Maximisation Dilemma

It is not unusual for developmental problems to be seen as a shortage or a lack of something, and the solution is therefore to increase the volume of that to the desired level. Climate enthusiasts can, of course, argue that in the case of greenhouse gases, the problem is seen as one of minimising something to the desired level. But that reduction itself is supposed to be achieved through an increase in the production of renewable energy alternatives. By extension this can be applied to any sector -- the task of minimising illiteracy can be tackled by maximising literacy and that can be achieved by maximising other variables such as the number and quality of schools, the scope and scale of literacy missions, the production of textbooks etc.

It is simply convenient for public institutions and bureaucracies to articulate a strategy for solving a developmental problem in the form of a mostly quantitative maximisation of that which is supposed to be the solution -- and the easier thing to do is always the tempting thing to do (and vice-versa).

Unfortunately, this tendency for measuring mission success in terms of maximising implementation very soon waxes into all kinds of irrationality. One of the main is of course that of cognitive dissonance about which I have written before. The more a development project becomes "successful" i.e. the more it maximises, the more the senior leadership starts losing touch with reality and ignores every possible feedback loop. The result can be visualised in the form of the following (fun) graph, where an (imaginary) index of cognitive dissonance keeps increasing exponentially along with the duration of project implementation. 

Jaga Mission - to Maximise or to Minimise ....WHAT ??

The complexity of a large and unique initiative such as Jaga Mission lay in the fact that some components had to be maximised, while others had to be minimised -- and these were, of course, interlinked.

Naturally, being one of the largest in-situ slum land titling initiatives in the world, the number of slum households covered by the Mission had to be maximised. Ideally, the coverage should maximise till all slum dwellers in the state are covered. However, the possibility of comprehensive coverage depends on the ownership of the land parcels on which the slums are situated. Despite the political will, the Mission was faced with the operational reality that it was possible for the state government to grant land titles only in those cases where the slums were located on parcels owned by various departments of the state government. As it was assumed that slums would most likely be located on public land parcels, it was not considered a variable of much importance.

However, once the geo-spatial datasets of Jaga Mission were prepared, it was discovered that there were quite a few slums which were either wholly or partly located on land parcels belonging to owners other than the state government. 

What to do in such a situation ?

Well, surely you would hope that the number of such slums are low or that one could find ways so that their number would decrease. However, a new complication arose, when an idea started getting toyed with that such slums could probably be relocated to very nicely designed new habitats.

The original aim of granting in-situ land rights to slum dwellers came into competition with the temptation of a new goal of building new habitats. On the one hand, the Mission wished to show that more and more slum dwellers were getting security of tenure in the locations were they were already living, and on the other hand the Mission also wished to showcase more and more newly designed habitats.

But one goal necessarily negated the effect of the other - in fact, the more of the latter would mean a failure of the former.

As prominent architects got involved in the Mission, the tendency to construct new habitats increased even more. After all, it is far easier for an architect to be excited about the prospect of finding a "design" solution to the slum problem in a new greenfield site than comb through cadastral maps and revenue data to find alternatives to relocation.

When a substantial fee to architectural firms is added to the whole equation, then all social awareness generally goes out of the window quite enthusiastically.

As Jaga Mission had an alert and wise leadership, such tendencies were curbed before they could do much damage. This was done largely by switching to Geographic Information Systems (GIS) to analyse the data of Jaga Mission rather than just use spreadsheets. Given the size of Jaga Mission, an analysis based on spreadsheets would tend to identify the status of land ownership in a binary format -- belongs to state government or does not belong to state government.

However, Jaga Mission was granting individual titles to slum households and not collective tenure to the whole slum site. Therefore, what was important was the status of land ownership based on the exact locations of the various houses in the slum. If only very few houses were located on parcels not belonging to the state government, then a relocation of the whole slum was neither necessary nor feasible. 

The solution therefore lay in minimisation based on the analysis of disaggregated spatial data. 

As a result of such an analysis the number of slums that might require relocation reduced to less than 4 percent of the total slums covered by Jaga Mission.

Such a solution not only maximised the achievement of the original goal of the Mission (to grant in-situ land titles) but also maximised the quality and significance of the few new habitats that had to be made. 

The maximisation of Mission success, was therefore achieved through a minimisation of new habitat construction.

