General discussion

Is math necessary?

As promised, I am starting a post to explore the value of applying a mathematical approach to defining sustainable development. My title (Is math necessary?) is stolen from the title of a humorous essay by James Thurber and E B White entitled "Is Sex Necessary?" So, please take the title with a little of the same tongue in cheek attitude expressed by Thurber and White in their book. 

So, the basic questions that I have include:

1. Does applying a "rigorous mathematical approach" to defining sustainable development help or hinder our ability to understand this concept? 

In support of the former, I would say the language of math adds precision to the approach taken to understanding and measuring sustainable development. In support of the latter position, I would say that this mathematical approach could give the impression of a greater sense of quantitative and theoretical understanding than actually exists. This is dangerous. 

2. Does a purely mathematical approach hinder communication?

Integrals and partial derivatives may only hinder our ability to communicate and discuss sustainable development beyond the "small club" of economists/mathematicians who relish the language of math over the language of conversation and writing. This is especially true the more mired in economic jargon it becomes. 

3. How appropriate is a rigorous mathematical theory of sustainable development?

Does such an approach imbue an inappropriately "scientific" understanding of a concept that is deeply ethical in nature? I question the value of trying to translate ethical principles in mathematical terms, even though I know this has been done by economists for many decades. I still struggle with the as yet unclear basis for saying that basic ethical principles lead to an acceptance of a positive discount rate (!@$#^@$&%!!!). But I will try to find the Koopmans paper from 1960 that allegedly proves this point.

4. Have we simply replaced a vague understanding with a shadowy interpretation?

Expressions such as U(t), V(t), M and W(t) hide a wealth of ignorance. Is this a case of just making ourselves feel better because we have packaged all these unknown and potentially undefinable relationships in compact mathematical forms? I have to say the idea of talking about V as a function of this all encompassing variable we call M for the political economy is--well--a little absurd.

And then there is the "shadow price"--a term conspicuously close to Plato's shadows of the real world observed from inside a cave. Not only is the concept of measuring shadow price incredibly daunting, but I question whether our ability to measure a shadow prices does anything more than help us climb a local hill and never get to the real peak we are seeking. 

5. Is the chasm between holistic theory and specific practice unbridgeable?

The only practical applications of shadow price offered by Dasgoupta are very narrow cases in which it is possible to easily translate an ecosystem service into a comparable cost for a technology alternative. This may be the best we can ever do. If so, what relevance is the broader holistic theory?

6. Tautology in mathematical terms?

The long sequence of mathematical development leads, as far as I can tell, to a reinterpretation of the final derivation in terms that simply restate the logic embedded in the body of ethical premises adopted at the start and translated into mathematical terms. 

Anyway, that's enough for now.

John

Good topic!  I'm firmly in the "yes, math is necessary" camp, and not just because I loved the show Square One as a kid.  (Anyone else?  Angle Dance?  Tessellations?  No?  ok...) 

I don't believe sustainability is just an ethical debate and I think we absolutely need to know how much of particular resources we are working with to determine if there will be enough left for future generations.  Population seems to be a driving force in whether or not we'll make it (will we have the resources to feed and support upwards of 10 billion people on this planet?)  Population models, projected growth rates, etc, are all critical to any firm policy decisions that attempt to preserve humanity.

In simpler terms, the level of math necessary is linked to the level of involvement in sustainability one is.  Everyone can and should know the basic principles and premise of sustainability, but not everyone needs to think about M and V(t).  Similarly, everyone knows that about gravity, some need to know that gravitational acceleration is 9.8 m/s2, and some need to calculate more precise values for g based on pressure and altitude.  If we purport to write the book on sustainability science, we need to include the math.  Readers can take as much as they want from that. 

At the very least, if these equations and definitions aren't ultimately the best or most important, at least it's an attempt to quantify where we are now, where we are going, and how we should get there.

Previously John Sheehan wrote:

Is math necessary?

As promised, I am starting a post to explore the value of applying a mathematical approach to defining sustainable development. My title (Is math necessary?) is stolen from the title of a humorous essay by James Thurber and E B White entitled "Is Sex Necessary?" So, please take the title with a little of the same tongue in cheek attitude expressed by Thurber and White in their book. 

