Posted on Fri 26 February 2016

more bandwidth, please

Is there an upper bound to the amount of bandwidth that people will demand?

First, a brief history of my personal bandwidth consumption.

I was lucky enough to be born into the beginning of the age of bandwidth, with computers being available in elementary schools and telephone modems just emerging into consumer usage. My first modem was a 2400 baud Zoom with no special features. When I used it, nobody else in my family could use our one telephone line. We did not have an answering machine, but that would not have worked, and voice mail was not a thing that could be ordered for any sort of reasonable cost.

I can read faster than 2400 bits per second.

When I went away to college, I lived in the first dorm on campus to have ten megabit ethernet in every room. It was very forward thinking: there were two jacks in every room.

In my second apartment in Boston, I got one of the first cable modems. It was a big ugly grey box with a lot of heat-radiating fins on it, and I frequently managed 10 megabits through it.

Nowadays my “cheap” cable modem service at home is 50Mb/s down, 5Mb/s up, and it feels reasonably quick. Delays are more often caused by the older clients connected to our 802.11 g/n wireless network.

What is the most bandwidth a human could want?

To a first approximation (that means I am wildly guessing), I would say that full immersive, uncompressed sensory data for 5 senses at a resolution approximating the perceptible limits of humans is a good proxy for maximum data usage. How much is that?

  • Visual data

A field of view about 180 degrees wide, 135 degrees high, 1 arc minute in minimum pixel size, and updated 100 times per second… twice, to account for full stereography, and using 48 bits of color.

180 * 135 * 60 * 60 * 100 * 48 = 419904000000,

420 billion bits per second.
  • Audio data

Human ears can be fooled relatively easily. Simplest is binaural stereo, in which only two point signals are needed. Sample at 48KHz, 16 bits deep, and we get

48000 * 16 * 2 = 1536000

a mere pittance compared to visual bandwidth.
  • Haptic data

Fingertips have a tactile resolution of about 1mm, If we overestimate that such resolution applies all over the body, that a body has 2 square meters of skin, and that the necessary bit depth is around 8 and the refresh rate is about 100Hz, we get

1 * 2000000 * 8 * 100 = 1600000000

quite an impressive 1.6 Gbs dedicated to touch and warmth.

  • Osmic data

Taste and smell are going to be extremely difficult to estimate, but we should try. There are five or six taste sensor types – we will say ten – with a range of 8 bits or less, and the number of individually sensible scent components is unknown. Estimates that I have seen range from 5000 to a trillion. Let us guess at 16 million scents, which will fit conveniently in 24 bits. How fast can we register a change in taste or smell? It takes longer than a tenth of a second, so we can say 10 Hz.

( 24 * 10 + 10 * 8 ) * 10 = 3200

Almost insignificant in quantity.

Putting it all together, a human might demand 422 billion bits per second.

At the time of writing, such speeds are approximately equivalent to the full bandwidth of a $20,000 top-of-rack ethernet switch… which is to say, engineering will be fun, but physics itself does not say nay.

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