However, in the planning and development paradigm of India, where the possible solution to a problem takes a life of its own and gets progressively dissociated from the very problem it was created to solve, such self-corrections are rare indeed.

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.

Of Planning Tools and Synaptic Connections

In his last book 'Disintegration' , geo-political expert Andrei Martyanov described an interesting conversation. He wrote:

 

"Few years ago, when having a conversation with one of the former combat pilots from Russian Air Force - RuAF Officer Schools are 5 years, 6 days a week academies, same as Russian naval academies - he complained that throughout his career he never for once needed the course in Differential Equations he had to take while in the academy. 

 

The response from the group was unanimous -- they did not teach you to use Differential Equations everyday, they taught you to develop complex synaptic connections which are applicable for everyday life, including combat flying."

These lines made a strong impression on me, because they matched exactly my own experience when I first started writing scripts for solving planning tasks and then explored the applications of mathematical methods in urban planning. It is not that I particularly wanted to. My interest, experience and skills all lay in qualitative and community participation methods.

The need for that came from the real experience of having to deal with projects of the size and complexity which simply could not be tackled with qualitative and community participation methods. 

 

The most important benefit of using these techniques is not their direct effectiveness in solving planning tasks (important as that is), but the effect that their use has on the way in which we conceptualise and approach the problems that we wish to solve. 

They increase our ability to articulate complex problems clearly.

It's quite like the skills that one acquires on attending a theatre workshop. It is not important that the person actually acts in a play on stage. But the skills of communication, role-playing, improvisation, expression, dealing with an audience etc, all make a huge contribution to our day to day performance in our own professions - whatever they may be. 

The benefit is indirect - and crucial. They develop synaptic connections.

 

Exactly, like what was said by the friends of the combat pilot, the important thing is not whether mathematical methods are being used everyday to solve all kinds of planning problems, but the familiarity with the application of algebra, calculus etc to planning problems enables us to think about the problem quite differently than if we were totally ignorant of them.

How and why does that happen ?

In the last two posts we discussed the variables that effect the simple act of people going from one location within a city or a region to another location. We saw that this act of "going" is directly related to the number of people at the origin and the number of "attractors" (e.g. number of shops) at the destination; and inversely related to some power of the distance (physical distance or other barriers such as time, money etc) in between the two locations.

 

But what if we turn this problem from a relatively simple one of movement between two points to a movement between many many points ?

This is exactly the point when the practitioner trained only in qualitative skills ends up using the power of language to describe how overwhelmingly complex urban problems are. The solution to tackle that complexity is generally an open-ended call for more discussion, consultation, capacity building, participation.....and -- increasingly in present times -- for more data, as if all these processes would somehow magically resolve the problem. 

 

However, a practitioner with a more holistic education and training, would be able to do something far more powerful -- combine communication and consultation with matrix algebra !

 

If there are 20 zones within a city, then our holistic planner would make a table with 20 rows (referring to origins) and 20 columns (referring to destinations), thereby creating a "map" of numbers to describe the movement between these locations.

A more general way would be to use a variable instead of a fixed number, and say n points...instead of 10 or 20 or 50 points.

We essentially gave ourselves a highly effective "tool" that helps us to study multiple interactions using something as simple as a table with a certain number of rows and columns. Armed with this tool we are able to make far more solid and meaningful points in any community consultation process on urban mobility that we may attend.

While the equation described in the previous two articles helped us to imagine the variables affecting movement clearly; the matrix helps us to imagine the interaction between multiple locations clearly.

 

We start moving away from vagueness and confusion; and towards clarity and focus.

Similarly, when we try to algorithmise a planning task by writing a computer script, we are forced to think very clearly about the sequence of individual tasks that an overall complex problem can be broken down too.

It is not important whether the problem gets solved by the algorithm itself or not. But the very process of creating the algorithm gives us greater command over the problem we are facing.

 

The same can be said about powerful techniques of Operations Research such as linear programming. Whether we can apply it to all kinds of planning problems or not, linear programming helps us to internalise a fundamental characteristic of real planning -- the need to maximise or minimise an objective subject to a multitude of constraints.

This is extremely important, because most of this time, in complex professions like urban planning, we are not in the business of achieving a goal in totality. Most of the time we trying to optimise the situation by maximising a desirable outcome and minimising an undesirable one. And all the while we are having to do this in a context of various kinds of constraints and limitations.

