3 ms·
Without taking the time to read the rest of the book, I am suspicious of the author's claims that he has really solved the problem. Consider: - Wolfram Mathwo
by Fixnum 17y ago
Without taking the time to read the rest of the book, I am suspicious of the author's claims that he has really solved the problem. Consider:
- Wolfram Mathworld references this topic and claims Benford's Law was put on a rigorous footing in 1998 (http://mathworld.wolfram.com/BenfordsLaw.html http://mathworld.wolfram.com/BenfordsLaw.html), but this is not even mentioned in the book.
- the author makes "straw-man" type claims that (unnamed) prominent mathematicians view Benford's law as "paranormal". Also see the last two paragraphs on the first page of the original article, where the author dismisses the idea of a "universal distribution", which is used at Mathworld to give a heuristic derivation (suppose some rule governs this distribution -> apply scale invariance -> derive needed properties) - it seems like he misunderstood this.
- the author claims that he is the first to have solved this mystery, but doesn't reference any literature since 1976
- he claims on a blog (http://www.dsprelated.com/showarticle/55.php http://www.dsprelated.com/showarticle/55.php) that he tried to publish in journals, but was rejected because mathematicians weren't interested. He then published in a textbook, not even in some sort of paper. His "proof" is really long, uses very elementary mathematics and unnecessary computer programs, and refers back to other parts of his book (so that I don't want to actually try to parse the whole thing and see if I believe it).
Can anyone confirm or deny my suspicions?
That said, Benford's Law is really cool.
- brg 17y agoAfter reading the chapter and glossing over Hill's paper, I think I can deny your suspicions. Ted Hill's papers on Bedford's law are from 1995, and this chapter is from 1997. Wolfram's date is incorrect, although the secondary phenomona that choosing from a distribution which itself was chosen at random is log normal was proved at that later time. The 'straw-man' was misunderstood by you. The author points out in the conclusion of that paragraph that all of these pseudo-scientific or grandiose explanations where nonsense. The 'proof' is really an explanation that the phenomena presents itself to an easier analysis when viewed in terms of FTs. The computer program is there to show the reader the 'repeatedly divide by ten' action which is implicitly going on when we map from the unbounded domain to a small bounded domain. Its a nice explanation really, but as the problem was solved years earlier and this analysis isn't given with another application, I can see why it wasn't accepted for publication in a pure math journal.
- Fixnum 17y agoThanks!