Actually it was literally an asymptote in the first version of their models they posted to github. They had a term that they were dividing by that ends up going to zero, so the entire equation breaks! https://www.lesswrong.com/posts/PAYfmG2aRbdb74mEp/a-deep-critique-of-ai-2027-s-bad-timeline-models

So, now we can answer the question from before: what time horizon does the red curve above predict for 2030?

Well, if you plug it into wolfram alpha, you get a time horizon of “-2542 - 11372i”

Yes, that is negative, and that is an imaginary number in there.

What’s actually happening is that when the term in the brackets above hit zero, we end up dividing by zero, and hit infinity. Beyond that, we get a negative number to the power of a non-integer, which gives nonsensical complex numbered answers.

The infinity point for this equation happens at a time of t = To/alpha, and will always occur at some point, no matter what initial parameters you use.

In fact, this infinity point is completely independent of both the time horizon and the SC threshold. If you keep the same alpha and doubling time, you could start with a time horizon of a nanosecond, and have a superhuman coding threshold of 1 trillion years, and the curve will still claim that superhuman coding will arrive before the end of 2029.

And indeed, reddit user mambo-12345 tried modifying the simulation parameters to drop the initial time horizon to 15 nanoseconds instead of 15 minutes, and the resulting curve still had a peak for the estimated superhuman coder arrival at 2026.5 years and a median at 2035. Credit to them for inspiring me to take a closer look here: