[NKS book correction] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

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NKS book correction

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Posted by: Jason Cawley

In the notes to the NKS book, there is a particular note on Diophantine equations on page 1164 that contains a table of them with large minimal solutions, meant to be the largest minimal solutions of equations with coefficients limited to certain values. It turns out two of the entries in that table are incorrect.

The second one listed has a simple, much smaller integer solution, which a reader noticed and pointed out. We found that the particular build (of an internal, unshipped version of the code) used during the search involved in making that table originally, had an obscure bug (long since fixed) that let these slip through. Checking with modern corrected Mathematica, the correct answers for the 2nd and 3rd entries in the table are -


-1 - 2*x + 2*x^2 - y + x*y - 2*y^2     {562, 719}

and

-3 - x + 3*x^2 + 2*y + x*y - 3*y^2    {2642, 3119}


The smallest solutions for the equations listed in the book right now are {3,5} and {8,21}.


Posted by: Jesse Nochella

On page 196, picture (b) seems to have an extra node and an arrow going the wrong way out of it, on the left-left branch of the bottom right limb. The main text paragraph is still correct that the network does not have the same pattern of connections, but I am not sure if it forms an infinite tree.

On page 1034R, the two last pictures of the second to last row are identical. I assume that they were meant to be different.

Hope this helps alleviate some confusion.


Posted by: Jason Cawley

Yes, the page 1034 duplicate picture was caught a while ago and fixed in the 4th printing. You seem to be the first to have noticed the extra arrow in the picture on page 196 (to report it, anyway). Someone is looking at how that got there, now. Thanks.




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