Interesting article, **Multiverses & The Shroud of Turin**, by the curmudgeon at curmudgeograph:

Like the shroud, the jury about whether pure randomness explains everything, has not even been sent out for deliberation. The mystery still remains. Though I cannot see how such a universe can explain us, I’m not upset at the investigations. I’d like to say I can be fair and show criteria that would persuade me, but getting right down to it, it would be much easier to prove that the Shroud of Turin is only an artful hoax.

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To start with the discussion concepts like randomness and infinite, should be clearly defined beforehand, something than at the current point is far from being clear. The fascinating ongoing research in many fields on why certain laws like, Benford or Zipf seem to “wrap” randomness is a clear example. Why the first digits of the amounts in bank cheques used by millions of clients not previously connected must follow the Benfords law? Why banks can use this law to detect frauds? Why languages, meteorological measurements and a long list of apparently random parameters, when analyzed follow Zips law?

Randomness is currently something to be far from being completely defined in all its implications to be used in the realms of philosophy.

In the semesters I spent in graduate philosophy classes, I never found that the good and worthwile parts were the professional academic parts. Randomness is legitimate grist for the mill. We can talk about the pseudo-randomness that computers can give us, we can talk about not being able to account for the factors determining the roll of the dice, we can talk Schrodinger, we can talk Darwin, and we can talk spinning off universes wherein maybe we get back to the dice. Where not locked into one of the above, or other categories, I think the man-on-the-street’s concept works for me. Now you’ve got me interested in Benford & Zipf. But first I gotta pick up all the branches the wind blew down this week. “… after enlightenment, chop wood and carry water.”

Thanks for reading. I’ll check out your writings.

My interest with Benfords law comes from my scientific activities, but regarding the Shroud I have always thought that if pixel values of the coloured areas followed Benfords law, that would certainly have incredible implications.

Gabriel, Thanks for introducing me to Benford’s Law which I hadn’t come across before. Stat Math was once a significant part of my working life, so I guess I must be getting fairly rusty on it now, not keeping up. I was intrigued by the many applications. I found even the Wikipedia article amazing. That it could have election fraud, and auditing applications makes it a potentially powerful tool, and I see that courts have accepted its use for persuasive evidence in cases of fraud.

I suppose it’s fairly simple when you think about it. Many non-normal populations of datasets will have a uniform logarithmic distribution, which immediately implies an exponential distribution in the data.

I hadn’t come across Zipf as such either, although it seems to be related to Pareto. I was amazed that Riemann’s Zeta function seemed to be part of the theory, as this is also tied up with the distribution of prime numbers.

The notions of order and chaos in the intial posting above, sent me back to a one-time popular work (1983) “The Mathematical Experience” by Davis & Hersh. It has a chapter ‘Pattern, Order and Chaos’ and gives iterative maths examples of Order from Order, Chaos from Order, Chaos from Chaos, and would you believe Order from Chaos.

I’m intrigued as to your idea about implications of Shroud pixels following Benford’s Law, and would love to hear a few more hints about this enigmatic comment.

Daveb:

In my view, if a process follows Benford and/or Zipf’s law, this represents the signature of a phenomenon which takes place without intervining an external major vector trying to redirect that phenomenon.

In the case of banks, a systematic fraud in cheques changes the statistical profile of the natural/random convergence of millions of clients with their cheques.Another example: the population in American cities follows Benford’s law but for example, if the government -an external vector- enforced deportations and direct a significative amount of persons to several cities, this would alter the “natural” movement of population and a departure from Benford`s law would be detected. This is more evident with Zipfs law and even some

scientific peer-review literature is currently available in other fields like meteorology (*) suggesting something similar.

If we translate this to the Shroud we can find mathematical indicators that could be tested for compliance of Benford and/or Zipfs law.

I mentioned the values of colourized pixels -appropiately rescaled to freely move beyond the 0-255 boundaries-, but could be other dimensions or ratios of dimensions

of the Shroud. The rationale would be the same: if the Shroud has been generated by a -how could I make myself understood at this point?- “naturally flowing” process

like for example, the one suggested by Rogers, we could expect that those mathematical indicators could follow Benfords/Zipfs law.

If the process had been mainly directed by an external force, for example, scorching or painting, an important departure from Benfords law could be expected.

(*) C. Primo, A. Galván, C. Sordo, J.M. Gutiérrez, 2007.Statistical linguistic characterization of variability in observed and synthetic daily precipitation series.Physica A: Statistical Mechanics and its Applications

Volume 374, Issue 1, 15 January 2007, Pages 389–402