Secrets of Creation, Volume 1: The Mystery of the Prime Numbers by Watkins Matthew

Author:Watkins, Matthew [Watkins, Matthew]
Language: eng
Format: epub
ISBN: 978-1-78535-102-0
Publisher: John Hunt (NBN)
Published: 2015-03-27T04:00:00+00:00

LOOKING FOR THE RIGHT KIND OF PATTERN

Historically, the primes have frustrated pattern-seeking humans, as they seem to do what they want, to pop up whenever they feel like it. As Don Zagier put it,

“[D]espite their simple definition and role as the building blocks of the [counting numbers], the prime numbers… grow like weeds among [them], seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout.” [8]

The enthusiasm for seeking “big” primes is perhaps partly driven by an unconscious hope that if we could see just a bit farther out along the sequence of primes, a pattern might become visible.

The problem is that anyone motivated like this is looking in the wrong way – looking for the wrong kind of pattern.

We’ve discussed two kinds of patterns: “perfect” patterns involving numbers and geometry, and “imperfect” patterns which occur in the physical world (like weather patterns or the behavioural patterns of animals), where we can predict what will happen, with limited accuracy, by applying statistical thinking.

Clearly, the primes live in the “perfect” world of number. In fact, they inhabit the very heart of that world. Naturally, we would expect any “pattern” which they might contain or produce to be of the “perfect” kind. But, remarkably, the opposite is true.

The pattern discovered in the sequence of primes at the end of the 18tfh century has the “imperfect” or “statistical” quality possessed by real-world, natural, social and organic patterns.

The pattern in the prime numbers concerns their distribution. In other words, it describes some aspect of their collective behaviour.

As our “school of fish” metaphor suggests, individual primes can’t exist in isolation. They interrelate at some level, somehow “cooperating” in order to obey the observed “social” pattern, collectively, even though an individual prime/fish seen in isolation may appear to be “doing its own thing”.

You’ll surely agree that the movements of an individual willow warbler have no bearing whatsoever on the map of the distribution of willow warblers in the British Isles. Bearing this in mind, consider the following statement:

“Some order begins to emerge from this chaos when the primes are considered not in their individuality but in the aggregate; one considers the social statistics of the primes and not the eccentricities of the individuals.”[9]

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