In which ways could we imagine the vast amount of computational power?

An imagination experiment about the computational power of the human brain

It seems unearthly to estimate the gigantic quantity that is provided by the only 20 W consuming interconnected neuron computer in our heads, or even trying to convert that to something like a numeric value. But to get a little bit insight into the gigantic scale of the possibilities that would be accomplish-able with a combination of today’s not yet very advanced stand-of-the-art data processing techniques in connection with an imaginary supercomputer, whose computational power would be equivalent to the computational power of the human brain, we start today some imaginary experiments to get it into perspective. So if we trust science, that would be round about 38 PetaFLOPS (what’s that?), but very likely even higher like 38 * 80.000.000.000 = 3040 Billion PetaFLOPS – so I would say we take this one for the further assumptions, because humans tend to underestimate the real complexity of something before they finally understand it (and because quantum). So how could we imagine the vast amount of power? In my opinion the best opportunity we have is to compare it to today’s computational capabilities and algorithms, because we have to assume that the data processing techniques of the brain are very likely more advanced and efficient than our today’s stand-of-the-art zero and one bit systems.

Imagination-Experiment 1: How much Netflix-Streams could you process and display with that computational power?

Let’s start with something everyone who’s surfing the web already heard of, or more likely using it daily: video streaming. This is very suitable for our first and also our following experiments because moving pictures are something that can be easily imagined and the fact that you can read this also states that we already sitting in front of a (more or less big) display. So let’s get started…

If we say we would need 0.01 TeraFLOPS (equal to Intel i5 Core) and 2.4 TeraFLOPS for 1080p graphic processing (like a nVidia GTX 960) we could handle at least about 8 Netflix-Streams simultaneously. Summed up we are at 2.41 TeraFLOPS in total. If we compare that to the 38 × 80.000.000.000 = 3040 Billion PetaFLOPS, we are able to reason that we could handle ((38 × 80.000.000.000 PF) ÷ 0.00241 PF) × 8 = 1.01 × 10¹⁶ Streams in parallel. That are fucking 10 quadrillions of movies simultaneously! The data stream would equal 10 quadrillion Movies × 0.00125 GigaByte per Stream = 12.5 Billion GigaByte per second, that’s more than the entire internet bandwidth of the world combined.

Imagination Experiment 2: How big could be a TV that the brain would therefore be able to manage?

To make the gigantic number of 10 quadrillion video streams more conceivable we now try to imagine how big a TV would be that could handle these huge amount of entertainment material. So if we say we spring from having a 24″ screen @1080p by a ratio of 16:9 we are at round about 0.3 m in height and 0.5 m wide. To keep the ratio we take the root from 10 quadrillions which is approximately 3.1623 quadrillions screens per side (x and y). The measures of the screen that the brain would be able to manage is therefore 3.1623 QD × 0.0003 km = 948.69 Million kilometers in height and 3.1623 QD × 0.0005 km = 1.58115 Billion kilometers wide.  That’s the size of vaguely 1364 suns in height and 2273 suns wide. Wow…

Imagination-Experiment 3: How big would be the TV if we scale the resolution to that of the human eye (or why we only see a small fraction of what’s going on)?

The human eye has a much higher resolution than a 1080p, or even a 8K display. Of course it’s difficult to compare the peculiar anatomy of the eye to the the less peculiar engineering of a digital monitor, but to get into perspective we take 576 MegaPixels (120 degree field of view – here is also a nice Vsauce-Video to this topic, for all that prefer video instead of text) for the further calculations. Even if we are only able to focus on a smaller fractions of this overall view we still take this number to stay conservative.

This time the number crunching is quite easy. We compare the total amount of pixels of the 1080p screen to the human eye pixel quantity. 1080p resolves to 1920 × 1080 = ≈2.07 MegaPixels, that means the overall resolution is 576 ÷ 2.07 = 278.26 times higher and therefore the new TV would be this order of magnitude smaller, like 5  suns in height and 8 suns wide.

Why we only see a small fraction of what’s going on?

Imagine we would stand in front of this gigantic human eye resolution TV. How much of this pixel bombardment could we overview? Obviously only a small fraction. Clearly, as we remind us that the base of our calculations was only a simple form of processing the pixels (streaming), that is for sure orders of magnitude less computational expensive compared to the complex thoughts that are running in our heads. But even if we say processing of higher orders of complexity would mean a 1 Million fold increase in computational work, the TV scale remains at a size of round about 3.48 km in height and 5.57 km in width. And if we say we could actively observe a screen the size of say 50 m high and 88 m wide (16:9) we would only be able to perceive ≈ 1.625 percent of what’s going on in our brains consciously.

Now consider that we yet don’t even know how the, from our perspective, consciously observable part of our mind works, how about the other 98.375 percent?

I do not even dare to ask…

Imagination-Experiment 4: How much atoms could we potentially simulate with the computational power equivalent to one single human brain?

Now let’s conect our imagination experiments a little bit more into the (merely) physical world. We know that today’s supercomputer are able to simulate the behavior of a certain amount of particles. But what does it look like with regard to our brain?

Coming soon…