# Talk:The Limits to Growth

## Runge Kutta numerical integrations

I remember reading a thesis done at the Colorado School of Mines. A chap tried to reproduce the study on a CDC and couldn't. The original study was done on an IBM which has much smaller floating point precision. The chap found many of the numerical integrations were not converging.

I have since looked for but have been unable to find the thesis - it would have been printed about 1973-1976.

Finding this thesis and verifying what it says would be a good thing to do because it means the study was mathematically not correct in addition to all of the other criticisms. Bascially GIGO. terr 03:00, 14 September 2006 (UTC)

Hmm. I wonder what are the exact changes between World3/1974 and World3/1990, since World3/1990 was designed to run on PC's. Jrincayc 03:57, 14 September 2006 (UTC)
Actually, come to think of it, I replicated the non renewable resource equations in python using doubles, Talk:World3_nonrenewable_resource_sector without noticing any serious differences. Jrincayc 12:22, 14 September 2006 (UTC)
This would make sense. The PC uses an IEEE specified format which has 80 digits of precision in the FPU and 64 typically in the floats.... however 80 bit floats can be used. The CDC machines had 120 bit doubles. Whether you use Python or any other language doesn't really matter.
I don't know how we can prove whether the Runge Kutta integrations converge or not... I think you'll have to do some digging. Numerical Receipes might be a place to start. I have the FORTRAN version but I'm comfortable with C and other languages. I have never looked at the source code and I really don't have enough time to do so - however I would be willing to work with you and write some functions you could call from Python to crunch some numbers. The issue is I don't think we can get 120 bit and I do know that if we adjust the steps on the RK integrations we are not suppose to need the higher precision. I do not think the code is the problem... I think the problem is the step sizes... I'd try playing there first.
What we really need is to find the Thesis. We do not know _which_ integrations the guy was talking about. Hopefully someone will step forth. BTW. Replicating doesn't prove convergence... it might just prove similar non-convergance... IE. The algorithm can head into the hills but in both machines it might have headed in a similar (worng) direction.terr
It is possible that Jay Forrester's DYNAMO simulator was used to generate the results. I used DYNAMO to investigate international exchange rates ~1972 using open difference equations. DYNAMO was written in FORTRAN and should be available somewhere. It ran on an IBM 360/370 platform.--Ozzie66 17:31, 30 March 2007 (UTC)

## Exponential index formula

Limits to growth does not give the exponential index formula, so I had to rederive it. The question is how long with the resource be used up. Since the exponential assumes that there is a constant rate of growth, it can be done as so: ${\displaystyle S=\int _{0}^{b}e^{kt}dt}$ where S is the static index (this normalizes the first years use to 1), ${\displaystyle k=\ln(1.0+r)}$ where r is the annual rate, and b is the exponential index. So, after integrating and solving for b, this works out to ${\displaystyle b={\frac {\ln(k(S+1)}{k}}}$. Jrincayc 20:58, 5 Dec 2004 (UTC)

Here is an example. On page 250-251, Introduction to Nuclear Concepts for Engineers by Robert M. Mayo has the following quote: "For the year 1995, about ${\displaystyle 4.7\times 10^{30}}$ J of electrical energy was consumed worldwide. Catalyzed D-D burning of seawater can then supply this constant rate for more than 100 billion years. Even allowing for a very liberal growth in electrical energy demand and complete elimination of all fossil fuel burning still does not detract from the conclusion. There is more fusion fuel available than earth inhabitants will ever need." So, for this example, the static index in 100 billion years, or 1e11 years. Assuming a growth rate of 0.1 percent per year (low compared to growth rates of energy after the industrial revolution), k = ln(1.0 + 0.001) = 0.0009995, and b = ln(9.995e-4*(1e11+1))/9.995e-4 = 18429 years, which is only about four times longer than human recorded history, or definately less than all energy earth's inhabitants will ever need. Jrincayc 12:40, 18 May 2006 (UTC)

## Controlling the birth rate

Well said! (see above: Exponetial index formula) Very well said and well illustrated.

This is exactly the point. Unless humanity is willing to stabilize its birth rate which means there has to at some point be ZERO population growth - then humanity is doomed! None of the world's problems have a solution while people think they can have x number of kids where x is a number much greater than 2.

## Swipe at Skeptical Environmentalist

User:User:24.253.113.115 wrote: Swipe at Skeptical Environmentalist exemplifies deficiencies of the Limits to Growth approach.

What Limits to Growth actually has is the above table which has the current reserves for oil running out in 1992 assuming constant exponential growth.

Divorced from context, the above statement is misleading. The book very clearly predicted that we would start running out of resources in the 1980s, 1990s, and later unless we implemented radical changes to our economy and polity in the 1970s (changes of a magnitude that, as a practical matter, would have required central coercion and would have given people such as the authors inordinate power in shaping society).

The truth of the above quotation is central to the weakness of the book; the authors assumed constant exponential growth in consumption and arbitrarily decided that everything else (productivity, technology, replenishment) would remain relatively fixed. In essence, the authors chose parameters that guaranteed the desired outcomes but had little relationship to reality (the pace of evolution in the decades preceding publication suggested anything but a sudden halt).

Limits to Growth was a pseudo-scientific attempt to justify a radical environmental ideology. It was wrong and has negligible value. Such irresponsible work undermines legitimate efforts to improve the earth.

[1] Writing for the Michigan Law Review, Alex Kozinski discussed Limits to Growth at length at the beginning of his heavily sourced, comprehensive review of The Skeptical Environmentalist. Lomborg earned the enmity of the environmentalists because he demonstrated the manner in which many leading environmentalists manipulate statistics to bolster political agendas.

I was unable to find justification of the claim that: The book very clearly predicted that we would start running out of resources in the 1980s, 1990s, and later unless we implemented radical changes to our economy and polity in the 1970s. The 'standard run' chart figure 35 for example shows the industrial output collapse begining at around 2010. On page 66, Limits to Growth states: Given present resource consumption rates and the projected increse in these rates, the great majority of the currently important nonrenewable resources will be extremely costly 100 years from now. That would be in 2072. If you actually look at the growth rates of for example petroleum consumption from 1960 to 1970 [2], the growth rate is exponential at 7.9% (higher than the 3.9% figure that Limits to Growth uses). The primary reason that there was no collapse of oil was because of OPEC raising prices dramatically, instead of hitting a geological limit. Lomberg clearly claims that Limits to Growth states that we will run out of oil in 1992, but the reference is to the table of exponential indexs. This table does not say that we run out of oil in 1992. I can certainly believe that the book implies that we will start noticing running low of resources in the 1980s, but I question the statement that it very clearly does. If it very clearly does, than please enlighten me as to where? Thank you. Jrincayc 23:18, 6 Feb 2005 (UTC)

From its very title to its overall tone to its dire warnings, LTG strongly implies that the rundowns would begin in the near then-future--as you note. From the intensity of their implications, I think the inference that their implications rise to the level of predictions is reasonable.

