Probability, Gravity, Shakuni...and the tackling of Uncertainty in Urban Planning

'But it appears worthwhile to answer here one frequently posed question: "Does the Monte Carlo method help to win in roulette?" The answer is "no". It is not even concerned with it.'

- Ilya Meyerovich Sobol, 'The Monte Carlo Method'

Just as clarified by the mathematician Ilya Sobol in the line above, it is not the purpose of this article to encourage the reader to become a student of the methods of master gambler Shakuni of the Indian epic Mahabharata. However, a total ignorance of the subject of probability and the rules governing the behaviour of random phenomena can surely land the practicing urban planner in a situation similar to the hapless Yudhishthira in the game of dice. For sure, our planner would not lose a kingdom and head for a 13 year exile, but the feeling of powerlessness, overwhelming sense of failure and incompetence may last way longer. 

 

Shakuni facing Yudhishthira in the game of dice in Peter Brook's Mahabharata

 

The urban situation is not just complex, uncertain and random, but like the loaded dice of Shakuni, it can also be brutally unfair. The chances of a professional planner to be able to tackle the urban system without the appropriate toolkit are low indeed.

One could say, that the probability of a planner successfully tackling urban uncertainty without the knowledge of probability is rather low.

The uncertainty of urban systems arises from the fact that many urban phenomena are non-deterministic in nature. Urban systems are dynamic where many variables continuously interact with each other. In cybernetics, variety is defined as the number of states any given system can take, and it can be quantified. Large and complex systems can have very high amount of variety - i.e. the total number of states that their sub-systems can take and their combinations - and hence they can also be highly uncertain and non-deterministic.

Consider the following questions from David Foot's wonderful book on operational urban models, which could be explored using urban models -

• How would a large area of new residential development or inner city redevelopment affect the journey to work trip pattern and general accessibility of a region ?
• How would a large increase in employment resulting from the development of a new airport affect the surrounding region and what other housing and transport policies would be needed ?
• How would the development of a new hypermarket affect the shopping pattern of the region, particularly nearby shopping centres of smaller size ?
• How would a general change in accessibility due to a large increase in petrol prices affect the region ?

The answers to none of the above questions can be given in a static, deterministic way. There is a whole range of ways in which different actors in the city could react to any of the situations listed above. There is no easy way to anticipate or prepare for the consequences of such developments. But that does not mean it is impossible.

Urban systems are not deterministic. They are probabilistic.

Probability and the First Law of Geography

Understanding the role of probability in urban studies is intrinsically linked with the concepts of gravity, distance decay and spatial interaction. To estimate the probability of an event is basically the task of figuring out what is most likely to happen (or not happen). According to the classical definition of probability this is calculated according to the following formula -

P(A) = m(A)/n 

Where P(A) is the probability that event A happens; m(A) is the number of chances favourable to event A; and n is the total number of chances.

When we toss a coin we do not know in advance whether we will get heads or a tails , but we know simply from common sense, that the chance of getting either is 50-50. There are a total of two chances i.e. we can get heads or tails (so n=2) and we can get either heads or tails (so m(A)=1). And therefore,

P(A) = 1/2 = 0.5 = 50 %......as in, fity-fity

In urban systems this concept of likelihood gets linked to geographer Waldo Tobler's first law of geography , which states:

"Everything is related to everything else, but near things are more related than distance things."

This first law of geography is fundamental to understanding spatial interactions in urban systems. Given two equally nice cafes, which is the one we are most likely to visit ? In most cases, it would be the nearer one. While we may visit both depending on our wish, if we maintain a continuously updated data-file of our own movements, we would would discover that as the data piles up there is a marked tendency to visit the nearer cafe more frequently than the farther cafe. 

In urban modelling this is known as distance decay. Our likelihood of going somewhere is inversely related to the distance that exists between us and the location of that place. The distance can be physical distance in terms of kilometres (or miles), or in terms of money or time we have to spend or any other form of cost that we may have to incur to reach that place. I had illustrated this relationship as a graph in an earlier blog -

The graph basically shows at what rate the likelihood to go a certain distance would decrease depending on the way in which the influence of distance is measured in the equation. The green line shows the effect of simply being inversely related to the distance (1/D).The blue line shows what happens if distance is not only inversely related but also raised to the power 2 (1/D^2). Finally, the red line shows the most most extreme case, where the effect of distance is raised to the power of 3. 

