Is there a clear statement of the big question? Is it a good big question? Identify the reasons why there is (or isn’t) confidence that the big question is tractable.
Can you imagine what the solution might look like for the big problem?
What kind of answers might be possible? Be clear on whether you are trying to find an exact answer or are you trying to bound the range in which the right answer lies?
Lay out alternative recipes (or ‘routes’) to the solution to the big problem. Can you identify a series of steps that might lead to a solution?
What are there crucial steps in this chain? Are there any steps that are ‘deal breakers’, that they seem hopelessly complex or that no critical test can be defined? If so, either pick a different big problem, or pick a different set of steps to the solution.
Is there a clear sense that the solution to the bigger problem will arise from combing the understanding gained about the smaller problems? If not, either pick a different big problem, or pick a different set of steps to the solution.
Identify a smaller piece of the problem.
Search for a smaller piece of the problem that feels ‘right’ – arising from a combined sense of the tractability of the smaller problem and its importance for the big problem.
How does the smaller piece challenge the prevailing understanding of the big problem, or is it going to be mainly comfirmatory of (i.e., a positivist take on) existing ideas.
Is it clear that this smaller piece is essential for the bigger problem? If not, search for a different small question.
To what degree is the smaller problem a critical evaluation of an existing idea? Are you prepared to (can you) state your critieria in advance for what will constitute a failure?
What is the most precise statement of the smaller question? What is the most precise statement of the background knowledge that will be assumed, and what is the level of confidence that can be attached to it? It is tremendously important to clearly lay out the foundations of the work that will be done. In doing this, the path to the solution of the smaller piece will be clearest.
What is the goal of this work? Are you trying to simulate nature? Are you trying to achieve a theoretical understanding? These goals are different and typically are contradictory.
Plan the solution.
Think about this smaller piece. Think hard about it. Drink beer and coffee with your mates until you get an idea about it. Can you frame this idea as a potentially falsifiable idea?
In tackling this smaller problem are you critically evaluating something, or are you building a case in favour of your idea? Either can be productive, but the process should be clear.
Choose the model will you use to tackle your problem. Clearly state the tradeoffs you are making between generality, precision, and reality.
Define clearly the meaning of your combined model and problem. Are you trying to represent reality? Are you learning lessons from a toy model? Are you making deliberate distortions of nature to enhance understanding? Are your goals and the model you are using commensurate with each other
Is the model the simplest one appropriate for the thing you want to understand?
If it is more complicated than necessary, how might those complications constrain/affect the understanding?
“One of the worst possible outcomes of a simulation is the right answer, for if you know you have left something out of your model, it means that what you have included is incorrect”
“People don’t understand the world, but they want to. So they build a model of it. Then they have two things they don’t understand”
T.H. Huxley "That great tragedy of science: the slaying of a beautiful hypothesis by an ugly fact"
Follow the plan.
Are there any surprises from the model? How do those surprises challenge existing understanding.
Articulate clearly the implications of what has been done. How has the initial idea been confirmed or
Did the work done answer a different question from the one you began with? Is that question useful?
Review the solution and plan for the next step
Might a different model produce a different answer? How does that affect the interpretation of the answer.
Do you trust your answer? Under what circumstances can you conceive of a difference answer? If you can define an opposite answer, is that remotely possible, or is it only a questions of degrees.
Give the best possible statement of the understanding achieved, given the clarity of the answer achieved for the smaller problem, its importance for the big question, and the level of confidence in the background knowledge.
Don’t exaggerate the relevance of the what has been done. There is value in having solved
The Complex Polya List – Synthesis from discussion and all our lists Statement of the big problem:
Is there a clear statement of the big question? Is it a good big question? Identify the reasons why there is (or isn’t) confidence that the big question is tractable.

You should think hard and critically to construct a clear statement of the problem, and the goals that you have in solving the problem (understanding; realism; reduce uncertainty, etc), and to make an a priori statement of what it would take for you to be satisfied with the results.
Why do I care about this question? What is my motivation? Am I being honest with myself and others?
What is the problem? Is there more than one question? If so, restate the problem by breaking it up into separatelyanswerable questions or subproblems.
Do I have hypotheses or just questions? If I have hypotheses, are they falsifiable (by the available data and models)?
What are your goals? What do you want to learn/predict, etc? What is the goal of this work? Are you trying to simulate nature? Are you trying to achieve a theoretical understanding? These goals are different and typically are contradictory.
Iterate on your initial problem statement until to you get to a question you think you can answer.
Are you looking for a result that narrows down the possibilities, or confirms or falsifies the big question?
Will the end result be more a statement of a hypothesis, or will it really build new knowledge?
Does there appear to be potential that I can understand this problem in terms of a combination of simpler concepts that I (or somebody) already have a good grasp on?
A good problem might be one that has one or more of the following outcomes:

the result makes a surprising prediction that is verified;

the result significantly narrows the possible solutions;

the result reconciles some apparent discrepancies in data/models/etc.

Assess complexity of system.
This might create a list of subquestions, or subsystems that need to be understood.