Of course, the authors were surely aware that use of mere strong implication and qualifying language would allow them to straddle their quasi-predictions and abandon them without acknowledging how totally wrong they were--just as this technique would have allowed them to claim vindication had history proven them correct.

Inferences are interpretations, so by definition the book does not necessarily have to state expressly what I inferred. However, publishing a tract full of alarmist pseudo-science and then hiding behind qualifiers stinks of intellectual cowardice (citing OPEC is all fine and well, but it reminds us that LTG didn't take adaptation, market mechanisms, technology, etc. sufficiently into account, calling the entire premise of the LTG model's utility into question). To me, the thrust of their implications amounted to very clear predictions, but that might take the interpreting dangerously far.

So, I concede that "predicted," or "arguably predicted," or "very strongly implied" might have been better choices than "very clearly predicted;" and your agreement on "implies" is certainly defensible. Nevertheless, my mildly imprecise wording warranted rebuttal and not exile from the main page; my interpretation of LTG is a valid counterpoint. User:Chrisa798

I have no significant objection to you working on the phrasing and content of the article. And for what it's worth, I did not remove you text (I thought I was too biased to safely do so.). I certainly agree that the World3 model fails to take into account market mechanisms. I do wonder what would have happened if OPEC had not caused high prices in 1979, and instead the natural causes had caused an oil shortage in the 1990s. Meadows et al explicitly state that their model does not take into account political events, so I think OPEC is a fair reason for their ideas to fail. I encourage you to find examples of quotes where they are implying sudden collapse, or if that is difficult, find examples of contemporary (1970s) interpetations to that effect. I think those would be interesting and useful additions to the article. Thank you. Jrincayc 03:36, 25 Feb 2005 (UTC)
To quote from a Mobil add that appeared in the Oct 22, 1973 Time magazine, page 1, Vol 102, No. 17: "It takes nature millions of years to create an oil field. It takes man only 20 or 30 years to use it up. ¶ Some day, all the wells in the United Statse will run dry and die. We're sorry to have to tell you that most on land are past their prime. ¶ Fortunately, there is more oil to be found. Some will be discovered on land; but the really promising areas are at sea." I think that this is rather strong evidence that oil shortages are being noticed. Jrincayc 16:15, 20 Mar 2005 (UTC)
Howard Friel has provided more than adequate criticism of bjon lomborg, who is now sort of coming around Mercurywoodrose (talk) 02:07, 17 September 2010 (UTC)

## Price Effects

In addition, several economists believe that the books is false because it leaves out a key factor: price. If prices rise, consumers will conserve, and producers will produce more or substitutes will be found.
However, several people, including Julian Lincoln Simon, believe that as long as the human mind is free (Simon's "Ultimate Resource", this will not be a problem.

which was removed by User:Sunray with the comment: rv - actually the authors did discuss price and its effects; best you find a source for this and quote it

The authors of Limits to Growth do discuss price and its effects in Beyond the Limits and the 30 year update and possibly in the original book, but the world3 model is seriously lacking in some important price feedback effects. For example, the natural resources model allows the price to increase by a factor of 80 without any direct effect on resource use, instead the only effect is on the amount spent on obtaining the resources. The resource use is then decreased when the economy collapses, but this is a rather late effect. The book Models of Doom best describes this. Jrincayc 16:25, 6 November 2005 (UTC)

The effects of price are discussed in Limits To Growth, but only fleetingly. --crafty bison

## Removed LaRouche

Removed:

Another harsh critic of Limits to Growth was Lyndon LaRouche, who authored a 1983 book There Are No Limits to Growth and included the Club of Rome prominently in his view of a global Malthusian conspiracy. [3]

LaRouche's views are not significant to anybody except LaRouche and his tiny band of followers. --Robert Merkel 05:33, 5 May 2006 (UTC)

## Sentence about the "point" of the book

I removed the following from the text:

Nevertheless, many today think that the overall message was accurate: the resources of the Earth are finite and are thus, inevitably, subject to natural limits.[4]

I think this sentence is pretty content-free. The authors made specific, dire predictions, which, as we know, did not come to pass in any way, shape or form. The authors did not assert, "Hey, these things are finite. They're going to run out some day in the indeterminate future". They claimed these resources were going to run out and gave dates. I think it's pretty clear from even the most cursory observer that their modelling was wrong.

It is not clear at all that their modeling was wrong, actually, and nobody has been able to cite a reference in the original work where they gave the dates you describe. Some critics have taken data or quotes out of context to try and make this point, but the original text makes no such claims.Ericy (talk) 13:11, 11 March 2008 (UTC)

Now, this quote says that they were essentially right because of a fact which has nothing to do with their assertion, and is trivial besides. Of course resources are finite, noone argues this. The argument is how much of it we have. And it is clear that these authors had some serious problems in their modelling. (And, hey, I should know. I just gave a final in my Intro to Math Modelling course. w00t)

Well as you say, from this point one can conclude that the resources will run out at some point in the indeterminate future, and hence there really are limits to growth. The only point open for debate then is roughly how long will it be before we reach these limits.Ericy (talk) 13:11, 11 March 2008 (UTC)

Seriously, the sentence I removed is analogous to something like someone predicting "The Chicago Cubs will win the World Series in 2006," and when they don't, an apologist coming along and saying "Well, the commentators overall message was accurate: it stands to reason that if baseball is played long enough, the Cubs will win the World Series at some point." --Deville (Talk) 04:04, 9 May 2006 (UTC)

(Off topic discussion moved to new section Predictions)
Followup: we're also getting a bit far afield here anyway. This section originally started when I mentioned that that earlier sentence was useless. Do you agree?--Deville (Talk) 13:06, 11 May 2006 (UTC)
I think that the earlier sentence is at minimum badly written, and taking it out is acceptable. Jrincayc 12:25, 12 May 2006 (UTC)

