Human brains are incredibly efficient compared to the best AI systems currently in operation today. A digital AI running with 175 billion parameters (e.g Chat GPT) consumes about 9MW of power compared to a human brain which demands a paltry 20W (450 million times less power) in spite of processing information across 100 billion neurons. This isn't really a fair 'apples to apples' comparison however. For instance digital brains can execute billions of operations per second at the transistor level whereas individual biological neurons are slow. A single neuron has a refactory (or reset) period of about 2 milliseconds which means it is limited to conducting around 500 operations per second. However, what the human brain lacks in component speed, it makes up through the massively parallel nature of connectivity between neurons with up to 1,000 connections between any single neuron and its respective neighbors. It is estimated that a brain can deliver up to 1 exaflops (or about 1 billion billion mathematical operations per second). At the time of writing, the world's largest supercomputer could deliver 4 exaflops, but this is a massive facility spread across huge warehouses consuming prodigious amounts of electricity.

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So what is the reason for this huge disparity in performance?

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The answer lies in the responsive yet messy nature of analogue biological systems which get to the answer directly against the cold, deterministic precision of digital hardware which need to build solutions in piecemeal form. 

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Before we get into the weeds of the differences between analogue versus digital computing, it's worth taking a step back into the history of computers which, from their inception, were accompanied by deep questions around the parallels that could be drawn with the human brain. A famous starting point is of course the story of the Analytical Engine, a formidable mechanical computer which rivaled early electrical machines built more than 100 years later in the 1950s. The Analytical Engine was, at heart, a digital (or perhaps more accurately, a discrete) system and glacially slow in comparison to modern computers with an operating speed of around 7 flops (around a billion, billion times slower than today's super computers). In spite of this limitation, Ada Lovelace, a famous proponent of the system (designed by Charles Babbage), imagined a future in which the Analytical Engine could compose music and took it upon herself to write the first ever software program (which she developed to compute Bernoulli numbers). This was impressive foresight considering the Analytical Engine was too complex in its day to be built! Ada also understood the temptation to imagine that a mechanical computer could in some way 'think' but cautioned that “the Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform," this line of thinking was unbelievably prescient, considering she noted it down in 1842. 

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​Figure 1: A portion of the analytical engine (which was never built in full)

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In the beginning, discrete mechanical computers, which could count one number at a time, made sense since this reflected the way in which human 'computers' (people who calculated things for a living) operated when creating arrays of numbers used for mapping out celestial objects during navigation or for compiling logarithmic tables. However, ​the complexity of doing this work mechanically quickly becomes apparent when trying to formulate complex functions used for solving practical problems. 

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A concrete example from the 19th century centers around the challenges of predicting tides. This has clear practical consequences, if you can't predict tides when navigating around the coast or inland estuaries, you are likely to wind up with a beached ship. The tidal range is determine in large part by the position of the sun and moon relative to Earth. The gravitational pull on the ocean creates a bulge in the sea which moves around throughout the course of the year. The tidal range at any given point along any coastline will take the form