The second case corresponds to the law and the corresponding equation by Reilly, which stated that -

"A city will attract retail trade from a town in its surrounding territory, in direct proportion to the population size and in inverse proportion to the square of the distance from the city."

The fun of spatial interaction begins when we consider that it is actually a tug of war between the attractiveness of the place we wish to reach and the distance that separates that place form us. In Reilly's equation the population of the larger city acts as a proxy for its attractiveness. The fact that it is inversely related to square of distance was empirically derived based on his study of cities in the USA. 

In other situations the power function may, of course vary, and whether it would be distance raised to the power 2 or any other number is determined during calibration of the model. In terms of attraction one could select any other relevant variable instead of population. In retail models, a variable that is used to represent the attraction of a place as a commercial area is often the total area of retail floorspace. Similarly, an area's attraction as a residential area could be measured using a variable such as total residential floorspace available. The following equation shows the relationship between the flow of people from a residential zone i to a commercial facility in zone j -

T_ij = F_j/d_ij^y

[ Where: T_ij  is the flow of people from i to j ;  F_j is the attraction of zone j (e.g. total square metres of retail commercial space or number of shops in the zone ; and  d_ij^y is the distance between zones i and j raised to an appropriate power of y]

Let's assume that there are a total of 3 zones in our study area. Then, using the probability of a person of zone 1 to go shopping in zone 2 would be given by the ratio of the chance that the person goes to shop in zone 2 and the total number of chances (i.e. all the ways in which the person may go shopping in any of the three zones)

Using the formula of probability and the formula of spatial interaction given above :

m(A) = probability that a person in zone 1 goes to shop in zone 2 =  F₂/d₁₂^y

n = total number of ways in which a person from zone 1 can go shopping in any of the three zones = F₁/d₁₁^y + F₂/d₁₂^y + F₃/d₁₃^y

Putting it all together, the probability that a person in zone 1 goes shopping in zone 2 would be given by -

Pr₁₂ = (F₂/d₁₂^y) / (F₁/d₁₁^y + F₂/d₁₂^y + F₃/d₁₃^y)        

So much for today. In the next blog, we will look deeper into the above formula and calculate the value of the probability by punching in some numbers.

To be continued...

Set theory, Systems and Jaga Mission

In his classic book 'A System's View of Planning', George Chadwick wrote:

"Not only can the whole of mathematics be developed from the concept of a set, but, as foreshadowed, the idea of a system stems naturally from that of a set." (p-28)

While we all studied set theory in high school mathematics, its usefulness in making sense of the structure and behaviour of complex systems encountered regularly in urban planning, was never discussed adequately in planning school. The consequence is the absence of yet another powerful tool from the contemporary planners' toolkit and the state of confoundedness that naturally follows.

Created by the German mathematician Georg Cantor in 1874, set theory "stems from the simple idea of a number of things which have a common property or properties and thus can be represented as elements of a set." (ibid)

The relationship of set theory with the systems view of planning is made amply clear when we consider that, "the commonly accepted definition of a system is a set of entities and the relationships between them."

Regions and Sets

Let us consider how set theory helps us to tackle the complexity in Jaga Mission, the flagship slum land-titling and upgrading project of the Government of Odisha, India. But before plunging into that, let's have a quick look at how set theory came to be an integral part of regional science already by the 1960s. 

In his classic paper, 'Mathematical Aspects of the Formalization of Regional Geographic Characteristics' , the Soviet geographer B.B. Rodoman wrote that, if a region is viewed as a set of subregions, then one could "convert into the language of geography the theorem of the five alternative relationships which is part of set theory." 