 

Often, we hear planning professionals complain about the impossibility of achieving the goals set by their profession given the tremendous limitations of resources, time, capacities etc. A planner who has internalised the science of linear programming would not complain about such a situation, because to such a professional these would be the essential and "normal" attributes of the job that he or she is trained to do. 

 

Does a fisherman grumble because the fish are in the water and they swim from one point to another ?

 

And does it not make sense, then, to continue to learn the art and science of "fishing" ? 

To Go or Not to Go --> (Urban Planning and the Distance Decay Function)

The fine art of problem articulation 

The important thing about mathematical urban models is not the mathematics itself but its application to simulate urban phenomena that we are trying to understand. Therefore, even a failed attempt at creating a model may help an urban planner understand and articulate a phenomenon with greater clarity. Trying to explain an urban phenomenon in the form of an equation compels us to cut through the fog of vagueness and confusion in our minds and seek clarity.

Try to imagine what we expressed by the equation --> A=f(B, C, 1/D) in the previous blog and then try to explain it in words instead of the equation.

We would have to say something like - "When we consider shopping or any such pattern in a city...it depends on how many people are shopping....where they are shopping...it depends also on which shopping areas are large or attractive...also we must consider which are far away or close by...its a pretty complex process....but also very basic etc etc"

While the equation used just 5 letters and 1 digit, the verbal explanation used about 250 letters (and counting). 

This is not to say that the equation is better than the description, but that one should attempt to formulate an equation from the description - if only to check if that is even possible. It is an iterative process where a description helps us to form an equation and the equation in turn helps us to give a clearer description and so on.

Distance decay and the Gravity function

Distance is a crucial topic in urban planning. As we have seen in the previous blog, "distance", in this case, is not just a physical distance, but the measure of difficulty (or ease) involved in reaching where we wish to reach -- it could be kilometers of roads; delays due to traffic jams; the high cost of petrol; the physical and emotional stress of spending hours in travel etc.

The funny thing with transportation is that it is the only land-use that does not exist for itself, but for the primary purpose of facilitating interaction among other land-uses. We are generally not on a road because we want to "go" to the road. We are on it because it links where we are (our point of origin) to where we wish to go (our destination).

The other funny thing is that distance...decays.

What this essentially means is that when distances increase between us and a particular destination, our desire to go to that destination also decreases (or decays). This is easy to imagine. Let's say that there are two cafes which are equally attractive to you. Would you rather go to the one that is 500 meters away from you or to the one which is 12 kilometers away ?  

This is what we expressed in our equation as 1/D, i.e. as D increases the A (number of trips) decreases. But by how much ?

Way back, in the 1930s, the American economist William J. Reilly discovered from his empirical studies on the flow of retail trade, that the volume of trade between cities increased in direct proportion to the population of the cities and in inverse proportion to the distance between the cities. The trade not only decreased  but it decreased in proportion to the square of the distance between cities. 

Based on these observations, Reilly formulated a law which states:

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

Mathematically it is expressed as -

R_i = P_i / d²_ki

Where R_i is the attraction of city i felt by city k; P_i is the population of city i; and d_ki is the distance between city i and city k. It has an uncanny similarity with Newton's law of gravitation where the attraction between two bodies also decreases in inverse proportion to the square of the distance between them. 

Reilly tested his model extensively by studying the breaking point between cities in the United States.  

If we accept Reilly's findings for now, then we have already developed our original equation further and we now have this -

A_ij = f(B_i, C_j, 1/D²_ij)

Nothing Super-Natural about it

It is clear from the way we constructed our equation, that there is nothing super-natural or god-given or mysterious about any of it.

We are just trying to analyse and describe how a certain kind of spatial interaction takes place.

This implies that there is nothing holy about the fact that the distance is raised to the power 2. Depending on the local context, it may be something else. In fact, empirical work over the years has shown that it tends to vary between 1.5 and 3 depending on a range of contextual factors.

However, many planning text books in India (including the venerable book on transportation planning by L.R. Kadiyali which every planning student is familiar with) continue to use distance to the power 2 without explaining that while it was derived out of extensive empirical research, that research corresponded to large cities in the United States, separated by an average distance of about 100 miles and was conducted in the 1930s.

(The fact that the equation still holds was precisely due to Reilly's empirical rigour - something that our scholars and researchers tend to shy away from most of the time.)

