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Worth the Read: The Mathematical Radio

In this review, Buc Fitch says "this book fills a big gap in literature"

In this column, Radio World’s longtime contributor Buc Fitch reviews the book “The Mathematical Radio: Inside the Magic of AM, FM and Single-Sideband” by Paul Nahin. Comment on this or any article. Email radioworld@futurenet.com.


Most of us in this business — and hopefully all of our listeners — feel that radio, and broadcast radio in particular, is composed mainly of magic.

Magic to entertain, inform, influence in a positive way, keep lonely folks company and be a companion to all of us in our daily lives.

All that magic is mainly in the sound, but additional magic exists in the science as well.

Cover art from “The Mathematical Radio: Inside the Magic of AM, FM, and Single-Sideband”

Alright Buc, you might be a little too poetic and romantic here but physics has to be part of the phenomena of radio too.

Americans think that any industry has to begin with an inventor.

But reflect on this: Because of the electrical basis of radio, the birth of our business begins a little further back with essentially the recognition that Hertzian waves must exist. 

After that, broadcast radio becomes an application of that nascent science.

So, how does one describe a conceptual power when you know that force must exist but no one has ever seen or touched that reality? You use a language. And since waves are essentially powers, MATH — ultimately the most accurate and true language — is the best way to proceed.

In this book, our author proceeds with a deep dive into the subject to satisfy all the number lovers out there. AM, SSB and FM are covered in a progressive exposition.

If you have not thought about the concepts and relationships of this physics for some time, this tome is a sensational review.

If math is heavy going for you, some alternate motivation exists for you to wade through the pages. Our distinguished writer brings a parallel narrative to his scholarly treatment borne out of his obvious love of radio.

He provides us with a very interesting historical narrative of how we got from conception (magnetic waves) to conclusion (the wonderful world of radio that we have today).

The gentleman annotates the social impact of radio, but mainly highlights the people who made it happen. Some of these people may be new to you as they were to me. 

The Mathematical Radio by Paul Nahin is available direct from the publisher (Princeton University Press) and from all the usual places such as Amazon and Books-a-Million. 

Copies are available as well at most libraries for loan as this book fills a big gap in literature and is well worth the shelf space in the reference room on a par with Kraus’ Antennas. 

That literature gap is the span, the connection that bridges the physics of radio and the engineering application of the same.

Physicists want to know why something works so they can take these laws and send us or take us to where we need to go … the future, a clearer truth, etc. 

Engineers want and need to know how something works so they can use what we have and the new knowledge we are given in a practical manner.

This book, a carnival of numbers, takes us on a very interesting journey through both worlds.

After you finish reading, please let me know if you agree with my assessment.

To share your thoughts with Buc, email fitchpe@comcast.net.

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