How not to be Wrong - Thoughts on the book

Demystifying the world around by learning it from Jordan Ellenberg.

There are so many questions that we have about the events in this world and somehow we want to understand it but we are confused about the tools that we need to pick up to learn it. Recently, I thought what if I pick up a book.

There are some series of posts that I want to write to assimilate the concepts that are discussed in the book. Keeping thoughts in control is the toughest part of self grooming. Actually, after completing my Data Science specialisation, I have some time that I can use to understand story telling in a better way.

Learning the basics helps afterall.

I too feel that maths is part of our lives but mostly hidden as it makes the world around us too boring to discuss. Moreover, it makes the world too formal, which most of us don’t like.

Preface of the book resonates so much with my life; I never thought that I will be at a stage, where it will be important for me to learn the language to express my thoughts. I also completed my executive MBA, where I was introduced the world of statistics and how it helps in analysis of the data and take effective decisions; These decisions can be about the career that we either choose or are forced to choose. For example, I met a guy who wanted to learn intricacies of cyber security just because he was asked by management to take up a position with their red team. When I met him, I thought he could be a better fit to be part of blue one.

Data Analysis and decision making is the field that we all are trying to demistify; I would like to stick to that thought for now at least :).

Answers to our naive questions such as, “When am I going to use it ?” is answered in the preface of the book. I also feel that we are like that student who has been given the task of solving difinite integrals on the weekend so that she can assimilate the maths in such as way that it becomes her habit to think mathematically and apply them when needed in her career.

Those integrals are to mathematics as weight training and calisthenics are to soccer.

I never played soccer but I played football and I am sure weight training and calisthenics are very applicable there too. Jordan claims that he can be that coach who we all (and the interested readers) are searching for. He is so confident to make us meet the hidden maths that we all use conciously or unconciously with confidence. I am not going to put his claim on hypothesis test. Why ? I simply went by the ratings received by the book on Amazon and becuase I bought the book already.. :D

I hope to make most out the book and to augment my learning I have enrolled myself as a teacher with Khan Academy. I could enroll as a student too but that doesn’t seem to sync with the ego that I need to maintain. However, I feel that we all are life long learners and learning has no bounds.

This book has 18 chapters, which are divided into five parts:

• Linearity
• Inference
• Expectation
• Regression
• Existence

Oh my God ! I am already having chills. I hope I have made the right decision. It is a good choice if I want to play, at a competitive level, “ignoring lot of boring, repetitive, apparently pointless drills”.

Abraham Wald and the Missing bullet holes

This story is about a Jew mathematician, who was part of The Statistical Research Group during WWII and worked right next door to Columbia’s wing of the atom bomb project. He did not developed any explosives but weapons of diffrent types called equations. There were diginitories such as Fredrick Mosteller, who founded Harvard’s statistics department and Jimmie Savage, the pioneer of decision theory & great advocate of the field that came to be called as Bayesian mathematician and the creator of cybernetics.

There is a very nice account of the problem on finding airplane parts where armour could be placed so that you save your planes from getting shot down. Armour is heavy . Too much and too less armour on planes have their respective limitations and problems. Somewhere there is an optimum. Finding that optimum was the reason that officers and mathematicians gathered under a roof.

Data brought by military is shown below:

I leave it to the readers to think about the data and do some initial analysis.

In next few pages, before Part-1, Jordan has tried to build his argument that mathematics is not so different from common-sense. Mathematics actually augments our common sense. There are times when we do not think about the oblivious while making our deductions and while doing some analysis. Focusing on oblivious might result in neglecting the features that are more relevant to the underlying problem. A common structure, which appears here is called Survivorship bias.

If you are still wondering about Wald’s recommendations then I must write it down.

The armour, said Wald, doesn’t go where the bullet holes are. It goes where the bullet holes aren’t, on the engines.

Why Wald gave these recommendations? How could he come up with such recommendation, which was put into immediate affect. He knew that missing bullets were on the missing planes. Planes that got hit on the engines are the ones that did not return. Hits on the fuselage still could be tolerated. Engine is a point of total vulnerability and it made lot of sense.

Lessons to to be learnt for us to be thinking like a mathematician are;

What assumptions are you making ? And are they justified ?

Our assumptions are limited to the data that we see and the unexplained can remain unexplained. There is obviously more to this explanation but we might see and understand more of it in later part of the book. Moreover, fomalisation of Wald’s deduction is also given in the book. However, I need to read more to understand and interpret it in a mathematical lingo.

A similar example on performance of existing mutual funds is presented in the book and I leave that for your reading.

Maths is an extension to our common sense. It is not about list of rules that we have to mug up. We cannot do calculus using common sense, but it is derived out of common sense. For example we could take Newton’s theory and apply it to the problems for which we had no equations.

I loved the analogy of Tony stark punching a hole through a brick wall with the help of servomechanisms powered by a compact beta particle generator, which he uses to power his Iron suite.

Then there is a section on What kind of mathematics will appear in this book?. In this section Jordan tries to convince us by showing our position in mathematical universe into four quadrants. We are placed into the one in north west. Simple and profound. More than simple and shallow and not falling into either shallow/Complex or Profound/Complex.

Jordan promises that we will do some maths too because It’s pretty hard to understand mathematics without doing some mathematics. There will be no homework and there will be no test.