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Our greatest shortcoming is our inability to understand the exponential function

206 points| itistoday | 16 years ago |youtube.com | reply

124 comments

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[+] netcan|16 years ago|reply
A lot to learn from this video about explaining things:

- Know your stuff. It's obvious he's been over all of this hundreds of times.

- Figure out great analogies and other aids. Part 3: 5:20 he makes an analogy out of multiplying bacteria in a bottle that fill it in an hour to show us at what point of the exponential function you notice your in one. It's got two parts and is very effective. It allows him to say things like "5 minutes before the bottle is full."

- Introduce your aids gradually and keep using them. Make clever decisions about your aids and make sure they accumulate to a powerful toolset. After that analogy which all the time he introduces the analogy above he has:

  - A trick for calculating doubling time 70/annual growth in %
  - A graph
  - A table 
  - An example (Boulder) that he keeps running scenarios on. 
  - The bacteria analogy 
  
By the time he's 20-30 minutes into a lecture, this guy has a very powerful vocabulary built up. He can take something like oil consumption and examine it with you very quickly using these tools. The bacteria in a bottle analogy is a great example of this. Once he's explained it (kind of hard) and practised it once or twice, he can say "What time is it?" and immediately have his audience understand something relatively complex. .
[+] mhartl|16 years ago|reply
Before people freak out about exponential growth, please consider John McCarthy's Slogan. (Yes, that John McCarthy; Lisp isn't the only thing he's done.)

  He who refuses to do arithmetic is doomed to talk nonsense.
http://www-formal.stanford.edu/jmc/progress/index.html

Based on reactions to this video (among other things), I'd add Hartl's Counterpoint:

  Just because you're willing to do arithmetic doesn't 
  mean you're not talking nonsense.
In case you're wondering why you shouldn't freak out, I offer you this: http://en.wikipedia.org/wiki/Logistic_function
[+] wazoox|16 years ago|reply
Huh. This guy is simply making the very basic point that politicians, economists and bankers selling us "growth" as a solution to unemployment, debt, etc are plainly lying. Growth (population, GDP, energy availability, etc) will stop at some point. An economy that relies entirely on growth to merely function is doomed to fail spectacularly at some point in time.
[+] gursikh|16 years ago|reply
Dr. Albert A. Bartlett is fully cognizant of that point. He says in part 8 of that video:

  "Except for the petroleum graphs, the things I tell you are
  not predictions of the future. I am only reporting facts and
  the results of some very simple arithmetic." (1:22)
He acknowledges the potential fallibility of his estimations. He goes on to say:

  "Please you check the facts. Please check my arithmetic. if
  you find errors, please let me know. But if you don't find
  errors, I hope you take this very very seriously."
[+] seabee|16 years ago|reply
The video also makes the point that people are ignorant of the exponential function's effect, believing that constant growth is possible, when it clearly is not.

The Dr. also mentions that 0% growth is inevitable, so that is covered - but I had no idea it was called the logistic function, thanks.

[+] rsheridan6|16 years ago|reply
In the context of population growth, the logistic function means that something has made it stop. He dealt with this is the second video - he says we'll get zero population growth one way or another, because exponential growth forever is impossible.

Around minute 7 of the second video (did you actually watch it?) he points out that many of the checks on population growth are generally considered bad things - war, famine, disease (the alternative being birth control). This is hardly a reason not to freak out.

[+] abrahamsen|16 years ago|reply
To the point: What seems like exponential growth often turn out to be better described as S-curves.
[+] fburnaby|16 years ago|reply
The reason that the curve levels out for biological populations is that the rates at which members start starving to death or killing each-other increases to cancel out the birth-rate. That does seem to be of some concern.
[+] jluxenberg|16 years ago|reply
Neat math trick from the video:

70 / x = number of years of constant growth required for a quantity to double given that it grows at x percent

The example used in the video: if the price of lift tickets goes up by 7% per year, in 10 years, that price will double.

(and actually, the constant 70 is an approximation, the actual constant is ln (2) * 100)

[+] chaosmachine|16 years ago|reply
It's also a useful way to tell when your investments will double in value. 5% interest: 70/5 = 14 years to double your money.
[+] jackowayed|16 years ago|reply
I've thought about his point that lowering the death rate makes the problem of population growth worse a lot, especially in the context of Africa and the like.

