Illustrating exponential growth using movement towards a target, revisited

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

Professor Albert Bartlett (19232013)

Back in May, I used a series of photos taken at regular intervals along a footpath in an attempt to illustrate exponential growth. Last month, I happened to be walking that same path once again. That day was not a bright, sunny one; it was instead bitterly cold, and a freezing fog obscured the view ahead (cue the ignorant climate science deniers crying, “Global warming? What global warming?”). Halfway along the path, it suddenly struck me that this would be a far better way of portraying a journey into a murky future. I retraced my steps to the start of the path so that I could repeat the exercise, once again taking snapshots fifty steps apart….

… this one was just 15 paces farther on.

As I was preparing this post, I realised something else: I had been walking at a steady pace along this 415-step-long path. But our collective acts of destruction of Spaceship Earth are not happening at a constant rate: the suicidal fixation on growth of Those Who Lead Us (while they give lip service to the need to address the climate emergency) is accelerating the damage we’re doing to our home.

So, perhaps an even more appropriate representation of the reality would be if these snapshots were taken, not at regular intervals, but at increasing ones. The choice of the rate of increase is, of course, an arbitrary one; let’s take 7%, which, in financial terms, represents a ‘modest’ doubling time of ten years. If the second photo were taken at 50 paces, at such a growth rate the third would be at 53.5 paces (50 times 1.07), the third at 57.245 paces, and so on. The set would comprise just eight images, not ten. I’ll have to wait for another freezing fog day to take those photos; in the meantime, I’ll leave its visualisation to your imagination.

When I reached the end of the path, I noticed the green sign on the gate. That was there back in May, and I’m pretty sure it’s been there for years. I’ve passed it many times, but have never paid it any attention: ‘familiarity breeds contempt’; we tend to remain oblivious to the obvious.

Here’s a close-up of that sign:

Samaritans invitation: 'Talk to us, we'll listen', telephone 116 123 (UK).
Samaritans invitation: “Talk to us, we’ll listen”

In the context of the climate emergency, this notice is ironically, bizarrely, appropriate. If you’re on any stage of Paul Chefurka’s ‘Ladder of Awareness’ that’s causing you distress, I hope that you’ll reach out for help.

In Pandora’s Box
Hope’s frosty note lay unread:
“Down pub getting drunk.”

Me, 2021

As for me, I’ve been in ‘Stage 5 Awareness’ for some time, oscillating between despair and (perhaps foolish) hope. Paul talks about dealing with ‘Stage 5’ via either an ‘inner path’ or an ‘outer path’. I’m now on what I like to think of as a ‘holistic path’, a combination of the two. Although I find it implausible, given the overwhelming numbers who are still ‘dead asleep’ (as Paul puts it), humanity may yet be able to avert catastrophe. Despite the word ‘woke’ having been hijacked as a term of denigration by those determined to carry on with business as usual whatever the cost, I believe that whether our civilization (or indeed our species) survives is wholly dependent upon how quickly those currently oblivious to, or in denial of, the reality wake from their complacent slumber. (If they don’t, we’re all truly screwed.) I won’t stop banging the ‘alarmist’ drum, because it’s crucial not to abandon all hope.

‘Climbing the Ladder of Awareness’

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.

9 Responses to Illustrating exponential growth using movement towards a target, revisited

  1. Dr Bob Rich says:

    To me, the best example of exponentials is the story of the invention of chess.
    “What reward would you like for this magnificent game?”
    “Majesty, I will be satisfied with one grain of rice on the first square, two on the second, four on the third, eight on the fourth, and so on to the end.”
    This would have amounted to 18,446,744,073,709,551,615 grains
    which was more than the entire stock of the empire. So, the emperor put the fellow to death instead.

    Another great illustration is: a waterweed seed lands on a lake. It grows into a plant, which sets seeds, and once the process is started, the weed-covered area doubles each day. Today, the lake is half-covered. Right, how many days until all of it is covered?

    Liked by 1 person

    • peNdantry says:

      I don’t deny that those aren’t good examples, Bob – for those who are comfortable with numbers. What I’m trying to do here is use the ‘a picture paints a thousand words’ idea.


  2. Amazing stuff, but my head is still like that fog. 🤣😎🙃

    Liked by 1 person

  3. Does this path get busy? I wonder what prompted the sign on the gate. Quite… random? I like it though!

    Liked by 1 person

    • peNdantry says:

      That footpath is well-trodden; it leads from the village to the railway station. I suspect that the sign on the gate (which is an entry to the station platform) may be for those who pass who may be considering throwing themselves in front of a passing train. (I have actually been in that situation myself, but that was long ago, and I got over it.)

      Liked by 1 person

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