# (1/8) De meest belangrijke video die je ooit zal zien (deel 1 van 8)

0 (0 Likes / 0 Dislikes)

It's a great pleasure to be here, and to have a chance just to meet with you and talk about
some very simple ideas about the problems we're facing.
Some of these problems are local, some are national, some are global.
They're all tied together. They're tied together by arithmetic, and the arithmetic isn't very difficult.
What I hope to do is, I hope to be able to convince you
that the greatest shortcoming of the human race is our inability to understand the exponential function.
Well, you say, what's the exponential function?
This is a mathematical function that you'd write down
if you're going to describe the size of anything that was growing steadily.
If you had something growing 5% per year, you'd write the exponential function
to show how large that growing quantity was, year after year.
And so we're talking about a situation where the time that's required
for the growing quantity to increase by a fixed fraction is a constant:
5% per year, the 5% is a fixed fraction, the “per year” is a fixed length of time.
So that's what we want to talk about: its just ordinary steady growth.
Well, if it takes a fixed length of time to grow 5%, it follows it takes a longer fixed length of time to grow 100%.
That longer time's called the doubling time and we need to know how you calculate the doubling time.
And it's easy.
You just take the number 70, divide it by the percent growth per unit time and that gives you the doubling time.
So our example of 5% per year, you divide the 5 into 70, you find that growing quantity will double in size every 14 years.
Well, you might ask, where did the 70 come from?
The answer is that it's approximately 100 multiplied by the natural logarithm of two.
If you wanted the time to triple, you'd use the natural logarithm of three.
So it's all very logical.
But you don't have to remember where it came from, just remember 70.
I wish we could get every person to make this mental calculation every time we see a percent growth rate of anything in a news story.
For example, if you saw a story that said things had been growing 7% per year for several recent years, you wouldn't bat an eyelash.
But when you see a headline that says crime has doubled in a decade, you say “My heavens, what's happening?”
OK, what is happening?
7% growth per year: divide the seven into 70, the doubling time is ten years.
But notice, if you want to write a headline to get people's attention,
you'd never write “Crime Growing 7% Per Year,”
because most people would know what it means.
Now, do you know what 7% means?
Let's take an example, another example from Colorado.
The cost of an all-day lift ticket to ski at Vail has been growing
about 7% per year ever since Vail first opened in 1963.
At that time you paid $5 for an all-day lift ticket.
What's the doubling time for 7% growth? Ten years.
So what was the cost ten years later in 1973?
Ten years later in 1983? Ten years later in 1993?
And what do we have to look forward to?
This is what 7% means.
This is what 7% means.
Most people don't have a clue.
So let's look at a generic graph of something that’s growing steadily.
After one doubling time, the growing quantity is up to twice its initial size.
Two doubling times, it's up to four times its initial size.
Then it goes to 8, 16, 32, 64, 128, 256, 512, in ten doubling times it's a thousand times larger than when it started.
You can see if you try to make a graph of that on ordinary graph paper, the graph’s gonna go right through the ceiling.
Now let me give you an example to show the enormous numbers you can get with just a modest number of doublings.
Legend has it that the game of chess was invented by a mathematician who worked for a king.
The king was very pleased. He said, “I want to reward you.”
The mathematician said “My needs are modest.
Please take my new chess board and on the first square, place one grain of wheat.
On the next square, double the one to make two.
On the next square, double the two to make four.
Just keep doubling till you've doubled for every square, that will be an adequate payment.”
We can guess the king thought, “This foolish man.
I was ready to give him a real reward; all he asked for was just a few grains of wheat.”
But let's see what is involved in this.
We know there are eight grains on the fourth square.
I can get this number, eight, by multiplying three twos together.
It's 2x2x2, it's one 2 less than the number of the square.
Now that continues in each case.
So on the last square, I’d find the number of grains by multiplying 63 twos together.
Now let’s look at the way the totals build up.
When we add one grain on the first square, the total on the board is one.
We add two grains, that makes a total of three.
We put on four grains, now the total is seven.
Seven is a grain less than eight, it's a grain less than three twos multiplied together.
Fifteen is a grain less than four twos multiplied together.
That continues in each case, so when we’re done,
the total number of grains will be one grain less than the number I get multiplying 64 twos together.
My question is, how much wheat is that?
You know, would that be a nice pile here in the room?
Would it fill the building?
Would it cover the county to a depth of two meters? How much wheat are we talking about?
The answer is, it's roughly 400 times the 1990 worldwide harvest of wheat.
That could be more wheat than humans have harvested in the entire history of the earth.
You say, “How did you get such a big number?” and the answer is, it was simple.
We just started with one grain, but we let the number grow
steadily till it had doubled a mere 63 times.
Now there's something else that’s very important:
the growth in any doubling time is greater than the total of all the preceding growth.
For example, when I put eight grains on the 4th square,
the eight is larger than the total of seven that were already there.
I put 32 grains on the 6th square.
The 32 is larger than the total of 31 that were already there.
Every time the growing quantity doubles,
it takes more than all you’d used in all the proceeding growth.
Well, let’s translate that into the energy crisis.
Here’s an ad from the year 1975.
It asks the question “Could America run out of electricity?”
America depends on electricity.
Our need for electricity actually doubles every 10 or 12 years.
That's an accurate reflection of a very long history
of steady growth of the electric industry in this country,
growth at a rate of around 7% per year, which gives you doubling every 10 years.
Now, with all that history of growth, they just expected the growth would go on, forever.
Fortunately it stopped, not because anyone understood arithmetic, it stopped for other reasons.
Well, let's ask “What if?”
Suppose the growth had continued?
Then we would see here the thing we just saw with the chess board.
In the ten years following the appearance of this ad, in that decade,
the amount of electrical energy we would have consumed in this country would have been greater
than the total of all of the electrical energy we had ever consumed
in the entire preceding history of the steady growth of that industry in this country.
Now, did you realise that anything as completely acceptable
as 7% growth per year could give such an incredible consequence?
That in just ten years you'd use more
than the total of all that had been used in all the proceeding history?
Well, that's exactly what President Carter was referring to in his famous speech on energy.
One of his statements was this:
he said, “In each of those decades (1950s and 1960s)
more oil was consumed than in all of mankind's previous history.”
By itself that's a stunning statement.
Now you can understand it.
The president was telling us the simple consequence
of the arithmetic of 7% growth each year in world oil consumption,
and that was the historic figure up until the 1970s.
There's another beautiful consequence of this arithmetic.
If you take 70 years as a period of time
—and note that that's roughly one human lifetime—
then any percent growth continued steadily for 70 years
gives you an overall increase by a factor that's very easy to calculate.
For example, 4% per year for 70 years,
you find the factor by multiplying four twos together, it's a factor of 16.
A few years ago, one of the newspapers here in Boulder
quizzed the nine members of the Boulder City Council and asked them,
“What rate of growth of Boulder's population do you think it would be good to have in the coming years?”
Well, the nine members of the Boulder City council
gave answers ranging from a low of 1%