"Oh they're starving because they get almost no rain, so that land really shouldn't support anywhere near as many people as are there. Let's give them food aid."

10 years elapse, and say they're getting 7% per year growth thanks to food aid keeping them from starving, lack of contraception, etc.

"Oh, there's twice as many of them now, so they're starving despite our current food aid. Double the food aid!"

Repeat until you realize that you can't double the food aid forever.

[+] fleitz|16 years ago|reply
"We" won't need to give "them" food aid forever, population growth levels off as wealth increases. Possibly the best thing that could be done for Africa is to end farm subsidies and argicultural tarrifs in the developed world.

Here is a great link to the farm subsidies recieved in Manhattan, it's odd how one never notices the wealth of family farms surrounding central park. http://wildgreenyonder.wordpress.com/2007/10/

[+] ihodes|16 years ago|reply
The trick is realizing that the last 3 words of your third sentence are the most important part of your slightly offensive post. That, and education.

Starving a people until they can eat off of the barren land they inhabit is certainly one way of taking care of the problem. Educating them on the merits of contraceptives, and teaching them how to use their land to greater effect is another.

[+] derefr|16 years ago|reply
Then send them yams and pomegranates. ;)

(For those unaware, they both contain progesterone; wild yams were the first plant to be used in synthesis of birth control pills.)

[+] prodigal_erik|16 years ago|reply
I'm not usually a fan of long talking-head videos but this was absolutely worthwhile. What's most chilling is the story of the bottle and the bacteria, and the realization that somehow finding a whole new planet would only tide us over for a couple more generations, after which we'd need two more....
[+] DaniFong|16 years ago|reply
There is no sustainable growth without sustainable decay. Makes you wonder about those financial systems based on economies with compounded interest -- exponential growth -- which are supposed to be resident on a finite planet.

The population bomb is kinda heading the other direction though. People moved to cities, where kids were a liability instead of an asset, life was exciting, and women had opportunities. Now birth rates in modernized countries are below the replacement rate (which causes exponential decay as impactful as exponential growth), which is largely made up through immigration.

In the limit case, birth rates in modernized countries are close to zero, and the entire population is comprised of newcomers from the places that are above the replacement rate. These countries could places for opportunity, not familyeither be like companies (where people work and live much of their lives but don't replenish themselves), or they could be like retirement homes.

[+] zemaj|16 years ago|reply
But it's all considered in a vacuum. Even though the majority of the population don't understand the problem, this is ok. We have an economic system that benefits those who predict impending needs and place themselves in situations to provide for them.

Take a look at the green industry ramping up. In the not too distance future, I think most of us here expect oil replacement to be highly profitable.

I disagree with these doomsday predictions from pure arithmetic. It seems to me that the reverse is true - exponential "problems" provide the core drive for our economy. What drives the entire start-up industry? I'd say it's identifying profitable exponential growth scenarios and providing for them. To me, this explains how primarily capitalist countries tend toward stability, until them become strangled by ever increasing regulation (that's not to say I'm against regulation in general, but I think we need to be as proactive about removing it as we are about adding it [wow, I went off topic there]).

[+] barmstrong|16 years ago|reply
Certainly a great video.

But one thing I didn't like about the bacteria in the bottle story was that he conveniently switched to 100% growth for that example. And then made it sound like Boulder was in the same position "it's 11:59 in the Boulder valely" etc.

But still his main point it dead on.

[+] jackowayed|16 years ago|reply
The best illustration of the concept, imo, is that with sustained 1.3%/year world population growth, we'll reach a population density of 1 person per square meter of land in only 780 years.
[+] redorb|16 years ago|reply
give me some context; how many meters per a person are we at currently? / Then give me some focus; what will it be at in my life span... 50 years?
[+] robryan|16 years ago|reply
At some point though there will be some kind of event to bring this down. Might be a population number or a resource usage spot, very unlikely to the world could remain at peace as certain countries loss large chunks of people to famines ect, people that have nothing to live for wouldn't want to go down without a fight.
[+] pmiller2|16 years ago|reply
People don't understand exponentials very well because human perception is scaled logarithmically. For example, both the apparent magnitude scale for celestial objects and the loudness scale for sounds (measured in decibels) are logarithmic.
[+] raimondious|16 years ago|reply
If our perception is scaled logarithmically, wouldn't that give us an intuitive sense for exponentials?
[+] aresant|16 years ago|reply
Part of the problem is that the distant future to humans is never any further out than ~70 years - eg our lifespans.