So, the basic questions that I have include:

1. Does applying a "rigorous mathematical approach" to defining sustainable development help or hinder our ability to understand this concept? 

In support of the former, I would say the language of math adds precision to the approach taken to understanding and measuring sustainable development. In support of the latter position, I would say that this mathematical approach could give the impression of a greater sense of quantitative and theoretical understanding than actually exists. This is dangerous. 

2. Does a purely mathematical approach hinder communication?

Integrals and partial derivatives may only hinder our ability to communicate and discuss sustainable development beyond the "small club" of economists/mathematicians who relish the language of math over the language of conversation and writing. This is especially true the more mired in economic jargon it becomes. 

3. How appropriate is a rigorous mathematical theory of sustainable development?

Does such an approach imbue an inappropriately "scientific" understanding of a concept that is deeply ethical in nature? I question the value of trying to translate ethical principles in mathematical terms, even though I know this has been done by economists for many decades. I still struggle with the as yet unclear basis for saying that basic ethical principles lead to an acceptance of a positive discount rate (!@$#^@$&%!!!). But I will try to find the Koopmans paper from 1960 that allegedly proves this point.

4. Have we simply replaced a vague understanding with a shadowy interpretation?

Expressions such as U(t), V(t), M and W(t) hide a wealth of ignorance. Is this a case of just making ourselves feel better because we have packaged all these unknown and potentially undefinable relationships in compact mathematical forms? I have to say the idea of talking about V as a function of this all encompassing variable we call M for the political economy is--well--a little absurd.

And then there is the "shadow price"--a term conspicuously close to Plato's shadows of the real world observed from inside a cave. Not only is the concept of measuring shadow price incredibly daunting, but I question whether our ability to measure a shadow prices does anything more than help us climb a local hill and never get to the real peak we are seeking. 

5. Is the chasm between holistic theory and specific practice unbridgeable?

The only practical applications of shadow price offered by Dasgoupta are very narrow cases in which it is possible to easily translate an ecosystem service into a comparable cost for a technology alternative. This may be the best we can ever do. If so, what relevance is the broader holistic theory?

6. Tautology in mathematical terms?

The long sequence of mathematical development leads, as far as I can tell, to a reinterpretation of the final derivation in terms that simply restate the logic embedded in the body of ethical premises adopted at the start and translated into mathematical terms. 

 

Anyway, that's enough for now.

John

While the JFK quote John gives us is very illuminating in its own right and an excellent articulation of the limits that GDP and GNP have for measuring our success as a given nation, I think further discussion of whether the "mathyness" of the chapters we looked at this week is needed to convey the point is important.  

Now that I posted this, I see that John had a much better analysis of whether the math is helpful or not in another thread (why two threads?). His analysis is much better than mine so go read that. 

Hopefully my response has some value, but John basically made a much more articulate version of the argument I made, so probably not.

Previously Alicia Harley wrote:

While the JFK quote John gives us is very illuminating in its own right and an excellent articulation of the limits that GDP and GNP have for measuring our success as a given nation, I think further discussion of whether the "mathyness" of the chapters we looked at this week is needed to convey the point is important.  

The wonderful thing about the chapters is that the careful economic/mathematical analysis allows us to be very very explicit given a particular definition of sustainability what are the arguments that go into it and how these play out. It is elegant and internally valid/consistent and does not allow hand-waving on what we mean by sustainability and what the implications of that meaning are. Internal validity in a definition of sustainability is hard to come by, so I applaud of chapter for that. 

Could these ideas have been conveyed without the use of such complex/mathy economics, using ethical and intuitive arguments instead? The answer is most likely yes. However, the mathematical rigor in the chapter is nice because it is very convincing that no hand-waving has taken place and that all of the assumptions make sense internally in the model. 

The problem with an highly quantitative model is usually external validity. After assumptions have been made to make the model internally valid we often get lost in the internal validity of the model and forget that the basic assumptions are only assumptions and if they dont hold in all situations, or perhaps should not hold in all situations, then the model has external validity questions. 

I am still trying to decide for myself whether I am convinced that the model is free of an implicit assumption that more is always better in terms of consumption of manufactured and natural capital. I do think that it is worth being extremely careful about this if it is going to be what we build off of in sustainability science. 

