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 🙂

Posted in ... wait, what?, Communication, Education, illusion, People, Phlyarology, Strategy | Tagged , , , , | 16 Comments

Yeah, I got Issues about Climate Change.. Turns out a Lot of People do..

I can sympathise with this.
(Note: the comment thread is revealing, too.)

Climate Denial Crock of the Week

What about it?


NEW YORK (Thomson Reuters Foundation) – Depression and anxiety afflict Americans who are concerned with the fate of the environment, according to a study of the mental health effects of climate change.

Most hard-hit are women and people with low incomes who worry about the planet’s long-term health, said the study published this week in the journal Global Environmental Change.

Symptoms include restless nights, feelings of loneliness and lethargy.

“Climate change is a persistent global stressor,” said Sabrina Helm, lead author of the paper and professor of family and consumer sciences at the University of Arizona.

Risks to mental health from climate change are a “creeping development,” she told the Thomson Reuters Foundation.

Due to climate change, scientists predict sea levels are on track to surge as temperatures rise, posing threats such as deadly heat, extreme weather and land swallowed by rising water.

World leaders mobilized…

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Posted in ... wait, what?, balance, Biodiversity, Climate, Communication, Core thought, Environment, GCD: Global climate disruption, Health | Tagged , , | 7 Comments

How to increase your blog following

TL;DR ~~

  1. Using the floaty ‘Follow’ button in WordPress only makes posts visible in the WordPress Reader. If you want to ‘follow’ someone and be notified by email when they post, you need to ‘follow by email’, which is different.
    Bottom line: Put a highly-visible follow-by-email button on your site.
  2. Gain an immediate (and impressive!) follower count boost by linking your accounts on Facebook, Twitter and other platforms to your WordPress account. But beware: if your blog has a high post count before you do, you may upset your followers…

For years, my follower count was at 130. It didn’t matter what I wrote about, nor how objectively ‘good’ the posts were; that number remained resolutely static.

And then I discovered The Daily Post‘s First Friday, a weekly open thread where any new blogger can share a link to their very first post with the larger WordPress.com community. Spending some time visiting, liking, commenting on and following the new blogs advertised there pays dividends; my follower count increases steadily when I do this, although it is a pretty time-consuming exercise.

(The Daily Post also features Community Pool, where more established bloggers can highlight their own blog posts every Monday. This is one way to reach a new audience.)

Some (not all) bloggers have a ‘follow-for-follow’ policy, so anyone who follows them gets followed back. I know of one blogger who owned up (and kudos to them for their honesty) to using this technique to build up a following of over 1000 in a relatively short space of time. You may — or may not — wish to utilise such a tactic yourself.

But the really big surprise came when I linked my Twitter and Facebook accounts to my WordPress blog: my follower count jumped from 196 to 503! So perhaps this is how those blogs I see with ‘followers’ in the thousands get those silly numbers?

I did some digging in the support forums, and found this:

If you have connected any of your social networking services (such as Facebook or Twitter) through our Publicize feature, counts for your followers on those services will also be shown.

… the sad thing (for me) is that I found one day, soon after I’d allowed the connection between WordPress, Facebook and Twitter, that The System was reposting old posts (like, from long, long ago) to my Facebook and Twitter feeds. Needless to say, I immediately disconnected these erring things — spam sucks, and no spam sucks more than old spam. Sure enough, my follower count dropped back to near 200 once again.

I got in touch with a WordPress Happiness Engineer about this spam problem. I was told that ‘Publicize’ will share old posts if they weren’t shared in the past, and that if I didn’t want certain posts to be shared, I could disable it on specific posts.

The problem is: I currently have over 400 published posts… and the thought of going through all of those and manually disabling the shares on each of them gives me a severe case of the screaming heebiejeebies!

The Happiness Engineer admitted that the only option is to automatically share each post and then manually turn sharing off again after publication. One other idea is to skip the automatic publishing and use the share buttons to manually share the posts instead. Neither of which is ideal (and for the purposes of this post, neither one increases your follower count).

So, learn from my mistake: if you’re going to share your blog to other platforms, do it before your blog post count gets too high!

Posted in ... wait, what?, Communication | Tagged , , , | 58 Comments

Seeing three dimensions in two dimensions

Let me tell you right off the bat here that this isn’t an April Fool’s post. I promise you that.

I’ve just learned from The Observation Post that April is apparently ‘National Humor Month’*; this post isn’t meant to be funny. I promise you that, too.

I can already hear you asking: “Well, if this isn’t meant to be a jolly jape, what are you blithering on about, man?”.

I’ll tell you what I’m blithering on about: autostereograms.

Here’s one (click on image to embiggen):

An autostereogram to demonstrate 3D viewing of a 2D image

Image credit: Gene Levine via Wikimedia Commons

It’s not a very exciting example, but there are no copyright restrictions on my using it here.

