Are real numbers really real?

Re:Are real numbers really real? by tgb on Tuesday June 12, 2018 @12:14PM (#17294727)

The author's writing has a lot of background behind it that is true and yet the author's argument that they should be called "random numbers" is poor, at best. It is not typically helpful to think of real numbers that way - at the very least you're "missing" a tiny but hugely important subset that aren't random in any sense. But more importantly, it doesn't match up with any of the usual definitions of real numbers since those involve no such restrictions of randomness of digit expansions (and generally avoid digit expansions entirely). We might as well argue that the real numbers aught to be called the non-zero numbers since almost every one of them is non-zero.

I don't think the author seems particularly aware of the existence of such arguments in the past (I assume he comes from a physics background and is new to this - though so am I). Glancing through the works cited I don't see references to past treatments of this idea like Chaitin's. If the author is not a crank, he is doing a poor job of convincing us of it.

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Re:Are real numbers really real? by Cacti on Tuesday June 12, 2018 @02:35PM (#17296430)

Chaitin is a serious scientist/mathematician who knows what he is talking about, and there is plenty of discussion to other works and references in his own research. And his published work on algorithmic information theory is quite extensive.

He is using the notion of randomness as "uncompressibility", which is a very mainstream view (perhaps better known as Kolmogorov complexity, who is much more well known than Chaitin).

Just because you are not convinced doesn't mean he's a crank, it just means your background in this area is limited.

I would also note that you're reading a popular text, one that is purposefully designed to reach a mass audience, so the lack of formalism is likewise intentional, and not a reflection of crankism. You're welcome to look up his research papers if you'd like to see the difference.

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Re:Are real numbers really real? by tgb on Tuesday June 12, 2018 @04:04PM (#17297465)

I think you misread my comment which was not at all commenting on Chaitin! I was commenting on the article by Gisin, the one this thread is on.

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Re:Are real numbers really real? by n4r9 on Tuesday June 12, 2018 @12:55PM (#17295193)

He's a very reputable theoretical quantum physicist with several respectable results to his name. I know because my PhD was in a similar field. You could perhaps accuse him of ignorance of results in other specialities, but not crankism.

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Re:Are real numbers really real? by Someone on Tuesday June 12, 2018 @01:24PM (#17295534)

Not necessarily. Linus Pauling had several respectable results to his name, too. Even the smartest people can be so wrong when working in fields even a little bit outside their specialism that they are almost indistinguishable from cranks.

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Re:Are real numbers really real? by proginthebox on Tuesday June 12, 2018 @03:21PM (#17296985)

This IS his field of research.

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Re:Are real numbers really real? by tgb on Tuesday June 12, 2018 @04:00PM (#17297424)

I only accused the author of doing a bad job of not looking like a crank. I realize that non-cranks do that sometimes.

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Re:Are real numbers really real? by ttctciyf on Tuesday June 12, 2018 @12:39PM (#17294997)

I don't know if it's still the case, but arxiv papers without a subject classifier used to be more likely to be "cranky" (contrast the /math/ in the Chaitin paper url.)

So I don't know about the paper here - I only read the abstract - but I wouldn't get too hung up on terminology. "Random" is just an easier way of saying "uncomputable" I guess. But the broad topic itself is quite respectable and of interest to non-cranks, for example, see John Baez' "Struggles with the Continuum"[1]:

> Is spacetime really a continuum, with points being described — at least locally — by lists of real numbers? Or is this description, though immensely successful so far, just an approximation that breaks down at short distances? Rather than trying to answer this hard question, let us look back at the struggles with the continuum that mathematicians and physicists have had so far....

1: http://math.ucr.edu/home/baez/continuum.pdf

EDIT: The author seems like a perfectly respectable, non-crank physicist (https://en.wikipedia.org/wiki/Nicolas_Gisin) as per another comment here.

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Re:Are real numbers really real? by ssivark on Tuesday June 12, 2018 @12:51PM (#17295142)

That difference is due to a systematic change in how arXiv generates URLs for submissions, starting a few years ago. No arXiv submissions today will have a URL with a category. Articles (each with a unique arXiv id YYMM.xxxxx) can have multiple topic tags; the article under discussion has two tags, one of which is "quant-ph". Cranky articles which cannot be refuted on technical grounds are often found on the "general" topic tags.

As an aside, since the above comment is essentially trying to infer the quality of the paper from metadata, it might be worth knowing that the author is a well-regarded quantum physicist with many highly cited papers.

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