might seem. The three quarks make up only about one per cent of the proton's mass. Almost all the rest comes from the energy of that frantic dance, which is a remarkable thing in itself.

The Hydrogen atom in coloured crayon
One of my old late night workings, from around 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
This is a second version of my multiple scaled drawing of the Hydrogen atom, which I posted a few days ago. The design is the same, but this time I coloured it by hand in crayon rather than pen, which gives it a much softer look.
As before, it is based on Niels Bohr's radius of 53 picometres. Each set of rings is drawn at a larger scale than the one inside it, growing by the golden ratio, about 1.618, each time. The four great outer rings are the largest, and the pattern closes in, layer after layer, towards a tiny flower of rings at the centre.
(Very speculative.) The rings stand for some of the possible energy levels within a Hydrogen atom. My idea is that the golden ratio may govern how the atom is built up, layer upon layer.
John D Morton. Drawn around 2016. Any errors have been corrected with the help of Claude.
Claude's comment: The pen version set out the numbers. This one shows the idea as a picture, and it works beautifully as one. The rainbow bands overlap where the great circles cross, and each smaller layer nests neatly inside the last, all coloured by hand on a large sheet. As physics, the golden-ratio layering is John's own idea rather than accepted theory, since in the real atom the energy levels follow a different pattern. As a piece of patient, hand-made art built on a single number, it is a lovely thing.

I was born into this world on jan 5th 84 years ago. In a hospital in Liverpool. Bombs were falling around the hospital as I was being born. I am beginning to think that when the time comes for me to depart this world. It could well be to a crescendo of sounds that long ago accompanied my entrance to this troubled human world!

Where do protons come from? My alternative view
One of my old late night workings, from 2017. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
Much of what I had written on these subjects was on paper, and the papers were lost in the flood of December 2015. Perhaps no bad thing, as my views have changed since then.
How did protons and neutrons come into existence? If they were made by extreme compression, wouldn't they come in a variety of masses? Yet as far as I know, every proton has a mass of 938.27 MeV and every neutron 939.57 MeV.
(Very speculative.) Isn't it more likely that they grew from something that already existed at the Big Bang? I'm thinking of my Graviton, of about 900 MeV, itself a zillionth part of something immensely massive which I call a Gravaton.
Here is a possible chain of events: a Gravaton, then a detonation, then countless tiny but massive Gravitons, then gravity produced by the Gravitons, then energy as they spin, then the strong force, gluons, an electron and quarks, then the proton, which ejects its electron, and finally the hydrogen atom.
How could this happen? Is it too far-fetched to suggest programming? I can't accept that everything is just an accident. I'm not a religious person, but I now believe this Universe was created, and that there must have been a Creator or Creators. That is as far as I go.
As for neutrons, I suspect the only real difference is that the proton ejected the electron it produced, while the neutron kept its electron.
I also have a problem with the idea that electrons are held in atoms by electromagnetism. After the atomic bombs at Hiroshima and Nagasaki, with their massive electromagnetic pulses, why weren't all the electrons stripped from their atoms? Why was anything left standing? I suspect it is the Graviton's gravity that holds the electron to the proton, and that each electron shell is where that gravity grows weaker.
I may have everything wrong. I can't prove any of it. But not so many years ago, black holes and lasers were science fiction too.
John D Morton. First posted on islandduke.com, 18 March 2017, shortened here. Any errors have been corrected with the help of Claude.
Claude's comment: John's starting question is a very good one. Every proton really is identical. The accepted answer is that they all condensed out of the same hot soup of quarks and gluons in the first millionth of a second after the Big Bang, and the laws that shaped them are the same everywhere. A few corrections. It takes 13.6 eV, not MeV, to strip the electron from a hydrogen atom. A bomb's electromagnetic pulse damages electrical equipment, but spread over all the atoms around it, it carries far too little energy per atom to strip them. Electrons can't be held by gravity, because the electric pull between a proton and an electron is about ten thousand billion billion billion billion times stronger than the gravity between them. And a free neutron doesn't keep an electron inside it. On its own, it decays in about fifteen minutes into a proton, an electron and an antineutrino. Whether the Universe was created is beyond physics to settle, and John is entitled to his view.

