Exponential Growth: The lillie pond riddle

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?


http://www.ecofuture.org/pop/images/worldpopline2.gif


http://www.geoman.com/jim/images/tibbsbox.gif

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

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...

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
:cool: :cool: :cool:

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!!:D

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.

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Originally Posted by 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.

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

When I'm 98?

P

:eek: :eek: :eek:

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

"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,

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:

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

Cheers,

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Originally Posted by 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.

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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... :p

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Originally Posted by SilentC

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.

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Isn't that the 30th day?

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Originally Posted by Midge

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".

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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.

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Isn't that the 30th day?

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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.

30 days huh!

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

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Originally Posted by Grunt

We've got to start somewhere, so we should start with ourselves. Australia is growing at 200,000 a year. We are damn good a consuming.

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I agree completely, although I'd like some ideas of how you think we should do that. If we all set off and do the "alternative" lifestyle thing, the world would suffer a glut of handwoven alpaca mohair ponchos in about one afternoon.

My own ideas of how we could go about this are fairly simple:

1% population growth is not significant, and if everyone undertook a 10% reduction in consumption we've have a net gain.

Lets' introduce a supertax on non-renewable resources. For fuel for example, say $3 per litre. That would force us into smaller more efficient vehicles, reduce trip distances and frequencies and put the price of goods up to the extent where the meaning of "luxury goods" would be restored to its literal place in our language.

We'd be spending more on food, so couldn't afford to have two teles. Manufacturers would have to rationalise packaging to gain a competitive edge.

"Climate control", heating and airconditioning should be banned, we should have to adapt to the conditions we live in, not have our environment adapt to us.

Travel wouid become expensive, encouraging us to live in clusters, (previously known as villages).

Eventually these villages would become high density clusters, much like the original settlement villages in Sydney (Paddo for example). As the density increases in these nodes, the cost of servicing will go down commensurately, and the proceeds from the tax could be used to demolish large tracts of suburbia, re-establishing green agricultural belts on previously fertile ground, and creating a food production source close to the residential one.

Overproduction could be exported in exchange for supertax rebates, so that efficiency is rewarded.....

Or we could just turn off lights in rooms where we're not using them I suppose.

Cheers,

P

Why don't we just spray the bloody lily with 245T ?

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Originally Posted by outback

Why don't we just spray the bloody lily with 245T ?

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or we could gild it...

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Originally Posted by outback

Why don't we just spray the bloody lily with 245T ?

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'cause it'd bugger up the ozone layer, global warming would happen, the lake would overflow into the next paddock, then the pineapple crop would die and we'd all get the rough end of it! :eek:

Come on Grunt, you started this, give me something to work with here!!

cheers,

P
:D

A 1% growth rate means that the population of Australia will be over 40 million by 2076. Not all that long from now. The worlds population would be 13-14 billion.

Growth is not a sustainable option.

I think everyone needs to really ask themselves what they need rather than what they want. After all, you'll never reach nirvana with desire.

Globalisation is really evil. Why did my dinner tonight travel 10s of thousands of kilometers to get to my plate? Why do we dig holes in the ground to get iron ore, send it by boat to some other place to have is sent back in another shape?

The only real answer is to depopulate. However, chosing a method of doing so is tough. Those who survive will need to be part of a community, that largely provides for itself. This is how it was done before industrialisation.

How about:
Stick a pineapple up where the sun don't shine for everyone who turns 65. If they don't die of constipation, they can stay.
Kill all Collingwood supporters, or anyone thinks about being a Collingwood supporter.
Any child who annoys me, gets one chance before they're sent to the knackers.

Any other ideas?

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Originally Posted by SilentC

No because the Earth will still be capable of supporting more life but external influences will start eradicating it quicker than it can grow.

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The Earth is a closed system (with the exception of some sunlight, sunspots and a bit of gravity from the moon). Which external influence do you mean? Starvation and disease are the main tools of nature to reduce populations.

