12.45 Restate My Assumptions: Complexity and Control

[My talk at the Café Curie event within PROBE: Research Uncovered at Trinity College Dublin, September 29th, 2017]

“12:45, Restate my assumptions:

1. Mathematics is the language of nature.

2. Everything around us can be represented and understood through numbers.

3. If you graph the numbers of any system, patterns emerge.

Therefore: There are patterns everywhere in nature.

Evidence: The cycling of disease epidemics; the wax and wane of caribou populations; sun spot cycles; the rise and fall of the Nile.

So, what about the stock market? The universe of numbers that represents the global economy. Millions of human hands at work, billions of minds. A vast network, screaming with life. An organism. A natural organism.

My hypothesis: Within the stock market, there is a pattern as well. Right in front of me. Hiding behind the numbers. Always has been.

12:50 press return.

I look for simple patterns in complex systems. Or in official terms, I’m working on Complexity and Control of Massive MIMO.


Think flocks of birds, the people out in the Front Square or your phones communicating in the telecommunication networks of the future. Even though we often disagree on the definition of complex systems, we agree that these are some of the prominent examples of complexity. They are often composed out of a vast multitude of components, usually set up randomly, and yet they exhibit unique, surprising, complex behaviour.

But I’m not in for complexity: it’s the simplicity I am after.

The Irish Times puzzles page seemed like a good place to draw the examples of Ulam spirals. TCD Probe advertisement was conveniently placed in the middle.

Here, take Ulam spiral as an example: the simple rule for generating prime numbers says we just circle numbers that have no other divisors but themselves and unity. And once we put them in a spiral, we get intricate diagonal patterns, not trivially following from the simple rule of the system generation. And instead of telling you where to draw diagonals, I just tell you the simple definition of prime numbers. Kind of like a recipe for pastry: it’s more than the sum of its components, and it’s easier to both reproduce and document in a book if I give you a recipe. Me describing the heavenly taste of it won’t help much in making it.

That is how complex systems scientists sometimes trade complexity for simplicity, two words coming from the same Indo-European root, *plek meaning to plait, to braid. Simple strands of hair, a complex haircut of the universe!

Now, my quest for complexity in the communication networks of today and tomorrow isn’t just aimed at documenting the haircut fashion styles or recipes of the radio waves enabling our society as we know it today. I have much more sinister intentions.


I intend to control that radio mess. I want to know the simple rules it follows when thousands of antennas roam the space and another thousand serve them content, from cat videos to reports from their self-driving cars. Once I know that I’ll know where to make just a little push to make things move in the preferred direction, offering you more 4K cat videos in augmented reality. We can try controlling it without knowing the underlying rules, sure: but that’s fixing your TV set by banging it on the side. It may work sometimes, but the odds aren’t on your side.

Controlling a complex system when its nature is known to us is a beautiful process of its own. We get to see amazing transitions and new patterns emerge, we tame it just to unleash its full potential and let it shine. It might be because complexity lies at the fine edge between order and chaos, so it delivers the best of both worlds.

So what’s so sinister about giving you more cat videos and making beautiful patterns? Nothing much, but there’s a common negative perception of the term control as something restrictive, mundane and dangerous. Hence the “sinister” character of control plans.

Massive MIMO

By the way, the technology I’m investigating is called Massive MIMO. Not really a household name today, I know… But it doesn’t really matter. Its effect is what counts.

If mathematics is the language of nature (Assumption 1), understanding scales and orders of magnitude is fluency in this language. Let’s give it a go then.

You all remember the day when the number of devices with an antenna you owned wasn’t bigger than the number of heads you have. Right now, the number of those antenna monsters is approaching the number of fingers you have, but you’ll have to be ready for the day when it surpasses the number of bones in your body. When the day comes, tenfold or hundredfold more antennas around you will take care of your devices’ connection to the world.

Once the number of antennas reaches the number of bones in your body, that’s approximately 200 antennas and a tenfold more to support it, leading to 2,200 or if we round it up, 2,500 antennas. With eight billion of us that will mean that we’ll have 20 trillion antennas, 10% of those being user equipment and 90% being the telecom infrastructure.

The number of bee colonies in the world is approximately one billion, 10% being domesticated beehives and 90% being feral colonies. In each of them there are ten to fifty thousand bees –let’s pick 20 thousand as our value. That gives us 20 trillion antennas.

It wasn’t a back of an envelope I did the calculations on, it was The Irish Times racing page (now there’s a complex system!)

The wireless of the future will be the equivalent of one of the most impressive complex systems of nature, the bee population. 10% of the antennas will be your domesticated beehives, and 90% is the feral telecom infrastructure keeping you connected.

That will be Massive MIMO looking after your wireless lifeline.

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