Understanding the complexity of the system: can a subsystem be defined by medium? By temporal scale? By spatial scale?

Can you imagine what the solution might look like for the big problem? What kind of answers might be possible? Be clear on whether you are trying to find an exact answer or are you trying to bound the range in which the right answer lies?

Make a plan

Have other people attempted to solve the same or a related problem? What was their approach and why did it fail? What prior knowledge is there that could shed light upon my question? How much will I be dependent upon that knowledge? What is the quality of that knowledge?

Is there an analogous solved problem that I can steal methods from?

Lay out alternative recipes (or ‘routes’) to the solution to the big problem. Can you identify a series of steps that might lead to a solution?

Can this problem be approached by isolating components of the system or by defining subproblems or a smaller piece of the big problem, then understanding these components/subproblems, and then piecing them back together? What are there crucial steps in this chain? Are there any steps that are ‘deal breakers’, that they seem hopelessly complex or that no critical test can be defined? If so, either pick a different big problem, or pick a different set of steps to the solution.

Is the core of this problem understanding one of the pieces or understanding the interactions between the pieces? Do I know?
4. Defining the smaller subproblems:
In determining the smaller problem/subproblems, ask yourself the following:

Does the smaller piece of the problem feel ‘right’? (Is it clear the smaller problem is tractable and it is importance for the big problem?)

Does the smaller piece challenge the prevailing understanding of the big problem, or is it going to be mainly comfirmatory of (i.e., a positivist take on) existing ideas.

Is it clear that this smaller piece is essential for the bigger problem? If not, search for a different small question.

To what degree is the smaller problem a critical evaluation of an existing idea? Are you prepared to (can you) state your critieria in advance for what will constitute a failure?

What is the most precise statement of the smaller question? What is the most precise statement of the background knowledge that will be assumed, and what is the level of confidence that can be attached to it? It is tremendously important to clearly lay out the foundations of the work that will be done. In doing this, the path to the solution of the smaller piece will be clearest.

Revisit your problem statement and goals. Is the problem solvable? Does your plan address the problem and will you achieve your goals if you follow your plan? Do you have the skills to solve the problem?

How much time will be required to solve the problem? … to solve each of the subproblems? How much time are you willing to put in (or can you afford) to solve the problem?

If you solve all the subsystem questions, how do you know that in gluing them together you will get something sensible (ie, relevant to the big problem you are trying to solve). Is there a clear sense that the solution to the bigger problem will arise from combing the understanding gained about the smaller problems? If not, either pick a different big problem, or pick a different set of steps to the solution.
5. Plan the solution for the subproblems:

Think about this smaller piece. Think hard about it. Drink beer and coffee with your mates until you get an idea about it. Can you frame this idea as a potentially falsifiable idea?

In tackling this smaller problem are you critically evaluating something, or are you building a case in favour of your idea? Either can be productive, but the process should be clear.

What tools (model, data, theory, etc) are needed to solve each of the subsystem questions? Clearly state the tradeoffs you are making between generality, precision, and reality.

Define clearly the meaning of your combined model and problem. Are you trying to represent reality? Are you learning lessons from a toy model? Are you making deliberate distortions of nature to enhance understanding? Are your goals and the model you are using commensurate with each other?

Is the model the simplest one appropriate for the thing you want to understand? If it is more complicated than necessary, how might those complications constrain/affect the understanding?

For each subsystem question, what are the assumptions? What are the uncertainties? Do you need key collaborators from outside your expertise to solve one or more subsystem problem? What do you require from each of these subsystems (what results are you aiming for?) to move on to the bigger problem?

What type of result is required from examining each subsystem, such that it makes sense to go the next step and glue the subsystems together?

Assess the results:

Are the results plausible? Are there any surprises from the model? How do those surprises challenge existing understanding? Are they consistent with what we know (about the climate system)?

Might a different model produce a different answer? How does that affect the interpretation of the answer?

Do you trust your answer? Under what circumstances can you conceive of a difference answer? If you can define an opposite answer, is that remotely possible, or is it only a questions of degrees.

Give the best possible statement of the understanding achieved, given the clarity of the answer achieved for the smaller problem, its importance for the big question, and the level of confidence in the background knowledge.

Articulate clearly the implications of what has been done. How has the initial idea been confirmed? What is new? Does your solution suggest new questions to be answered or dilemmas to be resolved?

Did the work done answer a different question from the one you began with? Is that question useful?

Go to the next subproblem ….

Putting the pieces together:
Need something here.

Selfcritique is critical at the end. Critical evaluation is essential.

An attitude of ‘skeptical enquiry’ must, eventually, be applied to all scientific research. There may well be intervals of time where an argument is constructed or ‘assembled’, during which it may be convenient or necessary to assume it is true and to explore the consequences But if the argument never gets critically tested, then fundamentally the work is not scientific. Building in mechanisms and tests for the argument to get challenged along the way ought to be seen as a very positive aspect of a piece of work.

Contributions that are not skeptical in attitude ought to clearly acknowledge the fact, or face severe criticism.
