Is consciousness a product only of matter, or of life?

No-one knows the answer to this question so it can’t hurt to present one line of thinking here. We will approach the issue not by asking whence arises consciousness, but rather by asking what prevents consciousness from arising. Begin with the assumption that your consciousness depends to some extent on your brain, and that the [...]

The creative discovery process in mathematics

Mathematicians appreciate the necessity of a long period of unconscious rumination of a problem for the eventual sudden appearance of the solution. Sometimes you can sit down with a problem and a piece of paper, and see the way forward almost immediately. But more often several days, weeks, months, years, or even generations of thinking, [...]

Our vast and beautiful universe

The galaxy I Zwicky 18 was apparently a bit of a puzzler because it looked like it stars began forming in it much later than other galaxies. Now it turns out that its stars are ancient after all, but the galaxy itself has retained a youthful appearance. Why and how are the new mysteries.
I couldn’t [...]

Dinosaur Comics does maths

It’s oh-so-true:

Problem solving

I follow the sage advice contained in a text which with every reading reveals new layers of nuance and meaning, new depths which I have barely plumbed. The book is called “Mr. Happy finds a hobby”, by that master Roger Hargreaves. The relevant page reads
It was whilst drinking a cup of tea the next morning [...]

Blox update: 4!

Elsewhere I’ve suggested adopting Hersch’s h-index to give a rough measure of the extent to which readers of a blog are drawn into the conversation. In this way, a blog’s blox is the number of posts which have at least that number of comments (including those from the author of the post). A lot of [...]

At least some of the time I’m an engineer

Let us first bear in mind that science is one way of looking at the world: precision is not the same as truth. I want to put those caveats at the beginning, because I want to share with you that it just occurred to me that quite a lot of what I do isn’t actually [...]

Gödel: intuition versus formality

(Left to right, top to bottom: Gödel, Hilbert, Chaitin, Turing.)
Such a heading deserves a longer and more detailed post than that which follows, but I would just like to bring a few topics and a tantalising paragraph to your attention.
In 1931 the mathematician Kurt Gödel showed that there are true statements in mathematics [...]

Richard Branson on Education

The supernaturally rich Richard Branson, starting from nought and now running companies worth over $25 billion, gives a fascinating interview which you can watch at TED. Fascinatingly, this creative, generous, productive, socially-aware, philanthropic, witty, charming, loving man says he did very poorly in academic work at school, that he would have “failed IQ tests”. This [...]

The value of longevity

I realise that the subject of longevity, the length of a human life, is somewhat off-topic for a maths blog, but since one of my aims is to learn to think about and discuss ideas clearly, to encourage such thinking in others, and to have fun interacting with ideas and the people behind them, I [...]