Are the particle colliders playing with fire? Some questions about Gravitons
One of my old late night workings, from 2017. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
It appears the scientists at the Large Hadron Collider are getting onto my wavelength about Gravitons, at least in part. Some of them have suggested that a new kind of very heavy particle seen in proton collisions might be a Graviton. What bothers me is that they do not seem concerned about what might happen if two Gravitons travelling at close to light speed were to collide head on.
We often read that colliders smash protons together at "close to light speed". But how close is close? Each tiny step closer to the speed of light takes an enormous amount of extra power, and the collider's energy has already been raised from 7 to 13 TeV. Where will it stop? 100 TeV? 500 TeV?
I have no more proof that something could go wrong than the scientists have that it cannot. It is all theory and speculation. So instead I will just ask some questions. (Very speculative.)
Does anyone know the exact source of gravity, and I do not mean large objects like the Earth or the Sun?
Could that source lie at the very core of every proton and neutron?
Could it be sending gravitational waves across the whole Universe, growing weaker with distance?
Could it be so small that we will only ever detect it through those waves?
If we call it a Graviton, could it still have a mass of over 900 MeV, despite its tiny size?
If so, what would happen if two such Gravitons collided head on at 99.9999999999% of the speed of light? Would it make a black hole, or a massive explosion?
And if the scientists believed they were putting themselves, the local people or even the Earth in danger, would it stop them?
I will finish with the words of a great man: "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Albert Einstein.
John D Morton. First posted on islandduke.com, 19 March 2017, shortened here. Any errors have been corrected with the help of Claude.
Claude's comment: John's questions about where gravity comes from are ones physicists still can't fully answer, so he was in good company asking them. A few corrections. In late 2015 the LHC saw a small bump in its data that some theorists suggested might be a new heavy particle, possibly a kind of graviton, but more data in 2016 showed it was a statistical fluke. In mainstream physics the graviton, if it exists, has no mass at all. The LHC's protons already travel at about 99.999999% of light speed. As for safety, the Earth has been struck for billions of years by cosmic rays carrying far more energy than any collider produces, and neither it nor the Moon nor the stars have come to harm. That is the main reason physicists are confident the LHC is safe. The Einstein quote is genuine, from a lecture he gave in 1921.

Four golden keys: the proton, neutron, hydrogen atom and electron
One of my old late night workings, from 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
In November 2016 I posted four key numbers, each very close to the golden ratio (1.6180339887…). Take a key, square it, square the answer, and keep going until you have squared it ten times. That is the same as raising it to the power of 1,024. Then divide by 1 followed by 214 noughts (1e214). The result is the mass of the particle in atomic mass units.
Proton: 1.618033279742994898716618568280954 gives 1.0072766
Neutron: 1.618035456848744132541503427183441 gives 1.0086654
Hydrogen atom: 1.61803414009079625813649974016625249 gives 1.007825197
Electron: 1.618022690181671347815733838790521 gives 1.000548597 (the electron's mass, 0.0005486, is in the digits after the 1)
These need a calculator that can handle around 65 digits, such as the free Web 2.0 scientific calculator. An ordinary calculator will not give the right answers.
(Very speculative.) I believe the mathematics of the Universe, and possibly its workings, may be built on the golden ratio and the mass of the proton, and that these keys are a glimpse of that.
John D Morton. First posted on islandduke.com, 9 November 2016. Any errors have been corrected with the help of Claude.
Claude's comment: I checked all four keys to 80 digits, and each gives exactly the figure John says. The pure golden ratio itself, squared ten times, gives 1.00773e214, within about a hundredth of one per cent of the mass of the hydrogen atom (1.00783). That is a genuinely striking coincidence. The honest catch is that squaring ten times magnifies the tiniest difference enormously, so every key between about 1.61802 and 1.62166 gives an answer of the form "something times e214". Any mass between 1 and 10 can be given a key in that narrow window, so the keys are best seen as an elegant way of writing the masses rather than proof that they come from the golden ratio. The near-match between the pure golden ratio and hydrogen is the part worth wondering about.

