Exponential Growth: The lillie pond riddle

[Grunt]

This is a post I swiped from elsewhere. Which I believe was swiped from somewhere else.


It is not hard to make a case that the human experiment on planet earth is beyond its limits. It is not hard to see that the present path of human existence is unsustainable. The future, to be viable at all, must be one of drawing back, easing down, and allowing the planet to heal its wounds. Population growth cannot go on indefinitely, in fact, we may have already exceeded the carrying capacity of the earth’s environment by billions.

Without significant reductions in material and energy flows, there will be in the coming decades an uncontrolled decline in per capita food output, energy use, and industrial production. We need a comprehensive revision of policies and practices that perpetuate growth in material consumption and in population and a drastic increase in the efficiency with which materials and energy are used. A sustainable society is still technically and economically possible, but not at these levels of growth in population and constant expansion of our economy.

The transition to a sustainable society requires a careful balance between long-term and short-term goals and an emphasis on sufficiency, equity, and quality of life rather than on quantity and speed of output. It must be based upon a recognition of the limits to growth and the fragile ecosystem upon which we depend, not GDP. This is nothing short of the most daunting task that has ever been put before mankind. Our entire modern industrial culture has been built upon the premise of perpetual material growth. Much of that growth is becoming exponential, even at a time of an obvious decline in many resources. If we are to make this transition, when must we take action to do so? Is it too late? Do we still have time? A traditional French riddle illustrates the surprising nature of exponential growth, and may help us realize the magnitude of the task and dilemma before us at the dawn of the 21st Century.

The Lily Pond Riddle
1. If a pond lily doubles everyday and it takes 30 days to completely cover a pond, on what day will the pond be 1/4 covered?

2. 1/2 covered?

3. Does the size of the pond make a difference?

4. What kind of environmental consequences can be expected as the 30th day approaches?

5. What will begin to happen at one minute past the 30th day?

6. At what point (what day) would preventative action become necessary to prevent unpleasant events?

7. With respect to human population, what corresponding day are we at in the world? The United States?
In 24 hours, I will post the answer to the riddle.
Answers to The Lily Pond Riddle
If a pond lily doubles everyday and it takes 30 days to completely cover a pond, on what day will the pond be 1/4 covered?

Answer: Day 28. Growth will be barely visible until the final few days. (On the 25th day, the lilys cover 1/32nd of the pond; on the 21st day, the lilys cover 1/512th of the pond).

1/2 covered?

Answer: Day 29.

Does the size of the pond make a difference?

Answer: No. The doubling time is still the same. Even if you could magically double the size of the pond on day 30, it would still hold only one day's worth of growth!

What kind of environmental consequences can be expected as the 30th day approaches?

Answer: The pond will become visibly more crowded each day, and this crowding will begin to exhaust the resources of the pond.

What will begin to happen at one minute past the 30th day?

Answer: The pond will be completely covered. Even though the lilys will be reproducing, there will be no more room for additional lilys, and the excess population will die off. In fact, since the resources of the pond have been exhausted, a significant proportion of the original population may die off as well.

At what point (what day) would preventative action become necessary to prevent unpleasant events?

Answer: It depends on how long it takes to implement the action and how full you want the lily pond to be. If it takes two days to complete a project to reduce lily reproductive rates, that action must be started on day 28, when the pond is only 25% full -- and that will still produce a completely full pond. Of course, if the action is started earlier, the results will be much more dramatic.

With respect to human population, what corresponding day are we at in the world? The Australia?

[Grunt]

An hour long but entertaining video of a lecture on exponential growth.

Albert Bartlett

For those who like to read.

"Reflections on Sustainability, Population Growth, and the Environment" by Albert Bartlett

[silentC]

It's a fairly simplistic view. It assumes that everything else is a constant and doesn't really take into account things like natural disasters and the distribution of population growth.

I think things will shut down long before we reach the 30th day. People will die from starvation and disease quicker than new ones are born.

Still, I feel bad for my kids...

[bitingmidge]

The flaw in the argument of course is that the rate of growth (and resource consumption) is not consistent nor is it static!

Neither are we dealing with one pond or one species of plant.

I agree with the underlying sentiment by the way, and think we have a moral responsiblity to reduce consumption at all levels, (providing we can still buy nice tools and have electricity to power them or for other uses between consenting adults in private).

The hardest part to deal with of course, is that for all the statistics about how much we consume as a nation (and per capita it's an outrageous amount), it's still not as much one major city (think London, Newyork, Paris, Beijing).

That's right folks, each of those cities consumes more of every kind of resource every day than our entire country!

So, if we all do the morally correct thing we could get our consumption down to the level of Rabbit Flat, but the rest of the world would still be "doubling".

