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There is a preprint on arXiv that states (in my own words).

If there are three numbers (digits) and task is to add all three numbers. First we well take two number to add, set aside third number. Then we will add third number in previous sum of two numbers. So, addition of three number requires two steps, because we cannot interact and manipulate more than two numbers in single instant. Our limitation to interact with only two number in single step has played very important role. This is one of reasons why Math axioms involve only two number e.g a.0=0, b.1=b etc…Similarly we cannot sort more than two numbers in single step. If there is a system that can sort three objects in single step it will be 200% more time efficient. The kind of sorting that involves three numbers in single step is not possible by humans or man-made machines (not even Turing machines ). But one such system is explained in the paper along with consequences.

The paper concludes

“It can be stated explicitly that computational complexity appears because of Mathematical Axioms that are constrained by and based on human cognitive limits as human cannot interact with more than two numbers at an instant”

Is above statement right?

Preprint Link https://arxiv.org/abs/1711.10874

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closed as off-topic by David Richerby, Evil, fade2black, Yuval Filmus, Juho Dec 17 '17 at 11:24

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not appear to be about computer science, within the scope defined in the help center." – David Richerby, Evil, fade2black, Yuval Filmus, Juho
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ "Are the claims of this paper correct?" isn't really within the scope of the site. Without carefully reading the paper, it's not really possible to say whether it's correct or not and, although the paper's fairly short, that's still more work than is generally appropriate for a Stack Exchange answer. $\endgroup$ – David Richerby Dec 15 '17 at 15:09
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    $\begingroup$ I wouldn't take this "paper" seriously at all. $\endgroup$ – Omar Dec 15 '17 at 15:10
  • $\begingroup$ @Omar you may, I don't want either, but questions raised in this paper are hard to ignore. $\endgroup$ – user81905 Dec 15 '17 at 15:47
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    $\begingroup$ I don't think so. The author does not even seem aware of the extended Church-Turing thesis, let alone that a "third-order comparator" or a "200%" improvement are particularly trivial suggestions/observations. $\endgroup$ – Omar Dec 15 '17 at 15:56
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    $\begingroup$ Sure. Such gates are possible with any constant number of inputs (not just three), and may result in any constant factor speedup. In complexity theory, that's not a big deal. It is very well understood. $\endgroup$ – Omar Dec 15 '17 at 16:08
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Who says we cannot add three numbers in a single step? We can, and if we use the fastest known methods to add integers, adding three numbers only takes a little bit longer than adding two numbers, not twice as long.

Most modern processors have instructions adding three numbers, for example the LEA (Load Effective Address) instruction on processors based on the Intel architectures.

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No. The paper appears to be total baloney. I noticed multiple unjustified statements in my first 60 seconds reading the paper. Don't waste your time with it.

arxiv is not peer-reviewed. Some papers on arxiv are great; some papers are arxiv are terrible and a waste of time. Its presence on arxiv says very little about its quality. It's like finding a paper on someone's personal website.

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  • $\begingroup$ The statement still might be right. But it is just not clear from that paper) $\endgroup$ – Eugene Dec 15 '17 at 22:17
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    $\begingroup$ I am fully with you, this is an awkward amateur's work, to speak politely. $\endgroup$ – Yves Daoust Dec 15 '17 at 22:21