In reality you are free to play around with the power of D in order to check which number makes the equation simulate an observed reality best. Consider the following graph which shows how the distance decay curve would vary if we assume distance to decay if we raise the D parameter in the equation to a power of 1 or 2 or 3 -

This graph shows how quickly the likelihood of traveling a certain distance will decline if we increase the power of D in the model.

As the power increases from 1 (the green line) to 3 (red line) the tendency to travel farther declines. The red line corresponds to a reality where the tendency to travel decreases precipitously when distance increases from 0 to 3 kilometers and becomes almost nil when distance increases beyond 5 kilometers. 

Understanding the rate at which the tendency to travel declines based on increase in the distance can help us understand how appropriately or inappropriately important facilities are located with respect to each other in a city. It can also help us to concretely evaluate planning decisions aimed at locating facilities in a certain way. 

In the next blog we will play around with this equation a bit more by applying it to situations familiar to us.

Overcoming the fear of mathematics in planning education and practice

A vital contradiction in our education system

The former chief scientist of Airbus, Jean Francois Geneste said in a brilliant talk delivered at Skoltech, that when it comes to large and complex systems, 

"We can only master, what we can measure and mathematics is a discipline for measurement -- it is measurement theory."

What he said has great implications for our own field of urban and regional planning too. It is important to measure and to measure correctly, before planning decisions affecting millions of people, thousands of businesses and hundreds of hectares of land-uses of different kinds can be taken. 

Yet, precisely when there is a growing fascination with data and digital technologies, there seems to be a relatively low understanding of the role of mathematics in planning. A substantial part of the problem lies in the fear of the subject itself and the inability to apply it effectively in real situations.

We are all aware, that due to the peculiar limitations of the Indian education system, there is a rigid and unnatural separation between the sciences and the arts. 

This leads to a situation where people trained in engineering techniques are often completely devoid of an awareness of social issues and of creativity; and the people trained in humanities are often clueless when it comes to physics, mathematics etc.

Truth be told, this challenge exists in urban planning education outside India too, though, perhaps, not as severely. As Brian Field and Bryan Macgreggor noted in the preface to their book on forecasting techniques,

"...we had both come to planning from numerate first disciplines and, in planning schools at opposite ends of Britain, had independently concluded that there was an obvious gap in the literature on this particular subject."

The important word here is numerate - which means having a knowledge of mathematics and the ability to work with numbers. It is the mathematical counterpart of the word literate, which is the ability to read and write.

The complex is essentially simple 

The complex is essentially simple, because it is also a function of our learning, experience and skill. To someone who has never stepped into a kitchen, even making a cup of tea may seem like a forbiddingly complex task. However, to most people it is just a regular task -- a simple task. 

The funny thing is that mathematics seems more difficult when it is taught but it seems easier when it is applied !

When it is taught - especially in our schools - its difficulty is cranked up to meet the needs of the engineering entrance exams, whose purpose is to eliminate large numbers of students through a process of cut-throat competition. It is easy to see that this "goal" has nothing to do with solving practical problems of life and society.

Even when students master that gigantic syllabus and get extremely high grades, they may not have internalised the logic behind the topics and may fail to apply them creatively in real life situations. 

However, when one begins to study science because one wants to understand and solve real life tasks, then the relevance and applicability of the topics are automatically evident and the human mind understands and internalises them faster.

Let's try to understand this using an example of a model, where we go from the simple to the complex and then realise that it's essentially simple.

Distance decay and equations that make you run away

Urban models are essentially mathematical equations that describe essential features of an urban system and can enable us to simulate and predict its behaviour.

Consider the following equation from Field and Macgregor's book (I will refer to this book  and David Foot's book on operational urban models many times in these blogs, as they are just brilliant) -

A = f(B, C, D)

This equation basically means that the variable A is a function of (that is, in some way, depends on) three other variables - B, C and D. Therefore, the value of A will change if there are changes in the values of B,C and D.

But what do A,B,C and D stand for ?

Let's assume that we want to understand how many shopping trips are made from various residential areas in the city to commercial areas. We can describe the components of our model in this way --

A = Number of trips made for shopping purposes (what we wish to find out)

B = Population of the residential area 

C = Number of shops in the commercial area

D = Distance between the residential area and commercial area.