“But what is it?” I hear you say…

Well, this image has been created in such a way that if you unfocus your eyes in just the right way, you’ll be able to perceive it in three dimensions, not just the two it appears to be. Your best bet is to click on the image here so that you can see a larger copy of it. Just relax your eyes and try looking through the image. It may take you a few minutes before you get it.

You can tell if you’ve succeeded by moving your head from side to side; if you’ve got the right focus you’ll be able to see depth to the image.

As I mentioned, this isn’t exactly the most exciting example of an autostereogram. But there are loads of them on the web, just search for autostereogram. Some images are better than others: here’s a particularly good one by Scott Pakin.

You can get posters of autostereograms to hang on your wall to amaze your friends. I have a couple myself, one’s quite an impressive example, featuring an underwater scene — the way the shark leapt out at me the first time was quite an experience, let me tell you…

… and if you do think I’m pulling your leg, please let me know in the comments 🙂

* Going by the u-less spelling of ‘humour’ I assume that the ‘nation’ in question is the USA.


Posted in ... wait, what?, art, illusion, Phlyarology | Tagged , | 21 Comments

Climbing the Ladder of Awareness

Just so there can be no doubt, the following are not my words, they belong to Paul Chefurka. I reproduce them here because I believe they are insightful and worth repeating.

Climbing the Ladder of Awareness
by Paul Chefurka

This article may be reproduced
in whole or in part, in any manner
and for any purpose whatsoever,
with no restrictions.

When it comes to our understanding of the unfolding global crisis, each of us seems to fit somewhere along a continuum of awareness that can be roughly divided into five stages:

Dead asleep. At this stage there seem to be no fundamental problems, just some shortcomings in human organization, behaviour and morality that can be fixed with the proper attention to rule-making. People at this stage tend to live their lives happily, with occasional outbursts of annoyance around election times or the quarterly corporate earnings seasons.

Awareness of one fundamental problem. Whether it’s Climate Change, overpopulation, Peak Oil, chemical pollution, oceanic over-fishing, biodiversity loss, corporatism, economic instability or sociopolitical injustice, one problem seems to engage the attention completely. People at this stage tend to become ardent activists for their chosen cause. They tend to be very vocal about their personal issue, and blind to any others.

Awareness of many problems. As people let in more evidence from different domains, the awareness of complexity begins to grow. At this point a person worries about the prioritization of problems in terms of their immediacy and degree of impact. People at this stage may become reluctant to acknowledge new problems – for example, someone who is committed to fighting for social justice and against climate change may not recognize the problem of resource depletion. They may feel that the problem space is already complex enough, and the addition of any new concerns will only dilute the effort that needs to be focused on solving the “highest priority” problem.

Awareness of the interconnections between the many problems. The realization that a solution in one domain may worsen a problem in another marks the beginning of large-scale system-level thinking. It also marks the transition from thinking of the situation in terms of a set of problems to thinking of it in terms of a predicament. At this point the possibility that there may not be a solution begins to raise its head.

People who arrive at this stage tend to withdraw into tight circles of like-minded individuals in order to trade insights and deepen their understanding of what’s going on. These circles are necessarily small, both because personal dialogue is essential for this depth of exploration, and because there just aren’t very many people who have arrived at this level of understanding.

Awareness that the predicament encompasses all aspects of life. This includes everything we do, how we do it, our relationships with each other, as well as our treatment of the rest of the biosphere and the physical planet. With this realization, the floodgates open, and no problem is exempt from consideration or acceptance. The very concept of a “Solution” is seen through, and cast aside as a waste of effort.

For those who arrive at Stage 5 there is a real risk that depression will set in. After all, we’ve learned throughout our lives that our hope for tomorrow lies in our ability to solve problems today. When no amount of human cleverness appears able to solve our predicament the possibility of hope can vanish like a the light of a candle flame, to be replaced by the suffocating darkness of despair.

How people cope with despair is of course deeply personal, but it seems to me there are two general routes people take to reconcile themselves with the situation. These are not mutually exclusive, and most of us will operate out of some mix of the two. I identify them here as general tendencies, because people seem to be drawn more to one or the other. I call them the outer path and the inner path.

If one is inclined to choose the outer path, concerns about adaptation and local resilience move into the foreground, as exemplified by the Transition Network and Permaculture Movement. To those on the outer path, community-building and local sustainability initiatives will have great appeal. Organized party politics seems to be less attractive to people at this stage, however. Perhaps politics is seen as part of the problem, or perhaps it’s just seen as a waste of effort when the real action will take place at the local level.

If one is disinclined to choose the outer path either because of temperament or circumstance, the inner path offers its own set of attractions.

Choosing the inner path involves re-framing the whole thing in terms of consciousness, self-awareness and/or some form of transcendent perception. For someone on this path it is seen as an attempt to manifest Gandhi’s message, “Become the change you wish to see in the world,” on the most profoundly personal level. This message is similarly expressed in the ancient Hermetic saying, “As above, so below.” Or in plain language, “In order to heal the world, first begin by healing yourself.”

