When I started university I thought I would be a math major.  I had always been pretty good at math, and, just as importantly, I had always enjoyed it.  Things went well reasonably well until the second semester, when we started working with n-dimensional matrices.  Because I couldn’t visualise n dimensions, I had real problems with this.  It was all those extra dimensions that knocked me off the math track.

Reading The Trouble With Physics by Lee Smolin brought this memory back to me. It is an excellent book, which I strongly recommend. Smolin describes the state of play in physics today. His primary question is why haven’t we had any major empirically supported breakthroughs in physics in the past twenty years? He discusses several reasons for this – but his main contention is that the reason is that physicists have spent the bulk of that time on string theory, which, while beautiful, is very difficult (impossible?) to verify empirically.  The story will be interesting to anyone curious about modern physics, or in the scientific process as Smolin spends the last 1/3 of the book discusssing how physicists might best proceed given some the difficulties with their dominant research program, string theory.

Smolin’s discussion of difficult technical issues is outstanding.  One thing that struck me is that most of the versions of string theory that are possible require extra dimensions – usually 10 dimensions plus time.  This is what sent me back to freshman year math!  It also got me thinking – most of us actually struggle with just three dimensions when you add time in.  This was brought home quite strongly when I ran across a post on The Long Now Blog which talked about a website called Artificial Owl (the source of the picture at the top of this post).  Artifical Owl contains a series of posts describing and showing abandoned man-made creations.  This is overwhelmingly appealing for anyone that has ever been a fan of Ozymandias… It’s also interesting for anyone involved with innovation.  There are two key points to consider.  The first is that new innovations always (well, nearly always) destroy existing technologies or ideas.  In innovating, we are making newly abandoned man-made creations. In other words, the innovations don’t just exist in three dimensions, they exist in three dimensions plus time.  Artificial Owl shows us how often we underestimate the impact of time.

The second point is that all innovations have a lifespan.  We often forget this.  If you haven’t yet, be sure to read the cover story from the March issue of Wired, which describes the rise and fall of the Gaussian copula function.  This formula originated in 1999, and then became the mathematical foundation for a number of financial innovations, including most forms of Credit Default Swaps and especially Collateralised Debt Obligations.  In light of recent events, most of these innovations had a lifespan of about 8 years.  Many innovations last longer than this, and quite a few don’t make it this far.  In my innovation strategy class, several students have been interested in sustainable innovation.  I’ve told them that the key to sustainable innovation is to develop ideas that are likely to have a long lifespan.  Which means that again we have to be able to think well in three dimensons – plus time.

As the years have passed, I still struggle with n-dimensions.  But I’ve gotten quite a bit better at thinking about time and working in four dimensions.  I think this is an important skill for all of us to develop.  It’s time to start innovating in four dimensions instead of just three.