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Originally Posted by Grunt

Why did my dinner tonight travel 10s of thousands of kilometers to get to my plate?

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1) Because you like stuff grown in a sunny climate and you're too lazy to move here.

2) The stuff you had last night was from near your home and it made you fart.

3) There is a famine in Victoria, but we are always looking to help our fellow man.

Cheers,

P (who had stuff from a fridge right in his own house - how's that for acting locally!)
:D :D :D

For the record, what I am doing to reduce my foot print is to:

Build a strawbale house on our 11 acres in Lancefield. The house will be solar passive and will require very little externally supplied heating (a wood heater) and no cooling.

I will grow a sustainable permaculture garden which will provide more food than we can eat.

I will continue to work but continue to telecommute to work as long as they let me.

I've been thinking, I may have to turn to the darkside. :(

I'll install some solar panels and have a backup diesel generator. I'll grow enough vegie oil to power the generator and small tractor. Around 1000 litres a year.

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Originally Posted by Grunt

How about:
Stick a pineapple up where the sun don't shine for everyone who turns 65. If they don't die of constipation, they can stay.

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And up yours too!

Cheers,
64 years old Graeme

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Originally Posted by Grunt

The only real answer is to depopulate.

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Won't that make it harder for your dinner to travel 10's of thousands of kilometres to your place??

If there's no-one to drive the delivery trucks, you could be in deep do-do's.

I'm doing my bit, I promise not to have any more kids between now and 2076.

cheers,

P

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Originally Posted by Grunt

For the record, what I am doing to reduce my foot print is to:

Build a strawbale house on our 11 acres in Lancefield. The house will be solar passive and will require very little externally supplied heating (a wood heater) and no cooling.

I will grow a sustainable permaculture garden which will provide more food than we can eat.

I will continue to work but continue to telecommute to work as long as they let me.

I've been thinking, I may have to turn to the darkside. :(

I'll install some solar panels and have a backup diesel generator. I'll grow enough vegie oil to power the generator and small tractor. Around 1000 litres a year.

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Your'e funny :)




You are being funny aren't you? I mean you can't actually be serious about all of that............can you?

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Won't that make it harder for your dinner to travel 10's of thousands of kilometres to your place??

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No, I'll just drive down to the take out alot.

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I'm doing my bit, I promise not to have any more kids between now and 2076.

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But the seed you've already sown is already out there doing there bit for the economy. You know, 1 for her, 1 for him and 1 for the country,

I took my children to the vet and had their bits removed as soon as they were old enough.

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And up yours too!

Cheers,
64 years old Graeme

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My point was that it's really hard to work out an equitable way to depopulate. Unless we have any volunteers?

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Originally Posted by Grunt

For the record, what I am doing to reduce my foot print is to:

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I don't in the least want to devalue what you are doing (except for the poncho weaving bit), however, there are a few arguments that can never be won here.

Depopulate you said, yet you haven't got killing anyone on your agenda.:eek:

Seriously, we have to accept that we have a fabric of society, and while you may live in a way which is very self-fulfilling, and I make compromises in my thermally efficient, veggie gardened suburban dwelling, scrounging second hand timber for my projects, riding my bicycle and generally minimising personal consumption, our tokens are just that: tokens that remind us of how irresponsible the rest of the world is.

What will be the catalyst to educate the masses? (I almost said the great unwashed, but that's you and your straw-baled hippie mates)

Maybe making stuff expensive. Paying the true cost for water, and as I have suggested above, supertaxing anything that uses a non-renewable resource will help.

What won't work, is moving everyone onto self-sufficient plots, our climate wasn't designed to sustain veggie farms 12 months a year, and spreading out further is self defeating, requiring a whole new set of resources.

Perhaps if we were to look to how China lives now, in self-sufficiency, sub-urban structure and transportation terms, we could develop a model.

The trick is to convince them to stop developing further, but they've seen what we have, and I don't blame them for wanting it, even if we see the evil in our ways.

Practically, how does the local snack bar employee telecommute?

