A New Kind of Science: The NKS Forum > Pure NKS > Further Improvements & Errata
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Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

Further Improvements & Errata

I have scanned most of the notes section and I think I came across a couple of errors.

This particular error that I have in mind at this moment in time was first pointed out by Professor Shallit in "Automatic Sequences: Theory, Applications and Generalizations". NKS mistakenly claims that Loxton and van der Poorten had proved that automatic numbers were either rational or transcendental. In fact, they proof contained an fallacious error. Plainly speaking, the mistake rests heavily upon a method which was introduced by Mahler.

I hope this helps ....

Evangelos Georgiadis

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11-21-2005 06:43 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

page 1153 Tarski's axioms

I don't agree with this axiom.
Tarski would not have chosen this one for purposes of continuity.

-evangelos

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11-22-2005 07:47 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

page 976 Signs

I think there is something wrong w/ the signs, in particular the minus sign. I am referring to the 'note to page 325'.

-evangelos

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11-22-2005 08:01 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

Simulating Rule icons for Turing Machine on page 669

I am very much surprised of how 24 rule descriptions [bottom half of that page] can be sufficient for this simulation. Clearly, at least 26 rules are needed.

I hope this helps.

-evangelos

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11-23-2005 03:22 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

page 336 - bottom description

Currently it reads :

" ..... while if the total is greater than 6, it becomes black. If the total is exactly 5 ..."

The correct version should really be:

" .... while if the total is greater than 5, it ...."

-evangelos

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11-25-2005 03:30 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

Further errata on page 673 ...

On page 673 :

Bottom right description.

[as is]

"An example of how a simple arithmetic system can emulate a register machine. ........ The rule is set up so that if the value of n is written in the form i+5, 2^a, 3^b then ...."

[should really be ]

" An example ..... in the form (i+5) (2^a) (3^b) then ..."

In other words, the commas have been ill-used since multiplication is needed in that place.

-evangelos

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11-27-2005 03:32 AM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

.... and more errors .....

I would like to thank Professor Jeffrey Shallit for being the first person to point out the the following errata :

Page 913, Line 5
Current Claim: Newton's Method for Sqrt[n] produces t^2 correct digits after t iterations.

Correction: Since the number of digits approx. doubles at each step, clearly one should replace t^2 by 2^t.

---------------------------------------

Page 142 :
Current Claim: "a nested digit sequence ... never corresponds to a number that can be obtained by the mathematical operation of taking the roots."
On page 913, line 30, it is claimed that "The fact that nested digit sequences do not correspond to algebraic numbers follow from work by Alfred van der Poorten and others in the early 1980s."

Correction: The truth of the first statement is not yet known, and the second is incorrect. As pointed out on a previous post.

-----------------------------------------------------

Page 1146, line 2 :
Current Claim: " ... finding an Euler circuit that visits once every node is in P."

Correction: The Definition of an Euler Circuit is that it visits every edge once, not every node.

-----------------------------------------------------

Page 870 :
Current Claim: "The fact that the odd binomial coefficients form a nested geometrical pattern had apparently not been widely noticed before I emphasized it in 1982."

Correction: In 1966 on page 130 in a column of the Scientific American, Martin Gardner pointed the aforementioned out ...

---------------------------------------------------------

I hope this helps.

-evangelos

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12-02-2005 08:21 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

Mis-reference ....

On page 595, line 6: Some form of misreferencing occured.
(d) and (e) -> (e) and (f) maybe this was what was really meant ? Well ...

... I think so.

- evangelos

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12-03-2005 09:55 PM
Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

On the last, yes it is clearly e and f that are meant. If you look back on page 593 start of the last paragraph, it is written as though there are only 3 examples of the simples before the two semi-randoms. Obviously the number of images increased, with one being inserted in the first 4, sometime after those sections of the main text were written. Perhaps to balance the graphic, when the last "key" icon moved down to the same box as the caption.

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12-08-2005 08:55 PM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

mismatch ... page 870

on page 870 : line 5-6 : it reads

"In the pictures below, this map has the form ....(compare page 153)."

My comment :

Hmmm ... what pictures below ???

I hope this helps.

-evangelos

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12-13-2005 02:57 AM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

Boolean Formula Mis-match page 869 - Error

Page 869 right column 2nd paragraph :

Another mis-match :

Rule 110 : Xor[Or[p,q],And[p,q,r]]

this boolean formula does indeed correspond to 124 not Rule 110.

Thanks,

Evangelos Georgiadis

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01-07-2006 02:55 AM
Evangelos Georgiadis

Registered: Oct 2003
Posts: 17

Boolean Formula Mis-match page 869

(since I've been approached multiple times about how the correct boolean expression for rule 110 would look like: I'd like to post it for sake of completeness):

Xor[Or[r, q], And[p, q, r]]

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01-11-2006 11:17 PM

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