## Predictions

I will send $5 US to the first person who can show me a definative and non-trivial prediction that the authors made in the book Limits to Growth and that has not come true. I reserve the right to choose what I consider definative and not coming true, but this should be easy to pass if there really are specific and dire predictions that should have happened already in Limits to Growth. Put the page number, the prediction, and evidence that it did not come true in a comment below. Good luck. Jrincayc 12:32, 9 May 2006 (UTC) Try "the world population will be 7 billion in 2000". PayPal to my address, please. --crafty bison Hmmm, let's see: • "there will be a desperate arable land shortage before the year 2000" • we will run short of gold by 1979 • we will run short of silver by 1983 • we will run short of tin by 1985 • we will run short of zinc by 1989 • we will run short of mercury by 1990 • we will run short of petroleum by 1990 • we will run short of natural gas by 1992 Except for petroleum, all these commodities are markedly cheaper than they were when the book was written. And the recent price spike in petroleum quite probably has more to do with geopolitics than supply, but, hey, I'll give that to you. That's seven predictions which are flatly wrong, do you own me$35?  :)
Seriously, predictions like this are wrong all the time. People use models they like, and sometimes these models work, and sometimes they don't. This is ubiquitous in science, and especially so in such a complex and (at the time) new field of environemental science. The science is a lot better now, although admittedly it still has a lot of problems. But in any case the world didn't end in the mid-90s.
And, for what it's worth, even the sentence I removed conceded that few, if any, of their predictions came true, but then claimed that this was alleviated by the fact that they claimed something was finite, and of course it is finite, so they were in some sense "right". --Deville (Talk) 13:43, 9 May 2006 (UTC)
Well, since you didn't provide page numbers, I am assuming that these are the 'predictions' you are refering to:
• there will be a desperate arable land shortage before the year 2000. Full quote page 51. "Figure 10 shows that, even with the optimistic assumption that all possible land is utilized, there will still be a desperate land shortage before the year 2000 if per capita land requirements and population growth rates remain as they are today." This is a conditional prediction based on per capita land requirements and population growth rates staying constant, therefore, as I read it, there is no specific dire prediction here because the two conditions failed.
• we will run short of gold by 1979, we will run short of silver by 1983 ... You are probably refering to the "Exponential Index" of reserves that appear on pages 56-59. As the Limits to Growth article already discusses this is again a conditional prediction depending on no new reserves being found and on continued exponential growth.
So, I don't consider anything that you have put to be specific predictions. As User:Chrisa798 stated earlier in this discussion: "Of course, the authors were surely aware that use of mere strong implication and qualifying language would allow them to straddle their quasi-predictions and abandon them without acknowledging how totally wrong they were--just as this technique would have allowed them to claim vindication had history proven them correct." I don't think that the authors of Limits to Growth are completely correct by any means. In particular, the Non-renewable resources model in world3 should be taken out and shot. However, I have not found any non-trivial, definitive prediction that is in Limits to Growth that would have come true or false by now. Good luck in finding them. I look forward to seeing what you come up with. Jrincayc 02:07, 10 May 2006 (UTC)
Ok, fair enough. What you're saying, then, is that the book makes no predictions at all? If yes, what predictions did it make? --Deville (Talk) 13:01, 11 May 2006 (UTC)
Well, I am reading over the book looking for predictions, and so far I have seen dire quoted predictions, but not a single unconditional prediction. Most of the predictions are partially irrelevent now because they have the condition of continued exponential growth at approximately the same rates. However, the growth rates of population and resource consumption have decreased quite a bit from what they were in the 1960s (at the cost of a recession or two, a couple civil wars, a new disease, and quite a bit of intentionial lowering of consumtion and population growth). So, I am looking for predictions, and my $5 offer still stands. I will make a comment here when I finish the book. Jrincayc 12:25, 12 May 2006 (UTC) I finished reading Limits to Growth. Here are two predictions in it: "Given present consumtion rates and the projected increase in these rates, the great majority of the currently important nonrenewable resources will be extremely costly 100 years from now." (page 66 LTG). "We can thus say with some confidence that, under the assumption of no major change in the present system, population and industrial growth will certainly stop within the next century at the latest." (page 126 LTG). The only really define predictions that don't have loads of qualifiers are quite a bit in the future (as in the 2070 or so range). So, yes, there are some predictions, but most of them will not be tested for awhile. I think that the 2.2 percent population growth of the 1970 was definitely not sustainable for very long, and I don't think the current oneish percent is very sustainable for very long either. I think I was rather disappointed in how little the ideas have changed between Limits to Growth and Limits to Growth, the 30 year update. For example, where is the hard consideration as to what really slowwed the 2.2 percent population growth, and the 6% (in US) growth of use of oil? Where is the thoughtful examination of how the model actually implements nonrenewable resources. Back, to the previous question, I was unable to find any predictions that have been proven false. It would still be interesting to find them. Jrincayc 14:43, 14 May 2006 (UTC) There is a reason that they updated the text - first in 1992, and then again in 2002. Mainly to compare and see how well their scenarios hold up, and also to re-run the computer model with the latest data. I should also add that the authors don't claim that their work is in any way prediction - they are scenarios. They run a number of different scenarios with differing assumptions, and by comparing the results, they can conclude that some ranges of futures are unrealistic, and other futures are more likely. In the preface to the 2004 book, they state that they will once again update in the year 2012, when they expect that there will be "abundant data to test the reality of overshoot".Ericy (talk) 12:22, 11 March 2008 (UTC) So, I guess what you're saying is, not only were they not right, they weren't even wrong? --Deville (Talk) 22:48, 14 May 2006 (UTC) I think the agricultural model they used in World3 might be right. The nonrenewable resource model is mostly wrong. Population, sorta right. I think they are more right then their detractors admit and less right then they think they are. I personally am eagerly awaiting the world4 model. So, yes, they are not right, and they are not wrong, but somewhere in the middle (and you put that wonderfully). Jrincayc 01:57, 16 May 2006 (UTC) ──────────────────────────────────────────────────────────────────────────────────────────────────── I hate to return to a 4-year-old thread, but "not even wrong" is an expression meaning (in this context) that the book actually makes no testable predictions. I'm not sure that Deville meant that at the time, but it seems a reasonable comment about the book if someone actually said that. — Arthur Rubin (talk) 01:45, 8 August 2010 (UTC) I think the book makes surprisingly few testable predictions. My$5 offer still stands. I think there are parts of the world3 model that are blatantly wrong, such as the non-renewable resource section (it lumps together things like oil (limited, energy use non-recycleable), limestone (of which there are massive quantities) and aluminum (large quantities, recyclable)). It also has things like the exponential reserve index, that an understanding of is very important. I think this is still an interesting thread, even if it is about a three decade old disscussion. Jrincayc (talk) 13:27, 8 August 2010 (UTC)

## The correct title is "The Limits to Growth"

The title of the 1972 book began with the word "The". The 2004 update did not.

