# Misc

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

The Exponential function is used to describe the size of anything that’s growing steadily, for example, 5% per year.

We are talking about a situation where the time that is required for the growing quantity to increase by a fixed fraction is constant.

If it takes a fixed length of time to grow 5%, then it follows that it takes a longer fixed length of time to grow by 100%. This longer time is called the doubling time.

We can calculate the doubling time:
T2 = 70 / (% growth per unit time)
Thus, a growing rate of 5% per year has a doubling time of:
T2 = 70 / 5 = 14 years

Doubling time for 7% growth = 10 years.

In just 10 doubling times it’s a thousand times larger than when it started.

The growth in any doubling time is greater than the total of all the preceding growth!

```Growth Rate                           Factor
1% per year                            2 = 2
2%                                 2 x 2 = 4
3%                             2 x 2 x 2 = 8
4%                        2 x 2 x 2 x 2 = 16
…
7%                                 2^7 = 128```

Imagine bacteria growing steadily in a bottle. They double in number every minute.

At 11:00 am there is one bacteria in the bottle.
At 12:00 noon the bottle is full.

```11:54 am                1/64 = 1.6% full
11:55 am                1/32 = 3.1% full
11:56 am                1/16 = 6.3% full
11:57 am                1/8 = 12.5% full
11:58 am                  1/4 = 25% full
11:59 am                  1/2 = 50% full
12:00 noon                     100% full
12:01 pm                       200% full
12:02 pm                       400% full```

We cannot let others do our thinking for us.

Growth of populations and growth of rates of consumption of resources can not be sustained.

Central to the things that we must do is to recognize that population growth is the immediate cause of all of our resource and environmental crises.

The Positive World Manifesto is a vision of a better world that strives for high levels of well-being for all animals (including humans), ecological efficiency, social justice, and a better mindset of ethics; a world where the sum total of the effects of humanity on the natural world is positive, and increase over time.

The first step toward making a change is to properly define it: the Positive Business Manifesto is a declaration of my principles as an entrepreneur and the basis of all my business dealings.

Today’s marketplace is an essential and central part of our world but its rules (or the lack of it) make it a completely unsustainable economic system. By permitting and rewarding selfish greed it creates conflicts that result in an outstandingly negative effect on our world.

A Positive Business, on the contrary, is striving for innovation and sustainable change. Although it shares the same objective of earning profits, it has a higher purpose beyond just money.