Maybe a few well-placed nuclear catastrophe's could do us the world of good! :eek: :eek:

Thanks Grunt, for starting my day in such a loving and caring way,

Peace man,

P

[Andy Mac]

Thanks Grunt,
I have been tossing up whether to start a similar thread after the "Dam" debate, but wouldn't have come up with anything quite as graphic, so well done!
I have been rereading Tim Flannery's book, The Future Eaters, which I mentioned before. Basically a history of mankind's impact on Australia, comparing it to NZ and PNG, written from the perspective of someone who knows a great deal about species extinction (Flannery is paleobiologist, head of the Museum of SA). He extends his argument to the ideal population for Australia, and comes up with something like 12-15million people, which we have already exceeded. Any dramatic growth above that, in his opinion, will mean a decrease in our living conditions, as the environment is placed under too much stress. Our arable land in Australia would not be considered arable in most developed countries, its marginal, and that's without the added degradation of pollution, overclearing, salinity, drought.
I think Flannery's key point in the whole book is that this unique country of ours is old, washed out, dry, with very low natural nutrient levels. For anything to prosper it has to be frugal with what it uses, like the Eucalypt, like the kangaroo, and dare I say it, like the Aboriginal people. Agricultural practices from the Old World, and that includes forestry and fishing (which are about harvesting, not plundering), will simply not work here, not on any long term, sustainable level.

I think you made a point in the "Dam" debate about the vocal ratbag Greenies...the way I see it, that particular group, the archetypal dole bludging, dreadlocked, anti-development hippy, is an absolute neccessity! Not because I agree with them neccessarily, or aspire to be one, but simply because they are extreme...the living, breathing expression of a point of view in opposition to the extreme conservative, pro-development, money hungry types. They are both as bad as one another in a way, but any debate needs the extreme views before a reasoned middle-ground can be found. Its not about agreeing with either party wholeheartedly, and I, for one, wouldn't want the pro-woodchipping fraternity running the country, despite their promises of jobs and $$!

Anyway Grunt, I hope we can expect some lucid, robust debate about this one!!

[Wongo]

This is sad, very sad. I don't know why but for many years I always believe that 2050 is the year and it is still a bit optimistic.

I hope I am wrong.

[bitingmidge]

This is sad, very sad. I don't know why but for many years I always believe that 2050 is the year and it is still a bit optimistic.

Will you still need me,
Will you still feed me,

When I'm 98?

P

:eek: :eek: :eek:

[Iain]

Of course there was 1984.........
And I think there was some signifigance with 2001

[silkwood]

"I think you made a point in the "Dam" debate about the vocal ratbag Greenies...the way I see it, that particular group, the archetypal dole bludging, dreadlocked, anti-development hippy, is an absolute neccessity! Not because I agree with them neccessarily, or aspire to be one, but simply because they are extreme...the living, breathing expression of a point of view in opposition to the extreme conservative, pro-development, money hungry types. They are both as bad as one another in a way, but any debate needs the extreme views before a reasoned middle-ground can be found. Its not about agreeing with either party wholeheartedly, and I, for one, wouldn't want the pro-woodchipping fraternity running the country, despite their promises of jobs and $$! Andy Mac

What well reasoned comment Andy Mac. With regard to the highlighted bit, do you think we're in trouble because they already are?

Cheers,

[bitingmidge]

We're all sitting here using electrical power, sending pulses along a network of materials that were mined from the earth and clad in some sort of petro-chemical product, using computer's that are destined to be obsolete within a few short years.

We are exchanging ideas, thoughts and personal abuse and wishing the world would stop consuming, just so we can keep doing stuff like this.

Or have I got it wrong?

Cheers,

P :confused:

[Andy Mac]

Hi silkwood and Midge,
You're both right...shot myself in both feet

Cheers,

[Skew ChiDAMN!!]

We're all sitting here using electrical power, sending pulses along a network of materials that were mined from the earth and clad in some sort of petro-chemical product, using computer's that are destined to be obsolete within a few short years.

We are exchanging ideas, thoughts and personal abuse and wishing the world would stop consuming, just so we can keep doing stuff like this.

I'm semaphoring my posts to this board using two sticks with leaves tied to the ends. (Which conveniently explains my typos... ever tried to semaphore an umlaut or ampersand? It's so hard to get just the right swish. [sigh])

What happens to my wigs and wags after they leave my line of sight is white man's magic... and what you're using at your end to interpret 'em is entirely up to you...

[Grunt]

I think things will shut down long before we reach the 30th day. People will die from starvation and disease quicker than new ones are born.

Isn't that the 30th day?

So, if we all do the morally correct thing we could get our consumption down to the level of Rabbit Flat, but the rest of the world would still be "doubling".

Yes. We've got to start somewhere, so we should start with ourselves. The western world criticises the 3rd world for population when the U.S. is growing at 3 million a year. Australia is growing at 200,000 a year. We are damn good a consuming.

As individuals, we can become less of a burden on the environment, however as along as there are 6.5 billion of us we're kind of stuffed. I think the human population is in overshoot. If the population of a particular species gets to plague proportions the the population is in overshoot. Nature has a way of causing die off which will bring the population back to or below normal.

Through history, the average population has been around a billion. I suggest that over the next 50 years the population will decrease to around 500 million. That is if we don't get into full scale nuclear exchanges.

[silentC]

Isn't that the 30th day?

No because the Earth will still be capable of supporting more life but external influences will start eradicating it quicker than it can grow. Unless you are into the whole Gaia Mother Earth thing, in which case in one sense you are correct.

[Wongo]

30 days huh!

Luckily the wood show is on tomorrow. Tough luck Mexicans.