Krishna
As playful as the tongue in cheek pun in the title, the book is absolutely brilliant. What magical concepts to explain mathematics! And yes, I reference the innuendo in the pun of the title. That is in sync with the entire style in which this book is written.
Take only one example from Steven, the author. He explains why the sum of all odd numbers from one to any number turns out to be a perfect square (1, 4, 9, 25 etc to infinity). It is all done with pebbles (or ‘rocks’ if you want to call it by the name author chooses to explain). If you are an ardent fan of mathematics (I confess I am) or, especially if you are not a fan of mathematics, this book is definitely for you. It will nudge your curiosity and bring you closer to the world of numbers. The author had me at page 2!
There is a lot of etymology here too, to add to the pleasure. Calculus and Calculate come from Latin word Calculus, which means ‘count with stones’.
The easy way to count from 1 to (say) 10 using stones is absolutely impressive! Better than learning by rote the formula n * (n+1) / 2. Ultimately you realize that it is exactly the same we are doing here, but visually. How enthralling!
Again with the equivalent of stones, Stephen explains easily why multiplication is commutative. That is, why 7 x 3 is the same as 3 x 7. Simple indeed but mind blowing for those of us who learnt it purely by rote.
More on the same vein. He uses stable and unstable relationships (and the fact that two negatives, when multiplied form a positive) to analyze World War I coalitions! No, he does not imply that these predict the results but some of these equations elucidate stable and unstable states and apply to real world problems due to different, practical, considerations.
Look at how he explains division. By sharing. Then he talks of fractions if you cannot share it equally. (Fractions are ratios and therefore called rational numbers. Neat, huh? )
Also he talks about the roman numerals and their similarity to earlier tallying III is like three sticks and V is like the strike across to make five in tallying. It comes from our having five fingers! In addition, he tells us that Babylonians counted in 60s because it is convenient for divisions and that is where hour into 60 minutes and minutes into 60 seconds comes from. Fascinating!
Even digits, the name for roman numerals, comes from the word ‘digit’ meaning fingers and toes.
If you take an equation like x – 7 = 12, you find x by ‘adding’ both sides with 7, which gives you the answer x = 19. This concept came from Baghdad, where Muhammad ibn Musa Al-Khawarizmi, a mathematician named the process ‘the restoration’ or in Arabic ‘Al-jibr’. The term algebra was a morphed term from that Arabic expression. In fact, even more interestingly, the logical process of finding an answer also later borrowed inspiration from his own name Al-Khawarizmi, and became algorithm.
Again, for “easy” quadratic equations, like the example of his which is x2 + 10x = 39, he solves it by imagining a square with side x and a rectangle with sides 10 and x and solves it visually. This is his introduction to quadratic equation and it is as fascinating as his earlier pebble examples.
After the initial surprises, when the author gets to quadratic equations and exponentials (and its reverse called logarithms) even he cannot keep your enthusiasm up as much. It is still interesting because you understand that for the musical notes, do re mi fa so la ti do, the pitch does not increase linearly but rather exponentially to produce that perfect music pitch! The Richter scale for earthquakes or the Ph rating of acidity / alkalinity are also on logarithmic scales which is why if you go a bit higher in Richter scale for example, it is a far more devastating earthquake than the slightly smaller number because the effect is exponential!
Hie reinterpretation of the functionality to the real world is still fascinating.
The sparks of ‘aha’ come and go throughout the book. For instance his elegant proof that all three angles of any triangle add to 180 degrees by simply drawing a line parallel to the base on the apex and reasoning it out. Very nice!
And it stays fascinating! His explanations on parabolas – and the principle of the places which seems to connect seemingly distant places in a building for clear communication where anywhere inbetween it is totally ineffective – are fabulous. He then links ellipses and parabolas to cross sections from a cone. Brilliant, and without any trace of complex mathematical equations. You seem to see geometry in a totally different light after reading this book! If you are at all interested in mathematics or even just numbers, this is a very educational and at the same time, fun read.
Equally fascinating history to calculus. We learn that Calculus is a study of infinitesimal pieces. A very different notion indeed. And the author proves it by calculating the area of a circle by cutting a circle into first four, then eight and then more pieces and arranging them in a specific way. Brilliant again!
The differentials are slopes and he says they are everywhere. (He does not go to the second and third derivatives as they are more complex to explain in this book that wants to teach the joy of mathematics). He talks about everything being a sine wave – the ripples in water after a stone has been thrown in it, the sound waves, everything.
The integrals get the treatment next. Leibnitz chose the integral sign ∫ – which is elegant like a musical symbol – simply because it looks like the letter ‘S’ for Summation.
It is indeed summation through other means. To find a shape of a curve, you make up very tiny rectangles and add up all their areas – or you use Integrals (as formulae).
Even Steven cannot, with all his obvious enthusiasm for mathematics, prevent you from glazing over when he explains how electomagnetism and magnetism work and how, through mathematics, early scientists realized that light was also a wave.
But still it leaves enough to admire. When the author explains how confusing an infinite series can be, by demonstrating three different answers to the same infinite series depending on how you parse the series, it gets fascinating! (All of that caused by the fact that the series never ends!). He even shows that the sum should be half of its own sum! Math doesn’t get much more fun than that!
When a book leaves you hanging and just about when you want more, it is a well written book. By that definition this passes.
So, in spite of the ‘eyes glaze over’ parts, this book deserves a 8/10
— Krishna