In the 1950s, it was estimated that if all the connections in the human brain were modelled with valves (or tubes in American English), that “brain” would be the size of what we now call Greater London. I don’t quite understand how this happened because Greater London wasn’t in existence at the time. I seem to recall that that administrative unit was created by drawing a circle twelve miles in radius around Charing Cross and including all the boroughs which its circumference passed through, but that seems to be too small. In any event, this is an area of 1569 km². This was during the time of the first generation of digital computers, when the switching elements were valves.
Later on, transistors had replaced valves. These are effectively solid state switches which can be turned on or off by the application of a current, hence their tripodic nature, and were initially made of germanium, an element I used to think was called “geranium” for some reason. Later transistors were of course silicon, but in both cases they’re “doped” with small amounts of another element, often arsenic. If a human brain were to be made of that kind of transistor, it would be the size of the Albert Hall. This is a large public building in Covent Garden, near Charing Cross in fact, which is elliptical seen from above, and has axes of almost seven dozen and six dozen metres. Taking the mean diameter, this gives it an area of 4778 m², and this gives me pause because it’s so much smaller than the first figure. Did they actually mean Greater London at all?
By the early 1960s, engineers were starting to put several transistors in the same package. Incidentally, these were not the first integrated circuits. Earlier, valve circuitry was being put into the same evacuated chamber and it was possible to make a valve comprising several discrete components, which was sometimes done in radio receivers. However, the real advance was putting components onto the same wafer, because it became feasible to make a single chip which worked as a logic gate, and later an arithmetic and logic unit and eventually an entire CPU. In 1965, Gordon Moore made the observation that the number of transistors which could be made to fit in the same area of silicon seemed to be doubling every year, and this became known as Moore’s Law. Incidentally, in my alternate history known as the Caroline Timeline I tried to imagine what would have happened if advances in this area had been linear rather than geometrical, with progress proceeding at 1979 levels. I call this Vannevar’s Law. In 1978, the BBC TV science documentary series ‘Horizon’ noted that it was now possible to fit an equivalent number of transistors to the human brain in a five metre square room. Moore’s Law no longer applies. The doubling was revised to once every two years at some point and it seems to have broken down in the late ‘teens. Assuming ‘Horizon”s room was 5x5x3 metres, or 75 m³ in 1979, there would have been eighteen iterations between that year and 2015, which would’ve reduced the size by a factor of 2¹⁸, which is 262 144, equivalent to a cube less than seven centimetres on a side, or about the same size as a Rubik’s cube. It would’ve been about the same size as a human brain in 2011 or so by those calculations. Does that mean it’s been theoretically possible to build a gynoid or android with the equivalent of human abilities for a whole decade then? That would assume that human brain functions can be precisely replicated using hardware in the form of logic gates, and that’s not clear.
I actually want to go the other way with this.
This image is not ideal. It excludes the Shetlands and includes about half of Ireland and bits of France, but I want to focus on Great Britain here. But we’re not quite there yet. Back to Greater London and the Albert Hall.
It wasn’t clear to me what kind of plan the human brain in the first two scenarios had. Was it supposed to be a two-dimensional or three-dimensional equivalent? Is the Albert Hall in particular supposed to be filled with transistors or is it just a flat surface covered in them? Brains are not like that, and the human brain is even less so due to being very wrinkled. This brings up a bit of a quandary for me. My head has a feature called cutis verticis gyrata, where my scalp is convoluted in a brain-like manner. Its cause is unknown but it gives me cause to wonder, is my scalp folded in the same pattern as my brain? Feeling it certainly seems to divide it up into similar lobes, gyri and sulci to the presumed brain underneath it, but if so, is that because there is some geometrical reason why the folds would be in the same place as the brain, or is there some connection between my gyri and the skin of my scalp? Is it like my cortex somehow communicates with my dermis and causes it to pile up in that manner? I don’t know. Nor does anyone else actually: the condition is entirely mysterious.
An unfolded version of the human cerebral cortex would have an area of about two thousand four hundred cm², but even then it’s a three-dimensional object and there’s more to the brain than the cerebrum. Perhaps counter-intuitively, there are several times as many cells in the cerebellum than there are in the cortices, and these are in a similarly folded arrangement and there are plenty of other bits inside the brain such as the hippocampus, thalamus, hypothalamus, amygdalæ, corpus callosum, basal ganglia and so on. Producing three-dimensional circuitry is an unsolved problem in microelectronics, but if the brain can be understood correctly as circuitry, the problem has been solved.
