This would certainly explain how ‘Zipf’s law seems to turn up everywhere’ if it is a manifestation of the Central Limit Theorem.

]]>For 0< n,m in N let’s denote the relative chance of drawing n vs. drawing m by: P(n)/P(m). Then P(n)/P(m) = (log (n+1)/n)/(log (m+1)/m), see the series posted last year on my blog fwaaldijk.wordpress.com. These relative probabilities can be derived heuristically, and are in accordance with Benford's law. The heuristics are interesting I think, but also quite speculative.

A `discrete' or `Zipfian' case can also be stated, which then yields P(n)/P(m)=m/n. But I did not study this in any detail.

I would be happy to receive some feedback on these ideas. Kind regards, Frank

]]>The paper on perfect randomness of cancer:

]]>i am well aware of a weak form of maxwellian demon who is looking ceaselessly after all these threads.

i have recently seen him at work. he is cleaning things up very helpfully.

i am trying to make a meaningful point here.

in doing so, various fragments of this post are slightly missing the focus of this thread’s subject matter.

perhaps more slightly than is tolerable by the blog administrator.

also, please accept my apologies for all that self promotion after you have read this entire post.

this is an empirical experiment on the acceptable limits of commenting.

if the experiment does not go terribly wrong,

i am excited about becoming a happy participant of this lively community.

any feedback what so ever highly appreciated.

thank you very much for your attention.

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Dear blog administrator,

in the event that interference with this post is inevitable,

please inform any one concerned, by any means deemed necessary, of what is going on.

thank you.

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Dear Oded,

you were so promptly drawing my attention to your paper.

i could not fail to notice how many times you drew attention to some one before,in the previous couple of years, on this very thread.

you deserve a feedback.

so i felt obligued to commit my quiet time to your paper.

Oded, i am very sorry but you are not deriving all these laws.

i want to believe your concepts, am almost there, but not quite, no.

you have truly stunning ideas and you firmly know your stuff.

but in its current form, i am not able to comprehend your paper fully.

your narrative is bumpy – that is, lengthy in the easy parts but non existant in the dificult (and interesting) parts.

also i am too lazy to do all of your research (again).

therefore it is not possible for me (and i suppose not very much any one) to have a meaningful discussion of its content.

(as if i knew anything !!)

Let me draw your attention to Terry’s wonderful (as usual) advice “on writing” here:

http://terrytao.wordpress.com/advice-on-writing-papers/

You tripped some of those land mines, if not most of them.

Your paper needs major pimping in order to be taken seriously.

On a different level:

exactly the form of your paper (which i just criticized so cruelly)

reveals much of your personality.

a personality that reminds me much of my self when i was at graduate school.

*** self promotion alert, start ***

oh how i love the proof by excel sheet !!

also, i am reminded (painfully so)

of how the pursuit of academic maturity is so incredibly painful.

and it never stops once it got started.

academic maturity has little to do with academic status or glory.

sorry i was stealing that line from somewhere. i will do it again.

having studied neither pure math nor computer science,

i bet aspirants in both these fields get as good a deal of masochistic drill as in any discipline (except medicine where doctor training aims at sadistic tendencies).

i have failed to achieve ph.d. status on three separate accounts and have never ever published anything.

one such failure relates closely to me being fed up with latex. latex sucks!

i assure any one caring to ask:

academic status is non essential and academic maturity is unlearnable from university alone.

academic status in fact hurts certain career options.

i have met math doctors working for a fraction of my income,

*** self promotion alert, end ***

and i earn low coin.

Dear Oded, you are well on your way.

You need to cheer up and keep going.

Please do your homework: pimp that paper and re-load it.

You owe it to your self.

And the community.

If you re-load, i promise i will re-view.

Perhaps i will motivate myself and do some home work of my own.

Turbulence needs fixing, after all.

Most sincerely,

Roland

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In relating to the subject matter at hand, i know of other good Benford examples i like to share:

my undergrad math teacher (with a background in telecommunication) talked about huge samples

of lengths of telephone conversations.

it seemed there was no way of predicting how much longer a conversation (in progress) is going to last, given it is in progress already for so many minutes.

so conversation statistics would be more perfectly chaotic than death statistics.

in analogy to Oded’s notion, there are more conversation boxes than death boxes.

everything else from said math class (which may very well have been about Benford) i have genuinely forgotten by the way.

coincidentally, i stumbled on a very enlightening non math article elaborating on (among other interesting things) the randomness of cancer. cancer positively qualifies as the mother of all Benfordian statistics with an infinite number of boxes.

I fell in love with the wording. Two thumbs up !!

For more reading O. Kafri “The distribution in nature and entropy principle” arXiv:0907.4852 and references therein. ]]>

I was actually looking for turbulence, where also this blog provides some brillant food for thought, guess am becoming a new fan.

Never heard about Benford before so I appreciate especially the Benford application to country population.

It is beautiful in, conversely, showing that

a) national borders are perfectly chaotic

b) since Benford overestimates 1, but consistently underestimates 2..9, that human population is far from infinite.