I'd love to chew the fat a bit over it. It makes the IR concerns a bit irrelevant eh?

cheers,

P
:D :D :D

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Your'e funny :)

You are being funny aren't you? I mean you can't actually be serious about all of that............can you?

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It'll keep me out of trouble.

Midge, I don't actually think what I'm doing will make one iota of differnce to the world. It just makes me feel better.

The things that need doing won't get done because they'll be killers on election day for any government that implements them.

Sadly, by the time the general population agrees that something needs to be done, it'll be too late.

I have stopped worring about the IR laws.

Has anyone ever wondered why, in Oz, it doesn't seem possible to be a greenie and get organised without joining the archetypal dole bludging, dreadlocked, anti-development hippy, Peter Garret wanker community?

I just wish there was a fascist enivormental movement. After all Fascists need to eat and breathe too.

Personally, I think Lovelock (?) got it right with the Gaia concept. Maybe staph aureius, AIDS, bird flue etc are just the ranging shots in Earth's fight back.

A couple of footnotes:

Our Seppo mates extensively utilise 'outdoor air-conditioning' in such hotbeds of PC actors such as Florida and CA. But never fear, both Taaaaam Cuz and Angelina have traded in adopting orphaned, third world peasant progeny for the real, live child (Ceasar natch!) - although I understand there is some debate over Taaaam's role in the conception.

For reasons I don't understand, the hole in the Ozone over Antartica is closing and will be gone in a couple of years. Mr Garret is not amused!

Hey Bodgy,

Maybe we should start our own green group. We could invite Shedhand to join us.

Chris

Absolutely, Grunt!

I'm gonna have fun thinking of a name for us.

Interestingly, this is exactly what the Tory party in the Old Dart is doing. They must have seen an opportunity, although Blair is self destructing and well past his use/by.

(Having just spent the last month over there - it was the wettest period since the 18th century and I was denied my in-alienable right to teach the Poms Oz sledging. My 4 x cricket games all got washed out)

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Originally Posted by Bodgy

For reasons I don't understand, the hole in the Ozone over Antartica is closing and will be gone in a couple of years. Mr Garret is not amused!

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It was (alledgedly) never a problem, just an excuse to ban a product that was running out of its patent (fluorocarbon). Funnily enough the company that owned the patent (and stood to lose mega-millions in royalties after it expired) also had the replacement. They (alledgedly) were also kind enough to fund the greenies in their campaign against the fluorocarbons.

Oh, and the ozone hole? NASA determined in 1957 that the enlargement and reduction of the hole was a natural phenomena linked with the oscillation of the earth around its axis.

Oh yeah, alledged hole, alledged NASA. There was a book about it - no really - there was.

All I know is that I am no longer building a pond in the backyard if I have to get rid of the plants every month when they get too big! The fish might get cold!

Groggs

Wanna join our nascient Greenie Party?

Isn't solar power, like, a huge waste of resources? Shouldn't we have, like, a sustainable sun that will last for a Brazillion years and not cause cancer causing sunburn? I mean, wouldn't it be great if we could turn it off at night and just save it from burning all that gas unnecessarily?

And if the ice caps melted we could just turn it down a little? Or turn it up when we need to grow food or get a tan?

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Originally Posted by Bodgy

Groggs

Wanna join our nascient Greenie Party?

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I'm in, the NGP huh? Sounds like a sparkplug! We'd have to have a different colour or we'd never be able to hold a rally without having an identity crisis. How about brown shirts? No, that's been done hasn't it. What about nice greyish blue, like the Melbourne sky?

(I better stop, sorry everyone, it's been one of those days - I claim jetlag.)

Great idea Groggy, the western hemisphere might complain when we turn the sun down during our night.

I suppose they don't matter, it's mostly Seppos and Poms.

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Originally Posted by Grunt

Great idea Groggy, the western hemisphere might complain when we turn the sun down during our night.

I suppose they don't matter, it's mostly Seppos and Poms.

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Let 'em build their own sun. :D