What if you started a colony of bacteria inside a bottle at 11 o’ clock and it doubled every minute? Assume that at 12 o’ clock the bottle was full, meaning that the bacteria population has reached the point where the environment inside the bottle can sustain no more of them. Now, at what time before that happened was the bottle half full?
The answer to this question is that it was half full one minute to twelve. That is what doubling every minute means. If the bacteria could think, when do you think they would start to realize that something was wrong, that they were running out of space, and rapidly so?
These and many other very disturbing questions are asked by Dr. Albert Bartlett, Professor Emeritus of the Department of Physics, University of Boulder Colorado in this lecture named “Arithmetic, Population, and Energy” that you can find in these 8 video clips.
Because bacteria are not the only organisms that have to deal with the effects of exponential growth. Many human phenomena also follow this growth pattern, like population growth, migration, economic growth, consumption of consumer goods and energy etc. etc.
Might it also be so, that we find ourselves at the time “a couple of minutes to twelve?” Now, a lecture with an old professor in front of a group of students is usually not something you would think about as terrifying. And sure it lacks the extremely graphic images of a war or a terrorist attack, but if you listen carefully and understand what he is saying, you will probably find this video more terrifying than just about anything.
The video does not only show that the human race is in bigger trouble than most people think. It also shows the mathematical fundamentals behind why we will not discover the problems until very shortly before we run into them.
By the way, you don’t need to possess university level skills in mathematics to follow this lecture.
“The greatest shortcoming of the human race is our inability to understand the exponential function.”
Dr. Albert Bartlett
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This video is informative indeed. It should be seen by millions!
@Christen Krogvig
Yes, at least almost a million viewers have seen the first of these 8 clips so far on YouTube, where we have embedded it from. The counter on YouTube is showing 952,886 views at the time of writing. But it should be seen by many, many more.
You could say that the number of people to see it ought to grow exponentially
When it comes to “consumption” of this video, lets hope it will reach billions.
Our readers can help spreading this highly important video. Send an email with a link to this page to all your contacts and ask them to pass it on.
You can also share the link on many different social media. If you look a little below the last of the video clips there are many icons for social media where you can share the link.
Not only does this video show that the human race is in far bigger trouble than most people think. It also shows the mathematical fundamentals behind why we will not discover the problems until shortly before running into them, big time.
@Christen Krogvig
Green Life Innovators would like to thank you for donating Norwegian Kroner 1000 to be used for Google ad campaigns, to make this page with this important video known to a larger audience.
The person who wrote the piece wasn’t thinking too clearly either.
If the number of bacteria doubles every minute for an hour, then the number at the end of the hour is 2^60, or roughly 10^18, times as many as the number at the beginning. Suppose each bacterium is shaped as a cube, one micrometre on each side. (That’s smaller than most bacteria.) Its volume is 10^-18 cubic metres. Suppose there was just one bacterium in the bottle at the beginning. At the end of the hour, the total volume of bacteria is one cubic metre. They wouldn’t fit into a normal bottle.
After another hour, the bacteria would fill a cube 1000 km on each side. After a third hour, they’d fill a cube three times larger than the earth’s orbit around the sun
Exponential growth is scary.
@David Williams
It does not invalidate the point of professor Bartlett what you write, it just makes it stronger, I believe
Yes. My observation does not invalidate Prof Bartlett’s point. It just shows that the idea of having bacteria double in numbers every minute for an hour inside a bottle is unrealistic.
As I’m sure you know, the sum of the infinite series 1 + 1/2 + 1/4 + 1/8 …. is finite, and equals 2. So the sum of the entire series is just twice the first term. If you look at the series in the reverse order, it represents exponential growth, and the sum is twice the final term. The number of humans on the earth is doubling in less than a human lifetime. If this has been true for the entire history of the species, then the total number of humans who have ever lived is less than twice the number who are alive today.
Later…
David
@David Williams
I sometimes use this fact as a background for a joke about statistics abuse. Saying that the probability of dying is 50%, since of all the people who live and ever have lived we have observed 50% of them to have died and 50% of them not to
very useful and informative in this and future critical times. how can i have a copy of dvd so I can use in my profession as environmental planner. thanks
nick tabungar
@Nestor “Nick” V. Tabungar, Jr.
As you can see, we have embedded these 8 video clips from YouTube. We do not have a copy of it on DVD. For a DVD of the lecture, I suggest you contact the University of Colorado, Boulder, where this lecture has been recorded, and ask them if they have one
Generally I like your blog a lot, but I’m not so impressed by this video (the math must be interesting for those who don’t grasp exponential growth, but I dissagree with many of the political concusions he draws and his predictions) and here is why:
First of all, let’s look at population growth. It has grown exponentially in the past, but that doesn’t mean that it will keep on doing so. We see that woman in developed countries in have a lot fewer children than they used to, so few that the population barely grows at all – and had been sinking in some places if it wasn’t for immigration, and this is expected to happen in the rest of the world sooner or later as well. The UN estimates guesses that the world population will stabilize at 9-10 billion. We certaintly won’t see continued exponential growth (unless society changes drasticly by humanity colonizing the universe, living a lot more space-efficiently by using viritual reality, or something like that).
But that’s not my main problem with his pessimism. He forgets that technology also grows exponentially! It grows more exponentially then consumption and population growth. Actually, both if we look at the statistics and expect technology to grow at the same exponential rate and if we look at what’s reasonable to expect with the emergence of nanotechnology, the advancement of computers, the re-engineering of the human brain functions, etc., we have reason to be extremely optimistic on behalf of humanity. I will write more about why I think this on my own blog in the future. (In the meantime I recommend this short presentation: http://howisearth.wordpress.com/2010/02/14/ray-kurzweil-on-how-technology-will-transform-us/ and this video: howisearth.wordpre…/12/21/did-you-know/.)