A proper fix to this would include renaming the article, and providing redirection for the old title, because other articles link to it.

Agreed it's strange without The, in particular with a picture of the first edition clearly showing "The". Since the article is mainly about the first edition I will go ahead and try to make the the change. Fothergill Volkensniff IV (talk) 01:12, 24 November 2008 (UTC)

## 2 vs 5 for factor of reserves

In the criticism section, there is some confusion over which factor was being used. For individual materials, they used both the actual reserve values and a factor of 5. For the overall amount of resources (where they aggregate everything into one lump) they use both a factor of 1 and a factor of 2 (and in Dynamics of Growth in a Finite World I think they also use a factor of 10). So if you are talking about individual resources, it is 5, and if you are talking about total resources it is 2. The section could be more clear about that. Jrincayc (talk) 13:38, 18 February 2008 (UTC)

Total resources seems more relevant where this discussed in the article.Ultramarine (talk) 14:19, 18 February 2008 (UTC)

## removed

removed this quote from Exponential Reserve index for inaaccuracy:

For petroleum, neither assumption was correct in the years that followed due to the OPEC's oil embargo, followed by a return to increasing production.

Oil is still finite, as opposed to the view espoused by the author, and in addition the world has since reverted to an "undulating plateau" period, not growth. ays (talk) 16:55, 30 April 2008 (UTC)

Okay. I agree that oil is finite. What I was trying to say when I wrote that was that oil production was not increasing at an exponential rate, and neither was it constant. Do you agree with that statement? Jrincayc (talk) 12:36, 1 May 2008 (UTC)
Yeah, that's significantly better - the earlier sentence is just misleading because it sends out the notion that production has increased constantly since that period, which is just false. I appreciate the work you've put into the article, though. ays (talk) 05:56, 3 May 2008 (UTC)

## Extraterrestrial reserves?

In the "criticism" section, just before the "neutrality" tag, there's the suggestion of the possibility of extraction of raw materials from outside the Earth. I think it's too far fetched to be placed as an alternative in such an optimistic manner. It's also somewhat argumentative in a way that the article stretches a bit beyond the book (I guess), and start to look somewhat like original research. Perhaps there's some way to phrase this alternative in a manner that better suits the context, but maybe it should be removed altogether and dealt with in a specific article (if there's really a problem with that, anyway, I'm not making a strong case against it), but for while I'll just find some way to add a link to the "space mining" article/stub. --Extremophile (talk) 22:31, 17 August 2008 (UTC)

Given the time scale of the forecasts for which the models apply, it is in fact certainly arguable that consideration of terra-forming other nearby planets or discovering more advanced energy sources is a reasonable point of view..

## CSIRO review

Someone with better editing skills than me may want to add this in: CSIRO believe the book's model has held up pretty well compared to real-world data http://www.csiro.au/news/The-Limits-To-Growth.html —Preceding unsigned comment added by 121.73.160.57 (talk) 20:27, 12 November 2008 (UTC)

Interesting. Here is a link to the actual paper: http://dx.doi.org/10.1016/j.gloenvcha.2008.05.001 I don't have access to the article but it is probably correct that the world3 model is matching real-world data, since some of the problems with the model (such as the non-renewable resource subcomponent) aren't really going to show up yet. Jrincayc (talk) 03:38, 15 November 2008 (UTC)
I added some info and a link to the full report, it's a PDF. I'll add the doi.org link also since that is more official. Fothergill Volkensniff IV (talk) 01:24, 24 November 2008 (UTC)
Interesting, I just skimmed the pdf and looked at the graphs. Thanks for the link. One more thing to read over my holiday break :) Jrincayc (talk) 03:52, 24 November 2008 (UTC)

The fundamental point of TLTG is the assumption that problems grow exponentially but solutions grow linearly. Since an exponential curve will inevitably end up cutting a linear curve, their model is foreordained to predict disaster. I think the article really ought to make this obvious point somewhere.

Malthus, too, made the apparently arbitrary, and as experience has shown incorrect, assumption that food production grows linearly with time, rather than the more natural assumption that it grows with unit-of-effort-expended, ie proportional to population.

A second order point is the primitiveness of the model (at least by modern standards). They have only one variable for "pollution". For CO2, they projected exp growth and 380 ppmv by 2000 (fig 15). They were correct. For lead, they noted exponential growth to ~1955 (fig 21) and though they weren't incautious enough to predict the future, since this is folded into their one "pollutant" variable they were effectively predicting continued exponential growth. This didn't happen; they were wrong.

William M. Connolley (talk) 22:06, 19 June 2009 (UTC)

I agree that LTG generally tends to assume that problems grow exponentially but solutions grow linearly. world3's food production model basically has a 'production possibilities frontier' that allows a certain amount of production of food for a given set of land, fertilizer and labour inputs. So the disagreement over food is production is more a disagreement on the form and coefficients of the equation. As for better models, I am curious if there is a newer model of equivalent scope. Jrincayc (talk) 22:25, 21 June 2009 (UTC)
The 30 year update uses a new model (World3) - I'm not sure if this is what you mean. William - your comments seem to be drifting towards original research. LTG correctly predicted world population 30 years in advance. Food production has grown linearly recently btw, and I hope it continues to.... The reason for using simple variables such as "pollution" rather than many smaller and more complex ones is to simplify the results. In the most recent version they are trying to show what the main effect of changes will be rather than trying to foretell the future. They realise that their model is incorrect but it is one of the best global models available. From what I've read of both the original and more recent update the whole point of the books is to try show what effects our current behaviour is having so that we can take action to try and improve things. Whether their predictions are accurate is pretty irrelevant. Smartse (talk) 12:52, 22 June 2009 (UTC)

