🔇 👨🏾‍🤝‍👨🏻 👨🏾‍🎤 Investigation of the logistic function as a law of industry development ◻️ 👼🏻 🙅🏽

Hello dear community. In this article I want to share part of my observations on the development of technology and industries.

Studying the development of a particular industry, I often notice a development picture similar to the stage of acceptance of the inevitable.

1. Denial

The first prototype appears, the main function of which is to show the operability of the new technology.

The new technology is denied by the scientific community with reference to its inefficiency, high cost of manufacture, complexity of management, etc.

2. Anger

After the hungry innovators did not give up, but continued their search, the first industrial design appeared that could be sold if it were not catastrophically expensive.
The scientific community is angry and begins to take preventive measures: reduce the cost of their technologies, reduce the cost of resources for old technology, increase the cost of resources for new technology, etc.

3. Trading

The new technology begins to take over the market in large chunks and the time is not far off when half of the consumers will use the new technology.
The scientific community is angry, sighs and begins to bargain with new technology.

4. Depression

And now the overwhelming majority uses the new technology, while the old one is still alive and took refuge in ever-decreasing market segments.

Among the "old people" a panic is going on. They understand that the collapse of their technology is already on the horizon.

5. Acceptance.
All the "old people" were either fired, or managed to hold out until retirement, or went over to the side of the enemy.
Full acceptance of defeat by old technology.

The result of such observations in my head appeared a picture resembling the following function.

This is a sigmoid. You can read about it here .

From the whole sigmoid family, the most suitable for my further searches is the logistic equation .

The equation has the form:

where
where the parameter r characterizes the rate of growth (reproduction), and K is the supporting capacity of the medium (that is, the maximum possible population size).

This equation is a model for describing population growth in conditions of limited resources, i.e. if no one died in the population and everything was enough for everyone, then it would grow exponentially, but the presence of external factors (death, predators, limited resources) leads to the fact that population growth deviates from the exponent and comes to a logistic function.

Do not you think that this model is perfect for describing the history of development of a single technology?

So, let's get started ...

For the object of study, I chose the history of cars with an internal combustion engine (ICE). I gained my knowledge about this industry at the university, and you can also get acquainted with the history of this technology here , here or here .

For the cut-off at a temporary school, I accepted the following dates:

1. The era of innovation (denial and the beginning of anger).Early gas experiments were carried out by Swiss engineer Francois Isaac de Rivas in 1806, who built an internal combustion engine running on a hydrogen-oxygen mixture, and the Englishman Semuel Braun, experimenting with his own hydrogen-fueled engine. The Belgian hippo Etienne Lenore with a single cylinder internal combustion engine using hydrogen fuel made a test run from Paris to Joinville-Le-Pont in 1860, covering about nine kilometers in about three hours.

2. The appearance of the first industrial design (anger and bargaining). One of the first gasoline powered four-wheeled vehicles in Britain was built in Birmingham in 1895 by Frederick William Lanchester.

3. Market capture (onset of depression).By 1927, the Ford Model T was the most common car of the era.

4. Death of the steam engine (adoption). The industry has been producing steam trucks for the longest time — until the 1960s. Farmers were very actively used by farmers in the USA and Great Britain: there are 6 types of agricultural steam equipment that worked on farms until the 1950s.

Let us analyze this function with respect to the coefficient K , which implies a growth rate and affects the population growth limit. This coefficient describes the growth potential of a new technology in principle, i.e. at low K values, the technology will not be able to capture the entire market, but will only be able to win back the market segment in which it will be more interesting than the previous technology.
As can be seen from the formula, the function value can never exceed the limit in K .

Below are the graphs with r = 1 and K = [0.2, 0.4, 0.6, 0.8, 1.0].

As we can see, at low K values, the technology may disappear altogether without entering the market.

It is noteworthy that at the point of transition from obviously dead technology to tenacious very unusual things happen, but this is a completely different story.

Since today we do not see steam cars on the streets, it is safe to say that K is close to 1 .

Now let's look at the equation for the coefficient r. It affects the growth rate of market share, as it stands in the exponent. The higher this ratio, the faster the new technology will absorb the market, i.e. Each year, technology should become more interesting to more people for its convenience. If the growth of interest in technology is low, then the new technology will fight for a long time with the existing one for the market, as it will be able to offer few "goodies" for the consumer every year, otherwise the technology will immediately capture the market due to its undeniable convenience.

Below are the graphs with the value of K = 1 and r = [0.2, 0.4, 0.6, 0.8, 1.0]

So, to start the analysis of the industry, we will accept the following assumptions:

since the function is centrally symmetric with respect to the point (0, P0), the reference point is 1900 as zero;
in 1800, for 1000 cars, only one worked on an internal combustion engine (P (-100) = 0.001);
in 1900, the market was divided equally between steam engines and internal combustion engines (P0 = 0.5);
in 1950, the entire market was occupied by ICE machines, excluding small sectors (P50 = 0.99);
in 2000 there were no steam engines left on the market (P100 = 1.0);
coefficient K = 1.0

In such a simplified version of the study, we need to find the coefficient r relative to our assumptions.

After some simple calculations, we find the coefficient r equal to about 0.0935 .

What we understood in such a rough analysis:

(K 1) . , .
, . , (r 0.0935).
, «». , .
Based on my knowledge of electric motors, I believe that the segment of heavy specialized machines (agricultural machinery, construction equipment, etc.) will become the last frontier of the ICE struggle.

Continuation: “When will everyone ride electric cars?” .

Finally

Thank you for your attention, if you liked this approach, then I can highlight the following questions in the framework of this study:

Progress as a predator-prey model;
Hype curve as an analogue of water hammer;
When will everyone ride electric cars ?;
When will Moore's law stop working? When to wait for a quantum computer;
Where to look for innovation. How the industry is born and how it dies;
Analysis of the prospects of technology development based on statistical data.