Quantum trading! And tunnels through the Earth!

Remember when we used to place data centers in whatever cheap abandoned warehouse was nearby? Well, that’s a quaint notion in an era where trading advantage and arbitrage depend more and more every day on the speed of light and link distance.

Sara Winge passed around this cool article about the optimal placement of financial trading nodes. The idea is that with information moving at the speed of light, effective trading locations need to be carefully positioned on the Earth’s surface to best optimize the average trading link distance relative to the light speed / distance cone, or something like that.

Of course that placement ignores all kinds of things, like the relative value of the achievable arbitrage compared to the cost of floating New York Stock Exchanges in the middle of the Indian Ocean (which, by the way, I’m all for if it gets some of the bankers out of Manhattan and brings rents down). When you are dealing with very small slices of very big numbers the optimal solutions can change dramatically when real costs are added to the model.

Today worldwide economic activity is measured in what, hundreds of trillions of dollars? Maybe after another couple of orders of magnitude of growth (assuming there is any planet left to grow it on) it might actually make sense to stick trading nodes and links around the world according to this model.

Why stop there? Growth marches inexorably on and my back-of-the-I-can’t-seem-to-find-an-envelop calculations show that when total planetary economic activity reaches 22 petadollars it will be cost effective to drill through the Earth’s crust and directly route the optic cabling between nodes on chord-lines that are tangent to, and almost touching, the earth’s mantle at the link midpoint. To reach this conclusion I’m assuming average drilling costs of ~$1m/inch and arbitrage opportunity on the order of 1×10^-12 % of total economic output varying at a rate of $0.52/nanosecond of link time.

I take it as providential that the light-cone optimal link distance also happens to be the exact arc-to-chord Sagitta length that will permit perfectly straight chord-line drill bores without mantle immersion at the mid-point. Because of course drilling through the mantel would melt stuff. It’s as if God selected the Earth’s circumference and crust thickness to simultaneously and exactly optimize both financial arbitrage and our pleasing-to-the-eye (and gravitationally optimized) physicality. We have an aesthetically ideal height to weight ratio.

The bore-web will be a non-trivial engineering effort, but by taking a short cut through the Earth’s crust we will decrease the average trade signaling distance by the ratio
2sin(θ/2) / θ. Where θ is the angle at the Earth’s center inscribed by the radii terminating in the trading nodes. The result will be materially shortened signaling distances and naturally, once the first floating trading node starts drilling, the rest will have to follow suit to remain competitive.

It’s actually a bummer that the speed of light isn’t slower because then the surface arcs would be longer and the economic break even point for drilling would be correspondingly lower as the chord paths became more direct relative to surface laid cable. A speed of light in the 1.2×10^8 m/s might pull the break even point into the teradollar range, but of course then we would still be waiting to see what happened on Alpha Centauri.