## Peter A. Victor redlink removed too quickly?

Peter A. Victor redlink removed too quickly? 209.255.78.138 (talk) 17:59, 7 April 2011 (UTC) Do not be afraid to create links to potential articles that do not yet exist (see Red links below), per Wikipedia:Manual_of_Style_(linking)#What_generally_should_be_linked, also Wikipedia:Red link "One study conducted in 2008 showed that red links helped Wikipedia grow". Since this a critic in this article, I'd hope a wp article would be created. Mr. Rubin, please "give hope time" (said with all due cynicism). 209.255.78.138 (talk) 19:47, 7 April 2011 (UTC)

"A red link to a non-notable person can end up being a link to a different person of the same name." — Arthur Rubin (talk) 21:45, 7 April 2011 (UTC)
That makes sense, but isn't 209's point the speed at which you delete redlinks? It obviously is not a link to the wrong article now, as it is a redlink. 99.19.47.120 (talk) 06:04, 8 April 2011 (UTC)
If this person is not notable, should they be removed from this article? 99.181.155.158 (talk) 03:54, 22 April 2011 (UTC)

## Exponential reserve index formula is wrong

The formula

${\displaystyle y={\frac {\log(1-(1-g)\times {\frac {R}{C}})}{\log(g)}}-1}$

is wrong. The -1 at the end is incorrect.

Instead of using g = 1.026, use g = 0.026 where g now becomes the annual growth rate factor. Thus substitute 1 + g for every occurance of g in the above formula. This turns the formula into

${\displaystyle y={\frac {\log(1+g\times {\frac {R}{C}})}{\log(1+g)}}-1}$

Now as ${\displaystyle \alpha \rightarrow 0}$ the expression ${\displaystyle log(1+\alpha )\rightarrow \alpha }$. Thus if ${\displaystyle g\rightarrow 0}$ in the expression above. Then

${\displaystyle {\frac {\log(1+g\times {\frac {R}{C}})}{\log(1+g)}}-1\rightarrow {\frac {g\times {\frac {R}{C}}}{g}}-1={\frac {R}{C}}-1}$

Hence in the limit of ${\displaystyle g\rightarrow 0}$, the expression in the Exponential reserve index section becomes

${\displaystyle y={\frac {R}{C}}-1}$

This is obviously wrong. In the limit of ${\displaystyle g\rightarrow 0}$, there is no exponential growth and the years to use up a resource should R/C, the static limit. The -1 in the expression is wrong and should be removed. I do not get a -1 when I derive the equation. — unsigned comment by Pionade (talk) 07:56, 9 August 2011 (UTC)

You're right.
${\displaystyle R=\sum _{i=1}^{y}{C\times g^{i-1}}=C{\frac {g^{y}-1}{g-1}}}$
reverts to the formula as you wrote it. However, we need to report what appears in the book, not the correct formula. — Arthur Rubin (talk) 08:42, 9 August 2011 (UTC)
Bloody hell, Rubin, are you serious? This mocks our esteemed Wikipedia is about verifiability, and not about truth policy, and turns it into something out of Monty Python. Isn't there a reference that has the correct formula? --Epipelagic (talk) 10:29, 9 August 2011 (UTC)
This article is about the book, not the concepts. If the book has it wrong, and we can find a reference with the correct formula, we should mention both in the article. I don't have copy of the book, myself. That being said, my mother's book Set Theory for the Mathematician had at least 120 errors in the first edition, 30 of which derive from an uncaught conceptual error on cofinality, so if it's corrected in a later edition, we probably shouldn't comment on the error. — Arthur Rubin (talk) 19:03, 9 August 2011 (UTC)
I'm actually more curious why the formula wasn't written
${\displaystyle y={\frac {\log(1+(g-1)\times {\frac {R}{C}})}{\log(g)}},}$
As the growth factor g is usually greater than one. — Arthur Rubin (talk) 19:12, 9 August 2011 (UTC)
Keep in mind Wikipedia:No original research. 97.87.29.188 (talk) 20:43, 9 August 2011 (UTC)
Here is the formula from page 60, limits to growth.
${\displaystyle exponential\,index={\frac {\ln((r*s)+1)}{r}}}$
Jrincayc (talk) 03:22, 11 August 2011 (UTC)
That makes more sense.
${\displaystyle R=\int _{0}^{y}Ce^{\rho t}\ dt={\frac {C}{\rho }}\left(e^{\rho y}-1\right)}$
reverts to
${\displaystyle y={\frac {\log \left(1+\rho {\frac {R}{C}}\right)}{\rho }}.}$Arthur Rubin (talk) 03:39, 11 August 2011 (UTC)
See #Exponential index formula above. — Arthur Rubin (talk) 07:34, 12 August 2011 (UTC)
Changed in the article text. Jrincayc (talk) 03:18, 17 August 2011 (UTC)

## Unclear as to why this was completely deleted ...

In 2011 Ugo Bardi analyzed the The Limits to Growth, its methods and historical reception and concluded that "The warnings that we received in 1972 ... are becoming increasingly more worrisome as reality seems to be following closely the curves that the ... scenario had generated." [1]

Deleting editor's comments were "Doesn't belong in the lede; not clear that it's the author's _opinion_, even though nominally reliable." Not sure what was the attempted intend was, but it doesn't sound as if complete deletion was warranted. Also who is Ugo Bardi? 99.181.132.165 (talk) 05:01, 12 August 2011 (UTC)

