“2+2 Doesn't Always Equal 4”, Sabine Hossenfelder(youtube.com)

“2+2 Doesn't Always Equal 4”, Sabine Hossenfelder

https://www.youtube.com/watch?v=0WPY5cfOOIM&ab_channel=SabineHossenfelder

1 comments

When most normal people talk about 2+2=4, they are referring to addition of natural numbers under the axioms of Peano arithmetic, where 2+2 indeed equals 4.

Sabine Hossenfelder's point is that if we abandon the Peano axioms then we can arrive at different results. For example, under the rules of modular arithmetic, 2+2 may not equal 4. Which is perfectly obvious. Of course if you define "+" to mean something different, then you get a different result. Why is that worth mentioning?

The purpose of language is for clear communication. In ordinary contexts, when someone uses the addition operator, everyone would understand that they're referring to integer addition under the Peano axioms and not modular addition or polynomial addition or something else. Engineering manuals do not need to preface all calculations with "Under the Peano axioms...".

When NASA engineers design a rocket, do they need to worry "what if 2+2 doesn't equal 4?"? Do we need to redesign all of our computer systems and rethink all of our scientific theories? If I'm writing a function which requires 2+2=4 to be always true, do I now need to write code to deal with the case where 2+2 does not equal 4? Of course not, but this is the most natural interpretation of the phrasing "2+2 doesn't always equal 4" which is the title of the video.

Of course it is just clickbait, but it seems to me that this kind of content only serves to confuse people and does not really help anyone. I don't want to use the word "sophistry" here but I can't think of a more appropriate word to describe this video.