Great, this helps me understand my confusion regarding what counts as early stage science. I come from a math background, and I feel that the cluster of attributes above represent a lot of how I see some of the progress there. There are clear examples where the language, intuitions and background facts are understood to be very far from grasping an observed phenomenon.
Instruments and measurement tools in Math can be anything from intuitions of experts to familiar simplifications to technical tools that helps (graduate students) to tackle subcases (which would themselves be considered as “observations”).
Different researchers may be in complete disagreement on what are the relevant tools (in the above sense) and directions to solve the problem. There is a constant feeling of progress even though it may be completely unrelated to the goal. Some tools require deep expertise in a specific subbranch of mathematics that makes it harder to collaborate and reach consensus.
So I’m curious if intellectual progress which is dependent on physical tools is really that much different. I’d naively expect your results to translate to math as well.
So I’m curious if intellectual progress which is dependent on physical tools is really that much different. I’d naively expect your results to translate to math as well.
This is an interesting point, and it’s useful to know that your experience indicates there might be a similar phenomenon in math.
My initial reaction is that I wouldn’t expect models of early stage science to straightforwardly apply to mathematics because observations are central to scientific inquiry and don’t appear to have a straightforward analogue in the mathematical case (observations are obviously involved in math, but the role and type seems possibly different).
I’ll keep the question of whether the models apply to mathematics in mind as we start specifying the early stage science hypotheses in more detail.
Great, this helps me understand my confusion regarding what counts as early stage science. I come from a math background, and I feel that the cluster of attributes above represent a lot of how I see some of the progress there. There are clear examples where the language, intuitions and background facts are understood to be very far from grasping an observed phenomenon.
Instruments and measurement tools in Math can be anything from intuitions of experts to familiar simplifications to technical tools that helps (graduate students) to tackle subcases (which would themselves be considered as “observations”).
Different researchers may be in complete disagreement on what are the relevant tools (in the above sense) and directions to solve the problem. There is a constant feeling of progress even though it may be completely unrelated to the goal. Some tools require deep expertise in a specific subbranch of mathematics that makes it harder to collaborate and reach consensus.
So I’m curious if intellectual progress which is dependent on physical tools is really that much different. I’d naively expect your results to translate to math as well.
This is an interesting point, and it’s useful to know that your experience indicates there might be a similar phenomenon in math.
My initial reaction is that I wouldn’t expect models of early stage science to straightforwardly apply to mathematics because observations are central to scientific inquiry and don’t appear to have a straightforward analogue in the mathematical case (observations are obviously involved in math, but the role and type seems possibly different).
I’ll keep the question of whether the models apply to mathematics in mind as we start specifying the early stage science hypotheses in more detail.