Illustrating exponential growth using movement towards a target

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

Professor Albert Bartlett (19232013)

Ever since I first encountered this quote (in Professor Bartlett’s seminal lecture ‘Arithmetic, population and energy‘) I’ve been trying to think of ways of highlighting the problem, hoping that, in some small way, I might contribute to finding a solution. Examples of my humble offerings include ‘Bacteria in Bottles‘ (from that lecture), various attempts to publicise the ‘Impossible Hamster‘ video, and a kind of imagination exercise. I’m revisiting that last here, as I think I can do better.

… this one was just 15 paces farther on.

This is the white gate I referred to in my post four years ago (‘Understanding the exponential function‘), and, for completeness, here’s what I said in that:

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 to 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.

With thanks to Brendan Leonard (@semi_rad)
for his kind permission for me to use
the image in the header.

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, Core thought, Education, GCD: Global climate disruption, People, perception, Phlyarology and tagged , , , . Bookmark the permalink.

34 Responses to Illustrating exponential growth using movement towards a target

  1. Your climate change illustration says it all!

    Liked by 1 person

  2. No! I meant it explains exactly how the exponential function works. Trying to understand algebraic equations makes me crazy. :)

    Liked by 1 person

    • peNdantry says:

      Ah, I see. I thought you were referring to the image in the post’s header – which may not be visible to you anyway if you’re using a dumbphone. (Just in case that’s the case, here’s a link to it.)

      I don’t want to make you crazy, but I do want to ask you what your answer is to Bob’s ‘weedy’ question, below

      Liked by 1 person

      • As I am probably the last person on the planet that does not have a mobile phone, I am always able to see everything on my PC. :D
        I’m guessing the whole pond will be covered in weeds. Unless, due to climate change there is a raging wildfire, and the entire pond is dried up… ;)

        Liked by 1 person

        • peNdantry says:

          Wow, I’m impressed! I held off getting a dumbphone for years, myself, and only succumbed when my brother ‘upgraded’ his phone a couple of years ago and gave me his old one (which still works fine, though its capacity is a bit limited). I can’t deny it has its uses, but IMO it still deserves to be called a ‘dumbphone’ rather than the more positive label, as its functionality, compared with a desktop PC, is severely limited.

          (My brother, meanwhile, has ‘upgraded’ again since, and has again gifted me with his cast-off gadget: I’ve yet to switch to that as the ‘Smart Switch’ application – spun as ‘easy to use’ – doesn’t do what it says on the tin. Go figure!)

          Liked by 1 person

  3. Karenhoffen says:

    Great visual representation

    Liked by 1 person

  4. Well explained :-) <3

    Liked by 1 person

  5. Dr Bob Rich says:

    My standard illustration is more weedy.
    One seed lands on a pond. It germinates, and a water weed grows. After a set time, it generates a number of seeds, each of which grows into a new plant.
    For simplicity’s sake, each plant takes the same time to mature, and produces the same number of seeds, but this doesn’t matter. To be even more simple, let’s make this one day, and two seeds.
    OK, today, only half the pond is covered in the weed. How much of it will be covered tomorrow?
    :)

    Liked by 1 person

  6. I’m with magicmermaid – the cover illustration explained things nicely.
    The photos would have been great if we encountered a wolf at the end of the path instead of a gate.

    Liked by 1 person

  7. I love the gate analogy Cool
    ;;
    ;;
    ;;
    Laughter is like sunshine!!

    Liked by 1 person

  8. Catxman says:

    The impossible gate is similar to the river that is never the same river twice that you dip your toe into. Both are metaphysics of a lying sort. Technically it may not be the same river, but has it really changed? The impossible gate may seem far away, but doesn’t it exist in the same reality close as it does far?

    — Catxman

    http://www.catxman.wordpress.com

    Like

    • peNdantry says:

      I fear that you may be missing the point I’m trying to make. The gate is not ‘impossible’, it’s ‘inevitable’. The crux of it is the speed at which it zooms into the field of our perception (but only in the final stages, by which time we’ve habituated ourselves to the plod, plod, plod of onward ‘progress’, and are incapable of even considering changing our ingrained behaviour, even when it’s obvious what’s happening).

      Like

  9. Jean and I have now watched Prof Bartlett’s lecture. It is extraordinairly good and leaves me with a profound sense of uncertainty for anyone under the age of possibly 50; definitely 40. I have yet to read his papers, some of which were linked to in the description of the lecture, but I will. Predicting the future in 30 years is impossible, well that is how it appears to me.

    Liked by 1 person

    • peNdantry says:

      Good for you for watching the lecture, Paul! (In my opinion it needs to be aired weekly on all channels on the idiot boxes around the world.)

      I, too, cannot predict the future. But I do not think it will be a happy one for homo fatuus brutus, not to mention all the other beings on Spaceship Earth while we remain at the helm in our unenlightened, avaricious, war-mongering state :(

      Liked by 1 person

  10. Forestwood says:

    Oh I love the Hamster example. I have always wondered why there is this obsession, no this obsessive fixation with exponential growth when the earth and its resource are finite!

    Liked by 2 people

    • peNdantry says:

      I put it down to greed, myself.

      Liked by 1 person

      • I think it is more complex than just greed. There are huge swaths of the population who have very little and many have a desire to improve their lot. Then a very small proportion of people get hooked on taking more and more, and that includes power and influence. And It is all very well for me to say that because I have sufficient and am at the age where I haven’t got many years left. But years ago I ran my own business and was intent on growth and never stopped to consider the wider implications of what I was doing.

        Then there is the question of population. It is too large and yet still complex because who is to say that group B can continue to grow larger while group A have to restrain them selves. As Forestwood says is, for some, an obsessive fixation. But still more complex and I do not have the answers; far from it!

        Liked by 1 person

        • peNdantry says:

          I still think it’s greed. Those whose needs aren’t satisfied strive to satisfy those needs… and when their original needs are satisfied, they find that they have other unsatisfied needs that they didn’t recognise before. Rinse and repeat; it becomes an addictive habit; one that can never, ever be satisfied.

          As for your observation on population; I’m not sure where that’s coming from, nor how it relates. Who are your ‘group A’ and ‘group B’, and in what manner are they treated differently? I see no ‘groups’; I see a seething mass of humanity ‘sharing’ (yeah, right) Spaceship Earth. Population growth is population growth, and even a ‘tiny’ 1% annual growth means the population will double in just one human lifetime.

          Like

          • I agree about population growth in general. But those that are ethnically disadvantaged are encouraged to get themselves out of the mire, not literally of course, whereas those that have life’s’ advantages are told enough is enough.

            Like

          • peNdantry says:

            I think it a crying shame that some can’t find it in themselves to use their more than enough resources to help their neighbours who are disadvantaged (in whatever manner) out of their (often quite literal) mire.

            Especially when, in many cases, it’s the former who have directly created the plight of the latter.

            Like

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