This past week I answered a reader’s question to Decoded Science with the online article, “Practical Uses of Matrix Mathematics“. That reader wanted to know about using matrices in daily life; but so much depends on one’s own day-to-day life.

Learn to Apply Matrix Math

Actually there are many, many fields in science that use matrix arithmetic. These include statistical applications (from sociology through “hard sciences”), chemistry and physics, and electrical engineering. As well, the discipline of mathematics studies how matrix math works: the rules, the tricks, and the relationships with other disciplines.

Before applying matrix mathematics, you have to learn the math; and also learn about the discipline to which it applies.

I just glanced over some courses offered by the University of Waterloo, where I earned my B.Math degree several decades ago. The Math faculty introduces matrix mathematics in the linear algebra courses; this provides a strong theoretical basis for matrix math. Meanwhile, an Electrical Engineering class approaches matrices from the practical side, where you solve simultaneous equations to analyze electrical circuits. In my view, the University of Waterloo remains one institutions of higher learning in Ontario.

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So if you’re heading for university in some discipline, check the course lists for topics like “matrix” or “vectors and matrices”; “linear algebra”; or “simultaneous equations”. If that’s part of your future, plan to enjoy manipulating rows and columns in matrices.

Thirsty for more information on this topic? Start with the paperback “Linear Algebra for Dummies” from Amazon Canada or Amazon USA. Mary Jane Sterling introduces vectors and matrices, simultaneous equations, and explains how to compute determinants and eigenvectors. Plus, she finishes with “real-world applications”… which is just what my Decoded Science reader wanted.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy, and DeHaan Fitness. That’s why we highlight these online articles on this blog page.

Read my writing tip in “Quick Response for Matrix Math Application Examples“, in my Blog of Writing. I based this writing tip on my preparation for the Decoded Science article.

To only see our Toronto events (for things to do in Toronto) or fitness articles, please click on the appropriate category in the “Categories” section at the bottom of the right-hand margin.

Thank you for reading about practical matrix mathematics in Canada.

My recent Decoded Science article, “How Modal Logic Proved Godel was Right, and God Exists“, explains the basics behind a brief but bold claim by 20th century mathematician Kurt Gödel.

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Introducing Gödel’s “God Theorem”

Gödel’s “God Theorem” garnered news internationally in the past month because German researchers succeeded in running a variety of computer programs that verified the “modal logic” which the theorem used.

My article summarizes the logic of Gödel’s God Theorem, and then puts the focus on modal logic. (The very quick synopsis: modal logic deals with “possibility” and “necessity” on top of more common logical terms such as “true/false”, “for all”, “if-then”, and “there exists”).

Gödel is most famous for his “Incompleteness Theorem”, which states that sufficiently powerful mathematics can not possibly be “complete”. (Such a powerful mathematics cannot generate every statement which is true within its own framework).

Earlier, Gödel had proven a “Completeness Theorem”: sufficiently simple math can generate all true statements within its framework. (For example: if you start with the number ‘1’, and only allow addition, and allow {1+1=2, (1+2=3, 2+1=3), (1+3=4, 2+2=4, 3+1=4),…}, then eventually you will generate any “n+m=[n+m]”. Simple, yes? Almost too simple).

For this DeHaan Services article, I tried to find a Canadian connection for Gödel. The closest relationships that I found were essays written at Canadian universities, such as the PDF “Kurt Gödel and Computability Theory” from the University of Calgary.

In another promotional article, my “The Proof of God: a New Niche for Kurt Godel” includes a niche writing tip.

Learn More about Kurt Gödel and his Incompleteness Theorem

Learn more about the man behind the Incompleteness Theorem, in the Canadian or American version of “Incompleteness: The Proof and Paradox of Kurt Gödel” via Amazon Kindle.
Hofstadter’s “Godel, Escher, Bach: An Eternal Golden Braid” is a fun and easy-to-read explanation of the Incompleteness Theorem. Amazon sells the paperback to Canadians and Americans.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy and DeHaan Fitness. That’s why we highlight these online articles on this blog page.

Thank you for reading about Kurt Gödel’s proof that God exists.

My recent Decoded Science article, “Free Will, Determinism and Turing’s Halting Problem” helps explain Prof. Seth Lloyd’s insights into these issues.

A Quick Look at the Halting Problem and “Free Will vs Determinism”

Some scientists would argue that our brains are “simply” complex machines that make deterministic decisions, based on the physics and chemistry inside our skulls.

Yet we all have the feeling of enjoying free will, the ability to make decisions and also to change our minds of our own volition.

On the other hand, some people may sometimes appear to be trapped by fixed patterns of behaviour. Perhaps they do not have free will, if their decisions can always be predicted?

MIT prof. Seth Lloyd argues that deterministic decisions, whether made by computers or people, could still defy prediction and appear to be examples of free will.
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Read my article to see how Prof. Lloyd applies Alan Turing’s Halting Problem to resolves this conundrum.

Learn more about Alan Turing’s real-world heroics in “Alan Turing: The Enigma” (Amazon’s Canadian paperback or Kindle in the USA pages).

Writers and editors should read my “free-will” writing tip in my other self-promotional article, “Halting the Free Will versus Determinism Debate“.

Professional Writing by DeHaan Services

DeHaan Services writes web site or advertising copy for clients. Our skills are demonstrated in online articles in Decoded Science, Decoded Pregnancy, and my Fitness and Weight Control blog. That’s why DeHaan Services highlights these online articles on this site.

Thank you for reading about the Halting Problem approach to “free will vs determinism”.