In summary, I think that the quantitative nature of the chapter is very helpful as an exercise. I am less convinced of its applicability in policy and I think no matter what the quantitative arguments need to be framed within a democratic discussion of their implications and the ethics of their implications.

I must say, John, that this is a very well-articulated and thought-provoking take on this issue.  However, as someone intending to make a career out of applying rigorous quantitative analysis to problems of sustainability, I fully support 'math' in sustainability.  As such, I will do my best to address some of your concerns.

The most important point here (hence why it is its own paragraph) is that your claims addressing the fact that math is not always used appropriately in sustainability science does not necessarily imply that it should not be used.  Instead I would argue that you have illuminated some areas in which it should be used better.

I will more specifically address some of your individual points below: 

"1. Does applying a "rigorous mathematical approach" to defining sustainable development help or hinder our ability to understand this concept?" 

- People should not view math as this 'black box' method that is opposite to basic verbal reasoning.  Math is designed to be the formalization of logic, and well-used math serves this purpose exactly.  In other words, for every logically-sound verbal argument, one should be able to mathematically represent it.  Similarly, for every logically sound mathematical expression, one should be able to verbalize it.  The advantage of using the language of mathematics is that it makes it harder to make accidental errors in logic, and it also sometimes makes it easier to see the logical implications of one's assumptions that one maybe hadn't thought of yet.  The disadvantage of using the language of math is that its assumptions are often less clear.  Clearly, ideal analyses should often incorporate a combination of mathematical and verbal reasoning.  However, one has to be careful to address the shortcomings of each.  In other words, the more heavily one relies on mathematical argumentation, the more one must be sure to specifically and clearly address their assumptions; and the more heavily one relies on verbal argumentation, the more one must be methodical in verifying the logical soundness of their argument (which may require using math anyway) and checking for possible interesting extensions/implications of their reasoning.   

"2. Does a purely mathematical approach hinder communication?

Integrals and partial derivatives may only hinder our ability to communicate and discuss sustainable development beyond the "small club" of economists/mathematicians who relish the language of math over the language of conversation and writing. This is especially true the more mired in economic jargon it becomes." 

- Good math that is accompanied by clear verbal reasoning should not have this problem.  Again though, in the pathological cases you mention, I would place the blame on the mathematician, not the math.

"3. How appropriate is a rigorous mathematical theory of sustainable development?

Does such an approach imbue an inappropriately "scientific" understanding of a concept that is deeply ethical in nature? I question the value of trying to translate ethical principles in mathematical terms, even though I know this has been done by economists for many decades. I still struggle with the as yet unclear basis for saying that basic ethical principles lead to an acceptance of a positive discount rate (!@$#^@$&%!!!). But I will try to find the Koopmans paper from 1960 that allegedly proves this point."

- This ties in very well with my point in Session 1 about sustainability scientists and their 'hats'.  The math used in sustainable development seeks to predict optimal courses of action, given assumptions about human goals/values.  While these assumptions clearly require verbal clarification and debate (that has a normative aspect), the math still has a role in applying whichever assumptions are deemed most appropriate.

4. Have we simply replaced a vague understanding with a shadowy interpretation?

Expressions such as U(t), V(t), M and W(t) hide a wealth of ignorance. Is this a case of just making ourselves feel better because we have packaged all these unknown and potentially undefinable relationships in compact mathematical forms? I have to say the idea of talking about V as a function of this all encompassing variable we call M for the political economy is--well--a little absurd.

And then there is the "shadow price"--a term conspicuously close to Plato's shadows of the real world observed from inside a cave. Not only is the concept of measuring shadow price incredibly daunting, but I question whether our ability to measure a shadow prices does anything more than help us climb a local hill and never get to the real peak we are seeking. 

- I think you have raised a good point here that often people see math and, without taking the time to understand it, skip to the verbal summary in the accompanying document and assume the conclusions therein are somehow bullet-proof and all-encompassing.  This again is not the fault of math itself.  The mathematician should be making the shortcomings and assumptions of his/her work more clear and the READER should be making more of an effort to understand the full extent of the argument rather than getting lazy and playing broken telephone.

5. Is the chasm between holistic theory and specific practice unbridgeable?

The only practical applications of shadow price offered by Dasgoupta are very narrow cases in which it is possible to easily translate an ecosystem service into a comparable cost for a technology alternative. This may be the best we can ever do. If so, what relevance is the broader holistic theory?

