As is the case with our parents, there invariably comes a moment when a teacher reveals themselves to be utterly, fallibly human. Rather than being a reliable source of knowledge, with one stray remark they reveal themselves to being as prone to misconceptions and ignorance as the rest of us. We learn that whatever instruction they offer should be treated provisionally.

One such moment from my own youth: sixth form, in morning assembly — a venue for our teachers to share wonderfully secular homilies. The teacher taking the assembly that morning explained that when he was himself in school he witnessed the first computer arrive in the classroom. At that time it wasn’t clear what function this intimidating new appliance should serve. “For some reason,” he told us, “they decided to send it to the mathematics department.”

Sitting there I understood quite intuitively that the maths department would have been the obvious and appropriate place to send the computer. After all, what is a computer except a machine for performing a long sequence of mathematical operations? The teacher seemed to believe computers were elaborate typewriters with the additional capabilities of playing a game of solitaire or selling you something.

I will add that this was the same teacher who I had heard, from a reliable and highly placed source (another teacher), that perhaps the maths department should start offering an “applied math” course, stripped of all the impractical and superfluous “pure math”. You know, only the math a good worker would actually need. As if maths teachers were some kind of freaks who insisted on inflicting abstract suffering on on students before grudgingly teaching them useful stuff: statistics.

In retrospect, sat in that school assembly, we were living through a significant moment. Broadband had arrived along with youtube. Facebook was only the latest in a string of social media platforms. I got a gmail account, with its bottomless inbox. Teachers were beginning to be drilled on the importance of making use of online resources. Certain educators dictated long and complicated urls to us that we had to copy down carefully so that we could make use of them later. I’m not talking about the home page of a site — we were sent to pages deep within the site-map; urls trailing all kind of database tokens and php residue that we would someday learn was susceptible to the unpleasant sounding “link rot”. This is the future, those educators presumably thought to themselves as they had unhappily transcribed those web-addresses. No doubt they were far from convinced that any of this would ever be *convenient*.

Only a decade later and we would enjoy boomers falling into candy crush addiction. And computers became even less recognizable as machines of mathematics.

As part of a professional realignment, I have been learning the ropes of cyber security. The past month was dedicated to mastering low level memory exploits. Or at least the low level memory exploits of twenty years ago. Real zeros and ones stuff. Well, hexadecimal stuff really. Staring at (virtual) memory locations. Format string exploits. Messing around with debuggers. You might think that would have brought me to the mathematical heart of our digital engines. But no. I have instead had an almost gnostic revelation about the true nature of the Matrix.

Certainly, there is a lot of deep mathematics playing a fundamental role in the workings of all the code. To take a particularly central example: the existence of one-way-functions is the underpinning assumption of almost all cybersecurity. The cryptographic protection we enjoy (whether you realize it or not), is provisioned on the understanding that an adversary does not have the ability to reverse certain mathematical operations with reasonable efficiency. This assumption may well hold up. Quite likely P does not equal NP, and it is entirely possible that quantum computers are a physical impossibility. I may not live long to see such profound questions resolved.

But there is another side to our PC world. From where I am sitting, they are simply huge bureaucracies. Mathematical bureaucracies to be sure, but bureaucracies nonetheless. There are replete with elaborate filing and organizing systems, protocols with carefully written standards, and all the input and output amounts to a certain kind of paperwork. From this perspective most security breaches are the product of improper filing, out of date standards, and old fashioned mail fraud.

There is no undoing all the bureaucracy either. The further we get from the golden age of pre-broadband the more the bureaucracy swells; not only to deal with the non-tech-savvy hoi-polloi, but to integrate the hoi-polloi into the very system itself. The age of nerds noodling around with open source code and experimenting with new kinds of hardware has given away to a world of corporations and start-ups where every other college grad needs to get their “workflow” in-sync with their fellow internaut.

As with parents and teachers, the original architects of the cyberspace have revealed themselves to be shortsighted and ideologically blinkered human beings with their own unique set of foibles. It took us too long to see it. That teacher who revealed his digital ignorance to our year group happened to teach economics. I never took a class with him, but if he knew anything of economic history then there was a chance that he might have been able to teach us certain truths about technological advancement that we had overlooked.