# Algorithmic Mathematics

Algorithmic Mathematical Art

## Discrete Algorithmic Mathematics Third Edition

go to link B Non-algorithmic math. Thread starter Blue Scallop Start date Oct 13, Blue Scallop. Related General Math News on Phys. Scott Homework Helper. Most math is non-algorithmic. In general, math makes declaratory statements.

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In contrast, algorithms make imperative statements. When executed, it will cause a variable "N" to be incremented. Taken as a Math statement, it is a declaration which is false. Scott said:. I did read "The Emporer's New Mind", but not recently enough to remember clearly. As I recall, "algorithmic" in that context referred to any process that was equivalent to how conventional non-quantum computers process information.

He was arguing against the generation of consciousness by "algorithmic" information processing by arguing that all such processing was the equivalent of reading the algorithm from a printed document and working it out manually. Since that printed document exercise does not elicit its own "consciousness", neither would any other mechanical or electronic equivalent. I searched all instances of the words "Non-algorithmic" in Penrose book and saw the following: "In Chapter 10, I shall try to present arguments to show that the action of our conscious minds is indeed non-algorithmic i.

I first read the book about 10 years ago and my first impression was non-computable means can't be solved by math. So I thought non-algorithmic means it can't be solved by math. But then are there maths that are non-computable? Any examples?

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Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular. This is the textbook for the course MAS Algorithmic Mathematics. notation [ ϵ] indicates that mathematical symbols are not permitted in the.

Many thanks! Blue Scallop said:. You meant Penrose was saying quantum computers were non-algorithmic yet still describable by math? I'm trying to search his book now where he strings the word "math" and "non-algorithmic" together..

There are non-computable functions. This means that for the function there is no algorithm, which can compute the function for any input. The standard example is Turings halting problem. There is however widespread belief that the Church-Turing thesis is valid and that computers and human brains are insofar equally powerful that any non-computable function for one is also non-computable for the other, and that computers can solve any mental task that a human can solve.

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It is known that Quantum computers are also in that sense equivalent to conventional computers, even though they are likely faster for certain tasks. FactChecker Science Advisor. Gold Member. I think of an algorithm as being a sequence of steps to solve a problem. Scott correctly points out that Shor's Algorithm is called an "algorithm" and I don't know if that use of the term is because it is done is a two step sequence traditional computer step, then quantum computer step or not.

Usually mathematics is a set of equations and facts that are all simultaneously true, not done in a sequence. In my interpretation of the term "algorithmic", that would make most math "non-algorithmic". I think the question in OP can be interpreted in a few ways. Regardless even if one believes the first statement, it would still leave some important points unanswered. Assuming the first statement to be true, it seems that Godel is really talking about "potentiality".

Edit: Also, given the disjunction, there seems to be a certain implicit assumption in the second statement hopefully just mentioning it doesn't add more confusion. To talk about it more meaningfully, suppose we restrict our "space" to just number-theoretic statements to avoid trouble with more difficult issues.

## Discrete Algorithmic Mathematics

It seems to me that the second statement implicitly assumes that the boundary between "knowable" and "unknowable" should be algorithmic in some sense? But then again, I am not sure why this can reasonably be taken as more plausible than say the boundary being non-algorithmic?

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Order by , and we can deliver your NextDay items by. The same function may have several different algorithms". Solid stacks of cubes is called Polycube a 3-dimensional version of polymino. One also needs to encode the geometric layout, namely, the circle's positions and sizes. Stephen Wolfram's book A New Kind of Science, for example, contains many pleasing images of cellular automata, although not for the express purpose of visual art. Hodges, Andrew

Perhaps I am missing something Edit2: Also I personally feel unease with such a disjunction unless one is very clear about exactly what "statements" are included in the second part of disjunction for example, a restriction to number-theoretic statements as in "Edit" above is perfectly fine. Students will need computers individual or pairs and the teacher may want to use data projection.

Detailed information on software is in the Teachers' Guide.

Introduction to Algorithms