Nanotechnology has the potential to help us make a lot of “stuff” that’s not resources today into resources, recycle everything we want, and be a lot mor efficient than we are today.
What we can do with computers and our understanding of the human brain are both growing exponentially (doubeling quite often), and it’s a question of time before we can make machines that are smarter than humans (and the arteficial inteligence we are able to make will keep on increasing exponentially also after that), which will speed up our scientific progress a lot.
I don’t think there is any doubt that we will be able to live confortabely on other planets and in space well within the end of the century.
There is no reason to worry about getting enough energy to cover our needs in the future. Even if we ignore what we will be able to do with next-generation nuclear power the energy from the sun will provide more than enough energy. This I have already written a post about which I think you will find very interesting: howisearth.wordpre…gy-renewable-energy/.
As mentioned, I will write posts in the future on my blog on why I’m so optimistic about the growth of technology, and what it will enable us to do.
By the way, I also think this post will be of interest: howisearth.wordpre…ring-climate-change/.
@Tor
First of all I would like to say that I wouldn’t mind if your techno-optimism turned out to be correct. It would be nice if human ingenuity could design us out of every challenge with single sided supply side solutions. I just happen to believe that we need to do something about the demand side as well and in particular with the current growth of the world population. The tragic thing is that we do have access to rather simple and cheap technology to do so. It is called contraceptives. Too bad that a large portion of the world does not use them enough, especially since some of the reluctance towards birth control comes from old religious taboos.
As to professor Bartlett’s lecture. The conclusion he draws from extrapolating the current growth to the point that we will have one square meter of land per person within some 600 years, if it continues, is not that this will happen. He quite clearly states that what this shows is that zero population growth will eventually happen. The question is only how. Mother Earth is notorious for not being very “motherly,” so to speak, when she “interferes” with the unchecked growth of a species through some of her limiting factors.
As a general rule, no phenomenon that grows exponentially for a period in its evolution will continue to grow exponentially in perpetuity. I will illustrate this with a rather simple mathematical example. Well, simple to anyone who has studied calculus anyway.
I will use the spreading of a rumour as the example
The model that describes this and many related phenomena is that the rate of change is proportional to what you already have.
If we assume that N is the number of people that have heard the rumour, then the rate at which it spreads, if we assume that it’s proportional to the number of people that have already heard the rumour, is modelled by the simple differential equation
N’=c*N
Now, the only function that is its own derivative is the exponential function. Hence the result is exponential growth
But, of course, the model will then predict that the number of people that have heard the rumour eventually will surpass the entire population on the planet and that clearly is not going to happen. So, we need to modify the model to take that into account.
Say that P is the entire population
Then a better model is
N’=c*N(P-N)
Which is to say that the rate of change is proportional to the number of people that have heard the rumour and proportional to the number of people that have not yet heard it.
Now, this is a harder differential equation to solve, but it can be solved by the method of partial fractions. And the solution gives a function that can be plotted as an S-shaped curve, that starts out with the familiar exponential growth to begin with, but then eventually flats out and approaches P asymptotically.
This is what happens to real phenomena that grow exponentially for a period of time. The growth is eventually halted by some external limiting factor.
As to the growth of certain technologies. The most prominent example of a technology that grows exponentially and has been doing so for decades is the processing power of computers, that has been following the so called Moore’s law up to now. But that technology will probably eventually also hit a limiting factor. And as a general rule, not all technologies grow exponentially. The speed with which we can travel does not for instance, and neither does the fuel efficiency in motor vehicles, as far as I know.
Optimism is in general something I consider a good thing. But I consider realism even better. There are things that we can do and there are things that we can not do. The big challenge is to know the difference between the two. It would be nice if “nothing was impossible” for man kind to achieve. But this is not quite the way the world works. Actually, we have even devised technical application based on what is, for all practical purposes, impossible. I am thinking about cryptography here, where the basic idea is to construct an algorithm that is easy to do for coding a message, whereas its reveres algorithm, to break the code, is impossible to complete over any practical time span.
Thank you for your answer!
I agree that there are limits for how many people we can be on planet earth, but with more advanced technology it can be pretty high. And we can also expand out to the rest of the universe.
There are physical limits to how fast computers can get, but they are not very limit. Exponential growth can continue for a long time.
I´ve just made a Youtube-video explaining why I have so great expectations for the future, and I highly recommend it: http://www.youtube.com/watch?v=dUOB4tdFDYM
Best regards,
Tor
What is the most environmentally damaging thing that many people do?
Drive gas-guzzling cars?
Live in poorly insulated houses?
Fly around in airplanes?
None of the above!
The answer, I am sure, is:
Have babies!
If you have a child, you are initiating all the environmental damage that will be done by that person during his lifetime. Furthermore, you are causing all the damage that will be done by the descendants of your child, indefinitely into the future. The total environmental impact of having a baby is stupendously greater than that of almost any other action you might take.
And yet it is hardly ever discussed, or even thought about. Last night, many people turned off their lights for an hour to show support for “green” living. So what do you think they did during that hour of darkness? Check the birth statistics nine months from now. The environment will suffer because of “earth hour”.
Why is this never discussed? There are plenty of reasons, but many of them boil down to one thing – religion. Many major religions still actively oppose population control. Even those that don’t oppose it still approve of having children. After all, the more followers a religion has, the more powerful its leaders become.
I often think I don’t belong on this planet.
I see this web is very good i like it so mutch
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