The Knee in the Curve
or, Progress in Our Time


Exponential functions are very interesting things. I’ve been encountering them a lot recently with my reading list. Most fiat currencies are, by their very nature, exponential. Chris Martenson’s excellent book “Crash Course” explains this very well. Population growth, in the presence of sufficient resources, is exponential. (Continuing our average of 2.2 kids per couple over generations is exponential growth.) Your bank account, if you are earning a regular rate of interest (don’t we wish) and not withdrawing (don’t we wish), would be exponential.

When you look at an exponential function, there is a visual point where it turns from being mostly horizontal to being mostly vertical. There is a “knee”, the point at which the game drastically changes. You might call this the “knee in the curve”, or “the tipping point”, or “the inflection point”. It’s when the nature of things really change.

Thought processes can be like this. I have found mine to be, anyway. A thought enters my mind, and I might consider it for a moment, maybe two. If it has some validity, it might linger, and so the graph heads slightly up. I consider it more, and, being attuned to the idea, notice it in my reading elsewhere. Up some more. I read a book on the topic, perhaps correlate it with other things I understand to be true, and… perhaps it shifts my thinking, embeds itself in my view of the world, and things change drastically. I’m now on the “mostly vertical” portion of the graph.

Hopefully your life doesn’t have more than a handful of such experiences in it. They may well fit an exponential curve, and they are certainly life-changing.

Obviously, building an analogy between exponential functions and the adoption of a meme is imprecise. At any point, I might see flaws in the idea, and therefore reject it (and so the graph plummets to zero.) Or the idea may not fully register with me, so I’m not attuned to it, and I remain in the “mostly horizontal” portion of the graph, maybe for years, decades, or for the rest of my life. Despite external inputs, human brains are not calculators. I have never been able to accurately predict human outputs from even the most binary inputs, so what triggers an “exponential” response in one might not even register in another.

One more caveat about exponential functions is in regards to the scale. If you adjust the scale – if you were to “zoom in” – the inflection point moves to the left. If your idea of “expensive gas” is $1.00 per gallon, that sets your Y scale, and the inflection point is some decades in the past. If your idea of expensive gas is $3.00, that’s a different scale on the Y-axis, and we passed that point in the past few years. But regardless of your idea of where the inflection point was (regardless of what your idea of “expensive gas” is), I suspect it’s headed up, and steeply.

Now to the idea that entered my head this evening. (Will the thought go exponential? Not sure yet; still on the horizontal.)

I just read an article in Time magazine, regarding changing conceptions of heaven. Okay, okay, how can the atheist have anything to say of any bearing on heaven? Why yes, the vegetarian believes the sirloin was exquisite, why thank you, yes, thank you. But the article was walking through changing views of heaven over the decades, centuries, eons. JC originally promised his followers he would be back within their lifetimes (I could look up the chapter and verse, and may well do so and edit this, but you can find this too.) That didn’t happen. Within a few hundred years, the “bible” as we know it in the western world was pulled together (by committee) and a more official church formed. By “writing” the bible and rewriting the rules (that is, forming a church), they could reinterpret the timescale. Zoom out, and move the knee far into the future.

Pause for a minute, and visually consider a graph. The X axis is years. The Y axis is “implausibility”. Jesus has been gone for a year. How plausible are his claims (all of this is assuming you were there to witness his claims)? Perhaps quite. Ten years pass. It’s still in your lifetime, so perhaps you still believe. One hundred years pass. Your great-grandfather met Jesus, who was supposed to return and build a kingdom on earth in your great-grandfather’s lifetime. You may well still be a slave. Plausibility factor? A bit less. By 500 years, the bible has firmly been canonized and a church organized, which you might consider as a slight “zooming out” of the graph. A big organization had rewritten the rules and then thrown its weight behind those very rules, so perhaps it would seem more plausible again. But continue looking forward – 1000 years? 1500? 2000? At what point does credulity wane, and we reach that knee in the curve?

I would be amiss if I didn’t point out examples of those who have prophetized the end of the world many, many times in the past. Harold Camping was the most recent high-profile one to do so. He made an extra fool of himself by doing it twice in near succession (May 21, 2011, and then Oct 21, 2011). People have been doing this for years, and in fact they have been doing it for previous gods. Harold’s mistake was doing it twice, in a timescale that fit in people’s memories.

But perhaps they’re on to something. No matter if you guessed the year wrong… change it! After enough time passes, no matter if you guessed the god wrong… change it!

But back to the Time article: One modern preacher is teaching that heaven is not a destination, not a place to go after you die, but God’s realm that co-exists with the earthly realm. Wow. He is attempting to define away the entire X axis. Time is no longer relevant. He is trying to define away the entire thought process of considering and ultimately either accepting or denying a proposition. Despite Jesus’ claim that he would return within his followers’ lifetimes (30 years, perhaps?), and we are now 2,000 years past that, he wants to drop that claim, and say, “it just is what it is”.

A question: If you could look forward in time, and could see the world progress, unfold, rise, fall, bubble, burst, strive, be born, die, rise and fall over the ages, how would that affect your religious beliefs?

Where is the knee in your curve of incredulity, and why?

If no God presented him/her/itself by year 2100, what would you think? What about year 2,500? 3,000? 10,000? One million years? Never?

At some point, don’t you have to change your thinking fundamentally? If God didn’t come back and “save us” for 10,000 years or more… why? That is a timescale so beyond human lifetimes and human comprehension – as is a “mere” 1,000 years! – that anything beyond it is simply cruel and unusual punishment (that is, if you subscribe to the writings in the bible). What would god prove or solve by coming back in the year 1,000 versus 2,000 versus 10,000?

And I shouldn’t have to do this, but let me point out that changing to a new god is admitting the previous one was bullshit. Do you really think in the year 10,000 “Jesus Christ” will be where the action is? I’m sure some other belief will have replaced it by then.

As this relates to exponential functions:

When I was younger, even slightly younger, I would not have imagined seeing a preacher try to downplay the return of “The Lord”. That sounds like new-age bullshit: “Heaven is here, heaven is all around us.” Or at least it would have sounded like new-age bullshit 20 years ago, but perhaps the clergy is being forced that direction to stay ahead of the flock. Perhaps the flock’s credulity is waning a little. And once the shepherd yields a little to it, the sheep take up the slack, and the cycle feeds on itself. That’s exponential, my friend.

But perhaps we always live in exponential times. It’s just a matter of scale.

Regardless, I’ll take that as progress.

April 13, 2013
1387 words


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