✦ Ideas & theories · 20 September 2026
When I asked my idea for numbers
I had a way of looking at the world that had been with me for years. At a certain point I wanted to know whether it held up. This is how it went.
I am not a physicist. I have an intuition about the world that I have carried around for years, and for years it was enough for me that it worked — in the sense that everything I read, or looked at, fitted inside it without any effort. Then I did the thing that ruins intuitions, and I did it on purpose.
The day I realised I was always right
The idea, stripped to the bone, is that the world is made not of things but of information, and that two matters which usually get run together have to be kept apart: how much information there is in a place, and how far it can move there. The river and its bed. I liked it because it did not merely describe: it forbade something. A permanent block does not exist in nature — water is diverted, it rises, evaporates, brims over, but it does not stop for ever.
The trouble was pointed out to me by the lens itself, one afternoon when I was explaining two opposite phenomena with the very same sentence and feeling pleased with both explanations. Whatever I had observed — that thing and its opposite too — I could have told as a configuration of information, and gone away happy.
Something that explains everything forbids nothing. And what forbids nothing cannot be wrong, so it is not an explanation: it is a frame, and frames look good round any picture at all. That is where the only question that could get me out of the circle came from: what if I asked it for a number?
The first thing I lost was my favourite
I had a result I was proud of, and had told many times to anyone who would listen: my lens seemed to explain the Hubble tension, that is, the disagreement between two different ways of measuring how fast the universe is expanding. Two teams, two instruments, two numbers that do not agree. And I had an elegant reason why they should not agree.
To do the calculation properly, I first had to say precisely what that famous river bed was — the capacity to propagate. I did. And when the writing was finally clean, that quantity did not resemble a component of the geometry of space-time: it was that component, written in my own vocabulary.
Which means that nothing I had derived from it in ordinary conditions was mine. It was Einstein’s, and had been for a hundred and ten years, and I had found it again in different words, believing I had discovered something. The explanation of the Hubble tension fell at that moment — not because a measurement disproved it, but because it had never been mine.
An effect that vanished when you changed the clock
The second blow I dealt myself, and it taught me more than the first.
I held that a star, radiating for billions of years, used up a little of the river bed. I had done the calculation, the quantity came out tiny, and that reassured me: a minute effect is plausible, it does not catch the eye, it does not ask to be defended. That is exactly where the error had hidden.
The factor depended only on time. And a quantity that depends only on time can be made to vanish by changing the way you measure time — it is like saying an object gets shorter when you switch from metres to feet. It is not a small effect: it is not an effect. And in the version where it might have meant something, there were measurements of the Sun, available since 2020, that had already ruled it out. I had never looked at them.
Since that day I have distrusted my small numbers far more than my big ones. A big number, I go and check. A small one puts me in a good mood, and I leave it alone.
Then it was the turn of the branch I cared about most, because it was the only one that was truly mine: the idea that every irreversible event uses up something finite, and that telomeres — the caps at the ends of chromosomes, which shorten with every cell division — were its bookmark, the measure of how much is left. The two readings I drew from it diverged by a factor of fifty-six, and had opposite signs. Withdrawn, that one too.
The night of the cross-examination
At this point I had a problem that good will does not solve: I am not a physicist, and I cannot contradict a calculation. For me, a mathematical criticism is unfalsifiable — I can believe it, or reject it out of pride, and neither of those is a method. They are two different ways of deciding according to mood.
So I had my own conclusions attacked by whoever had every incentive to demolish them, under a single rule: the lines of attack are written down before the calculations are done. That is the part that really counts. If you decide afterwards what you would be willing to count as a defeat, you will never lose once: you will always find the reason why that particular blow did not count.
In one night, two conclusions I had labelled as derived — the strongest label I had — were overturned.
But what stayed with me is neither of the two demolitions. It is a note in the margin, one I would never have seen on my own: my prose was systematically stronger than my numbers. Not now and then — always, and always in the same direction, the one that made the story cleaner. A random error goes wrong both ways; mine all went wrong on the side of the well-turned sentence. Caveats disappeared, assumptions became results, a “might” presented itself as a “therefore”.
An error that has a direction is not carelessness. It is desire. And you do not correct desire by rereading more carefully, because desire is exactly what is doing the rereading.
Something I was not looking for
Then, in the middle of all this losing, the most beautiful thing happened.
I was correcting an error in a quantity I called maximum density, convinced I was doing maintenance. It turned out not to be a constant at all: it depends on the size of the region you look at, and it changes by forty-five orders of magnitude — a one followed by forty-five noughts — between a black hole and the observable universe.
Applied at the scale of the whole universe, the corrected formula returns the cosmological critical density on its own: the number that decides whether the universe will expand for ever. I had not put it in by hand, I was not looking for it, and for a few minutes I sat there staring at the screen, unable to tell whether I had got something wrong again.
It is not a testable prediction, and I do not pass it off as one. But it came out of a definition done properly rather than out of a hope, and it is the reason I kept going when the books were all in the red.
Then I found out that the judge gets it wrong too
The last thing I learned is the most uncomfortable, because it calls into question the tool I had used for everything else.
I had got into the habit of treating a mathematical refutation as a verdict. But a refutation is a product like any other: it has an author, an execution, and nobody who has checked it a second time. Calling it “the calculation” hands it an authority it has not earned.
I found this out the worst way. A demolition had gone into my archive without passing through the cross-examination, because it seemed obvious; when I did put it through, it was overturned. For a good while I had believed a conclusion dead that was alive, and this time the culprit was not the idea: it was me, at the exact point where I had stopped applying my own method because I was in a hurry to be severe.
So I changed the question. No longer “has it been refuted?”, but: what does it cost me to check the refutation? Sometimes it is a few lines and I can do them by hand, as in the story of the clock — there the refutation is as solid as it looks. Other times it is a long calculation, run once by a tool, and then I am not checking anything: I am taking someone’s word for it. The difference is not philosophical. It decides which of my twenty withdrawals are final and which are still only promissory notes.
What is left
Today there are ninety-one claims on record, and twenty of them are withdrawn. Not one fell because an experiment said “false”: they all fell from internal rereadings, or from finally reading in full texts I had been citing at second hand. I do not delete them. They stay on the record, with their date and with the status they had when I believed them, because an archive that keeps only what survived is not an archive: it is a shop window.
What did not fall is the lens. And here I want to be clear, because the story so far might sound like a penance, and it is not one.
This is a blog, not a journal. I did not borrow rigour from anyone as the price of being allowed to speak: I imposed it on myself because I wanted to know how things stood. And it had an effect I did not expect — it made the vision freer, not less free. As long as the image is declared for what it is, a way of seeing and not a proof, it can stay even where the calculation says it is wrong. The strongest image I have is also the one mathematics corrects most, and I keep it all the same: it made me ask the right question, which is a different service from being right, and not a lesser one. You do not sack a metaphor for poor numerical performance.
What the method forbids is not imagining. It is presenting imagination as a result. They are two different sentences, and the whole difference lies in one line said before you begin: this part is a vision, and I am telling you so now, not after I have convinced you.
The practical upshot of the whole story is that at sixty I started studying mathematics again from scratch, from the signs and the brackets, with a paper notebook. Not in order to be right: in order to be able, one day, to check for myself the people who tell me I am wrong. It is the only answer I have found to being a man who has an idea and no tools to defend it with.
The river, meanwhile, goes on flowing on its own account, and takes no interest whatever in what I have written about it.
The whole story, with the reckoning and the withdrawn claims, is here.
And the text this story took apart is still where it was, with its date.