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Exponential change

Updated: Sep 8, 2021

How can it be that a 4% growth rate means a doubling in 20 years?  How can it be that if 1% of a market starts adopting something, that 100% will adopt it within half the time that the first one percent got there?    Wikipedia is a great first stop for understanding – and here’s the formula for Exponential Function.

exponential function

So, as x increases, b is increasing to the power of x.

hockey stick graph

This translates as slow takeoff until a tipping point is reached, then major acceleration. We understand this slow takeoff to tipping point from a marketing and branding perspective (and whipping cream – you whip for ages and ages and then suddenly, it thickens and can go too far in a nanosecond), but I’m now realising it applies to many things and doesn’t sit well with our largely linear thinking brains (what happened yesterday informs what happens today). I note that worryingly, the graph looks a bit like the hockey stick graph that has caused so much controversy in the climate change discussion.

climate change hockdy stick

Exponential growth in anything will always reach a tipping point that causes a graph to swing wildly upward.  We have exponential growth in terms of our population, technological development, our resource consumption and even in changes to our paradigms or world views (Hawkins (1983)).  Our consumption doubles every few years as indicated in the picture below from

Saravanan's image.png

Saravanan is an engineer from India whose blog has a great overview of the threats to human survival on the planet.

Science fiction is heading towards science fact as the digital age progresses and exponential growth in computing technology (Moore’s law) continues apace.  Futurists such as Ray Kurzweil believe we are headed for a singularity – the place where human and artificial intelligence meet.  Ray postulates that our minds (software) will become downloadable and our bodies (hardware) upgradable.  In his book The Singularity Is Near, Kurzweil argues that artificial intelligence will augment human intelligence as the next stage of natural evolution. He predicts a merging of human and machine that will allow humans to transcend biological limitations to the point where the singular (augmented) human will be immortal by the end of this century.

Hilbert and Lopez discuss the exponential nature of the world’s technological capacity. This from (retrieved Jan 2, 2016) referencing this February 2011 article from Martin Hilbert and Priscila Lopez.

“Between 1986 and 2007, machines’ application-specific capacity to compute information per capita has roughly doubled every 14 months; the per capita capacity of the world’s general-purpose computers has doubled every 18 months; the global telecommunication capacity per capita doubled every 34 months; and the world’s storage capacity per capita doubled every 40 months.”

Futurist Gerd Leonhard says we’re at the pivot point, or the tipping point of exponential technological change and that this will cause humanity to change more in the next 20 years than in the previous 300. This analysis is rooted in the exponential formula outlined above.  Gerd says that despite our knowledge of exponentiality, we still vastly underestimate the sheer velocity of change. We are facing exponential change in so many areas, that he’s coined a term – combinatorial – to describe multiple areas of digital change. Gerd’s slides available here

The ramifications for every area of our lives are massive, almost unfathomable.  Our responses now are what’s important – let’s not do an EMI records or other big names from that industry (forgotten what they were!)- and try to stop the tide.  You’ll die, as they have. Now after a period of time in the doldrums the music industry has found a new business model, but the profits aren’t going to the old record companies, it’s Apple, Google, Youtube, Spotify and Pandora that are making the cash. These tech companies have entirely disrupted this and other industries.  Google thinks of the new reality as an ‘ecosystem of intelligence: software, devices, the cloud, objects, things…and people’. (Gerd) . That looks like some serious change and serious disruption.  My sense is that every industry or organisation needs to start thinking about where exponential change might take it.  And one thing’s for sure…

In times of change, the greatest danger is to act with yesterday’s logic – Peter Drucker

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