However, the inner path does not imply a “retreat into religion”. Most of the people I’ve met who have chosen an inner path have as little use for traditional religion as their counterparts on the outer path have for traditional politics. Organized religion is usually seen as part of the predicament rather than a valid response to it. Those who have arrived at this point have no interest in hiding from or easing the painful truth, rather they wish to create a coherent personal context for it. Personal spirituality of one sort or another often works for this, but organized religion rarely does.

It’s worth mentioning that there is also the possibility of a serious personal difficulty at this point. If someone cannot choose an outer path for whatever reasons, and is also resistant to the idea of inner growth or spirituality as a response the the crisis of an entire planet, then they are truly in a bind. There are few other doorways out of this depth of despair. If one remains stuck here for an extended period of time, life can begin to seem awfully bleak, and violence against either the world or oneself may begin begin to seem like a reasonable option. Keep a watchful eye on your own progress, and if you encounter someone else who may be in this state, please offer them a supportive ear.

From my observations, each successive stage contains roughly a tenth of the number people as the one before it. So while perhaps 90% of humanity is in Stage 1, less than one person in ten thousand will be at Stage 5 (and none of them are likely to be politicians). The number of those who have chosen the inner path in Stage 5 also seems to be an order of magnitude smaller than the number who are on the outer path.

I happen to have chosen an inner path as my response to a Stage 5 awareness. It works well for me, but navigating this imminent (transition, shift, metamorphosis – call it what you will), will require all of us – no matter what our chosen paths – to cooperate on making wise decisions in difficult times.

Best wishes for a long, exciting and fulfilling journey.

Bodhi Paul Chefurka
October 19, 2012

Posted in balance, Biodiversity, Climate, Communication, Core thought, Education, Environment, GCD: Global climate disruption, Health, History, People, Strategy | Tagged , | 13 Comments

The main character in ‘The Wooden Groat’

So, anyway, I wrote this short story. It’s called ‘The Wooden Groat’. And I thought that the main character’s name was Andy, Andy Fletcher. There are two other characters in the story: one is Bernard Marlin, the other is Gerry Taverner. And all the while, while I was writing it, I was thinking that the main character was Andy… but it turns out that, at least according to WordCloud, I was completely mistaken:

If perchance, you’re interested in reading my short story, it’s available on Scribophile (you have to register to read it).

Posted in ... wait, what?, art | Tagged , | 10 Comments

The litany against FB

Hat tip to Dreamwalker’s Sanctuary for pointing me at this video:

Here are some words I wrote a few years ago (ok, so most of them belong to Frank Herbert, they’re taken from his fabulous Dune saga)…

No entry sign with 'FB' insideI must not FB.
FB is the mind-killer.
FB is the little-death that brings total obliteration.
I will face my FB.
I will permit it to pass over me and through me.
And when it has gone past I will turn the inner eye to see its path.
Where the FB has gone there will be nothing.
Only I will remain–
— ooooo, shiny! [This text should be invisible]

I’ll end this post with a link to a very insightful piece by Anya Bettoney on
social media anxiety.

Posted in ... wait, what?, balance, Communication, Computers and Internet, Culture, Just for laughs, Phlyarology | Tagged , , , , , , , | 23 Comments

Data Driven: Colbert on Cambridge Analytica

Finally, someone goes on air to highlight the dissonance between the mouthings and the motives of the advertising industry. Oh, and some other stuff, about Facebook…

Climate Denial Crock of the Week

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Posted in ... wait, what?, Business, Communication, News and politics, Phlyarology | Tagged , , , , | 14 Comments

New writers start here: Scribophile

I recently joined an online writing community called ‘Scribophile‘, following a recommendation from fellow blogger DHH.

Scribophile’s website is very well designed. There are the usual personal profile pages, forum, blog and FAQ, but for me the main draw is its comprehensive critiquing system, based on ‘karma’. It’s really quite neat: you earn karma for critiquing others’ works, and then spend your karma to post your own writing for others to rip apart comment on. It’s a mutually beneficial arrangement. It’s not possible to game the system; you can’t avoid doing your fair share of critiquing if you want to post your own work.

Possibly best of all, there’s a free option. It’s fully functional, although limited (for instance, as a ‘basic’ — free — member you can only have a total of two pieces of writing up for critique at any one time — whereas a ‘premium’ member enjoys unlimited works). So it needn’t cost you a penny to test the waters.

If this is of interest to you, when you get there please do look me up!

In other news, I’ve also joined a writing group near where I live, but that means I have to go out into the big wide world to meet people face to face… scary!

Posted in Communication, Computers and Internet | Tagged , , , | 33 Comments

Poetry word cloud

What better way to remember a nifty website address and thank the provider of same — than a reblog?

Blue Sky Days 365

I’ve been playing around on wordclouds.com

This is the word cloud of my poetry text, shaped as a heart as “love” is my most often used word with 22 occurrences in 52 poems… what can I say? I’m just a romantic at heart.

Poetry wordcloud

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Posted in ... wait, what?, Communication, Computers and Internet | Tagged | 17 Comments