Great Britain does not have a definite area, and there are two figures for it, for similar reasons as the difficulty in working out the true size of the brain and its equivalent. The United Kingdom, i.e. including the bit of Ireland still claimed by Westminster and therefore more than just Great Britain, can be considered to have an area of 242 495 km² or 243 610 km². There are two reasons for this discrepancy. One is illustrated by the idea that “if Wales were flattened out it’d be bigger than England”. The UK is not flat. The first figure is basically the area enclosed by the coastlines considered as a two-dimensional surface. The second takes into consideration the fact that there are hills, valleys and mountains involved. This is where fractals come into play. The resolution of the hills and valleys is important here too. Hills could be thought of as cones or pyramids, or they could be thought of as rough surfaces. However, this doesn’t make the area infinite because it converges on a limit. The question of the coastline and tides also arises, although area based on tides is standardised by some kind of international agreement. But the coastline is also fractal and this influences the area. By one measure, the coastline of Scotland is ten percent that of the whole of Europe, and Europe itself has an unusually long coastline compared to other parts of the world. I’m guessing this also converges to a limit. Scotland’s coastline is, remarkably almost half the length of the oceanic coastline of the whole of the United States, if the later is calculated by a method excluding firths, but more like a ninth if the Great Lakes and firths of the US are included. Scotland is convoluted. It’s “brainy”.
The other factor, which doesn’t influence Britain much, is the fact that it follows Earth’s surface. This gives it a slightly larger area than if it’s assumed to be flat, and also a slightly different area than if you assume it to be a 242 495 km² portion of the surface of a sphere, because Earth is not perfectly spherical but deviates something like 0.5% from the shape of a sphere, and not even in a particularly regular way. Hence there are difficulties.
For the sake of argument I’m going to assume that the area of Great Britain, i.e. the big island I live on, is 209 331 km². This excludes any claims made on Ireland and also Lewis, the rest of Na h-Innse Gall, Ellen Vannin/Man, Ynys Mon, the Isle of Wight, Sheppey and much of Portsmouth (which is on an island). However, it would include the likes of Bede and Frog Islands in Leicester, Dungeness and the Isle of Thanet, since those are not currently islands.
When I look at a map of Great Britain, it is of course very familiar to me, as it would be for most Brits, but when I look at a photograph, map or diagram of the human brain it is less so, unsurprisingly. The brain is also much more significantly three-dimensional than Great Britain is and my lacking spatial abilities are brought into play. Parts of Britain are familiar enough to me that I can fairly easily identify individual rivers, villages, towns and cities in some parts of the island on unmarked maps and photos, particularly if I know which way the compass directions are. What I want to know is, how familiar am I with the anatomy of the brain compared to the geography of Great Britain?
The human brain has a volume of about 1 500 ml. It isn’t entirely sensible to assume it to be a sphere, but it’s still probably the best I can manage as a means of estimating its horizontal cross-sectional area. A sphere with a volume of 1 500 ml would have a cross-sectional area of 158 cm². Compare this to the area of Great Britain, this means that every square millimetre of the brain is proportionate to thirteen and a quarter square kilometres, and I’m guessing that’s the size of a small town.
Like my knowledge of British geography, my knowledge of brain anatomy is very uneven. I know the lobes, some of the sulci and gyri, the structures I mentioned above and the connections made by the cranial nerves along with the ventricles, the basal ganglia and a few other things. I’m also aware of the general layout of the neurones and supporting cells on a microscopic scale. But please don’t ask me to do brain surgery or it’s “there go the piano lessons”, and you also have to contend with the fact that my spatial abilities are pretty poor. It took me a very long time to place even two minor brain structures in relation to each other. I’m talking months.
It amounts to this. There are small areas of Britain of which, like practically anyone else, I have detailed local knowledge. By the way, it’s an interesting exercise to assess the accuracy of Wikipedia by looking up one’s local areas and comparing the articles to what one knows to be true of them because in that respect we’re all experts. Most of us couldn’t do the same with articles of the nucleus accumbens or substantia nigra. The brain is also characterised by different systems marked out by their use of different neurotransmitters, which I might compare to things like the National Grid, the road network and the rail system, although like most other things they’re three-dimensionally arranged.
The body of a nerve cell is about 100 μm wide. A brain scaled up to the size of Great Britain would have such cells 300-400 metres in diameter, so they’d be about the size of a medium-sized park or small lake – perhaps part of a neighbourhood such as a street. You could probably jog round it in about five minutes if you were fairly fit.
I want to be more familiar with the anatomy of the brain just as I want to know the geography of Great Britain, but in order to be able to do that, I need my own brain to have sufficient abilities to grasp its own three-dimensional structure, which makes it a harder task than, say, “doing the knowledge”. But isn’t it odd how we can basically be such a complex organ without having any knowledge of what we are? It isn’t even the same as self-awareness. You could have any degree of that without having a clue about the brain. I can tease out individual bits of experience and correlate them to the nature of the brain, such as the visual system, sensorimotor homunculi, reticular system and others, and I’m aware of the probability of what this particular brain does with certain neurotransmitters compared to others, but like most other people my brain is in a dark bone box doing all this stuff and will forever remain a mystery to me, not least because in order to understand it fully, I would have to have a more complex brain which I wouldn’t then be able to understand, and so forth ad infinitum.
Life is strange.
A Box Of Chocolates 