“Yes We” can t-shirt design from tcritic.com.

There’s been a lot of interest and debate both from the public and within the government on the subject of population in Singapore (the fertility rate of, the import of, etc). One recurring topic has been what the maximum (or at least comfortable) population is that our infrastructure can support. However, I find that most of the discussion so far have been purely technocratic or utilitarian in nature–taking the total amount of infrastructure we have and dividing it by the amount needed per person gives us the required figure. However, I suspect that that the answer derived this way is far from both the optimum or the maximum.

Lawrence and I have been working on a project that looks at the importance of intangible input factors of production to economic growth. One surprising (at least to me) finding that came out of the project was the existence of elasticities of substitution between the tangible and intangible input factors [as according to a World Bank report here]. That got me thinking if perhaps tackling the population question purely from the angle of physical resources would perhaps not give us the best answer.

What are dimensions [and where do they come from]?

[Disclaimer: I'm not a scientist, just a science buff, so any misstatement of physics theories come from my own misunderstanding. Although I'm usually wary of stretching analogies too far, in this case I do think that there are some useful lessons.]

In physics, dimensions are best thought of as that which keeps stuff apart. This is best summed up by theoretical physicist John Wheeler who quipped: “Time is what prevents everything from happening at once”.

By this “definition”, it’s quite clear that time is similar to the 3 familiar physical dimensions in the sense that it prevents stuff from lumping together, the exception being that we travel along the time dimension in only one direction–forward.

[There was a big digression here on where dimensions come from, but I've moved it to the end of this post. Read on there if you're interested to understand where dimensions come from.]

Beyond physical dimensions

However, our world isn’t just made up of physical dimensions. For human beings especially, there are social dimensions (or layers of meaning). My introduction to this concept came at a series of lectures on social institutions by John Searle, a renowned social philosopher, during my halcyon university days. He gestured at the auditorium in which we were seated and said that the university wasn’t just bricks and mortar. The university was also made up of intangible aspects like the institution and the sentiments and meanings that we attach to it. I pictured it like additional dimensions that were layered on top of the physical structures, but which were invisible in our 3D space.

Similarly, we humans don’t exist purely within the physical realm either–our identities extend into social realms, for example. Moreover, the elasticity of substitution between the physical and the non-physical realms (beyond certain minimums, of course) is quite obvious. It’s conceivable that some people would choose to live with less physical space, worse infrastructure, or less material wealth if they can access more intangible “wealth” such as civil/political freedoms or more time/space/opportunities to socialize.

Accommodating more people–merely a problem of design?

Large cities with more than a million inhabitants have probably come into common existence only within the past century. It would be extremely arrogant for us think that we’ve mostly figured out how to pack people together. If the current hype on “urban solutions” is to be believed, there is still much improvement to come. Reading through the literature though, I get the impression that leading edge thinking is still attacking the problem from the logistical angle–better IT systems, waste management, transport infrastructure etc. I have not encountered anyone who asked if we can trade off the tangible with the intangible.

For example, in packing more people per square kilometre, do we at the same time try to shape culture so that people value “mental” space more than physical space? And if people are willing to make that trade off, have we designed our laws and regulations to free up these higher dimensional spaces for them?

Let’s look at how evolution tackles this problem with regard to metabolism (more specifically the basal metabolic rate–the resting rate of energy consumption) in animals as discussed in Melanie Mitchell’s excellent book Complexity: A Guided Tour. From a purely thermodynamics point of view, the basal metabolic rate should scale at a maximum of body mass to the power of 2/3. This is because an animal’s ability to radiate the heat away (surface area) grows only at body mass to the power 2/3. Thus, surface area becomes a bottleneck for metabolism and hence the metabolic rate can only grow at a maximum of length to the power 2/3. If it were higher, the animal would have trouble radiating waste heat and overheat. However, careful measurements over the next 50 years after this “surface hypothesis” was formulated  by Max Rubner in 1883 showed that the rate was scaled at a rate closer to body mass to the power 3/4 (called Kleiber’s Law after Swiss animal scientist Max Kleiber). It was only in the 1990s that researchers Geoffrey West, Brian Enquist, and James Brown at the Santa Fe Institute came up with the metabolic scaling theory that provided a satisfying (but still controversial) explanation to Kleibner’s Law.

In effect, their theory examines the way evolution has produced circulatory and other fuel/waste transport systems in the body and found that their fractal arrangement has approximated a fourth dimension (thus giving the 4 in the exponent) to make our metabolism more efficient. They put it this way: “Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional… Fractal geometry has literally given life an added dimension”.

By analogy (and I’m well aware of the dangers of stretching analogies too far), we should be able to accommodate many more people than we currently do in land-scarce Singapore if we figure out a way to tap on the “higher” dimensions.

One current example from Singapore is how LTA has put in place incentives to “time-smear” (my term, not LTA’s) travellers into off-peak hours. To me, it seems like largely a similar problem of design to “space/time/other dimensions-smear” people so that we can accomodate more of them more comfortably in Singapore.

For example, even if houses were getting smaller, I would think people wouldn’t mind if there was an efficient way to also share infrequently-used facilities, say storage or study spaces. To a certain extent, this already happens when residents in a condo share a swimming pool and tennis courts, and I suspect it can be taken much further, and further still if we tap on the intangible dimensions.

I’m gonna be a civil service shill here and direct anybody who is interested in how design can help improve the way your organisation works to contact Mr Leon Voon who heads up the Design Lab in the Public Service Division (and who co-authored my previous article on designing effective public policies). “The Lab” provides support to agencies within the public service interested to tap on design thinking. I’ve seen some of their work–it’s excellent.

Annex: Where dimensions come from

You would probably have heard that the universe originated in the Big Bang. But it’s not just the stuff in the universe that was created. Everything was–including space, and time. Asking what came before the Big Bang makes no sense because the dimension of time didn’t exist. Theoretical physicist Sir Stephen Hawking explains: “It’s like asking directions to the edge of the earth ['s surface]; The Earth is a sphere; it doesn’t have an edge; so looking for it is a futile exercise”.

To visualize how something can come from nothing, let’s use the some example that Paul Davies uses in his book The Mind of God. Imagine the expanding universe as an upside down cylindrical pyramid. The pointy end at the bottom is where the universe started. In our model, 3D space maps onto the 2D surface of the pyramid. Time moves from the bottom to the top towards infinity, so as the universe ages, it expands (as is the case in our current universe). Now look at the pointy tip of the inverted pyramid where space and time begins and round off the point so it looks more like a hemisphere. What you’ve done is that you’ve proven the equivalence of space and time since they “merge” into each other at the “beginning”. And these dimensions have emerged from nothing! Talking about the “outside” of the cylindrical pyramid makes no sense because there is no “outside”–the pyramid is the entire universe.