Tending towards infinity (when infinity equals one)

"If I could be bounded in a nutshell..."

Today I noticed a curious passage in Marx's Capital:

Just as a certain number of simultaneously employed labourers are the material pre-requisites for division of labour in manufacture, so are the number and density of the population, which here correspond to the agglomeration in one workshop, a necessary condition for the division of labour in society. Nevertheless, this density is more or less relative. A relatively thinly populated country, with well-developed means of communication, has a denser population than a more numerously populated country, with badly-developed means of communication; and in this sense the Northern States of the American Union, for instance, are more thickly populated than India. (In consequence of the great demand for cotton after 1861, the production of cotton, in some thickly populated districts of India, was extended at the expense of rice cultivation. In consequence there arose local famines, the defective means of communication not permitting the failure of rice in one district to be compensated by importation from another.)

Let's adopt Marx's reasoning for a few minutes. We'll grant, then, that population density isn't simply the ratio of inhabitants (p) to square miles (a); the speed and sophistication of the inhabitants' communications infrastructure (c) enters the formula as a variable multiplier. Given two land masses each with an area of 500 square miles, and populations that differ by a ratio of 2:1, the less sparsely populated area can have an equal adjusted population density (d_a) to the more populous area if the extent and efficiency of their communications network twice exceeds their counterparts'.

Marx doesn't explore the determinants of c's value in the formula for adjusted population density, and neither will we. I'm not remotely qualified to put forth a numerical efficiency value for, say, the Pony Express system or conjecture its difference from the c value represented by a network of telegraph lines and stations. Or: what is the disparity in the c values of home telephones and of desktop computers with modems, instant messaging software, and email clients? Or between a nation of people with desktop computers communicating via phone lines and a nation of people with mobile devices communicating via radio tower relays? Between mobile devices communicating via radio tower relays and mobile devices via satellite? And so on.

Moving along: telecommunications are transforming the Earth and its human inhabitants into a global country (neither "nation" nor "village" seem apt to me at this moment) with a growing population and an inhabitable area with a more or less fixed maximum. If the global network and the technologies it employs are continuously expanding in their reach and efficiency, could it be said that Earth's adjusted population density (at any moment) tends towards a singularity?

Again: we will assume that p is approaching some large but finite quantity, and if a represents the total area of Earth than can be made habitable, it more likely than not will arrive at some point of maximum possible development. That leaves c. Do we have any cause to believe that c can approach infinity? If we take the transhuman millenarians at their word, there sure is.

To get an idea of the appearance and operation of infinite communication efficiency, one need only read science fiction or singularity blogs. Imagine a world where a thought—a phrase, an image, a sensation, a statistic, any of the various packets of information which we presently rely on language, visual displays, or one of the various modes of artistic expression to convey—a thought flashing up in the awareness of an individual is transmitted, almost instantaneously, as a thought, to another person (or persons) anywhere (or everywhere) on the planet.

This would represent communication efficiency of an incredible magnitude—but not quite infinite.

Infinite efficiency would be attained when the transfer of information is instantaneous; when a thought bubbles up in the brain of one person on the planet, it bubbles up in the mind of everyone else on the planet simultaneously. Moreover, there must be a one-to-one correspondence between the information dispatched and the information received at its intended destination(s). This means that every time an idea whizzes across the grid (whatever the grid is, however the grid is, in whatever dimension the grid is) it must be understood, noticed, acknowledged, absorbed with zero percent noise or ambiguity by every human being plugged into the grid. This requires that that cognitive faculties of every human being on the planet become adequate to parse every last individual eV or byte of information bombarding them from every other human being on the planet—or that every human being on the planet is thinking the same thought simultaneously. The event of the former might well result in the situation of the latter: some eight or nine or ten billion human minds flitting about, remotely nudging each other like the particles of a dust cloud in space, each mote and speck gravitationally attracting every other mote and speck until the whole scattered mass coalesces into a single body.

We're making several assumptions here, sure, but I don't think they're totally unmoored from precedent or the present. The epoch-marking successes of Twitter, Instagram, Vine, Twitch, et al. suggest that instantaneous communication with as absolutely (potentially) broad an audience is what the wired world wishes for. Sharing is taking on the dimensions of a social imperative, while the private experience approaches undesirability. The platforms we use to share either include or wholly consist of audiovisual content, implying that we wish to convey our thoughts and experiences through the media correlating to our most salient sensory experiences. And we've already noticed how culture and communications are coalescing into monolithic structures within their own spheres. If we can expect these trends to continue without reverse or intervention, the infinity scenario seems like the ultimate and logical endpoint.

There's your millenarian future: as we refurbish the planet, extirpating (unintentionally or deliberately) all the spaces and species that are not integral to (or can't be co-opted by) the world-polis, humanity turns outward to and inward on itself, the individual experience becoming public, the public conversation becoming the individual experience, until one equates to the other.

I am reminded of a passage in The Human Evasion where Ms. Green is herself reminded of a book called Flatland

...in which an imaginary two-dimensional world is described. Towards the end of the book a non-dimensional being is encountered——a point in space. The observers listen to what it is saying (but of course, since they are of higher dimensionality than its own, the point being cannot observe them in any way). What it is saying to itself, in a scarcely audible tinkling voice, is something like this: "I am alpha and omega, the beginning and the end. I am that which is and I am all in all to myself. There is nothing other than me, I am everything and all of everything is all of me and all of me is all of everything..."

The human race has taken to producing similar noises.

The destination of our planet is an anthropic black hole.