Understanding the exponential function

Professor Albert Bartlett famously said:

The greatest shortcoming of the human race is our inability to understand the exponential function.

One of the reasons that this is a ‘shortcoming’ is simply that the term ‘exponential function‘ is obscure to many. I’ve been thinking about that for some time now, and I think I have a way to describe this term in a way that (I hope) is not too difficult to grasp.

Imagine you’re walking along a path through a field.  Ahead of you, in the distance, is a white gate.

Now, pause, hold up one hand, and frame the gate between your fingers.

It’s tiny, right?

Far too small too get through! :)

As you continue to walk through the field towards the gate, at a steady pace, the gate appears to get larger and larger. But, more than this, the rate at which it gets larger accelerates, even though you’re not moving any faster. As you walk towards it, the gate gets bigger and bigger until, when you’re about ten paces from it, it suddenly begins to zoom in your field of view until… it’s plenty large enough to get through.

That, in a nutshell, is the exponential function in action.

I hope that makes sense (if not: please leave a comment!)

Now, armed with this new knowledge, you can watch Professor Bartlett’s lecture ‘Arithmetic, population and energy‘ without fear of being befuddled :)

About peNdantry

Phlyarologist (part-time) and pendant. Campaigner for action against anthropogenic global warming (AGW) and injustice in all its forms. Humanist, atheist, notoftenpist. Wannabe poet, writer and astronaut.
This entry was posted in ... wait, what?, Communication, Education, illusion, People, Phlyarology, Strategy and tagged , , , , . Bookmark the permalink.

16 Responses to Understanding the exponential function

  1. I think I’ll just stick with explanation LOL :-)

    Liked by 2 people

  2. Eric Alagan says:

    “The greatest shortcoming of the human race is our inability to understand the exponential function.”

    That’s quite a statement.

    In my opinion, perhaps most are unable to articulate /explain exponential function, as you have done so well. But for the good professor to claim that that makes it a shortcoming – now, that’s quite a statement.

    “The greatest shortcoming of the human race is the inability to look in the mirror for our problems. We are so very good at looking out the window,” said Wannabe Professor Nobody aka Eric Alagan.

    “Now, that’s quite a statement too,” said Alagan, as he leaned on his window sill – and held up a handheld mirror.

    Liked by 2 people

  3. Excellent Analogy. IT is amazing how many of us, myself included, see the white gate in the distance, so small and clearly not big enough for us to get through and so stop walking towards it. I think we are often too easily put off. I will try to remember that gate and keep walking in future.

    Liked by 2 people

    • pendantry says:

      You’ve put a slant on this that I hadn’t considered (and, good for you, it’s a good slant!).

      As for me, I think (in the context of Professor Albert Bartlett’s lecture and the problems that we’re currently facing on this planet) that the problem with the exponential function is that we keep on plodding towards a future that is, for its part, rushing inexorably towards us. And the worst part is that on the whole we’re totally oblivious of this.

      It’s hard to describe… the best advice I can give is to watch the Prof’s lecture, then you might understand where I’m coming from.

      Liked by 2 people

  4. Paco Jariego says:

    I used to like the exponential functions. Exponentials and logarithms in mathematics are like the wonderful princesses of fairy tales. Then, the technology gurus came and started to talk about exponential technologies, and exponential innovations, and all that exponential yada yada yada. And you know, you are absolutely right. Paraphrasing Iñigo Montoya’s reply to Vizzini in the Princess Bride: “They keep using that word, and I do not think it means what they think it means.”

    Liked by 2 people

  5. Your word picture explanation is great and I watched the video..he sure wraps up a whole lot in that 9 minutes..I had to stop and start a couple times to make sure I was processing the numbers , he goes so fast…

    Liked by 1 person

  6. floatinggold says:

    You explained that quite well.

    Liked by 1 person

  7. Dr Bob Rich says:

    Well done, Colin. I agree, many of humanity’s historical problems are because people think in straight lines not exponentials.
    My usual analogy is the one water weed seed landing in a pond. It produces a plant in a day. That plant only produces 2 new ones, on the next day. On the 3rd day, each of those 2 plants duplicate. Right. Eventually, half the pond is covered. How long before all of it is?
    I used to describe this when teaching statistics to students who took an Arts course to get away from mathematics.
    Most of them COULDN’T WORK IT OUT.

    Liked by 1 person

    • pendantry says:

      I’m going to leave this as an exercise for other readers; but I can’t resist admitting I know the answer. I learnt it from Professor Albert Bartlett’s lecture (which I linked at the end of my post above). I’ll also admit I might have struggled had I not watched that lecture!


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