I don't know who Ugo is, but the reference seems to be a paper or book published by Springer, which would make it generally reliable unless it were an editorial or letter. The lede, however, needs trimming of specific criticism or support, in favor of summarizing the criticism and support which should be detailed in the body. — Arthur Rubin (talk) 06:16, 12 August 2011 (UTC)
Google shows Ugo Bardi as [professor of Chemistry in Firenze, Italy and on the International Board of ASPO. He is the author of a recent Springer book The Limits to Growth Revisited to which Springer gives free access to parts of here. Unfortunately most content is blanked out, but the citation introduced earlier is visible on page 3 in the introduction. I find the book a relevant addition to the discussion on Limits to Growth, as apparently did Springer. The book is academic, Bardi deals with the modeling used in 1972 and interestingly economic models about technological change in general, yet the focus of his book seems the public reception of 1972 Limits to Growth in the years since then. Others cited higher up in the lede already demonstrated that "reality seems to be following closely the curves...", so Arthur Rubin has a good point that the lede becomes too long by citing Bardi's book in detail. The citation does seem valuable though. Would it be an idea to expand the 'criticism' section further down below and call it e.g., 'reception', to allow for criticism, support and analysis of the discussion in the section? --EphemeralKnowledge (talk) 07:42, 12 August 2011 (UTC)
I agree with you EK. The critical commentary on this article does not reflect the current literature at all, and needs rewriting. --Epipelagic (talk) 10:41, 13 August 2011 (UTC)
Is this "ASPO" = Association for the Study of Peak Oil and Gas? 64.27.194.74 (talk) 19:43, 12 August 2011 (UTC)
That wp article shows peakoil.net as its official website; appears equal, yes. 99.181.128.152 (talk) 06:09, 13 August 2011 (UTC)

## Another equation

this youtube video by Albert A. Bartlett has an equation at 4:36 which differs from others here. its called the "Expiration Time or "T sub E", of a non-renewable resource whose rate of consumption is growing steadily". If anyone else thinks his equation is relevant, can they transcribe it? the math is beyond me.(mercurywoodrose)76.232.9.165 (talk) 02:00, 27 October 2011 (UTC)

## recent revert

This revert comment "this section is about the criticism that occurred soon after publication, not decades after publication" does not make any real sense. The changes I made only synched the content to the cited source, removing the op-ed content with a more detailed description of Wallich's criticisms. There is nothing in the change relating to criticisms from decades later. aprock (talk) 17:42, 3 November 2011 (UTC)

Here is what I originally wrote[5]: Yale economist Henry C. Wallich labeled the book "a piece of irresponsible nonsense" in his March 13, 1972 Newsweek editorial. Wallich's main complaints are that the book was published as a publicity stunt with great fanfare at the Smithsonian in Washington, and that there was insufficient evidence for many of the variables used in the model. According to Wallich, "the quantitative content of the model comes for the authors' imagination, although they never reveal the equations that they used." Considering that the detailed model and Meadows et al justifications were not published until 1974 (two years after Limits to Growth) in the book Dynamics of Growth in a Finite World, Wallich's complaint about "the peculiar presentation of their work and by their unscientific procedures" has merit.
Here are some more quotes from the article that I did not add to the original edit:
Quote: Economists often build models broadly of this sort. It is well known that a model can be made to produce any outcome that one wants--steady growth, stability, regular fluctuations, explosive upsurge, or collapse. It all depends on the interactions one assumes. Progress in economics has consisted in replacing these arbitrary assumptions by stable relations grounded in statistical research.
Quote: "Limits" is full of statistical material on natural resources, pollution, etc. The unwary reader is made to believe that these form the basis for assigning magnitudes to the interactions in the "world system." So far as I have been able to discover, this for the most part is not the case. The statistical material is illustration and anecdote; the quantitative content of the model comes from the authors' imagination, although they never revel the equations they used.
Quote: Their principal assumptions are, broadly, that natural resources cannot be expanded very much by new technology, that pollution cannot be very effectively controlled, and above all that people show so little foresight that they always overshoot the equilibrium point and land in disaster. In each instance, the opposite assumption seem to me more plausible, leading to the opposite results. Considering the unbelievable difficulties of halting growth and equalizing the world's income, which began to surface at the Smithsonian meeting, there can be no doubt which way the decision should go.
The cited source is March 13, 1972 Newsweek, and the article is "More on Growth" by Henry C. Wallich, page 86. I disagree with Aprock's removal of sourced material. Jrincayc (talk) 15:14, 6 November 2011 (UTC)
Editorials are generally poor sources for an encyclopedia. While they can be used to as a source for the author's opinion (for which the editorial is a primary source), it is preferable that secondary sources be used. The Atkisson book is a much better source for giving a broad overview of the sort of criticisms the book faced on release, and the overall context. To the extent that the op-ed should be used, it would be as additional support for content discussed in the secondary sources. aprock (talk) 17:20, 6 November 2011 (UTC)
I'm surprised to see that you have yet again removed that quote Aprock. A key part of the story about Limits to Growth is the manner in which its arguments were so vigorously dismissed by economists and businessmen. I do not understand why you seem to want to suppress this. --Epipelagic (talk) 03:05, 7 November 2011 (UTC)
I originally added the comments from Henry Wallich because I looked for what I could find on opinions about Limits to Growth right after it came out.Jrincayc (talk) 03:18, 7 November 2011 (UTC)
As noted above, the extent that the editorial is relevant is the degree to which is can support content from the secondary source. I was attempting to rewrite the section based on the broader treatment by Akisson, but was met with immediate push back by someone who didn't bother to review my edits. Removing quotes from a passing editorial that isn't noted by any other source isn't suppression, it's an application of due weight. I'm entirely happy to include a broader discussion of contemporary and current views on the work. Hitting immediate push back just bogs down the process, and makes in an exercise of constant parsing and reparsing. If someone feels this quote is central to the content, I invite them to add it back. That is distinct from reverting the other constructive edits I've made. aprock (talk) 03:29, 7 November 2011 (UTC)

## Removed Citation Needed on Petroleum performance

I don't see what possible citation is needed there... petroleum production and demand, such as they are, are not in dispute. The request dates from 2010. I went ahead and removed it, if we do need a cite, I need to know whether they want a cite from the book claiming exponential demand behavior (which seems uncontroversial given their methodology) or a cite from IEA or something on the oil performance. 12.208.4.65 (talk) 19:34, 27 December 2011 (UTC)

The citation is needed for the statement: "For petroleum, neither the assumption of constant usage or the assumption of constant exponential growth was correct in the years that followed.". This appears to be editorial synthesis. Reviewing the history, the statement was inserted here: "For petroleum, neither assumtion was correct in the years that followed due to the OPEC's oil embargo, followed by a return to increasing production." without a source, and subsequently modified without sourcing. I'll just go ahead and remove the statement. When sourcing is found, restoring similar content would be excellent. aprock (talk) 20:07, 27 December 2011 (UTC)

