I challenged my collaborator to try a different genAI: they got the exact same formula and a completely different wrong answer. Turns out the genAI cannot handle the large integer math, but rather than admit it cannot, it just reports some answer that is orders of magnitude incorrect.
Another example of AI failure.
I will not use generative AI. Full stop.
However, I have collaborators who will for minor purposes.
I was notes with one about a project and I outlined that one element was essentially a simple combinatorics problem (n choose r) and listed the very large number of possible outcomes in a table.
When we discussed it, we confirmed the formula was right, but whose numbers were correct, mine or theirs? (Mine obviously). I had calculated the values in Python, but then showed that I got the same values out if I plugged them into a website combinatorics calculator.
Unfortunately, I mangled my explanation slightly. My collaborator dumped the problem into genAI and got a formula and numbers out that did not match those in the table. They tested the formula for small values they could prove by hand (literally writing out every possible combination and counting them), so they knew the formula was correct.
@loke In normal terms, v can never exceed c, so v2/c2 would always be a value between 0 and 1 (if v=c and that ratio is 1, delta T would dilate to infinity). if we apply the same logic to imaginary terms, one would presumably assume that v could never exceed ic. If v = ic, the denominator would become sqrt(2) and delta T would shrink to ~70% of delta T prime. I think we must assume that imagination cannot reduce apparent time more than that.
Large values of v indicate material presented very quickly or which is very boring. Careful empirical analysis has indicated that for large lectures, v is approximately 0.9c (where c is the speed of light). For departmental seminars is is ~0.75c and for conference presentations ~0.8c.
The length of a lecture according to your mind is dependent on the confusion-boringness factor, v. This represents the relative speed at which your brain can absorb the material versus the speed at which is presented, corrected by the level of boredom generated by the lecture style and material.
Why lectures seem to last forever?
An explanation based on the time dilation principle of Einstein's special theory or relativity (1905).
Note 1: Also applies to many other types of presentations.
Note 2: I originally came up with this idea 35 years ago, after one week as a freshman college student.
Because your knowledge is remaining relatively stationary while the lecture is shooting ahead astronomically, you view the lecture from a different frame of references than it actually occupies. Since the actual time (dT') is measured by the lecturer, the apparent length of time according to your mental reference frame (dT) dilates and becomes longer than the actual time. According to the relativity formula, dT = dT' / sqrt(1 - v^2/c^2).
Based on this we can determine that the large 1 hour and 20 minute lecture with v = 0.9c, appears to last 3 hours and 4 minutes, the 50 minute seminar with v = 0.75c appears to last 1 hour and 16 minutes, and the 15 minute conference presentation with v = 0.8c appears to last 25 minutes.
Note that v could be an imaginary number in the imaginary case one actually find the material interesting, in which case time would shrink and the lecture would appear to end faster than it actually does.