- The broader holistic theory illuminates what empirical analyses/calculations are ideally necessary.  You may be right that we may not be able to measure shadow prices very well ever, but without the theory, no one would know that we ideally want to measure shadow prices, and thus nobody would be trying to measure them.  In other words, don't give up on math because it doesn't seem to solve all of our problems because it's doing a lot better than anything else right now.

6. Tautology in mathematical terms?

The long sequence of mathematical development leads, as far as I can tell, to a reinterpretation of the final derivation in terms that simply restate the logic embedded in the body of ethical premises adopted at the start and translated into mathematical terms. 

- You are oversimplifying I think.  It is true that sometimes people mathematically formalize commonly used verbal axioms and find only that they are logically consistent.  This may seem tautological, but the point of it is to test the logical consistency of the initial verbal argument/set of assumptions.  Sometimes, the formalization of the verbal assumptions leads to an inconsistent conclusion mathematically, which can be very illuminating in terms of pointing out the logical flaw in the initial axioms.

BIG POINT RESTATED:

Math is a tool that can facilitate great progress.  It makes the ceiling higher.  Its misuse and/or the misunderstanding of its purposes/limitations can hinder progress.  However, the solution (i.e. that which will lead to the greatest progress) should not be to get rid of math altogether, but rather to due our due diligence as scientists and practitioners to understand and explain math, its uses, and its limitations better.

Previously John Sheehan wrote:

Is math necessary?

As promised, I am starting a post to explore the value of applying a mathematical approach to defining sustainable development. My title (Is math necessary?) is stolen from the title of a humorous essay by James Thurber and E B White entitled "Is Sex Necessary?" So, please take the title with a little of the same tongue in cheek attitude expressed by Thurber and White in their book. 

So, the basic questions that I have include:

1. Does applying a "rigorous mathematical approach" to defining sustainable development help or hinder our ability to understand this concept? 

In support of the former, I would say the language of math adds precision to the approach taken to understanding and measuring sustainable development. In support of the latter position, I would say that this mathematical approach could give the impression of a greater sense of quantitative and theoretical understanding than actually exists. This is dangerous. 

2. Does a purely mathematical approach hinder communication?

Integrals and partial derivatives may only hinder our ability to communicate and discuss sustainable development beyond the "small club" of economists/mathematicians who relish the language of math over the language of conversation and writing. This is especially true the more mired in economic jargon it becomes. 

3. How appropriate is a rigorous mathematical theory of sustainable development?

Does such an approach imbue an inappropriately "scientific" understanding of a concept that is deeply ethical in nature? I question the value of trying to translate ethical principles in mathematical terms, even though I know this has been done by economists for many decades. I still struggle with the as yet unclear basis for saying that basic ethical principles lead to an acceptance of a positive discount rate (!@$#^@$&%!!!). But I will try to find the Koopmans paper from 1960 that allegedly proves this point.

4. Have we simply replaced a vague understanding with a shadowy interpretation?

Expressions such as U(t), V(t), M and W(t) hide a wealth of ignorance. Is this a case of just making ourselves feel better because we have packaged all these unknown and potentially undefinable relationships in compact mathematical forms? I have to say the idea of talking about V as a function of this all encompassing variable we call M for the political economy is--well--a little absurd.

And then there is the "shadow price"--a term conspicuously close to Plato's shadows of the real world observed from inside a cave. Not only is the concept of measuring shadow price incredibly daunting, but I question whether our ability to measure a shadow prices does anything more than help us climb a local hill and never get to the real peak we are seeking. 

5. Is the chasm between holistic theory and specific practice unbridgeable?

The only practical applications of shadow price offered by Dasgoupta are very narrow cases in which it is possible to easily translate an ecosystem service into a comparable cost for a technology alternative. This may be the best we can ever do. If so, what relevance is the broader holistic theory?

6. Tautology in mathematical terms?

The long sequence of mathematical development leads, as far as I can tell, to a reinterpretation of the final derivation in terms that simply restate the logic embedded in the body of ethical premises adopted at the start and translated into mathematical terms. 

 

Anyway, that's enough for now.

John