The following is a text conversation between film-maker Benjamin Yackshaw and his friend Kevin Crawford concerning a single word of a single sentence in the blog post introducing Blue Dragon Studios' Incomparable Man commentary.
Ben: Math question. If movie X earned 400 million and movie Y lost 2 million, would it be accurate to say that movie X made incalculably more money?
Kevin: Hmm. The engineer in me says that 402 million is an entirely calculable number. But, incalculably more money does sound better than calculably more money... I give it an official stamp of approval. Science!
Ben: Would it be more accurate to say that X outperformed Y by an incalculable percentage?
Kevin: Again, hmm. I think this hinges on the definition of calculability. X made infinitely more money. There's a divide by zero there. But, infinity may be a calculable number. Without looking into this for a real answer, I can't say for sure. I'd guess the case for incalculaby is stronger. Another thought is that the percentage profit difference just ends up being a negative number, which is kind of weird to think about.
Ben: This all sounds very calculable to me. X didn't make infinitely more money, it made 402m more, a finite value. And it sounds like the negative number prevents X from earning an infinitely greater percentage as well. So both incalculable and infinite would be technically inaccurate, right?
Kevin: I think it all depends on how the data is presented. Say X made 400% profit and Y made -20%. Then, it's a direct comparison, so you could say X did 420% better than Y. On the other hand, you can compare earnings above cost of movie normalized for cost, and you get X having infinitely better performance than Y. It's all relative. Basically, the data can be manipulated. It probably doesn't help that I'm almost certainly butchering business terminology.
Ben: This is for ROBO dialog. I feel it is important to get it right because ROBO would not make a mistake of arithmetic or terminology. I will send you what I have for approval before I publish it.
At this point, Ben sent Kevin an email with the blog transcript. He received the following in response.
Kevin: I did some research to confirm, and division by zero is officially mathematically undefined. Thus, division by zero is incalculable, and that term is safe to use.
Had I not been discussing this with you, though, I don't know if I'd interpret ROBO's statement as desired. I'm probably over-thinking it. The more I read it, the better it sounds in my head, so that's probably good? I don't really have a suggestion to improve it anyway.
I don't think it's worth it to change the statement, either. People (normal people that don't do math all day) probably won't even consider the math, or just accept it as is.
Ben: Well, I knew that was the likeliest outcome as soon as I raised the issue. Still, I was curious enough to double-check. At worst, it sounds like the terminology/math can be disputed. Since ROBO can't definitively be proven wrong, I think his programming would permit him to say what he said (especially when you consider that his primary objective in this instance is simply to make fun of me/hurt my feelings).
Kevin: Sounds logical/fair/good to me.
The blog post was published shortly thereafter.