Exponential resource waste, population growth, etc doesn't become a non-survivable event for a few more generations - at that point we may actually start to see realistic change.

[+] jwegan|16 years ago|reply
Definitely worth watching the entire series, but for those looking to save time: the first video covers the main point and the subsequent videos in the series just reinforce its significance.
[+] indrax|16 years ago|reply
I think we actually do have a deep implicit understanding of the exponential function, and THAT may be our greatest shortcoming. We don't understand it precisely, and we don't intuitively relate to "4^x".

But we very intuitively get things like "really big changes will come from small things" And we rate highly getting a seemingly small increase in personal ability. This is why videos like this can capture our attention at all. It seems like a basic ability to recognize and reason approximately about exponential growth is required to do agriculture.

I think this is why we like RPG's and katamari damacy, and talking about peak oil.

I think that this mental flag also makes us extremely sensitive of people 'from the wrong tribe' being in our area.

In short, I think that we were surrounded by exponential functions in our ancestral environment, and developed an ability to recognize them and see them as very important, with out really knowing what they are.

[+] iamwil|16 years ago|reply
I haven't gotten back into the habit of watching lectures in a while, but this was one of the best ones I've watched in a long time. Thought it was super cheesy at first, and didn't think I was going to keep watching, but it kept me rapt the entire time.
[+] ModelCitizen|16 years ago|reply
A note on the rest of the series: He spends the remaining time outlining some impending Malthusian catastrophe / peak oil scenario. For a counterpoint, check out anything by Julian Simon.
[+] skybrian|16 years ago|reply
Actually, he doesn't think much of Julian Simon and says why.
[+] madair|16 years ago|reply
In part three he brilliantly draws a distinction between the objective sciences and others and subtly, if I'm understanding correctly, critiques a proponent of uncontrolled population grown by pointing out that the proponents degree from the same university is not a degree in "mathematics, in science, nor in engineering".

Feynman made explicit observations on this topic, quite critical ones, if I remember right.

[+] KingOfB|16 years ago|reply
Anyone find any good graphs about population growth? I asked wolframalpha and was pretty dissapointed, google found this article which I found interesting. Second graph in particular. Seems at 1000 and 1400 there were some drastic growth rate shifts.

http://www.theoildrum.com/story/2005/12/18/1387/0641

[+] Tycho|16 years ago|reply
I've always had this idea in my mind that the 'legendary failure rate of IT projects' is best explained in terms of an exponential increase in points of failure (or even just points of activity) when you deal with computer systems. Are there any famous papers that flesh out this idea? Anyone?
[+] tibbon|16 years ago|reply
I'm curious what the average price of gall bladder surgery is now. In it his students project 25K by 2000, which we are obviously quite a way past. If you're uninsured, this amount sounds about right likely these days.

Great video. I'm on part 2 and I'll finish the rest in the morning.

[+] Empact|16 years ago|reply
The HealthCare Blue Book tells an interesting story:

* $16,435 for traditional gall bladder removal, somewhat below the estimate http://healthcarebluebook.com/page_Results.aspx?id=75&da...

* $6,934 for the modern minimally invasive equivalent, far below the estimate http://healthcarebluebook.com/page_Results.aspx?id=74&da...

More evidence that projecting trends without considering technical progress is bound to result the sort of overly pessimistic results that Malthus made famous.

For example, Dr. Bartlett's two-column view on population assumes that people will need some certain number of square feet of land. But why wouldn't we build up, ala NYC? Or settle the ocean (http://seasteading.org/)? Or colonize the stars? Or perhaps even transfer our consciousness to some more efficient representation?

Yes, exponential growth presents problems, but exponential progress in technology has the power to solve them. That's where we (and others like us) come in.

[+] chrischen2|16 years ago|reply
Well one benefit of increasing population is that we increase the chances of geniuses being born, and increase the diversity of the population.
[+] JBiserkov|16 years ago|reply
There's an old joke that says:

  The intellect of the planet is a constant, the population is increasing. 
genius != intelligence, but still :)
[+] stck|16 years ago|reply
All we now need is a system for harvesting those geniuses. Who knows how many Srinivasa Ramanujans the world has lost.