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Achilles And The iPhone

In the 5th century BC, a Greek philosopher named Zeno invented clever, paradoxical puzzles.  In the most famous, he argues that swift Achilles, racing a turtle that has been given a very modest lead, can never catch that torpid tortoise.  Twenty-one centuries later, two geniuses simultaneously and independently used Zeno's view of infinity and the infinitesimal to create calculus.  It took another 500 years for Steve Jobs's magnificent iPhone to newly define the infinite as Apple sold more than a billion devices, spawned a trillion dollar business, and inspired new forms of social and economic organization.

Isaac Newton
Mathematician, physicist, inventor, and scholar, England's Newton
developed calculus at the same time Germany's Leibniz had similar ideas

Zeno's inspirational paradox, briefly, is this: Imagine a footrace between athletic Achilles and an ordinary tortoise.  Achilles gives the tortoise a hundred yard lead and then tries to overtake it.  To do so, Achilles must run to the position the tortoise occupied at the start of the race.  By that time the tortoise has moved ahead.  Achilles must then run to the where the tortoise was when Achilles ran the next segment of the race, and again by that time the tortoise would have plodded on some distance.  So, while Achilles can always reach a point where the tortoise used to be, he can never catch up with the reptile, let alone overtake it.

Zeno's paradox inspired all the philosophers and mathematicians who followed him to think about the division of time and space into ever smaller portions and the way those portions might or might not be added together.  The notions inherent in this puzzle underlie the most powerful ideas behind calculus.

Gottfreid Wilhelm Leibniz
The German mathematician and philosopher developed calculus
so brilliantly that we still use his notation

In the 17th century two extraordinary scholars, Isaac Newton in England and Gottfried Wilhelm Leibniz in Germany, happened to think about ways to create a branch of mathematics that would address matters not amenable to analysis using the basic algebra of their time.  Each, coincidentally, developed what we call integral and differential calculus.  The first enabled the solution of problems involving the area under a curve and volume within a three-dimensional object.  The second provided a basis for describing rates of change.  The two branches of calculus complement each other and together form a complete body of knowledge.

Each of the two mathematicians had interests far afield from calculus.  Newton invented the reflector telescope, which he used to examine astronomical objects influenced by gravity.  He used calculus to describe the way gravity determined the paths of the moon and the planets.  Similarly, he applied his methods to things closer at hand, including falling objects, an inspiring one of which was an Apple.  Thus, Apple is a very good name for an inspiring company.

Leibniz was in some ways more of an academician than Newton.  It is his scheme of mathematical notation, including the elongated S commonly called the integral sign, that is still used to express the concepts of calculus.  Leibniz wasn't entirely devoted to the abstract, however.  He built mechanical calculators that performed the four basic arithmetic operations: addition, subtraction, multiplication, and division.  But in his abstraction of philosophical ideas he advanced the notion of simple objects that interacted with other objects in various ways.  These monads, as he called them, inspired scientists of the 20th century to develop theories of neurons, each independent but nevertheless part of an interactive whole, that helped reveal the secrets of the brain.  Smartphone users may be thought of as monads, too.

Steve Jobs And His iPhone
More than an invention, the iPhone is a vision,
one that nearly a decade later
has reshaped the world of communications

We will never know how Steve Jobs developed his wonderful vision of the iPhone.  Whatever the provenance of his inspiration, it guided the engineers, programmers, designers, physicists, mathematicians, and marketing specialists at Apple as they developed the device, its supporting technologies and its surrounding ecosystem.

In 2007, when the iPhone was announced, pretty much every observer of information technologies who took a good look at it was not merely impressed but dazzled.  And that was only the beginning, when the iPhone had, by today's standards, limited computational abilities and a very modest complement of apps.  That was before mobile networks offered particularly large bandwidth.  That was before geolocation technologies and related libraries of maps, atlases, and other reference materials became powerful in their functionality and at the same time eminently affordable.  That was before Apple was able to boast it had sold more than a billion iPhones, a milestone it passed last summer, even before the current iPhone 7 generation of instruments were yet to appear.

If Apple maintains the sales pace estimated by Gartner and other analysis firms, it could add another hundred million units to the population of smartphones by the end of this calendar year.  These phones typically sell for $750 to $900 each, for a total hardware value of $75 billion to $90 billion in half a year.  IBM's revenue for all of 2016 from hardware, software, and services is expected to be about $80 billion or maybe a bit less.  Apple's iPhone hardware business alone, then, is bigger than all of IBM.

In addition to phones, Apple's customers buy lots of apps, plenty of phone cases and other accessories plus communications services that usually cost more per month than a phone purchased on an installment plan.  For Apple, for carriers around the world and for all the companies that piggyback their activities on the lively market, the iPhone universe represents a very big business.

Apple is likely to ship an additional hundred million by units during 2017 even before it begins delivery what market watchers call the iPhone 8 generation of products, successors to today's phones.  That's another IBM's worth of revenue.  In 2015, IBM reported net income of just over $13 billion.  For the fiscal year ending in September 2015, Apple reported revenue in excess of $233 billion and more than $53 billion in net income; Apple did not say how much income was directly attributable to the iPhone.

The iPhone may be the best-selling model but Apple is not the best-selling brand of smartphones.  The leader, with many phone models, is Samsung, which sells phones at not quite double the rate that Apple does.  On Apple's heels come a number of Chinese rivals, led by Huawei, followed by a long list of other manufacturers, mainly from Korea and Taiwan.  What most of the contenders have in common is their use of Google's Android operating system.

Client Devices
Gartner research shows that smartphones sell at twice the rate
of all other client computers and four times the rate
of desktop and laptop PCs

Both the bigtime phone operating systems, iOS and Android, provide interconnected bundles for web searching, phone and app searching, navigation, email, messaging, contact management, telephony, web browsing, and cloud storage.  Phone users don't always have to use the OS-related apps for all these functions, but in many cases the core apps do the best job in the simplest way.  Still, there are lots of apps that are quite popular.  For navigation, Waze comes to mind, for email there is Gmail and the open source K9 client, for messaging there are quite a few popular apps, for telephony there are outstanding offerings like Skype, several web browsers are quite popular, and when it comes to cloud storage Dropbox and its ilk provide excellent alternatives to the cloud storage services offered by Apple and Google.

The importance of these key apps is that they are gateways to the outside world, gateways that often enable the monetization of glances and clicks.  The value of these gateways, particularly when it comes to searching, is so huge that they enable players like Google to treat the development and support of Android as just one of many costs of maintaining a lively business.

If and when Yahoo is finally sold, probably to Verizon, we will be able to see whether the combination of a common carrier and a gateway is greater than the sum of its parts.  Google, dabbling in the carrier game, thinks this might be the case.  Apple, still not a carrier (but that could change at any time), would certainly invent some new ways to operate if it decided to add carrier services to its stew of mobile device offerings.

And then there is Amazon, another giant that has some powerful services.  Amazon has tried and failed in phones, but succeeded with reader and media tablet.  Amazon is significantly different from the other companies offering cloud-based services.  Google sells the persuasive potential of its access while Amazon directly turns that click or glance into an actual purchase including the speedy delivery of goods.  Amazon seems to have learned that its culture is not fit to compete with Apple in the communications business.

Like Achilles chasing the tortoise, Apple's many and diverse rivals seem to be able to get to a position Apple occupied in the past only to discover Apple had moved on, remaining just out of reach.

— Hesh Wiener October 2016

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