Albert Barlett Exponential Function

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!

Steady Growth for 70 Years:

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.

by Albert Bartlett

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2010 has been a very challenging year for me during which I learned and changed a lot. It was the year of first times: co-founding a company, living on my own in a foreign country, attending a major conference, etc. It is also the year I dropped out of university.

Looking back at everything I’ve done, failed, and learned over the course of the last 12 months, I feel like I’m on the right path to achieve my goals. I’m stubborn, persistent, and that makes me confident in the future.

However, the amount of hard work required to make my dreams come true is at an all time high, having failed to achieve any of my goals last year. Therefore, consistent and intelligent work will be my primary objective for this year.

In the end, I hope that 2011 will mark the beginning of change for and from me, where what ought to be will finally be.

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Certainly one of our greatest powers is our ability to determine ourselves and decide of our attitude at any given moment. Though this freedom finds its limits in the conditions in which we live in, we are always free to take a stand, and even in the direst situations, to decide what to make of our existence.

How we use this freedom defines who we are and, as with every great power, there must also come great responsibility.

Freedom is only part of the story and half the truth. Freedom is but the negative aspect of the whole phenomenon whose positive aspect is responsibleness. In fact, freedom is in danger of degenerating into mere arbitrariness unless it is lived in terms of responsibleness.

— Viktor E. Frankl

Freedom allows for both good and evil; while our society tries to enforce that nobody falls to the dark side, it remains our responsibility to choose between the many different shades of good.

Furthermore, this new age of science and technology has expanded our choice and revealed to us the full scope of our freedom. While our ancestors could rely on traditions, such as religions, to tell them what they ought to do, we now stand fully aware of the infinite different ways in which we could live our lives.

Why is it that human beings, surely the most intelligent life form on earth, do not strive to achieve their maximum potential? The reason is simple: we have been given the freedom of choice.

— Jim Rohn

In facing a choice, multiplying the options does not always lead to a better outcome, for it then requires that we make up our mind and be strong enough to act. In particular, the former requires a certain level of knowledge that grows exponentially with the number of options.

In the case of life, some options are attractive at first sight but disappointing in truth, while others take great courage to choose but offer immense rewards in the end. Most important, some are unknown to us until we acquire the knowledge that will reveal them to our minds.

That is why I find acquiring knowledge to be one of the most important pastimes, because it broadens my view and understanding of the world, thus increasing my opportunities and improving my judgment.

We all have a remarkable potential and we must decide what to make of it. While some might be satisfied with less than others, many strive for more. Whatever we decide, we should not forget that everything is possible, so long as we believe, and put in the mental effort to become what we ought to be.

It is our responsibility to choose what’s best for us, our loved ones, and the world.

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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.

Read the Positive World Manifesto

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Imagination is one of the most precious faculties of man. In addition to “providing meaning to experience, understanding to knowledge, and playing a key role in the learning process” (Wikipedia), imagination gives man the faculty to see things (himself, in particular) beyond the present moment. Combined with freedom of choice it makes him the master of his fate.

Imagination has been the seedling of all human progress but it’s also the motive power of our individual lives. The more one uses it, combined with a burning desire for its actualization and a definite purpose, the greater one’s achievements will be.

With experience and intelligence, imagination becomes creativity—the ability to create new things with some kind of value—and can then be transformed into riches. The transformation is not an easy step but we are all capable of achieving it, unless we surrender to the manual.

Man’s obsession with creating maps and manuals for how to live his life goes against the human nature, for there is no limits to what he can achieve and become. Maps, in this sense, are counter-productive because they set boundaries where none existed before. They help avoid the mental effort of finding a path, but offer no surprise to what the destination will be.

In the face of an infinite sea of choices, it’s natural to put blinders on, to ask for a map, to beg for instructions, or failing that, to do exactly what you did last time, even if it didn’t work.

— Seth Godin

Life offers an infinite sea of choices because man is always able to choose what his existence will be in the next moment. In this frightening journey, imagination is our own personal navigation tool. It’s always available to us, but we must deliberately and repeatedly make the choice to use it.

Today’s world of factories has created countless manuals and mapped a vast number of paths which are followed by many. Our education system reinforces this by making us believe that the only way for us to succeed is to follow those paths. They offer a quick and easy fix to a broader problem that is the meaning of one’s life, but do not come free of charge.

While following a map can offer a temporary remedy to some of our fears, it will only take us where someone else wishes us to go, usually for his personal benefit. Moreover, if you’re not prepared to work without a map and be wrong, you cannot let free of your creativity and achieve your full potential.

On the contrary, following your imagination won’t give you the comfort of knowing what to do and where to go at any given moment, but its rewards are invaluable compared to the wages that you can expect by working at the office. Beyond success, it’ll bring you happiness and fulfillment, for you will be the man in charge.

Man’s only limitation, within reason, lies in his development and use of his imagination.

— Napoleon Hill

Within the laws of physics, the power of our imagination is simply limitless.

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I dream things that never were; and I say, “Why not?”