Attempts to produce a light bulb are exactly an example of what I mean.
Inventors in Ancient Greece would not have produced an electric light bulb, at all, even if thousands of them worked for hundreds of years. Early 18th century inventors could possibly have produced one if they had reason to put in immense effort. So rather than starting at Edison, this is where we should start that story. This is about the time period where p > 0 for a “trial” for the first time.
By the early 19th century the conditions were becoming ripe for the possibility of electric lighting, and some expensive and short-lived forms of electric light bulb were already being invented (Davy’s incandescent bulb and later arc lights). The techniques and materials still weren’t reliable or cheap enough at that time, and the theory and practice of electricity was still lacking, but people were attempting the task of making a long-lived, cheap and moderately efficient bulb and making progress with increasing degrees of success.
By the later 19th century there were dozens of successful incandescent light bulb designs, with the first patent granted about 40 years before Edison. Later versions were developed that had some narrow commercial use, and Edison’s bulb was an economically better incremental improvement that was sufficiently cheaper and longer-lived to go into mass production nearly 100 years after the first research prototype for incandescent lighting was developed.
I stated that the independent Bernoulli trial model does not work, except over the very shortest timescales, far shorter than the span of all attempts to make a thing. Edison’s attempts were indeed far shorter than the span of all attempts to make the thing.
The original post is talking about the span of all attempts to make the thing, and the constant-p model is not at all reasonable for that.
Attempts to produce a light bulb are exactly an example of what I mean.
Inventors in Ancient Greece would not have produced an electric light bulb, at all, even if thousands of them worked for hundreds of years. Early 18th century inventors could possibly have produced one if they had reason to put in immense effort. So rather than starting at Edison, this is where we should start that story. This is about the time period where p > 0 for a “trial” for the first time.
By the early 19th century the conditions were becoming ripe for the possibility of electric lighting, and some expensive and short-lived forms of electric light bulb were already being invented (Davy’s incandescent bulb and later arc lights). The techniques and materials still weren’t reliable or cheap enough at that time, and the theory and practice of electricity was still lacking, but people were attempting the task of making a long-lived, cheap and moderately efficient bulb and making progress with increasing degrees of success.
By the later 19th century there were dozens of successful incandescent light bulb designs, with the first patent granted about 40 years before Edison. Later versions were developed that had some narrow commercial use, and Edison’s bulb was an economically better incremental improvement that was sufficiently cheaper and longer-lived to go into mass production nearly 100 years after the first research prototype for incandescent lighting was developed.
I stated that the independent Bernoulli trial model does not work, except over the very shortest timescales, far shorter than the span of all attempts to make a thing. Edison’s attempts were indeed far shorter than the span of all attempts to make the thing.
The original post is talking about the span of all attempts to make the thing, and the constant-p model is not at all reasonable for that.