Another excellent Interesting today. Since then my head has been bursting with many of the ideas presented there, particularly the concept of being able to see radio waves, the Indian superheroes, frivolity, and what you might learn about yourself from collecting in depth data describing your thoughts and emotions.

As last year, I’m in awe of the speakers. It’s a difficult and potentially hugely embarrassing thing to do, to stand up and say ‘this is interesting’. What if the audience disagrees?

I’ve been considering for weeks about what I would do if I were speaking at an Interesting.

Most of the ideas get kicked out quickly, would require a huge amount of work, or refused to be put in a coherent shape.

The main (or perhaps remaining) one is an idea (touched on today) about modes of thinking, and how they relate to one another.

I don’t mean the thinking that sort of rattles around your head (or mine at least) all day – the ‘I’ve left the oven on’, ‘isn’t Johnny Marr brilliant’, ‘she’s cute’ type of chatter. Instead I mean, the sort of thinking you’re about to do when you say ‘I’ll have a cup of tea and think about that’.

And, I’ve found there are normally two good ways to solve an intellectual problem of this sort (aside from tea, which is required for both).

If I’ve got a topic that’s going round and round my head, and I want to figure it out, I can either try to forget about it entirely and wait for the answer to pop in to my subconconscious (this can take a while, so it’s not good if you’ve got a deadline), or I can start trying to write a half-arsed blog about it, and the process forces me to a conclusion. Often that conclusion isn’t the end of the whole thing, but it normally moves it forward. (Right now, I’m doing the later!)

Of course, these are solo methods. One of the great advantages of blogging is that someone random from Tennessee can jump in and supply the answer. Or, more accurately, an answer which can push you in the right direction. And a similar thing can happen in brainstorms (although I do remain quite skeptical about this particular activity) or just by going over-and-over it with others until you get somewhere. We could describe this as the ‘Rolling Stones’ method (Richards and Jagger having famously been locked in a room by their manager until they came up with an original song).

But- and here’s my thesis – there are fundamentally different types of thinking. And if they can be managed at all, they need to be managed in different ways.

This probably seems a trivial observation. But I’m not sure it is. Over the years, many perfectly rational philosophers (and some not so rational ones) seem to have driven themselves mad trying to achieve the sort of certainty, for example, which comes from mathematics. Trying to derive the equivalent of Pythagoras’ theorem for meaning or observation is a very short trip to the nut house.

Pythagoras’ theorem and things like it are great. A quick trip over to Wikipedia and you can see just how elegant the whole thing is:

In fact, Wikipedia shows 8 different proofs of the theorem (including one from a future US president). If you understand the symbols used and a couple of concepts of geometry and arithmetic, you can understand the proof. You cannot argue with it. Not just that, it is relatively easy for us to understand that the proof applies to all right angle triangle however extreme, even though we will help ourselves understand the proof with a particular drawing.

And then consider that there are three different (non-scalar) examples of Pythagorean triangles which work with whole numbers under 25 (3,4,5 and 5,12,13, 7,24,25). (Does that seem unsuprising? There are **no** whole numbers at all that satisfy a^{3}+b^{3}=c^{3}).

This is the sort of thing that people want truth to be like. Absolutely certain, simple and with the sort of ‘elegance’ that makes you feel there is order to the universe and you are just decoding it.

And so much of maths is like this: neat Ikea-style building blocks that continue to yield satisfying results. Pythagoras’ theorem sits on top of some neat geometrical ideas. And it is then used to derive equally satisfying ideas including (elements of differential) calculus. Calculus tells us that the gradient on a curve described by y=x^{2} is always 2x. And so on.

Not all mathematics is cuddly. You can keep going and prove statements that could hardly be described as intuitive, for example that the size of the natural numbers is the same as the size of the natural numbers squared or to prove that there are statements that are true but that cannot be proved.

But I don’t believe philosophy is like this. Descartes (another mathematician) was famous for ‘I think therefore I am’. A lot of Plato’s writings echo the same desire to believe in perfect objects and reference. These are attempts to put philosophy on as secure a rational footing.

But philosophy is about the meaning of concepts and their inter-relation. It is about the inside of our brains. It does not measure the world itself, and it doesn’t derive from a simple set of axioms, like mathematics. Searching for absolute certainty rather than seeking to understand inter-relations is like trying to find a yellow fantasy or a happy number, it is simply a misclassification of what is going on.

But the two do share something in common: they are both analytic. When thinking in such analytical areas, the thinker must understand the whole question, and must exhaustively run through all of the options that may contribute to the answer.

Science is different again, although many scientists have been drawn to the allure of mathematical (or philosophical analytic thinking). There are a potentially infinite set of sciences that could be brought to bear on explaining any particular set of observations. They are not true or false, rather useful or non-useful.

And then we get to creative thinking. This is not the same thing at all.

With creative thinking, it seems we are often trying to break down meaning, language, or concepts in a way which is deliberately non-sensical. We seek to remove the context of these thoughts, and to look at them through different belief and understanding systems. This is why social media can be creative when it is on a huge scale but less so when it’s focussed on consensus-orientated groups.

Of course, thinking about philosophy or science can be creative, because it can be about re-framing questions or crossing idea paradigms. The most creative thinking however, does not need to be useful – or at least it does not need to be immediately useful. We can play with ideas to our heart’s content, and only need take away what we find interesting or useful. It can be the most powerful skill and it really requires the opposite of philosophical or mathematical thinking, it requires the ability to remove restraint from the thought process.

A type of creative thinking is trying to derive ideas which will motivate others. These are ideas which need to have a particular use. Here we’re trying to use our brains not to examine rational paths but instead treating our own brains like a petri dish for any sort of idea which can inspire a certain emotion.

And then we have creative thinking which is not about utility at all, but about beauty. This is the creative thinking of art and music. Where ideas are generated just because they are ideas, and if other people like them then even better.

We saw a lot of examples of all of these types of thinking at Conway Hall today. One of the speakers said they’d come to the conclusion that creative imagination was a muscle that could be exercised, rather than a well that could be drained. Late in the day, I overheard one attendee saying they were ‘interestinged out’. It certainly was a (very lovely) work out for the brain.

So many conferences seem to train a particular mental muscle. Russell’s ideas fest certainly gave us an all-over full body work out, and reminded us that we need all the bits of our brain (not just the ones that we use to talk about social media) to keep thinking about things in interesting and useful ways.