One byproduct of playing around with #Python's matplotlib.pyplot library is that I can now rather easily create qualitative graphs to illustrate more informal relationships that I could previously only describe in words, or with a crudely drawn handwritten sketch. A workflow that I have found effective is to ask #ChatGPT for working code for a simplified example of what I want, and then I adapt and tweak the code until I get an output that matches what I had in mind. For instance, here is a graph I created this way (in a matter of minutes, after asking GPT at https://chatgpt.com/share/064ae58d-7400-4589-a027-d66a8a8a236e) to illustrate a point I made previously by text in https://mathstodon.xyz/@tao/110250470289337319 : I have found AI assistance to be of limited use in my primary specialty of research mathematics, but it has greatly increased my capability in secondary tasks such as coding (or in producing graphs like this), while also bringing my capabilities on general tasks up to at least a beginner level of expertise. (For someone who is expert in programming, but has only a secondary specialization in mathematics, I would imagine the benefits of AI assistance would be somewhat reversed.)
@tao Mentioning this because I didn’t see it in the ChatGPT conversation above. ChatGPT also has a built-in python interpreter. So, you can ask it to run the code that it outputs and it’ll give you the final plot as an image after running it through its interpreter :)
I would strongly prefer a hand-drawn scribble for communicating an informal idea like this. Then form matches content and can easily be interpreted as such. And it avoids all other drawbacks of using and normalizing these tools.
(Of course, in your specific example, the form also illustrates a point, but that will be the exception.)
What does the valley between primary and secondary field even mean? (The relative shift is bigger there!)
@SylviaFysica For images that I intend to convey a rather complex relationship, I have found it inconvenient to work with hand-drawn images, partly because of my terrible handwriting, but also because of the inability to easily edit a sketch that only partially conveys what I had in mind. With the Python graph, I could easily cycle through a dozen attempts before finding one that captured the nuances I intended. For instance, I deliberately did intend to have the valley between primary and secondary fields - which to me represents fields that are adjacent to both - receive a higher boost from AI assistance than a completely general field. For instance, I consider pure mathematics to be my primary field and computer programming to be a secondary skill; setting up and installing a machine learning software package would qualify for me as something which I am not directly experienced in, but is adjacent to both specialities, so I would place it in an intermediate location in this graph.
With respect to illusory exactness, I was hoping that the absence of numerical labels on the axes would already convey the informal nature of the image, but perhaps one could also create other signals to emphasize the informality of the graph, for instance by making the lines thicker and blurrier to more resemble a hand-drawn graph, and also choosing a less "professional" font. This is easy enough to do in Python (but would require redrawing the image completely if done by hand), see attached.
@SylviaFysica I just realized that I did, indeed, make a hand drawn sketch of the figure first before turning to chatgpt/python to generate further images. You can judge for yourself which type of image would work better.
@SylviaFysica Another adjustment to the graph, this time adding some cases in which it would not be advisable to use AI assistance: attempting to use AI on an intermediate difficulty task with little prior knowledge, or an expert difficulty task with only intermediate prior knowledge. (In this particular case, this update would be feasible on a hand-drawn image as well as it only requires adding new drawings rather than removing or modifying existing ones, but for many other types of revisions, using a hand drawn image as the master source would be inconvenient.)