data scientist goes coolhunting…

Intuitive coolhunting scales poorly. Here’s some math to help fix that problem:

Axioms of cool

Five axioms enable us to mathematically model cool:

  1. No one is intrinsically cool, individuals simply channel it.
  2. Ability to temporarily hold coolness varies by individual.
  3. Coolness naturally flows into some individuals more readily than others.
  4. Rate of coolness flow into an individual increases with the amount of cool stored within that individual’s social network.
  5. The rate at which cool leaves an individual increases as observation of cool’s presence in that individual increases.

Examining these axioms in more detail:

1. No one is intrinsically cool, individuals simply channel it

‘Cool’ flows into and out of individuals, as shown by the following stock and flow diagram:

Individuals can temporarily store some of this cool, in a manner resembling a capacitor storing electrical charge. We can for example imagine an individual’s step response to incoming cool:

We can describe this capacitive behavior in the stock and flow diagram with first-order dynamics:

2. Ability to temporarily hold coolness varies by individual

Individual capacity for storing cool differs. Given the same step input above, we might observe different responses for individuals A and B:

3. Coolness naturally flows into some individuals more readily than others

Some individuals channel cool better than others. We model this by varying the “natural” coolness input flow rate by individual:

4. Rate of coolness flow into an individual increases with the amount of cool stored within that individual’s social network

Individuals with cool friends tend to more successfully channel cool themselves. We model this by increasing influx rate according to a “coolness in social network” factor:

5. The rate at which cool leaves an individual increases as observation of cool’s presence in the individual increases

Once observed, cool tends to exit the individual it was observed in. We model this by increasing the coolness decay rate as a function of public observance of an individual’s coolness:

Source and sink of cool

Assume the universe provides an infinite source of cool. Similarly, assume existence of an infinite capacity sink for coolness that exits individuals. Also assume that everyone alive connects to this source and sink. It follows that individuals cannot “use up” the supply of cool or withhold coolness from others. Under the axioms, cool never transfers from one person to another—the relationships between individuals simply modulate the rate cool enters each person from the source and leaves each person to the sink.

Networks of cool

The last two axioms relate individual ability to receive and store coolness to the instantaneous state of their social network. To demonstrate the axioms in this social context, suppose the following friendship network exists among seven individuals:

Now suppose that Julie holds a lot of cool at a particular moment. It follows from axiom #4 that Guido’s instantaneous ability to channel cool will increase due to his connection with Julie. Similarly, if Di stores very little cool at a given time, Hardeep’s ability to receive cool will not benefit from his relationship with Di.

Hardeep’s coolness influx rate benefits from the combined cool stored within Emilio, Kaitlin, Di, and Abe. However, because of axiom #5, the fact that Emilio, Kaitlin, Di, and Abe observe Hardeep’s cool accelerates its exit from Hardeep. Due to the first-order dynamics described above, this exit of cool lags the influx of cool, giving Hardeep time to enjoy a temporary build up of coolness and time for Emilio, Kaitlin, Di, and Abe to benefit from its presence in Hardeep.

Simulating coolness networks

Using the mathematical framework developed above, we now simulate cool’s flow within the network described in the last section. Since we currently have no way to actually measure cool—and therefore parameterize the model—we run it with fictional initial conditions and examine the resulting system-level effects to see what happens.

The combined model for this friendship network is shown in the image below (sorry about the mess of arrows):

Simulating this model with arbitrarily selected initial conditions and factors yields:

A long way to go before this work is useful

As stated above, we currently have no way to measure cool, and therefore no way to validate and parameterize this model. Expect a Bayesian strategy to emerge shortly though. Until then, this work remains conjectural and exploratory.

Computation notes

Used Vensim PLE to draw and simulate the stock and flow systems, R to display the simulation output, and NetworkX to draw the example social network.

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