How would you model subjective opinions like “how fast time passes”?

Question

I was thinking about modelling mathematically (or finding the mathematical model) of the following experiemnt. Think about students $S_i$ saying how fast or slow they feel the lecture has passed - and I'd like to predict that.

Let's also suppose that I measure

• the data time $T_i$ the start time
• $D_i$ the duration of the lecture
• $O_i$ the temperature outside
• $I_i$ the temperature inside the lecture room
• $M$ the average passing rate for the course (i.e. how "difficult" it is)

My assumption is that

• the greated $D_i$, the more students will report that the time passes harder
• the higher the difference $|I_i - O_i|$, the more the effect of $D_i$ will be reduced
• the higher $M$ is, the more students will say that time has passed harder

How could I find out how good this model is and perhaps find out a better model to predict how hard (in fuzzy logic) a given student $S_i$ will say the time has passed (given the above parameters), if I collected all this information mentioned about and also reports from the student $S_i$ on how slow the time has passed?

Answer 1

You should make large scale experiments. Let $N$ be the number of random experiments that you do. Then the subjective assertions will approach to the objective ones when $N\rightarrow\infty$.

If some of the parameters that are introduced have no effects on the model, then your assumtions will fail; namely for example the greater the $D_i$ will have no effect on the feeling of the students that the time passed faster etc..

In such a case, those assertions should be removed from the model and the newer ones could be included. At any case, the results of such a model, after asssuming a good built of a model, will still be related to the common understanding of the humanbeings on time.