He elaborated further that, according to set theory, two regions A and B may have the following relationships with each other:

1) They may have no common territory

2) They may intersect

3) A may be part of B

4) B may be part of A

5) They may be identical

The relationships can be expressed as follows by using the symbols of set theory:

1) A ∩ B = ∅    [intersection of A and B is a null set]

2) A ∩ B ≠ ∅ ; A ∩ B ≠ A ; A ∩ B ≠ B   [intersection of A and B is not a null set]

3) A ∩ B ≠ ∅ ; A ∩ B = A ; A ∩ B ≠ B ; A ⊂ B   [A is a sub-set of B]

4) A ∩ B ≠ ∅ ; A ∩ B ≠ A ; A ∩ B = B ; B ⊂ A    [B is a sub-set of A]   

5) A ∩ B ≠ ∅ ; A ∩ B = A ; A ∩ B = B ; A = B    [A is equal to B]

By adding to the above the relationships of the sets with their complements (i.e. the elements present in the universal set but not in the set itself - basically the world outside of itself), one can show the full range of ways in which various overlapping or separated regions interact with each other. This was explained very clearly through an example of wheat growing regions, vegetable growing regions and corn growing regions in Golledge and Amadeo's paper titled 'Some introductory notes on regional division and set theory'

It is clear from the diagram above that every part of the three fields, no matter how complex, could be accurately described using the language of sets. For example parts 4 and 6, which occupy the central part of the fields, where all three type of fields intersect can be described using the following notations -

For part 4 --> (W ∩ V) ∪ (W ∩ C)        

[i.e. the union of the intersection of wheat and vegetable and the intersection of wheat and corn]

For part 5 --> (C ∩ W) ∪ (C ∩ V)

[i.e. the union of the intersection of corn and wheat and the intersection of corn and vegetable]

It is easy to spot the origins of the various vector operations in GIS using logical operations such as AND, OR, != (corresponding to intersection, union and not equal to) etc from the above discussion on set theory and regionalization.  

Slums and Sets 

Any slum land titling project is complex by its very nature, but Jaga Mission is quite the Godzilla of complexity due to its size and geographical coverage. Unlike, slum titling and upgrading projects that target a couple of major cities, the Mission covers all 2919 slums in all 115 cities and towns in the state.

However, by combining the necessary geo-spatial datasets corresponding to the various operational parameters of the mission one can readily apply set theory to simplify and automate the tasks. This was particularly true in the case of the trickiest component of any land titling project - the land parcels themselves. 

In fact, one is bound to spot the visual similarity in the following image of a slum of Jaga Mission shown below and the illustrative diagram of the three fields in Golledge and Amadeo's paper.

The above map shows the location of slum houses overlaid on land parcels which belong to three types - Leasable government land (on which slum land rights can be granted); Reserved government land (on which slum land rights can be granted only after a category conversion process); and Private land (on which slum land rights cannot be granted).

If A is the set of slum houses and B is the set of government leasable land parcels then the slum houses entitled to land titles straight away would be given by - 

A ∩ B    

However, if one would consider the total set of slum houses which are entitled to land titles once the land category conversion for reserved government land parcels are completed (reserved parcels given by set C), then that would be given by -

A ∩ (B ∪ C)

If private land parcels are the only category over which land titles cannot be granted (set D) then the set of entitled slum houses could also be given by -

A ∩ D'    [where D' is the complement of set D]

By defining the sets according to the specific parameters of the mission, the outcome of the interaction of various parameters could be computed by applying the theorem of alternate relationships.

Once such relationships are established then it really does not matter if the process needs to be done for one slum or for a 100 slum or for a 1000 slums. Nor is it any difficulty to divide a particular set into its constituent sub-sets (for example the reserved government land category itself is a union of numerous subsets of land parcel types distinguished by the land-use type and the ownership type -- these particulars can also be described as sets of their own).

Otto Neurath...Vladimir Putin...and the economy of real things

Just two days ago the Hindustan Times published an article with the headline, "US Senate clears long-delayed $95 billion aid package for Ukraine, Israel and Taiwan". A long-awaited proposal to continue the massacre of unlimited numbers of Ukrainians, Palestinians and to lay the ground-work for a similar future for Taiwan seems to have seen the light of day.