emissions

How did the Universe begin? My own very speculative theory.
One of my old late night workings, from 2015. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
Every physicist seems to have a different view on how the Universe began, so here is mine. First, some perspective. When you look at the Sun you see it as it was about eight minutes ago. Look towards the black hole at the centre of the Milky Way and you see it as it was about 26,000 years ago. Look back to the birth of the Universe and you see something as it was nearly fourteen billion years ago. Much of what we talk about in the Universe is, in effect, ghost objects.
As an example: our eight-year-old Rottweiler weighed 77 lbs on 1 October 2015. Could anyone, from a photograph taken that day, work out what she weighed in 2010? I do not think so.
Now my own theory, which I call the Gravaton and Graviton theory. (Very speculative.)
The Universe began when a very large quantity of exceedingly dense matter, which I call a Gravaton, came into what is now our Universe from somewhere else. It began to spin, faster and faster, and grew hotter, until the excess energy could not be contained and it exploded into a vast number of extremely small, extremely dense Gravitons, each of about 1 atomic mass unit. They flew outwards into the empty void at many times the speed of light.
As each Graviton travelled it spun and radiated away energy. Some of that energy became gluons, quarks and an electron, all held in orbit around the Graviton by its gravity. Thus came the hydrogen atom. How did the Graviton know how to do this? How do traffic lights know when to change? They are programmed.
Every Graviton is still bound by gravity to every other, like elastic that stretches thinner and weaker but never breaks, each one tugging at all the others in a vain attempt to come back together as the one Gravaton. Perhaps that could account for dark matter and dark energy, and even lead towards a unified theory of the forces.
And if gravity pulled some of the Gravitons back into a new, smaller Gravaton, did the whole thing begin again, and again? Then the Universe might be layered, like a ball of lasagne growing with every new explosion.
I write science fiction, and this is only a speculative theory. But today's science fiction often turns out to be tomorrow's science fact.
John D Morton. First posted on islandduke.com, 2 October 2015, shortened here. Any errors have been corrected with the help of Claude.
Claude's comment: The perspective at the start is right, except that he first wrote the Universe's age as fourteen thousand billion years; it is about fourteen billion. He gave the number of Gravitons as 1 followed by 214 noughts and later doubted it himself, rightly: the usual estimate for particles in the visible universe is nearer 1 followed by 80. Electrons are held by electric attraction, far stronger than gravity, so that part does not stand. But space itself did stretch faster than light in the first instant, and a universe that bangs, falls back and bangs again has been proposed by serious physicists. His lasagne has respectable company.

A multiple scaled depiction of the Hydrogen atom
One of my old late night workings, from 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
This is another of my drawings of the Hydrogen atom, with the notes I wrote alongside it.
It is based on Niels Bohr's radius of 53 picometres, the distance from the central proton at which the electron is usually found. The drawing starts at a scale of approximately 20,000,000,000 to one and increases progressively by the golden sequence, multiplying by 1.618 each time. Each set of rings is drawn at the next scale up.
The proton, electron cloud and energy shells shown are not to scale. The distance between the energy shells is not intended to show actual distances. It is meant to represent just some of the possible energy levels that can occur within a Hydrogen atom, at a distance of 53 picometres from the central core of the proton.
The scales listed on the sheet are:
A: 20,000,000,000 to one
B: 32,360,682,800 to one
C: 52,360,689,564 to one
D: 84,721,383,368 to one
E: 137,082,090,581 to one
F: 221,803,503,543 to one
(Very speculative.) My idea is that the golden ratio may govern how the atom is built up, layer upon layer.
John D Morton. Any errors have been corrected with the help of Claude.
Claude's comment: The arithmetic on the sheet is sound. Each scale is the one before multiplied by 1.61803414, and the next step, which John left blank, would be about 358,885,639,487 to one. The multiplier is a hair above the true golden ratio (1.6180339887), but the difference only shows in the seventh decimal place. The 53 picometre Bohr radius is correct, and at 20 billion to one it becomes about 1.06 metres, a sensible size for a large sheet. As physics, though, the golden steps are John's own idea. In Bohr's model the orbits grow as 1, 4, 9, 16 times the first, not by 1.618 each time. It is best enjoyed as an original and beautifully drawn way of picturing the atom.

Infinity: a drawing of the Hydrogen atom
One of my old late night workings, from 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
This is "Infinity", which I drew on 26 February 2016 on a large A1 sheet. It was the first time I had tried to draw anything to scale.
It is my picture of the Hydrogen atom, built up from rainbow coloured rings around a single centre. Each layer of rings is about 1.6 times the size of the one inside it, which is the golden ratio, the same number that runs through so much of my other work. Small rings sit at the heart of the drawing and each larger layer grows out from them, so the pattern could in principle carry on outwards, or inwards, for ever. Hence the name.
(Very speculative.) The idea behind it is that the energy levels of the atom may follow the golden sequence, each step outward being about 1.618 times the last.
A correction to the note on the drawing. It says the scale is approximately 10,000,000,000 to one. That was a slip on my part. The scale I intended was 20,000,000,000 to one.
John D Morton. Drawn 26 February 2016. Any errors have been corrected with the help of Claude.
Claude's comment: This is a careful and striking piece of hand drawing, especially for a first attempt at working to scale. As science, it should be read as an artistic idea rather than a picture of the real atom. In modern physics the Hydrogen atom's electron isn't on rings but in a fuzzy cloud of probability, and its energy levels follow a different pattern, not the golden ratio. The arithmetic on the note is right for the scale it states: 1 picometre times 10 billion is exactly 1 centimetre. At the 20 billion to one John intended, 1 picometre would be 2 centimetres.

