<?xml version="1.0" ?>
<tei>
	<teiHeader>
		<fileDesc xml:id="0"/>
	</teiHeader>
	<text xml:lang="en">
		
		<p>An &apos;optimal&apos; solution to a problem is, in<lb/> some sense, the &apos;best&apos;
			solution. It&apos;s the<lb/> shortest route to work, or the way of pack-<lb/>ing oranges
			that takes up the least vol-<lb/>ume. In science, optimality has long been<lb/> an
			organizing principle. Mathematical<lb/> physics views the Universe as unfolding<lb/>
			with dynamics that minimize a quantity<lb/> known as the &apos;action&apos; , whereas
			economists<lb/> and other social scientists often take opti-<lb/>mality as a guide to
			human behaviour: we<lb/> act, they say, to maximize our utility, be it<lb/> financial or
			otherwise.<lb/></p>

		<p>Looking at our networked and inter-<lb/>connected world, we may wonder<lb/> whether
			anything is optimal here,<lb/> from the food webs that underlie<lb/> ecosystems, to
			technological networks<lb/> such as the Internet. And science recog-<lb/>nizes that the
			real world often falls short of<lb/> optimality. Physicists know of many mate-<lb/>rials
			in which, as in glass, complex inter-<lb/>actions among the molecules prevent<lb/> the
			ordered arrangement of lowest<lb/> (free) energy; these materials per-<lb/>sist
			naturally in disordered, sub-<lb/>optimal confusion. Meanwhile, the<lb/>
			economists&apos; Homo economicus has been<lb/> replaced by a biologically more
			plausible<lb/> creature acting on the basis of fast yet fal-<lb/>lible instincts. We
			solve life&apos;s problems the<lb/> way we pack the dishwasher — not opti-<lb/>mally,
			after long calculation, but quickly<lb/> and more or less efficiently.<lb/></p>

		<p>What about networks? Is the Internet<lb/> optimal, in any sense? Is there a
			&apos;best&apos; way<lb/> to design the connections that link together<lb/> a collection
			of cells, people or computers?<lb/> This question has many possible answers<lb/> — which
			always depend on what, if any-<lb/>thing, a network is &apos;designed&apos; to
			do.<lb/></p>

		<p>In 1964, American engineer Paul Baran<lb/> conceptualized a layout for the command<lb/>
			and control network of the US military<lb/> aiming to withstand an attack by the
			Soviet<lb/> Union. He visualized it as a meshwork,<lb/> something like a fishnet, with
			roughly the<lb/> same number of links emanating from each<lb/> element. No one element
			would be a com-<lb/>munications hub — and primary target —<lb/> and the natural
			redundancy of paths would<lb/> allow messages to find a route through the<lb/> network
			even if much of it was destroyed.<lb/></p>

		<p>A few years later, US researchers had<lb/> Baran&apos;s meshwork in mind while
			devel-<lb/>oping the ARPANET, the seed of today&apos;s<lb/> Internet. Yet the Internet
			itself has turned<lb/> out to be wildly different from Baran&apos;s<lb/> hubless ideal.
			Although decentralized like<lb/> Baran&apos;s meshwork, it is in fact conspicuous<lb/>
			for its communications hubs — network<lb/> routers (or clusters of routers) that
			accu-<lb/>mulate far more connections than most<lb/> others. The network is especially
			sensitive<lb/> to any failure of these centres. In terms of<lb/> resilience, it is
			clearly not optimal.<lb/></p>

		<p>Of course, the forces driving Inter-<lb/>net growth have never been channelled<lb/>
			towards resilience, and its architecture<lb/> reflects the independent actions and
			deci-<lb/>sions of untold millions of people and<lb/> organizations. Quite possibly, its
			architec-<lb/>ture is not<lb/> optimal for anything.<lb/></p>

		<p>Yet in other settings the<lb/> notion of network optimality may have<lb/> considerable
			value. Suppose the popu-<lb/>lation in a certain country has a known<lb/> geographical
			distribution. How should<lb/> facilities such as hospitals be located most<lb/>
			conveniently? One recent study suggests<lb/> a relatively simple, if somewhat
			pecu-<lb/>liar, answer: that the density of facilities<lb/> shouldn&apos;t just be
			proportional to that of<lb/> people, but to that density raised to the<lb/> power of
			two-thirds. This puts more facili-<lb/>ties where there are more people, but not so<lb/>
			many more that they become redundant.<lb/> It is unlikely that urban planners
			currently<lb/> adhere to this principle, but it presents a<lb/> clear target for future
			policies.<lb/></p>

		<p>Another problem that a network might<lb/> solve is coordinating the activity of a set
			of<lb/> elements — by helping them to synchro-<lb/>nize their behaviour, for example.
			The<lb/> elements could be living cells such as neu-<lb/>rons, or anything else with
			rhythmic activ-<lb/>ity, and interact through signals of some<lb/> kind — electrical or
			chemical signals for<lb/> cells, or light for fireflies in a tree. It turns<lb/> out
			that the way such a network synchro-<lb/>nizes partly reflects its community
			struc-<lb/>ture, a community being any cluster with<lb/> far more links between its own
			elements<lb/> than to elements elsewhere in the network.<lb/> Studies show that under
			broad conditions,<lb/> the smallest and densest communities tend<lb/> to synchronize
			first, with larger-scale syn-<lb/>chronization arriving later.<lb/></p>

		<p>This suggests that a modular structure<lb/> of communities within communities may<lb/>
			allow for rich and varied dynamics — con-<lb/>ditions conducive to efficient
			information<lb/> processing and storage. In this sense, quite<lb/> plausibly, the wiring
			of the brain has been<lb/> crafted into optimal or near-optimal form<lb/> by the forces
			of evolution.<lb/></p> 
		
		<p>Yet in other cases, even proven mathe-<lb/>matical optimality may
			lack any exemplars<lb/> in nature. Researchers have identified a<lb/> broad class of
			networks that conspicuously<lb/> lack any modular structure, yet support<lb/> extremely
			efficient global coordina-<lb/>tion. These networks — named after<lb/> the renowned
			Indian mathemati-<lb/>cian Srinivasa Ramanujan — have<lb/> highly uniform
			architectures,<lb/> with additional long loops<lb/> lending them an
			&apos;entangled&apos;<lb/> character. They seem to be<lb/> almost optimal for many
			pur-<lb/>poses, for example by providing<lb/> networks that can be easily and<lb/>
			efficiently searched while avoiding<lb/> congestion. Even so, no one as yet has<lb/>
			found any natural network that adopts<lb/> this style.<lb/></p> 
		
		<p>What all this suggests is
			that questions<lb/> of optimality are rarely straightforward. A<lb/> network will
			probably reveal optimal form<lb/> only if it has a ready means for evolving<lb/> towards
			it, and time to do so. And the<lb/> nature of such optimality always depends<lb/> on the
			network&apos;s function. In many cases<lb/> today, even that remains at least a
			partial<lb/> mystery.<lb/></p>

		■


	</text>
</tei>