Number 1

We normally use Base 10 to count, 0-9. Sometimes we use Base 2, 0-1, or Base 16, 0-F, when working with computers.

But any number can be used as the base for a number system. Those of us old enough to remember log books will be familiar with that. And the fact that you can readily convert between bases, “10” = “A”.

So take a circle, the circumference of a circle is given by 2πR  where R is the radius. Now, if we go for Base π then the circumference of any circle would be expressed as 2R. By definition, 2R = the diameter of the circle so in Base π the diameter and the circumference of a circle are the same.

But the diameter is a straight line and as such can be expressed as a square, put 4 matches in a straight line and you will see what I mean.

So the circumference of the circle can be expressed as a square.

Hence it is shown that you can square a circle.

QED. 🙂


Wisdom of the crowd vs Regression to the mean

I am a big fan of Over the past couple of years it has become my default way of finding out about music. The way it learns your taste and (somewhat) challenges it is great and I have enough of the trainspotter about me to be interested in the charts it creates of the music I have most listened to in the past week, month or year., like everything in this world these days, has a social networking component, part of which allows you to join groups. I belong to two such groups, one for readers of Metafilter, the other for people who shop at PostEverything.

So, two groups, one aimed at a mainly American technology aware, socially minded group of people; the other for people who shop at an esoteric online shop for “interesting” music.

And when you look at the charts of most popular music in the two groups you find … a large degree of similarity. Radiohead … check, Coldplay … check, Portishead … check.

There is nothing surprising in popular music being popular. But it got me thinking about taste and popularity and the connection between chart position and tag clouds. One goes up and one gets bigger but both tell the same story.

And the concept of popularity always makes me think about the story of how architects define paths on campuses by letting people walk across the grass, organically creating links and these emergent paths are then used as the basis for the formal paths.

This is often quoted as an example of the “wisdom of the crowd“. The way in which a decision taken by a group may be smarter than that taken by individual members of the group.

But you can also think of it as an example of “regression to the mean“. The tendency of distributions to collect around the mean point. This is just a natural reflection of the fact that most things are around average, by definition, but we humans like stories, we like to think that what we are seeing is something real, not just a statistical artifact.

We see this time and again in life. A football manager is acclaimed one season as a genius and accused of failure the next, when you look at the stats all that has happened is that they won slightly more games than the form book would indicate in year one and slightly less in year two. Whenever things are at an extreme we either proclaim a new paradigm – “The Bubble is eternal!” or start looking for reasons to explain something which may just be noise.

I find myself thinking about what this might mean for social media and engagement. If we create a more agile public space, one which is as frictionless as possible. Where people can rapidly engage with and shape policy, is there a risk that we conflate noise and reality?