constant growth rates in response to exponentially increasing inputs is the null hypothesis
Yeah, that would be big if true. How sure are you that it’s exponential and not something else like quadratic? All your examples are of the form “inputs grow faster than returns”, nothing saying it’s exponential.
Toy model: Say we are increasing knowledge towards a fixed maximum and for each man hour of work we get a fixed fraction of the distance closer to that maximum. Then exponentially increasing inputs are required to maintain a constant growth rate.
If I was throwing darts blind at a wall with a line on it and measured the closest I got to the line then the above toy model applies. I realise this is a rather cynical interpretation of scientific progress!
If the progress in a field doesn’t depend on how much you know but how much you have left to find out then this pattern seems like a viable null hypothesis. Of course the data will add information but I’m not allowed to take the data into account when choosing my null.
EDIT:
More generally, a fixed maximum knowledge is not strictly required. We still require exponentially varying inputs if the potential maximum increases linearly as we gain more knowledge. Think Zeno’s Achilles and the tortoise.
Ok, I’m an idiot, this model doesn’t predict exponentially increasing required inputs in time—the model predicts exponentially increasing required inputs against man-hours worked.
The relationship between required inputs and time is hyperbolic.
When thinking like this it’s worthwhile of what’s meant with “field”. Is for example nutrition science currently a field? Was domestic science a field?
What would be required to have a field that deals with the effect of eating on the body?
Sticking with the throwing darts at a wall analogy, the linked post suggests that the problem is that no-one knows how close any of the darts are to the line. That problem would need to be solved before we could make progress.
Yeah, that would be big if true. How sure are you that it’s exponential and not something else like quadratic? All your examples are of the form “inputs grow faster than returns”, nothing saying it’s exponential.
Toy model: Say we are increasing knowledge towards a fixed maximum and for each man hour of work we get a fixed fraction of the distance closer to that maximum. Then exponentially increasing inputs are required to maintain a constant growth rate.
If I was throwing darts blind at a wall with a line on it and measured the closest I got to the line then the above toy model applies. I realise this is a rather cynical interpretation of scientific progress!
If the progress in a field doesn’t depend on how much you know but how much you have left to find out then this pattern seems like a viable null hypothesis. Of course the data will add information but I’m not allowed to take the data into account when choosing my null.
EDIT: More generally, a fixed maximum knowledge is not strictly required. We still require exponentially varying inputs if the potential maximum increases linearly as we gain more knowledge. Think Zeno’s Achilles and the tortoise.
Ok, I’m an idiot, this model doesn’t predict exponentially increasing required inputs in time—the model predicts exponentially increasing required inputs against man-hours worked.
The relationship between required inputs and time is hyperbolic.
When thinking like this it’s worthwhile of what’s meant with “field”. Is for example nutrition science currently a field? Was domestic science a field?
What would be required to have a field that deals with the effect of eating on the body?
Sticking with the throwing darts at a wall analogy, the linked post suggests that the problem is that no-one knows how close any of the darts are to the line. That problem would need to be solved before we could make progress.