However, headlines seem to be written primarily for those who read nothing more than the headline (or a tweet), for in just the second paragraph, the following is written:

"The legislation will now be submitted to the House of Representatives, which is controlled by Republicans, where there is little possibility that it would pass into law. US Speaker Mike Johnson has condemned the bill."

The Russians have said time and again that providing financial aid to Ukraine may prolong the conflict but would do nothing to change the outcome. Yet, this obsession with providing billions of dollars of aid continues. 

Such is the obsession with the magical power of money brought about by the unrelenting spread of neoliberal ideology and finance capitalism around the world, that it's hard for most people to get their heads around the fact, that money, by itself, is quite nothing.

It is the things that we can buy or rent or use with the money that is everything. There is not much use in having a lot of money during a famine when there is no rice to buy with it (just watch Satyajit Ray's classic film 'Asani Sanket' on the Bengal famine during World War 2 that claimed the lives of 5 million people).

This propaganda of money is particularly strong in India, where three decades of worshiping and trumpeting of finance capitalism has granted a god-like status to the super-rich. It matters little how the money is accumulated or what is being done with it. The mere possession of it is enough to attribute the virtues of greatness, intelligence, wisdom, talent, vision etc etc to the rich. If you are great then you will definitely be rich and if you are rich then you must be great !

However, there is not much use in releasing billions of dollars to fight a war if you neither have sufficient quantities of weapons and equipment to buy with it, nor have the industrial capacity to produce it. Already back in 2022 news articles appeared about the "donation" of 20000 rounds of 155 mm artillery ammunition to Ukraine by the US and Canada only to be followed by other news articles that would discuss the difficulties in producing and procuring sufficient quantities of shells in a short time.

And all that while, the Russian armed forces were firing about 60000 155mm shells on Ukrainian positions every single day. 

Money can buy shells if there are shells. Money cannot magically become shells. 

Apparently it was not part of the calculations of globalists that after having off-shored much of the industry to other countries to both maximise profits and break the backs of trade-unions; having set up military bases around the world to ensure that this global network stays in control; and putting in place all the financial institutions to deploy the sanction-weapons to put any mis-behaving economies in line, that they would have to see this day when they struggle to produce shells in their own countries while Saudi Arabia and Ethiopia line up to join the BRICS.

And we saw a similar situation recently with the Houthis. The peculiarly named 'Operation Prosperity Guardian' was faced with an embarrassingly prosperity-threatening prospect of having to shoot down couple of thousand dollars worth of Houthi drones with couple of million dollars worth of air defense missiles.

Already in February-March 2022, when the western powers hurled every possible economic sanction at Russia and then proceeded to freeze about 600 billion dollars of their sovereign funds, they were certain that as a result of these measures the Russian economy will tank and collapse in days.

Well, guess what ? We are in 2024 now and if this is what the Russian economy can do when it is tanked then I don't know what their economy is like when it booms. It's the sanctions that tanked, not Russia. Nobody even remembers Mr. Daleep "Sanction" Singh now.

There is no mystery to the resilience of the Russian economy. It is an economy of real things - or, as economists like Michael Hudson and experts like Andrei Martyanov have described ad nauseam - it is a REAL ECONOMY.

 

 

And this is nothing new, although it is almost always ignored by mainstream economists. Already in the 1920s the Austrian political-economist and the creator of the ISOTYPE method of pictorial statistics, Otto Neurath had discussed at length about "in-kind" accounting in economics based on his studies of war time economics. He realised that periods of crisis - such as war - clearly revealed the reality of a nation's economy and that is based on the simple fact that you can neither eat money, nor wear money, nor shoot money from money if you do not have the real goods that can satisfy all these needs in sufficient quantities.

Of course, it continues to be a mystery to scores of people in the west and also here in India. 

 

How come "rich" economies like the US and EU cannot bring a "poor" (gas-station-masquerading-as-a-country) economy like Russia to its knees with its earth-shattering sanctions ??

 

Well, as they say in many Hollywood films and series -- "Just follow the money"...and keep following it until the trail runs cold on reaching the dead site where the factories used to be.