But what to do if a city has multiple residential areas and multiple commercial areas and sometimes the residential areas are also commercial destinations and vice-versa ? We would like to express our equation in a way that shows interaction between any number of residential zones and any number of commercial zones.

We do it by introducing two more variables - i and j (where i stands for any residential zone and j stands for any commercial zone) and re-writing our equation thus -

A_ij = f(B_i, C_j, D_ij)

 Where -

A_ij - number of shopping trips made from zone i to zone j

B_i - residential population of zone i

C_j - number of shops in zone j

D_{ij –} distance between zone i and zone j

 

Our model represented by an equation comprising just a few alphabets can now handle a rather complex interaction of trips originating from any number of zones and terminating in any number of zones. 

We can refine the model further by considering the fact that A is directly related to B and C i.e. if B and C increase, chances are that number of shopping trips will also increase and B and C decrease then number of shopping trips would decrease. 

Furthermore, A and D are inversely related. If the shopping area is too far away (distance between i and j is too large) then the tendency to go and shop there would be low. Therefore as D increases, A would decrease. 

 

Therefore A = f(B, D) and A = f(1 / D)

 

Our model now becomes -

 

 

 

What we have discussed are the concepts of gravity (how strongly do different zones attract each other) and distance decay (how the intervening barriers between zones e.g. distance, cost, quality of infrastructure etc cause the interactions between them to decrease), which are key concepts in mathematical urban models.

 

When an equation just hits us out of the blue it looks difficult to understand, but when we break it down to its components and understand the logic behind their construction then it starts getting de-mystified. In fact, science is all about de-mystification. Once we get a grip of the logic then it not only does not seem complex, it actually seems very clear and basic. At that point we can begin to play around with it, understand its strengths and limitations and get comfortable with applying it.

 

Constructing mathematical models is a creative process

It is clear that what variables we choose to construct the model depend on us and on our understanding of the reality that we are attempting to study and predict. For example, attraction of commercial areas can be measured by number of shops, but it can also be measured by total floor area of shops in a zone. Distance between zones can be in the form of kilometers but it can also be in the form of the cost of covering distance or the time spent in covering it. 

It is pretty clear that one has to be extremely observant, imaginative and creative if one wants to create a model that is able to capture the essence of various urban phenomena.There are many people who may be experts in mathematics but have no understanding of urban processes or may just apply ready-made models blindly without considering how they ought to be altered or re-constructed given empirical realities.

 

As the Soviet mathematician Elena Wentzel correctly observed,

 

"The trade of model development is an art indeed with the expertise being acquired only gradually, as it would in arts."

In the next blogs we will look deeper into the role of mathematics in planning and explore how to apply it in planning problems we encounter in our day to day professional work.

Automating Planning Tasks 2 - (Programming with GRASS + Linux)

In the first part of this blog we had discussed how the various steps of a particular planning problem (in this case the slum-proofing problem of Jaga Mission) can be articulated, algorithmised and then automated. In the second part we shall see how the specific commands in the computer program work.

The technical steps necessary for achieving the goal (given the capabilities and constraints of government organisations executing the mission) were identified and are listed below -

(a) Identify the location of existing slums 

(b) identify vacant government land parcels near the existing slums 

(c) check them for suitability 

(d) generate map outputs for further visual analysis and verification. 

It is clear that the problem solution involves spatial analysis tasks to be performed on a Geographic Information System (GIS) software. 

While QGIS is the more familiar and user-friendly option, my preferred software for tasks like this is GRASS, which stands for Geographic Resources Analysis Support System.

GRASS is an extremely powerful and versatile open-source software, which was originally developed by the US Army - Construction Engineering Research Laboratory (CERL) and then by OSGEO - The Open Source Geospatial Foundation. 

A very useful feature of GRASS is that when you undertake any operation on it (e.g. clipping features in one map layer using features in another map layer), the command line version of the operation is also shown.

This is because GRASS is not just a point-and-click software (software which rely on a Graphical User Interface - GUI - for performing the operations by clicking with a mouse), but it also contains a command line option.

Most computer users are unfamiliar with the Command Line Interface (CLI) - even intimidated by it (I certainly used to be not so long ago). They, therefore continue to work on the user-friendly environment of the GUI and doing all their tasks with the mouse. However, by doing that they fail to harness even a fraction of the power of these wonderful machines - there is a reason why users who work comfortably with the CLI are called Power-Users. I have written about the advantages of the CLI in earlier blogs.

