Numbers

This is an excerpt from the fifth chapter:

Ω is a number 3 x 10-1 that measures the amount of material in our universe and is the ratio of the actual density to the critical density. At the beginning its value cannot have differed from one by greater than one part in 10-15

Any higher value and the universe would have collapsed long ago. Any lower and no stars or galaxies would have been formed.
(Martin Rees – Just Six Numbers)

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PRIMES
Cambridge & Leh
1989

“I describe myself as a “patternist”, someone who views patterns of information as the fundamental reality.” Ray Kurzweil

Hazael leaned back in his old leather swivel chair and looked out of the window into the ancient quadrangle below him. Dozens of students were milling about chatting and laughing and he thought back to his youth when he first arrived to read for his doctorate. Very little had changed in the interim. A long time had passed since he had first visited Leh to set in motion the processes for the collection of data, and as regularly as clockwork this data had been sent to him by Tensing, as promised.
Conventional thinking in academic circles was that at no stage would machines be able to come close to emulating the human capacity for pattern recognition. Hazael did not hold to this view and rigorously defended his argument in any forum in which it was debated. His bravest prediction at a recent conference on the subject was that current computer calculation capacity at around one hundred calculations per second would increase a thousand fold to a minimum of one hundred thousand per second over the next twenty years. At this point it would be at the knee-point of the exponential growth curve and thereafter accelerate away to ten trillion per second over the following twenty years.
With a consistent futuristic view of where his methodology was headed, and a quiet persistence in airing some of his groundbreaking mathematical ideas in international forums, he caught the attention of some of the major computer manufacturers and as a result he was always one of the first to be given the opportunity of trying out new hardware. When Intel managed to combine a million transistors into the 486DX processor, Hazael knew the time had arrived to use this latest version and input the immense amount of data that had been accumulated.
His top doctoral students had been working long hours with the new computers, fine tuning them to the task at hand, and had already loaded enough data to perform their first runs. They had called for a meeting earlier that morning and after a three-hour session they completed their presentation in addition to several additional runs at Hazael’s instigation. After reviewing in his mind the general thrust of their findings he placed a call to Aaron.

‘Good morning,’ Hazael said breezily, his excitement obvious.
‘Hullo. What do you have for me?’ Aaron answered; realising at once that Hazael might have made a breakthrough.
‘At first I processed ten samples with a minimum number of fifty-five letters per sample from each of the four key manuscripts and applied my latest modelling techniques using the fastest computers available at the university. The model reveals a single unique number for each manuscript, which repeats itself throughout the contents of the particular manuscript… ’
‘Let me guess,’ Aaron interrupted, unable to contain his own enthusiasm, ‘are they triangular numbers?’
‘Yes. 1, 3, 21 and 55.’
‘Is the Thomasite the 55?’ Aaron said, interjecting again.
‘Yes.’
‘You do realise that those numbers are also Fibonacci numbers?’
He thought for a moment before replying, ‘That hadn’t occurred to me as yet, but you’re right. As I was saying, I tested this further with additional samples from each manuscript and it turns out that this number repeats itself throughout the contents of a particular manuscript when I apply the model to any sample with fifty-five or more characters.’
‘And I don’t have to remind you that 55 is the last triangular number in the Fibonacci series?’
‘No, you don’t have to remind me,’ Hazael confirmed, adding ‘What’s also intriguing is that in the thousands available Prem has so far located only twenty-nine manuscripts concerning Muhammad, and only twenty-five concerning Issa, including the Thomasite of course. Do you have any view on these numbers?’
‘Let me think about that. Anything else?’
‘Not really, I’m just excited about this mini breakthrough, and I wanted to let you know that there seems to be light at the end of the tunnel.’
‘Well done. Now you are definitely on the right track and clearly the computers you are using are able to cope better with the volume of data at your disposal. Retest those numbers and validate them, then move on. A pattern will emerge which will make more and more sense as you proceed. I am really excited for you. Talk to Edwin and get back to Leh as soon as possible. For years now you have been content to sit back and wait for material to be sent to you, and that’s been all right given the processing constraints, but this breakthrough indicates you are on the cusp. It’s time for you to re-establish your connections there, face to face, and see what else you can find.’