Hand-incalculable Problems

Question

Let's define a "hand-incalculable problem" as a mathematical problem that can not be solved by available human calculation power (using only writing materials and utensils) at a specific date and geography, during lifetime of the person who posed the problem.

Given a specific date and problem can we strictly label the problem as "hand-incalculable"?

Edit:

We assume that algorithm to verify the solution is known.

Edit:

I am looking for a general classification similar to P/NP/NP-Complete which is used in computation theory. I wonder if we could define such classes for mathematical problems as HC(hand-calculable)/HI(hand-incalculable)/HI-Complete at any specific date. Even an absolute classification based on available human FLOPS and not related to a specific date, would be nice.

Edit:

HC: Hand-calculable at a specific date.
HI: Hand-Incalculable at a specific date.
HI-Complete: Hand-incalculable no matter how far mathematics will advance in future; consider a dynamic programming problem that needs millions of FLOPS of calculation power to be solved in reasonable time (during lifetime of the person who posed the problem).

Related: “I go back in time to 1847 and have lunch with Carl Friedrich Gauss. We are chatting about the developments in 20th and 21st-century mathematics, and because I am a horrible person, I mention that ${\left(\pi^\pi\right)}^{\pi^\pi}$ has been proven to be an integer. Gauss is incredulous, but I insist. After I leave, can Gauss convince himself that I am nothing but a troll?” Alexander Walker brilliantly shows that Gauss can do this. — MJD, Oct 22 '14 at 14:55
@MJD Thanks for your reference. I am look for a general classification similar to P/NP/NP-Complete which is used in computation theory. — Bahribayli, Oct 23 '14 at 09:10
Don't you think it would have been a good idea to say so in your question? Nobody here can read your mind. — MJD, Oct 23 '14 at 12:59
Human hand calculation power depends greatly on the theory developed up until that point in time and what has not been lost in the mist of history. I'm skeptical that this is a math question. Seems more like a history/anthropology/futurist question. — J. David Taylor, Oct 26 '14 at 07:09
@Taylor It is related to history of mathematics but can not be completely answered by historians. The question asks whether we can label a specific problem as HC at a specific date based on current knowledge about the era. Is it possible or not? If I pose a problem and ask whether is was HC around 11th century, can math community answer my questions? — Bahribayli, Oct 26 '14 at 07:30
Shortly, It is difficult to formalize such a notation, as the issue is raised by other parties as well. There are many parameters for such definitions and the bad is that the definitions are time dependent. No one would love to see such, especially when everything changes extremely fast. One day it is possible that a man is half machine. What will happen to your definitions? — Seyhmus Güngören, Oct 30 '14 at 20:27

Daniel Goldman · Accepted Answer · 2014-10-30T20:25:15.403

2

If you can determine big O for the problem and estimate calculations per hour for a person then you should be able to roughly determine your class.

This can, at most, be done for problems for which have algorithms to some them.

Also, since we can essentially be considered Turing machines, HI complete includes NC complete.

edited Oct 30 '14 at 20:25

answered Oct 30 '14 at 20:20

Daniel Goldman

942

Hand-incalculable Problems

1 Answers1