6 October 2020

How mathematics can help you to stretch towards exponential thinking

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People tend to say that humans, being linear thinkers, cannot cope with the exponential change in technology because both curves don’t match and have a different speed or progress. People can only take one linear step at a time, while the speed of new technologies doubles with each step. So, they make us believe that there is no relationship between linear thinking and exponential change.

However, if we look at mathematics, an exponential curve and a linear one do match. Why, … ever heard of ‘first derivatives’? Well, the first derivative of an exponential curve, is … a linear curve. 

In fact, this means that for every point on an exponential curve we can find a linear curve that is adjacent.

Wikipedia even states : “The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus.” Measuring the sensitivity to change, that is why we, being linear thinkers, are feeling stress with these new technologies.

“But how does this theory help us to stretch towards exponential thinking?”

An

In the early days of computing, we wanted to reduce the time for calculating and programmed the computers so that they could perform complex calculations for us. Calculating complex shapes was time consuming so we looked for support by computers. In fact, in the early days of computing, we called this ‘finite element analysis’.

With finite elements we divide a complex shape or curve in small infinite steps. We treat each element as a linear element and calculate the best fitting curve as alternative for the infinite small curve.

And thus, we have to do the same with the exponential changes. If we tackle the technology one by one, and learn in small linear steps what they mean, how they can help us, what they can do for business… we can grow steadily in catching up with the exponential change rate of technologies.

Of course, it is not possible to tackle all technologies at one time, but we cannot hesitate to start implementing them. These technologies are there to make us smart, to help us grow and catch up with new business or opportunities.

In fact, we should consider these technologies as calculators, meant to help us to think faster and smart.

So, being a linear thinker, how can we stretch towards exponential thinking and increase our speed of thinking?

“So, being a linear thinker, how can we stretch towards exponential thinking and increase our speed of thinking?”

An

If we take the basics of a linear curve then there are 2 options to increase the knowledge rate. Or we increase b, the Y-intercept, or we increase a, the slope of the curve. 

In an exponential changing world increasing ‘b’ means adopting new technologies as new skills, new leverages for thinking faster.

In that same world, we can increase ‘a’, the slope of our linear thinking curve by embracing these new technologies because we trust them to help us think faster in the future. By trusting them, we can surf on the slope of the change they realize, so a small linear step will end up higher than before.

For me, this is what hybrid thinking is about: exploring, adopting and experimenting with new technologies and embrace them as calculators so that we can think faster. 

And maybe one day technology is ready to be implanted in our brains so that connection with thinking is made compatible, but until then we can proceed enormously by adopting these new technologies and skills.

“In a way it’s funny, to realize that we used this methodology to program our computers and they evolved exponentially, where we as humans have forgotten to apply this methodology to our own thinking process. But there is still time left to catch up….”

An
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