When GRASS is launched, it opens three windows simultaneously - the Graphic console (for performing operations using the mouse) ; a display window (for viewing the maps and results of operations) ; and a command line window (for performing tasks by typing in commands).

An interesting thing happens when you do any GIS operation on GRASS. Let's say you wish to execute the module called v.extract , which creates a new vector map by selecting features from an existing map (quite like exporting selected features to a new map layer in QGIS). The series of steps is similar to that in QGIS, where you specify the input file name, the output file name (of the new file), any queries that specify which features are to be selected etc.

You will notice, that while you are specifying these details by clicking with the mouse and entering file names, the following line is getting typed at the bottom of the module window -

This line is basically the command line version of the v.extract operation. This is how it reads --

< v.extract input=bbsr_slum_houses@training where="ward_id = 16" output=ward_16_slum_houses --overwrite>

The command begins with the name of the module, then specifies name of input file, name of input file and the sql query (in this operation the query selects all slum houses that are located in ward 16). The optional --overwrite can be added if you run the operation multiple times and would want the previous output files to be overwritten automatically (useful during scripting/programming).

When you click the "copy" button in the module window, this command line gets copied to memory. You can then paste it in a text file to make it a part of your program.

A good practice is to run all the operations manually once using the mouse, just so that you are clear about all the operations and all the command line versions of the operations. With practice you would not need to copy the commands. You will simply be able to type them out from memory or my referring to the manual page of the respective module.

Turning individual commands to a script 

Commands are very powerful because instead of clicking with a mouse many times, you can just type a short line and get the job done. But the main power of the commands is that you can write a bunch of them down in a sequence in a text file and execute it as a program to automate all your computing tasks. 

Consider the following 4 commands written down in a sequence -->

(1) v.buffer input=centroids output=buffer type=point distance=$buffer

(2) v.clip input=orsac_tenable clip=buffer output=vacant

(3) v.out.ogr --overwrite input=vacant output=$LAYER_OUTPUT/$ulb\_vacant_$buffer\_m_buffer.gpkg format=GPKG

(4) db.out.ogr --overwrite input=vacant output=$LAYER_OUTPUT/$ulb\_vacant_$buffer\_m_buffer.csv format=CSV

Of course, it looks a bit overwhelming ! But nothing to worry, cos everything useful feels a bit overwhelming at the start. Here is what is going on -

In step 1, the v.buffer module draws a buffer of user defined distance around the centroids of slums and saves it in a file called buffer. In step 2, the v.clip module clips features from the land parcels layer using the buffer layer file. In step 3, the v.out.ogr module exports the clipped land parcels as a gpkg vector file and stores it in your chosen folder. In step 4, the db.out.ogr exports the attribute table of the clipped file (containing details of the land parcels) as a comma separated value (csv) spreadsheet file and stores it in your chosen folder.

When you run these commands as a script then all these tasks get performed automatically in this sequence. 

It is clear from the above, that you can tie together any number of commands in an appropriate sequence to handle analytical tasks of varying levels of volume and complexity. 

GRASS + BASH

Bash - an acronym for Bourne Again Shell - is basically a "shell", a program in Unix like operating systems such as Linux, which is used to communicate with the computer i.e. it takes keyboard commands and then passes them onto the operating system for execution. 

The unique thing about Bash is that it is not just a powerful method for passing commands to the operating system but also an effective programming language.

The advantage of combining GRASS with Bash is that you can take the GIS commands of GRASS and use them as it is in a Bash script without any change in syntax by adding a flag called --exec at the start of the command.

By doing that you can not only execute the GIS tasks but combine those tasks with all the other programs and the full power of your Linux computer.

For example, in the same script, you can select GIS files of a few specific cities, undertake all the operations that your need to undertake, then save them in a separate folder, extract the attribute data as csv files, undertake data analysis tasks on them, put them in some other folder, turn both the spreadsheets and the output maps into pdf files etc etc. 

I guess this is already somewhat of an overload...and I feel tired of typing too ! I will show the combination with Bash in the next blog.

The request and the reward

Using the command line and scripting with GRASS and Bash are extremely powerful, flexible and fun processes, but they do request a readiness to learn and an openness to be creative.

The rewards...well they are immeasurable.