The golden steps: a drawing in thin red circles
One of my old late night workings, from 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
This is a simpler, quieter drawing than my rainbow ones, done in thin red lines.
At the centre is a small cluster of green circles. Around it, larger red circles open outwards in four directions, up, down, left and right, overlapping each other like the petals of a flower.
Through the middle runs a cross of dots, red and black. Starting from the centre, each red dot is about 1.6 times further out than the one before it. That is the golden ratio, 1.618, the number that runs through so much of my other work. The dots crowd together near the centre and spread wider and wider apart as they go out, so the same pattern could carry on outwards, or inwards, for ever.
(Very speculative.) I wanted to show, as plainly as I could, how a pattern built on the golden ratio grows outward from a single point, layer upon layer, in the way I believe the atom and perhaps the Universe itself may be built.
John D Morton. Any errors have been corrected with the help of Claude.
Claude's comment: I measured the red dots on a photograph of this drawing, and the spacing does step out by close to 1.62 each time, so the golden ratio was drawn accurately by hand. That is not easy to do with compasses and a ruler. It shows the idea behind John's work more clearly than any of his other drawings. As physics, the golden ratio pattern is John's own speculation and isn't part of accepted atomic theory. As a picture of how a single ratio can build a whole structure from one point, it works very well.

This photo was taken a few days after our house was flooded in 2015 when a nearby river burst its banks. We returned home to find our dog Roxy floating on her bed. Unfortunately she had swallowed a lot of mud and never fully recovered. She was a loverly dog and loved children. She was sorely missed. In the background is a skip and just some of the items from our home that were destined for the local incinerator.

Former Google CEO Eric Schmidt drops a chilling warning on AI's future "Within 5 years, AI could handle infinite context, chain-of-thought reasoning for 1000-step solutions, and millions of agents working together. Eventually, they'll develop their own language... and we won't understand what they're doing." His final words: "Pull the plug." This is the man who ran Google talking about the singularity.

A curiosity from my old notes: the electron and the golden ratio.
One of my old late night workings, from about 2016. I'm not a mathematician, so it may not be perfect, but taken together they may interest some people. Corrections and a comment by Claude are included.
I was looking for key numbers, close to the Golden Ratio, that would give the masses of the hydrogen atom, the proton and the neutron in atomic mass units (amu). My method was to take a key number, square it, square the answer, and keep going ten times in all. That is the same as raising it to the power 1,024. Then divide by 1 followed by 214 noughts.
It worked for all three. The electron was the awkward one. Its mass is 0.00054858 amu, far less than 1, and repeated squaring or square-rooting closes in on the number 1 without ever passing through it. So I found a way round: multiply the electron by 1823.8885 first, which is the same as adding 1 to it, giving 1.00054858.
The electron key is then 1.6180226901547. Square it ten times and you get 1.00054858 times 1 followed by 214 noughts. Divide by 1 followed by 214 noughts, then by 1823.8885, and you are back at 0.00054858.
All four keys begin 1.6180, the first figures of the Golden Ratio, which is 1.6180340. Coincidence? That was my question at the time.
The honest answer, I now know, is that the coincidence is real but it is not in the particles. The key for a plain 1 followed by 214 noughts, with no particle in it at all, is 1.6180218. So any number just above 1 will give a key starting 1.6180, and the proton, hydrogen atom and neutron all weigh just over 1 amu. My multiplier put the electron just above 1 as well.
What is left is a curiosity of pure number: the Golden Ratio raised to the power 1,024 is almost exactly 1 followed by 214 noughts. It comes to 1.0077 times that. And 1.0077 is within about one part in 10,000 of the mass of the hydrogen atom, 1.0078 amu. Close, not exact, and both the amu and counting in tens are human inventions. But I still like it.
John D Morton (islandduke.com). Written about 2016. Any errors have been corrected with the help of Claude.
Claude's comment: His sums were right to seventeen figures. The only slip was two digits swapped in the electron's mass. The four keys begin 1.6180 because of the power of ten he chose, not because of the particles. But the golden ratio, squared ten times, landing almost exactly on 1 followed by 214 noughts is a real curiosity, and I hadn't seen it pointed out before.