# TAD and graph theory

One area that I find many students getting stumped is the actual application of mathematics. Thanks to the rote way of teaching and learning; I think schooling has done more harm than good when it comes to connecting one piece of learning in the actual real world around us.

I once met an engineer who had no clue what height a 10' ladder would reach if it was to be placed inclined against a vertical wall so that its foot is 6' away from that wall.

Of course I threw him out from my office. Think about it for a moment: This is a simple application of the Pythagoras theorem.

What is fascinating about the way we use the spaces in our buildings is that they can be represented by a mathematical graph. A “graph” here being a set of points a lines (called “edges” in graph theory) that connect some of the points. So there are multiple ways you can build a “graph” for a building. One way to do it is to see how each room is connected to each other room directly — thru a doorway in between.

So if I have a toilet, and a bedroom and a kitchen — along with other rooms; then it is often possible that the toilet would be connected to the bedroom. But it would be rare for the toilet door to open directly into the kitchen. (It does happen in some poor localities and primitive housing but go along with me for now)

So if I were to draw a graph where dots represents the rooms of my house and the lines are drawn if there are direct connections; then the “dot” for the kitchen will not have a line connecting to the “dot” of the toilet.

There; I gave you an idea of what TAD can be used for. TAD internally allows architects to “classify” spaces so that when architects use TAD to design buildings; they can leave behind inside the data they create in TAD useful graph information that can later on be used to get lot of insights.

All spaces can be broken down into 3 different categories into what I rather pompously named as the SFA classification (SFA = Sabu Francis & Associates) the architectural practice where this classification was first used.

The way we derive value from the spaces we inhabit are based on such graph traversals. We do not realize this directly but it is not hard to realize it if you dwell on it. If I am a poor person and I did have a toilet that really did open directly into the kitchen then the experience you will have at my poor house would surely be different from a rich man’s house — where the kitchen is not having direct connection to the toilet.

If you expand on this; you will find all these inter-relations played a major part in shaping our experiences in the buildings we happened to inhabit or use.

Many architects are blissfully unaware of all this but like said earlier even if you do not believe in mathematics, or understand it well; the mathematics will still apply for you too.

For years; nay centuries, some architects are made to believe that architecture is all to do with how it looks and “feels” (in deliberate quotation marks, to mark sarcasm — because nobody really knows or I can say would ever know how to transfer that “feeling” to another) … But moving ahead a lot more can be done if we went down to understanding this “graphical” aspect of spatial relationships (pun intended)

Life happens in architecture, and we must check the kind of life that need to happen as we design — just so that our mistakes are not cast in stone; and therefore can be corrected before the building turns up.

Walt Whitman, the great American poet, expressed it so well:

“All architecture is what you do to it when you look upon it, (Did you think it was in the white or gray stone? or the lines of the arches and cornices?)”

From “A Song for Occupations”

In an earlier article I had pointed out how we live with mathematical palindromes daily in our buildings (Look that up … it is there somewhere in my timeline. Or better still, let me put a shameless plug about my book “Designs on Life” here. It is available at https://store.pothi.com/book/sabu-francis-designs-life/ )

Enough digression.

Let me get back to graphs. It is not just that graphs can be made purely on “inter-connections” between spaces. But you can create graphs on other parameters too. For e.g. in the Islamic culture they have spaces that are marked “zanana” and those that are “mardana” — the former are predominantly for the ladies of the house and the others for the male members.

Similarly there could be other equations that could be at work here. Say in a joint-family, there would be lots of subtle human relationship issues — this person has a hobby that grates on the nerves of someone else’s hobby. Or the the job that one person does is not compatible with that done by some other person and so on.

Here is a fascinating video that I saw on “Numberphile” which talks about an important conjecture that was proved false a couple of years back after almost 50 years.

What I have been trying to do for last 30+ years is to create a framework for architects to deposit their design data in such a fashion that future usage of architectural data can become a lot more useful and insightful.

Today all architects we is to place a morass of jumble of lines, and arcs and circles into drawing paper; and then step back moronically trying to win brownie points purely on how a building looks. As a result, architects have been at the leading edge of causing major disasters in the world. Both acute and chronic.

It is not just chronic issues such as global warming, carbon footprint, etc that we architects have contributed to due to poor design. But even acute problems such as the explosion at Beirut (which could have been easily predicted by a simple graph analysis on the spaces of the godown) or take a look at the horrific deaths that happened in Bolivia where some young students lost their lives — when a super-packed jostling crowd broke open a railing and those students plunged down four floors…. Again, I see an issue of incorrect representation of the design representation. If that data was available as a “graph”, someone could have attempted the effect of overcrowding in spaces. And it is not just the first time a tragedy like this has happened.

Go thru this video and see if you can make a connection between graph theory and space usage of architecture. (There are many other fascinating such examples) Or would you want to be like that engineer who was perplexed why I threw him out because he did not connect the inclined ladder with Pythagoras?

… and if you are an architect, I hope you would get convinced to download TAD and start representing designs a lot more accurately, and responsibly — at least people in the future may be able to use your data in more ways than you thought of.

TAD is free. www.teamtad.com