Books: Infinite Powers - How Calculus Reveals The Secrets Of The Universe

 (Drivebycuriosity) - When I studied economics a long time ago I enjoyed the beauty of calculus. The rise of a curve, showing for instance oil prices responding to the demand for oil, can be measured by the first derivative. The faster the price rises, the steeper the curve, the higher the number of the derivative. When the rise slows, the slope gets less steep and the second derivative turns negative. A positive second derivative represents an acceleration, a negative stands for a deceleration.

To refresh my very dusty knowledge I read "Infinite Powers - How Calculus Reveals The Secrets Of The Universe" by Stephen H. Strogatz (amazon ). The title is a bit too ambitious, but many things came back in my memory and I learned a great lot of new things.

Strogatz can write and describes basic ideas very simple and with humor. He depicts the evolution of calculus  and refers to Greek likes Archimedes and later followers like Galilei, Newton, Fermat, Descartes, Leibnitz and many others, spiced with anecdotes.

The author does nor care about economics, but he shows many other applications of calculus: NASA flights, cell phone, microwave ovens, radar, computerized tomography and countless more.

I learned why a limit cannot be reached and Strogatz solved the famous Achilles/Turtoise puzzle (Turtoise cannot overtake Achilles). 

He defines calculus "by its credo: to solve a hard problem about anything continuous, slice it into infinitely many parts and solve them - and then putting the answers back together".

Calculus works with "differential equations. Such equations describe the difference between something right now and the same thing an instant later or between something right here and the same thing infinitesimally close by".

"An ordinary differential equation describes how something (the position of a planet, the concentration of a virus) changes infinitesimally as the result of an infinitesimal change in something else (such as an infinitesimal increment of time)". 

"Newton discovered that motion of any kind always unfolds one infinitesimal step at a time, steered from moment to moment by mathematical laws written in the language of calculus".

 

I did not know the rule of 72. Here it is:

"To estimate how long it will take to double your money at a given annual rate of return, divide 72 by the rate of return. Thus, money growing at a 6 percent annual rate doubles after about 72/6". Helpful when you think about investment into the stock market.

Highly recommended.