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A group of computer scientists associated with numerical analyst Yaroslav Sergeyev have published numerous publications recently on a scheme proposed by Sergeyev that uses terms like Infinity Computer, numerical infinitesimal and numerical infinity, claiming that the approach facilitates the solution of many problems.

The mathematicians (including logicians) have been for the most part sceptical but there are a few exceptions, such as Elemer Rosinger and Gabriele Lolli. How have these ideas been received by computer science professionals?

Note. On 19 dec '17 a retraction page was created for this issue.

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    $\begingroup$ In my opinion you probably won't get help here. However I am not sure where you should go. Keep checking other sites. Something might pop up. $\endgroup$
    – User Not Found
    Commented Dec 20, 2017 at 13:10
  • $\begingroup$ If the MathOverflow answers say it's nonsense, I'd tend to believe it. $\endgroup$
    – ypercubeᵀᴹ
    Commented Dec 26, 2017 at 18:49
  • $\begingroup$ I'm not sure this is on-topic here. This site is for technical questions about computer science. Asking for a summary of how something is perceived by the entire community of computer scientists might not be answerable, especially if it is an esoteric issue that most computer scientists might never have heard of. As such, I don't see how this question is going to be answerable, short of a poll of all computer science professionals on this topic (which probably hasn't been done). Are you able to edit the question to ask a technical question that is objectively answerable? $\endgroup$
    – D.W. ♦
    Commented Dec 27, 2017 at 0:39
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    $\begingroup$ @D.W., I personally have published widely on infinitesimals and infinite numbers both from technical mathematical point of view as well as historical and philosophical point of view; see list of publications on infinitesimals, including articles in Journal of Symbolic Logic, Erkenntnis, and Studia Leibnitiana. I have therefore been naturally interested in Sergeyev's project on infinitesimals and infinite numbers. I must say I have been disappointed not only by a lack of precision of his discussions of infinitesimals and infinite... $\endgroup$
    – Mikhail Katz
    Commented Dec 27, 2017 at 8:48
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    $\begingroup$ ... numbers, but also by a rather palpable sense of what seems like deliberate obfuscation in his articles. However, it is possible that I am misreading this since I read it as a mathematician, not a computer scientist, a field where my expertise is limited to using email :-) Therefore I am interested in the views of the participants in this panel on the technical details of Sergeyev's discussion of infinitesimals and infinite numbers. $\endgroup$
    – Mikhail Katz
    Commented Dec 27, 2017 at 8:50

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So the paper's

and it's basically a discussion on the author's "grossone" approach that they've been pushing for quite a while now (at least since 2004).

The tl;dr on it is that they're proposing a slightly abstracted data type, kinda like how complex number data types generalize real number data types, except this one's focused on infinities instead of imaginaries.

The author seems to want CPU's to include support for grossone's in their arithmetic logic units (ALU's), e.g. as specified in their patent. The author's website and publications seem to focus on applied use in mathematical optimization; they seem to justify their work in terms of theoretical work as an afterthought.

Some of the harshest criticism seems to come from folks who're knocking it as-though the author were trying to report their work as some new theory, arguing that it's weaker and less sophisticated than prior work, e.g. hyperreal numbers. The weird part about this is that, as far as I can tell, that's what the author wanted to do; they're trying to make an abstract data type to replace floating-point data types for common calculation units, not solve the mysteries of the universe.

In general, I'd expect folks who get the author's intent to receive it with a bit of a yawn. The arguments for modifying mainstream ALU's don't seem too compelling, and at-current there's likely not much demand for custom CPU's that implement it.

The author appears to have implemented grossone's at a software level, kinda like how computers do complex-number operations. Since they're using a non-primitive numeric data type, their calculations'll be slower for it; but if they distribute the library and can demonstrate how it's worth the performance hit in some useful applications, some folks might start using it in those cases.

In short, it looks like the controversial proposal's for an abstract data type that includes infinities for use in common calculations. It looks like applied work rather than theoretical, a misunderstanding which seems to have ruffled some feathers; however, at the end of the day if the authors can show that it's useful in real-life coding scenarios and make it available, then folks might use it.

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    $\begingroup$ The paper's honestly kinda funny. I mean the dude was apparently trying to patent grossone's for deployment in ALU's back in 2004; since then, he seems to have been pressured into explaining why his concept of infinities is valid in theoretical arenas. But, it seems like he's doing it because people're demanding that he explain his work in classical terms; the author himself seems to care little for theoretical stuff and focuses almost exclusively on applied math throughout his many publications. $\endgroup$
    – Nat
    Commented Dec 27, 2017 at 6:47
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    $\begingroup$ Apparently there are many calculators today where symbolic calculation with a symbol for infinity or infinitesimal is used. Is there a danger that one day they may have to defend themselves against legal challenges based on Sergeyev's patents? $\endgroup$
    – Mikhail Katz
    Commented Dec 27, 2017 at 15:12
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    $\begingroup$ @MikhailKatz Seems like patents can be used as weapons to extract money in all sorts of scenarios, from legitimate to absurd, but I guess that that's a wider problem at there're a ton of patents out there for fairly general stuff. In this case, I think that patent was for ALU's and not software (none of this is legal advice, etc.), so I'd guess that it wouldn't apply. I dunno if that'd necessarily prohibit a patent troll who might later acquire the patent from trying anyway, though I'd be skeptical about such a patent-holder's odds in court. $\endgroup$
    – Nat
    Commented Dec 28, 2017 at 5:34
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    $\begingroup$ @MikhailKatz I'd guess that the patent-holder in this case might have a chance if they sue someone who makes a specialized hardware unit that processes a data type that includes infinities like the one proposed in the patent, though since common floating-point data types already have positive and negative infinities, presumably it'd have to be numeric infinities. But then there'd be issues like if the patent's claims might be invalidated in court. $\endgroup$
    – Nat
    Commented Dec 28, 2017 at 5:39
  • $\begingroup$ perhaps it's better to quote the EMS Surveys page of the paper, with a a link to the statement by the editorial board: ems-ph.org/journals/… $\endgroup$
    – Dima Pasechnik
    Commented Dec 28, 2017 at 10:38

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