on modeling

"all models are wrong, but some are useful"

models are everywhere. math equations for physics. conceptual models for physics and chem (relativity, atoms, quantum mech). explanations of things. biology and neuroscience models of humans and animals. ecology models of evolution and ecosystems. even branding is a model.

anesthetics

building a model (double meaning haha) to represent the relationship between eeg and unconsciousness. this is almost certainly incorrect — we try to be general but it is not at all perfect, especially in bio this is common. although it is useful:

• with interp, can see structures of eeg not previously seen before
• maybe these proxy predictions can be useful in operations or controlled unconsciousness experiments

math modeling: environmental impact of data centers

the model is representing the relationship between data centers and environmental impact. almost certainly wrong — with real life things, the way to be correct is to just build the thing and then measure; equivalent to modeling the world down to an accuracy where accuracy doesn't matter anymore (in this case to the atomic scale) and getting results that way. but useful:

• maybe if it is somewhat correct, can understand things about the relationship
  • "is it just one or two factors causing all the damage?"
  • "do some factors not matter?"
• also maybe if it is somewhat correct, can predict and be somewhat accurate

the linear regression model explains this nicely

real data is hella weird. if it looks like our model will fit it decently, apply the model. this is important because we want the model to be the same shape so that it will be useful. the model doesn't capture all variance, and that is ok.

here is where the "same shape" comes in:

• given that it is roughly the same shape, predictions will be trusted much more (because it captures the pattern that exists in the data)
• but it captures it very simply, thus cannot be trusted that much

now that it's kinda trusted:

• can use it to understand pattern better
  • instead of saying "yeah they look about correlated" can say more rigorous things to gain clearer understanding
  • or, maybe you didn't even know there was a correlation and now you know (yay!)
• can make somewhat predictions

if it were not the same shape, maybe it could predict better (e.g. n-th degree polynomial for n data points, yay!!! r^2 = 1) but the fundamental pattern is not captured.

caveats:

• in real modeling problems, it is much harder to just "see" whether the model is the right fit or not, you just have to do it and then make an argument about how it is the right fit / can be somewhat trusted
  • you need to just build models and validate them with certain things
  • or build them alongside validation so as to not have to restart every time it's bad

math modeling: firefighters

the model is representing the relationship between input factors (type of strategy, # of firefighters, fire?, type of building, time of day, etc) and outputs (time taken, people died, certainty in headcount). kinda like a black box.

will this be used for predictions? hell no — like our thing will be very inaccurate in a high stakes environment. however, it will be used to gain insight about the problem. basically, it will act as the pitch for certain strategies with certain numbers of firefighters (things from your inputs that you can control). like you will be presenting the strategy and number to your boss and to really convince them you will say you modeled the situation in code and these performed the best. ofc it's not 100% accurate, but with other validation, it's somewhat trusted, and makes a case for those strategies in this simplified world. ofc the more accurate and validated the better, because then a better case is made and more is understood.

the limit: physics equations

continuing from the previous point — sometimes you go and go and go and the limit is basically physics equations such as maxwell's equations. the model is basically the ground truth now, because it has been validated so much. this is the limit of "understand more about the relationship" as well — it has literally completed your understanding of the relationship, and become the relationship itself.

maxwell literally just took magnet coil and magnets and batteries and played with them, refined the models more and more and came up with them.