"The Joy of Mathematics: Marvels, Novelties, and Neglected Gems That Are Rarely Taught in Math Class" by Alfred E. Posamentier

Publisher:Amherst, New York : Prometheus Books, 2017.

ISBN:9781633882973 

Characteristics:319 pages :,illustrations ;,23 cm

You must admit that “The Joy of Mathematics" is at the very least an intriguing title. I doubt very much if there's many people that really consider mathematics to be joyful, especially when you consider the way it's being taught in schools today. When I was in school everything was taught by rote memorization, learning your times tables memorizing theorums, doing problems, etc. I have no idea how many hundreds of times my various teachers in grades two through four made me and the rest of my classmates write out the times tables from 1 x 1 right through to 12 x 12. I guess though in all fairness it did work, but it was definitely not joyful. I’m not going to get into the fun of Algebra.

Now if I had had this book, or very least if my teachers had had this book I'm fairly sure that math would've been much more fun and interesting. 

On the other hand I loved geometry and trigonometry as they had practical applications. Good ol’ Pythagorus and his theorem is something I’ve used many times and the same goes for trigonometry. Calculus wasn’t offered in my school way-back-when, but seeing as it has practical applications I would likely have been interested in that as well.

The authors touch on a lot of different topics such as arithmetic novelties, algebraic explanations of accepted concepts, geometric curiosities, probability, and some common sense mathematics. And they do it in a way that is interesting to read, and they give great explanations and examples showing you why and how it works.

I would definitely recommend this book to any math teacher, as getting students to be interested in math can be a challenge, and as one of my math teachers told our class once “There is not a single thing you will do in your life that doesn’t involve math, and if you can prove me otherwise you automatically pass this course.”

So far I haven’t found anything to prove him wrong!

"Revolt in 2100" by Robert A. Heinlein (1907-1988)

New American Library

Copyright 1954

This book is actually a collection of three short stories / novelettes. The first is entitled "If this goes on -", the second is "Coventry", and the third is "Misfit."

"If this goes on-" tells the tale of a futuristic society centred in what is now the United States, that had been taken over a number of years earlier by a theocratic government. It goes on to tell how a small revolutionary force manages to overthrow this dictatorial government. The main character is a guard assigned to the Angels of the Lord - the personal bodyguard to the Prophet, who falls in love with one of the prophets harem.

"Coventry" tells the tale of a young man who is convicted of a crime (minor assault) and who has to choose between either being psychologically re-oriented (brain-washed into conforming), or being sent to a special reservation  known as Coventry where many criminals, and those who choose to live life in their own way now live. This story follows the first in this book by a number of years as the Coventry is now the law that governs the land and which was put in place following the revolution.

The third story "Misfit" in this book tells the tale of a young man who is a new member of the Space Marines, and who is part of the crew that is being sent to the asteroid belt with the goal of moving an asteroid into earth orbit so it can be mined. It follows the first two by an unspecified time period. This young man Libby, has a talent for mathematics, that does him a good turn.

All three of these stories are interrelated with each other, and form a a good read, that would be recommended to anyone who appreciates classic science fiction.

"The Discoverers" by Daniel J. Boorstin

Daniel J. Boorstin (1914-2004)
Publisher:New York : Random House, [1983]
Copyright Date:©1983
ISBN: 9780394726250
Characteristics: xvi, 745 pages ;,24 cm

The overview of this book says that it is "An original history of man's greatest adventure: his search to discover the world around him. In the compendious history, Boorstin not only traces man's insatiable need to know, but also the obstacles to discovery and the illusion that knowledge can also put in our way. Covering time, the earth and the seas, nature and society, he gathers and analyzes stories of the man's profound quest to understand his world and the cosmos."

This book is one of three Mr. Boorstin wrote in this same vein, the others being "The Creators" and "The Seekers".I haven't read either of these yet, but they are on my list, and will be reviewed in time.

The Discoverers was a fascinating book, and even thought it took me a long time to read it (684 pages of text) it was well worth the time. I believe this book (and possibly the other two mentioned above as well) would make fantastic texts for a history or anthropology class at the University level. Granted that the majority of students might not read them, but those that did would benefit immensely from the information to be gained.

The book is separated into four major divisions Time, The Earth and the Seas, Nature, and finally Society. Within each of these are sub sections that breakdown the divisions into more manageable works. These are sub sequentially separated into chapters dealing with a specific idea.

