The world changes; some people don't get that

I read something by a smart person that basically said: "90% of attempted X have failed, therefore X won't be viable."

The problem is that what that person really should have said was: "90% of the attempted X up to now have failed, therefore unless the underlying conditions have changed, X won't be viable."

Here's an example, adapted from a real situation in the past, with disguised (and simplified) numbers; smart person would have spoken up in year 20 and said: "people have been trying that for 20 years now, and trying in ever increasing numbers of attempts, and over 90% of the attempts have failed."

(click for bigger)

And while that's true, by the year 25, sixty-eight percent of all attempts made that year succeed! The secret is a change in underlying conditions (could be infrastructure, social acceptance, technology, economics, or other change).

The details of the model are the following:

1. Number of attempts in year $N$ is $A[N] = 2^{N-1}$.

2. Given a probability of success $p[N]$ in year $N$, the number of successes is the expected number (so we get rid of any stochasticity, for simplicity only):

$S[N] = p[N] \, A[N]$.

3. The probability of success in year $N$ is given by a deterministic difference equation,

$p[N+1] - p[N] = (a + b\, p[N]) (1 - p[N])$,

where the parameters $a$ (innovation rate) and $b$ (imitation rate) are between zero and one, with the specific values for the model above being $a=0.00001, b=0.6$, and $p[0] = 0$.

In other words, very slow innovation, but a large imitation rate (which leads to slow adoption at first then a cascading effect at some point, before saturation sets in). 

[The general form of this process is called a Bass model of evolution (used to analyze product diffusion in the past); I don't like it for data analysis or decision support (for a variety of technical reasons), but it's a convenient model for simulation when we take the parameters as given.]

Here's a real-world example of things changing, possibly one of the reasons of the current interest (institutional as well as individual) in cryptocurrencies:

But some people have this blindness: that just because something has been tried before and hasn't worked then, it must never work. And that something could be SpaceX landing its boosters, or the feasibility of Bitcoin, electric vehicles, small nuclear reactors, etc.

Fear is the mind killer. And not just for scions of House Atreides.

Fun with numbers for October 4, 2019

It's flu season, let's talk product diffusion

One of the classic marketing models people learn in innovation classes is basically a SIR(1) model without the R part: the Bass model of product diffusion.

The idea is that some fraction $a$ of the consumers are "innovators" who adopt a product without social pressure, while another fraction $b$ are "imitators" who adopt a product when they see others with it. The fraction $x$ of the market that has adopted the product at a given time is given by the following differential equation

$\dot x = (a  + b x)(1-x)$, 

and the behavior looks like a traditional product life-cycle curve (an S-shaped curve):

The process for a viral infection is similar: some people get the virus from the environment (those would be the $a$ fraction), some get it from contact with other people (those would be the $b$); the infection process has a third element, recovery, which we ignored here.

Growth confusion and punditry, part 1

Pundits throwing around growth numbers seem to be unaware that there are significant differences even with very small growth numbers.

Growth confusion and punditry, part 2

A pundit: "it's important to get the economics high-growth first, so that the slower growth starts from a higher number." (Paraphrased.)

Me: Gah! Multiplication is transitive. The order doesn't matter, what matters is that the high-growth period be the longer period.

Consider two periods, with $t_1$ and $t_2$, with associated growth rates $r_1$ and $r_2$. Starting from some value $x_0$, the result of period 1 before period 2 is:

$\left( x_0 \, e^{r_1 t_1} \right) \, e^{r_2 t_2}$,

and the result of period 2 before period 1 is

$\left( x_0 \, e^{r_2 t_2} \right) \, e^{r_1 t_1}$,

in other words, the same result.

These pundits get paid to go on television and say these things and to write them in Op-Eds. And influential people take them seriously. The innumeracy is staggering.

Having some fun with Tesla data

Downloaded some historical data from Yahoo Finance (yes, I have other better sources, but this one is public and can be shared) and played around with smoothing. Here's a nice view of the TSLA closing price for the last year using the same triangular smoothing I did for my bodyweight (in other words, a second-order moving average of (5,5)):

Throughout the first half of 2019 Tesla boosters on Twitter were fully convinced that this would be the year that heralded the end of the internal combustion engine car. In reality, this seems to be the year in which Tesla's financial shenanigans are likely to bring its valuation to a more appropriate level.

CYA statement: I have no personal position on Tesla and will not initiate one in the next 72 hours. This is not intended as financial advice and represents my personal views (of making fun of Tesla boosters) not those of my employer or our clients.

Also:

(Yes, it's sarcastic.Very, very sarcastic.)

Yet another infrastructure photo