## Another modern review

This looks like an excellent secondary source which summarizes the cultural impact of the book. I'm just adding this here for now so that I can work on it when I've got time: "Boom And Doom: Revisiting Prophecies Of Collapse"[2]. aprock (talk) 22:12, 7 February 2012 (UTC)

Having just skimmed the book, and finding it to be pretty dated and useless, I'm surprised how biased this article is - shouldn't there be a critique of some sort? (Btw, I do think we will run out of oil etc etc, but book ignores transformative power of technology and does basic Malthus assuming the conclusion. Whether or not you like nuclear energy, if we built 50 new stations US power output would be very different) — Preceding unsigned comment added by 76.110.79.198 (talk) 16:33, 8 January 2013 (UTC)

This illustrates the fact that most people are ignorant of the nature of the book. Nuclear energy systems cannot be funded without huge government subsidies. They do not factor in true costs, which are externalised by leaving problems for future generations. Most nuclear reactors have to be infinitely mothballed after 30-40 years of operation, as they become to radioactive for human safety. If the US built the reactors the poster proposes, the economic collapse would occur even faster. The only known use for nuclear "waste" is building nuclear based weapons.John D. Croft (talk) 10:34, 16 August 2013 (UTC)
If the shortcomings of the book are not apparent to you, try reading the critique that I refer to below to restore some balance. I appreciate that the talk pages are not debating places for the issues covered by the book, but I am concerned that the article itself should be more balanced than it is at present.
Gravuritas (talk) 09:41, 3 September 2013 (UTC)
Mr. Croft's comments are totally wrong. There are some problems with nuclear reactors which are externalized, but the major (US) government "subsidy" is the exemption from class-action lawsuits for damages without evidence of causation. The other statements are interesting, false, and not related to this article. — Arthur Rubin (talk) 09:52, 3 September 2013 (UTC)
If the shortcomings of the book are not apparent to you, try reading the critique that I refer to below to restore some balance. The critiques in this article _are_ insufficient; the book _does_ ignore the transformative power of technology; and it has indeed been described as Malthus with a computer. So Mr Croft's comments are not 'completely wrong'. NPOV please.
Gravuritas (talk) 11:23, 3 September 2013 (UTC)
I meant that Mr. Croft's comments here (in regard nuclear power, above) are totally wrong and irrelevant, except for the first sentence. The question of whether the assumption of cheap (nuclear) power are appropriate is relevant, but the particular errors Mr. Croft asserts are not. — Arthur Rubin (talk) 14:41, 3 September 2013 (UTC)

## famine predictions omitted

I clearly remember specific dates d0from the original LTG of 1975 for early famine starts, and 1980s as the upperlimit for a worldwide famine. Ive also seen CoR extend tthose initial confident predictions. Innovation is not accounted in LTG, and seems a common critique. 01:51, 23 July 2013 (UTC) — Preceding unsigned comment added by Heymikey80 (talkcontribs)

You are confusing "The Limits to Growth" with Paul Ehrlich's 1968 book "The Population Bomb". The Limits to Growth predicted the problems would really start in the mid 21st Century. John D. Croft (talk) 10:29, 16 August 2013 (UTC)
Interpolating from the 'standard run' chart in LtG, 'food per capita' and 'industrial output per capita' collapse very fast after a date before 2010. All the other runs show a collapse of one sort or another well before the mid 21st century.
Gravuritas (talk) 08:12, 3 September 2013 (UTC)

## False statement in first paragraph

The first paragraph states "on the assumptions that exponential growth accurately described their patterns of increase, and that the ability of technology to increase the availability of resources grows only linearly." The limits to growth made no such assumption. This assumption was made by Thomas Malthus 200 years ago, it is not found in The Limits to Growth". I have changed it as a result.John D. Croft (talk) 10:16, 16 August 2013 (UTC)

Exponential growth was indeed considered by LtG to be the natural pattern of increase for most of the variables in question. You are right that they did not assume linear growth in resource availablility: they assumed instead that resources are finite. I've amended the first para accordingly.
Gravuritas (talk) 08:32, 3 September 2013 (UTC)

Donnella Meadows has acknowledged that much of the data needed for the initial book were not available in 1972 and therefore proxies for many factors were required. Also the use of computer modelling was then in its infancy, and the World 3 model used was, at the time, state of the art. The simulations then required a huge amount of computer time to run. The article needs to be amended to reflect this. Criticising the article without mentioning these factors into effect is to take a false point of view. John D. Croft (talk) 11:04, 16 August 2013 (UTC)

I'm surprised that there is no mention of 'Thinking about the future: A critique of limits to growth' which was a near-contemporary criticism by the University of Sussex. I'm currently reading it, together with LtG again, and I'll add a section to this article when I've finished. This should improve the balance of this article considerably. btw John, the criticisms in this source do not depend on the power of the computer.
Gravuritas (talk) 08:37, 3 September 2013 (UTC)

12:51 September 3 2013 NewsAndEventsGuy has moved a comment regarding Malthus from the lead to an obscure position. This leaves the fourth para of the lead as a series of supporting statements and 'criticisms of criticisms' that are not beginning to be covered until later in the article. This now reads more like a publisher's puff piece than an encyclopedia article, and is terribly unbalanced. A bit of balance is more important than a style issue, so will revert the edit for now. I suggest that both criticism and support statements are postponed until after the introduction: maybe the whole para beginning 'In 2008...' should go much further down. Gravuritas (talk) 12:56, 3 September 2013 (UTC)

"This page in a nutshell: The lead should define the topic and summarize the body of the article with appropriate weight."
Malthus is not mentioned anywhere in the body of the article and therefore, your insistence that we take up valuable real estate in the lead's first paragraph to somehow "balance" another part of the lead, is non-compliant with the Manual of Style.
In addition, you call the place I moved it "obscure".... say what? The main body sub-section devoted to related books is an "obscure" location to list a related book?
Also, if were problems with the fourth paragraph, the solution is not to push the first paragraph out of compliance with the MOS as part of your crusade for "balance" in this article. Doing so smells a bit like WP:POV-ization. There's all sorts of approved tools available to you, when you run into perceived problems.
All that said, I happen to agree with you that paragraph 4 is an unreasonable bit of cherrypicking from the material in "books" and "reception" subsections, and I have moved it to those sections intact, and replaced it with (paraphrased) "The book continues to be the subject of fervent debate and subsequent writings." That should address what you claim was "false balance" in the lead (which I neither accept nor reject) while at the same time fixing two different WP:MOS problems with the lead.
Meanwhile, I think the "books" and "reception" section have too much overlap and not enough material to warrant different headings, and think they should be merged. One NPOV way to talk about the various perspectives is to simply summarize each in chrono order.

