# A SET OF HARD PROBLEMS

The theory of computation studies a class of problems called ‘NP Complete.’ These are problems that are considered computationally hard in the sense that all known algorithms to solve them require a non-deterministic Turing machine polynomial orders of time. The traveling salesman problem is a classic example of this set. They all share one characteristic – indeed it is the test of membership in the class – that they are all isomorphic. An algorithm that solves any of the problems would therefore solve all of NP Complete problems.

The problems that humanity faces collectively at the global level, constitute a similar set and there are some interesting parallels and differences between the two sets. The set of global problems includes at the very least the problem of environmental degradation, the economic system and the population problem. All of these basic problems are in a sense isomorphic and any solution advanced to solve any one would also automatically address the others. However, the difference between the computational problem set and the global problem set is that whereas you can address the traveling salesman problem in isolation without regard to the assignment problem, you really cannot attempt to solve any of the basic global problems in isolation.

The reason for this is the basic fact that all global systems are interconnected in the present age. The economic system is part of the socio-political system which is tied to the population which exists in the ecological system and so on. No man, nation, system, organization or institution, is an island. The consequences of this fact are sobering. Firstly, it is futile to attempt to try to solve just one of them while disregarding the others — there is considerable evidence to attest to that. Secondly, any solution advanced has to meet the requirement that it must not leave any losers in the deal; the solution has to create a win-win situation. To borrow from a biology lesson, every evolutionary stable strategy is win-win: the win-lose strategy is not sustainable – both predator and prey disappear for good.

To go back to the computational analogy for a bit. To solve computational problems for any real-world situation where the size of the input would rule out computing exact solutions due to the fact that such a solution would require more time than the age of the universe, heuristics are used which provide approximate solutions which can be arrived at in a reasonable time. In a similar sense, to address the seemingly intractable global problems, we need to apply heuristic methods which limit the search for a solution.

A BASIC SET OF AXIOMS

Consequently, there must be a set of axioms that can be used as boundaries to limit the search for sustainable solutions to the global problems. In my opinion, as a first cut, I present the following:

0. It is all interconnected.
1. Nothing inequitable is sustainable.
2. The solution must be win-win for all concerned parties.
3. The solution cannot incorporate a growth in the physical throughput of the system.
4. Competition for scarce resources must be replaced by cooperative use of the resources.
5. There are real limits to basic resources – land, energy and water – currently available to humanity.
6. Growth centered development is inherently unsustainable.
7. The attempted solution must be appropriate to the nature of the problem.

The 6th axiom is to make explicit that there is a distinction between growth and development. Growth is natural and healthy at specific stages of a system and has to stop when the system reaches an optimal size. Development of a system, however, need not stop if it is defined as the expansion of the potential of the system and does not necessarily imply growth.

The last heuristic is meant to guard against the common folly implicit in the dictum that to a man with a hammer, everything appears to be a nail. No point in trying to attempt an administrative fix to a sociological problem. Or a technological fix to a ethical problem. Or a political fix to a technical problem.

The global interacting system can be understood broadly as the environment, the economy, and the population. Every global problem has a component which affects and is in turn affected by each of these three subsystems. Take, for example, the fact that economic factors have shaped environmental trends and in turn affected populations. Demand for resources has escalated pushed by the engine of population growth and led to the unsustainable exploitation of resources. Deforestation is a direct consequence of population pressures which is partly responsible for the 24 billion tons of topsoil lost every year. The earth’s carrying capacity has been sorely tested and it is evident that the ecological space that humanity has in a sustainable ecosystem is nearly, if not already, full.

However, there are economists like Julian Simon who would argue that global resource scarcity is not a serious problem on the grounds that prices of resources relative to wages would tend to decline over time. This view cannot be maintained if one posits the finiteness of resources available at any given time. It becomes even more untenable if one were to consider the loss of resources which are non -substitutable like biological diversity. No amount of money can replace the value lost in the extinction of species.

## 17 thoughts on “A SET OF HARD PROBLEMS”

1. superb meta-article. waiting for the next part.

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2. gursant singh says:

plese send me more about environment problems

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3. Thanks
i m Gursant Singh i have just got this artical thanks thanks for this i m student of B.Ed. living at punjab India. Environment educatin is my subjectof study . & i want to aware the children about Env. problems. Because if ve teach the properly then We Are making our future bright.
Plese Keep sending me mails about environmental & wild life problems which ican tel to others .

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4. amar says:

Atanu,

A excellent analogy, followed up by a comprehensive “heuristic solution” to the real-world problem.

A small note: The complexity of the real-world problems fascinates some people. There are others that are fascinated fascinated by the simplicity of the problems in Computer Science/Mathematics.

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5. Hi!

Suggestions for the next cut!

3 and 6 go away if we introduce the second law of thermodynamics – Entropy. errr … rather they follow. 4 is partially true. Competition can exist provided resources are cycled. Mais oui, cooperation is known to be optimal. Again, borrowing from Biology, cyclic pattern of resource use where the waste of one is the food of another is one way to ensure development despite thermodynamics. Our current model of Technology is quite the opposite, and is growth centered.

I cannot understand the arguments behind global resource scarcity not being a problem as I am not very conversant with the mechanics of pricing. All I seem to understand is that a price is a (statistical average) of essentially a time bounded negotiation game between the trading parties. It appears to me that Energy cost/expenses could provide a better invariant (like the PGTEC) and universal currency consistent with your proposed axioms.

All IMHO. :).

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6. These global problems are separable and solvable, independently, at varying degrees of difficulty. For example, global warming due to anthropogenic surplus atmospheric carbon can be resolved at a cost of just under \$US 1bn/year, by distributing chelated Iron in nutrient-impoverished equatorial ocean waters. Overpopulation is a fantasy. Europe, Northern Asia, Australia, Japan are depopulating, even as Mexico, Nigeria, India, Bangladesh are overpopulating. Like starvation the issue is merely one of transportation. By dissolving the role of the nation-state as a barrier to immigration, the problem would resolve itself, to the benefit of all concerned.

The only truly terminal illness is stupidity. I fear that mankind may be too late for heroic measures.

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7. Rick Hull says:

axiom 3: you need to have a convincing argument to accept this axiom. this one sound suspiciously like 6.
axiom 4 is equally difficult to swallow without justification.
axiom 6: though this subsumes axiom 3, it still needs justification if we are to take it as an axiom.

An axiom is not just a convenient construction to hold an argument that you cannot prove. It is a necessary construction that must only be used for conclusions so primary that they are taken as given for anyone entering the discussion. These axioms do not meet the burden.

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8. I agree with A Mino Rex that global problems can be solved when seen in an isolated way. This exercise is interesting maybe, but is it needed at all or can it be implemented at all, even when the model is created, on the basis of the axioms presented?

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9. Guru Gulab Khatri says:

What would be a win win situation in bakri kasai (à¤¬à¤•à¤°à¥€-à¤•à¤¸à¤¾à¤ˆ)game that a bakri found itself in ?
Especialy if you are the bakri and
and other bakris are singing the virtues of bakri-kasai bhaichara and you are looking
at your soft rearside and are not sure when the kasai will go back to his ancestoral practice.
The solution for the bakri is to ignore the welfare of the kasai and make sure it has enough to eat so that it can grow its horns to gore the kasai if they come to close.
But some other bakris keep insisting that we bakri and kasais are the same and we should
(a)
ignore strategies which can starve the
kasai
(b)break our horns since they threaten the kasai.

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10. Arvind says:

A SET OF HARD PROBLEMS

Well said. Too hard to Understand!

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