The detail with which Mr. Boorstin was able to present this information is wonderful. An example of this from the section of Time is: "Part I: The Heavenly Empire" which deals with rudimentary astronomy and it relation to astrology and how it was connected with religion and how they all influenced various historical events.

"Part II: From Sun Time to Clock Time" traces the development of time keeping through its many phases. Including Calendars, Sun Dials, Clocks, Time Keeping at Sea which allowed for the determination of longitude, etc.

I could go on and give an overview of the entire book, but then you wouldn't have to read it, which is something you should definitely do! All in all this was a great book, and I'm looking forward to reading the next ones in the series, however I won't be reading them right away as it will take me a while to digest all the information presented in this volume.

Space is big, real big ...

I was doing a presentation at one of the schools the other day for grade six Sky Science (introductory astronomy for those of you not familiar with the Alberta curriculum) and a few of the students asked me about aliens, and UFOs, and such. I expected these after all this is what the various media outlets are feeding people now-a-days. In fact if you believed everything you saw in the media you probably think that every other person in the word was from another star system.

Now I don't want to sound like some type of a nay sayer, so to I'll make my stand clear. Yes, I believe that there is other life in the universe, and I hope that someday we will come in contact with them. This will likely be by detecting their radio transmissions, or some such as opposed to having a little green man knock on your door one morning and asking for a cup of anti-matter. But I don't believe they have ever visited us. Why? Read on for the first of my objections.

For those of you who have been weaned on a diet of "Close Encounters of the Third Kind", "Independence Day" and various other gems from Hollywood the chances of aliens having visited us are pretty slim, in fact they are essentially non-existant. Why? I knew you ask so I here goes:


"Space, is big. Really big. You just won't believe how vastly hughly mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space."

"The Hitchhiker's Guide to the Galaxy"
Douglas Adams (1952-2001)

Mr. Adams wasn't kidding either, and that's why I don't really believe that we've ever been visited - there's another reason too, but I'll get to that in days to come. So everybody agrees space is big, but how big is it? Well I just happen to have my copy the 2012 Observer's Handbook handy so flipping to page 291 (Table of Nearest Stars) we see that Proxima Centauri is 4.24 lightyears (ly), Alpha Centauri 4.36 ly, Barnard's Star 5.98 ly, and Wolf 359 7.78 ly distant. So this means that the light were seeing right this second from Proxima Centauri left there 4.24 years ago. For that matter if our sun was above the horizon as I write this the light that we would see from the sun left there 8.3 minutes ago (499.0047864 light seconds to be exact)

Now a light year is standard measure of distance. Sorry to break it to you, but Han Solo got it wrong in Star Wars IV when he said it was a speed factor. It is the distance light travels in one year. Now light goes 299728.458 kilometres per second (abbreviated as c)which when multiplied out gives you 9.458 x 10^12 or 9,458,000,000,000 km in a year (299728.458 x 60 x 60 x 24 x 365.25). A long way!

Now according to a certain rather famous scientist by the name of Albert Einstein it is impossible for an object of positive mass to reach (and therefore pass) the speed of light, so that means that any visitors would have to be travelling at a speed somewhat less than this speed limit. which therefore makes their journey that much longer. So if they were travelling at half light speed then Proxima Centauri is 8.48 years away.

By the way, for the time being I'm going to ignore all the hypothetical faster than light drives that have been postulated for many years in science fiction stories, as we have no idea if it is possible, and until someone rewrites the laws of physics as we understand them it really isn't worth worrying about. I'm also going to ignore the ideas of cold sleep / hibernation etc. in case your curious.

So what we have is a trip to Proxima Centauri that is going to take at least 8.48 years (at 1/2 light speed) and likely much longer (at 1/10 light speed it's 84.8 years). So what does this give us? Well, if a civilization was going to outfit a ship to travel from say Proxima Centauri to us, they would have to provide the crew with sufficient supplies (breathing gases, water, food, spare parts, etc.) to last the journey, and they would also have to devise a way for the crew to entertain themselves for the entire trip. Now I get bored on a car trip longer than a few hours, so I don't even want to imagine being stuck in some type of vehicle for 8.48 years (or 84.8 for that matter).

So as you can see one of the biggest arguments against us being visited is simply distance. Plain and simple. Now if you do accept faster than light drives, cold sleep / hibernation etc. this all changes, but that's what I'm going to talk about tomorrow.

TTFN