NewsAndEventsGuy (talk) 17:38, 3 September 2013 (UTC)

Come to think of it, books that do not explicitly discuss Limits to Growth really should be stripped from the text and placed in the a "Further Reading" or similar section. NewsAndEventsGuy (talk) 19:51, 3 September 2013 (UTC)
Thank you for pointing me to WP:LEAD- as a new editor I hadn't read it before though I think I was trying to operate to that sort of guideline anyway.
Agreed that Malthus is not mentioned in the body of the article. However, that's an indication that it's a poor article: why isn't Malthus mentioned in the body of the article? Because it's not balanced. LtG is in a along tradition of similar concerns & predictions, of which Malthus is the best known. Why isn't contemporaneous, serious, criticism mentioned? (e.g. the book I referenced elsewhere) Because the article is not balanced. So your endeavor to give an accurate summary as the lead to an unbalanced article results in an unbalanced lead. However, I'll leave the lead as it stands at present until the article itself is more balanced- then we can resolve the lead.
Why is "reception" limited to post-2000 comments? Because it's a poor article. As I mentioned elsewhere, I'm currently reading the critique and will soon add something appropriate to the "reception" section, which I think should logically be advanced ahead of the "books" section. At that point there should be sufficient material for the two sections to merit being kept apart, so please do not merge the two sections pending this addition.
Gravuritas (talk) 20:58, 3 September 2013 (UTC)
Actually, he was mentioned. I don't know how my text string search missed it before, but there is a reference to Malthus in the books section. Before you edit further, recommend you study WP:NPOV and follow the various links to learn about the tools available to editors wishing to fix what they see as POV problems. As for discussing a whole series of works on this subject, that's the task for some other article in the Environment tree of articles. We shouldn't shoehorn that literature review into the article about any one published work. NewsAndEventsGuy (talk) 21:11, 3 September 2013 (UTC)
Gravuritas (talk) 22:33, 3 September 2013 (UTC)
(A)The "whole series"/"literature review" was my critical assessment of having a section in the body of the article to list books on the approximately the same subject. In my view, the entire "related books" section should be removed, and the contents in that section put into other parts of the article. If they specifically address this book, Limits to Growth, they can go in the "reception" section. Otherwise, they might be better listed in the "See also" or "Further reading" section.
(B) You should also read WP:AGF, and then discipline your mind to not read any ulterior POV motives into my tech writing remarks. Because I have not addressed content at all. 100% of my remarks are to try to move the presentation of existing content closer to wikipedia's standards. In the process, I have not slammed the door on any new content you might wish to add. So go directly to WP:AGF, do not pass Go, do not collect \$200. NewsAndEventsGuy (talk) 23:44, 3 September 2013 (UTC)
(A)Very reasonable as far as it goes. However, given that you're making a number of edits and changes and have studied the "reception" section, I'm surprised that you haven't noticed that we get no breath of any contrary views or criticism of LtG until we get to "reception". Then within "reception", the contemporary criticism starts in para 4, after several supportive comments from the 2000s. Anyone with a NPOV would find that structure odd.
(B)No, you _haven't_ addressed content at all, which I suggest was & is the major problem with this article. You are trying to put a polish on a pig. You also haven't addressed most of the content of my posts in this thread. And as far as WP:AGF goes, re-read this thread, noting in particular your '..smells like WP:POV..', 'crusade' for instance. Glass houses and stones, sunshine.
Gravuritas (talk) 07:27, 4 September 2013 (UTC)
As a new user, here are a few more helpful things to check out.
SUMMARY: Let's see your proposed NPOV RS-based improvements and call this thread a wrap. Just know that at this time I am not interested in studying RSs on this subject (except for verification purposes). Just technical editing for the information that has been included thus far. That doesn't make me a POV ed. If you think there is POV imbalance, fine, try to correct it.... but work within the guidelines and processes and we'll get along great. NewsAndEventsGuy (talk) 19:04, 4 September 2013 (UTC)

## + source (Vaclav Smil)

Critique by vaclav smil in POPULATION AND DEVELOPMENT REVIEW 31(1) (MARCH 2005) page 157 : http://secure146.inmotionhosting.com/~vaclav5/wp-content/uploads/docs/smil-article-2005-pdr2005-1.pdf

fwiw --Kim Bruning (talk) 00:04, 22 March 2014 (UTC)

## The Guardian

theguardian.com 87.78.27.31 (talk) 16:29, 6 September 2014 (UTC)

## Food industry @Trackteur

LTG refers to food production. The Food industry, to which you are repeatedly trying to link, explicitly says: "Only subsistence farmers, those who survive on what they grow, can be considered outside of the scope of the modern food industry." So the link is very misleading in that the food industry as defined in WP does not include the produce generated by subsistence farmers, which LTG includes. I suggest you desist. Gravuritas (talk) 14:41, 20 September 2014 (UTC)

This article currently contains links, in the notes and the references, to Graham Turner's 2008 A comparison of The Limits to Growth with thirty years of reality. These direct the reader to two different pages within the CSIRO website, which in turn provide two different 'file not found' errors. A search of the CSIRO website was unable to locate it.

The document is available online at what appears to be a Colombian website, but I am not sure that this is necessarily an approved host. The paper does contain a copyright notice, indicating that rights to it have been reserved by the Australian government.

Other than this, the paper does not appear to be available - except via the WayBack Machine, where I was able to access it as part of a CSIRO snapshot as at 05 June 2011. Thus, two questions:

1. Does Wikipedia permit/encourage/accept that use of links to WayBack pages?
2. If so, is it reasonable for me, or for a reader of this comment if such is their wont, to amend the links to point to this?

Ambiguosity (talk) 08:41, 18 November 2017 (UTC)

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1. ^ Ugo Bardi. The Limits to Growth Revisited. Springer 2011 DOI: 10.1007/978-1-4419-9416-5 p.3
2. ^ MacKenzie, Debora (10 January 2012). "Boom And Doom: Revisiting Prophecies Of Collapse". New Scientist. Retrieved 7 February 2012.