On Learning Something New

The following quote is attributed to Richard Feynman: “We are trying to prove ourselves wrong as quickly as possible, because only in that way can we find progress.”

To paraphrase this, if you want to prove something first you should try to disprove it. When you have tried everything, then perhaps, perhaps you have a new idea. It is possible that don’t have enough information, to prove yourself wrong.

When I heard this on a podcast today, I had listened to a few other podcasts about mathematics. It was either on SGU November, or Science(ish) the episode about Pi.

When I consider knowledge I tend to visualise it like wet paint on a canvas flowing but not covering all the space. Different colours representing different depths of the material. We start off with a smattering of something and then we continue to cover the canvas or move to another one and leave this idea partially known, or learning a little.

This year to date, I have painted very slowly and very sporadically for reasons not entirely within my control.

A bit of light reading

Amir D. Aczel’s book Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers

I quite enjoyed this book, the story of one man and his search for the origin of zero. It turns into a trek across south east Asia, where he crosses the barrier from Hindu Arabic numbers to something a little stranger. It appears that while in the west numbers were used for commerce, in the east they had a lot to do with mysticism.

The book follows the questions of the author as a child from the first time the questions occurred to when where somewhat answered as an adult. The story has the author travelling around the world focusing on what used to be part of the French colonial empire that they called Indochine.

The author sadly passed away in the year of publication, 2015. One of the mathematicians he references Alexander Grotendhieck died in late 2014. What isn’t referenced as it wasn’t widely known at that time is at the end of his life  Grotendhieck relented on the retraction that is mentioned in the book.

Due to the inclusion of Grothendhieck the group Bourbaki gets a mention in passing.

Three photos from a little journey

During the summer we went for a little break to the Ardmore in Waterford.

These are three photos that remind me of those warmer days.



This little beauty is a hand bellows for a firew. It is in a tiny rural pub on the outskirts of Ardmore and it still works over a hundred years since it was made.


This cast of a half penny adorns the wall of a small dining area to the rear of The Spire Cafe, in Lismore. As I remember predecimal coins this was a bit of a surprise.

However this cafe gave me even more of a surprise, when I went inside I found the meter below on a shelf and they let me take it down and place it on a table to take a photo.

In a former life I used to use analogue meters on a regular basis.

My father had one from this manufacturer when I was a very young. That was when we had lead in solder.


Sometimes you should look at the back of a thing.


Kings Of The Wyld

Kings Of The Wyld

I finished it. If you like fantasy all action books, you could to a lot worse than this. 5/5

My usual reading in fiction are more Space Opera, this is outright fantasy.  It doesn’t suffer with an over complicated story. I enjoyed it from beginning to end.

It follows some good plot writing toolchains and this is a good thing.


If you need to spend some hours reading fiction, go on, treat yourself it’s great.


#kingsofthewyld #fiction #fantasy


My Favourite Mathematics Book

It is a hard a question to pick one book  to represent my favourite book. This challenge was set by person who started to organise a group of people to read mathematics books in a book club of sorts. What follows is what I wrote for them on that subject.

I’m going to exclude standard text books as they are used to practice the ideas we are playing with.
I’m going to exclude history of mathematics books, while I read them there are parts of history where I get excited, usually by thinking about how the person being discussed got to the point where they did whatever thing it was that is documented. For instance, Ian Stewart’s very nice ‘Taming the infinite the story of mathematics’, starts with the wonderful line, ‘Mathematics did not spring into being fully formed. It grew from the cumulative efforts of many people, from many cultures, who spoke many languages.’ Knowing this means that I can’t know how or why that happened to be, I can, I suppose, guess but I’ll not be certain without evidence, and then at this remove that evidence is not viewed as it was at the time, we can’t know what went on in the Babylonians minds. Frank Sweetz wrote a book titled Capitalism and Arithmetic, the new math of the 15th Century. We also know that people approximately counted seasons and years from the Mayans to the Celts through the legacy of stones in various trigonometric designs. So I will abandon these books for their distance of the journey.
This thinking has me reflecting on three of my favorite books, in the series about people, in no particular order:
Siobhan Roberts excellent book on John Conway, Genius At Play. Levels of Infinity by Hermann Weyl a collection of his essays including one on Emmy Noether, which is reason alone enough to read the book.
Lastly in a category all on it’s own Lymm Gladwell’s excellent Mathematics and Art, which if you want to characterise it you might say it is a coffee table book, it is also a nice history of mathematics but not in the style of the general history books which tend to be very much aimed at course work. It is beautifully illustrated and just a joy to dip into now and again.
This however leaves whole subsections of mathematics alone, it causes me some grief not to mention the Princeton Companion to Mathematics, edited by Timothy Gowers, or Mathematics From The Birth of Numbers, by Jan Gullberg both of which are tomes and well worth the investment. In this short survey of my shelves I’ve left out a few brilliant things, anything by the popularising group Keith Devlin, Ian Stewart, Marcus Du Sautoy.
Now comes the reason I can can’t name a single book, there is a series that takes a bit of work at times, be that as it may, you can skip the hard parts now and again and still get significant gain from working though this little set of books. It is called The Best Writing in Mathematics and it has been an annual release since 2010 edited by Pitici they are a joy in and of themselves and cover a broad swathe of the subject.
With all that in mind I think you might see why I have problems picking a single book.

John Horton Conway on Surreal Numbers

This is a great lecture (in my opinion) that John Conway gave in Toronto in 2016 on how he came to discover Surreal Numbers. With that in mind be aware that he doesn’t do proofs early on, he states assumptions which he deals with later.

I’ve not written anything in a couple of weeks here because I started to write about infinity and I’m still unsure what I want to say about it. There is so much you could say about it.

Popular Television & Physics Comedy

There is a mathematician named Douglas R Hofstader, another one named Sheldon Katz, both rather interesting in their own way.

The former is the author of several books. Godel Esher Bach is most likely the most well known of them.

The latter Sheldon H. Katz is an American mathematician, specializing in algebraic geometry and its applications to string theory. In 1973 Katz won first prize in the U.S.A. Mathematical Olympiad (Wikipedia). This is him talking about something I understand some of the words but not in that order, it is way over my head. Sheldon Katz – Elliptically fibered Calabi-Yau threefolds: mirror symmetry and Jacobi forms