THE MATH OF HOUSES
The design of a house can be expressed in a mathematical formula. So let us see how we can incorporate mathematical equations as part of our design process.
When a client approaches you with their requirements for a house, without question, there will be a list with elements, such as living, kitchen, dining, entry, bedroom, mudroom, etc. Further, each of these elements will have a probable adjacency relationship: the dining should be adjacent to the kitchen, etc. How a house works is governed by the sequence of these elements. Volume generally tracks with importance. And we generally input variables such as the direction of south, direction of the best views, etc.
Let’s put those factors into a math formula, as shown below:
where n is the number of independent elements, p is the number of possible adjacencies, q is the quantification of importance, v is variable input, and h is the quantity.
And there you have it, the design of a house expressed in a mathematical formula! I’m just kidding. The formula above, while it looks impressive, is merely an approximation of what this could look like if it actually worked. It doesn’t work.
Still, it could. Far greater interdependent scientific probabilities are summarized with math formulas. Don’t you feel a seriousness just looking at that equation? In our culture, we fervently believe that it is not a science until it can be expressed mathematically. When something become scientific, subjectivity and culture are removed. Making something scientific means that it can be bought and sold in the marketplace for big bucks.
Another question, have you ever noticed how design gets serious every time there is a mathematical overlay? Think of the mathematics demonstrated in Alexander’s Notes On the Synthesis of Form, excerpted below. Open most any page of Thompson’s Growth and Form, and there will be mathematics. Or think of Corb’s Modulor. If there is math, suddenly we must be getting somewhere serious.
The design of a house is what is called a Markoff Process: there are a finite number of possible system states, the probabilities of a relationship are dependent upon a preceding element, etc. And Markoff processes are summarized with mathematical formulas all the time.
This is an invitation for any reader who is mathematically adept to have a go at this. Writing mathematical expressions is a creative process: the mathematical expression adjusts to fit the syntax of what you want to solve. And I should know; to write the formula above, all I did is type strings of words into AI Chat, and presto, an impressive looking formula!
When it comes to math, the common concern is owners’ equivalent rent (OER). OER measures how much money a property owner would have to pay in rent to be equivalent to the cost of ownership. OER also measures how much money a property owner would have to pay in rent to be equivalent to their cost of ownership. I suppose another measure is cost per square foot—plans, building materials, labor cost, bids from subcontractors, lot prep, interior finishes, plus porches, garages, driveways, and unfinished spaces like attics, etc. But cost per square foot is a terrible measure of the costs associated with building a new home. Maybe just skip the formulas? Mark Ellison’s cranky book (cranky about owners and architects) Building—A Carpenter’s Notes on Life & the Art of Good Work is illustrative of the difficulties in estimating time, effort, and costs of building. In any event, your formula is a nice joke, but that pink in the illustration is dreadful. Cheers, KO!