EVERYTHING YOU NEED TO KNOW ABOUT "2+2=5". As a former mathematician, I have things to say. 1/

Statements like "2+2 = 4" are abstractions. What that means is they're generalizations of "something". You should always think of these statements as associated with an underlying reality. As a data analyst, I love numbers but It's my job to connect them to reality. 2/

Literal-minded people might sometimes say things like I put a rooster and hen together and I came back a year later and there were three of them (1+1=3) or they might say I left a fox and a hen together and later I came back and there was only one (1+1=1). 3/

People like this sound stupid but they are making a tremendously deep point. Our numbers, our quantitative measures, are abstractions of real underlying things in the universe and it's important to keep track of this when we use numbers to model the real world. 4/

This is a great lesson for a junior data scientist to remember. Whenever you create a numerical construct like IQ or an aggression score or a sentiment score, it's important to remember that properties of this score might not mirror the real things being measured. 5/

The very act of turning something into a number is an assumption. 6/

You can think of an arithmetic as coming from entities living in an underlying space. For instance, 2+2 could mean 2 oranges plus 2 oranges. In which case, "2+2 = 4" means 4 oranges is the same amount of oranges. 7/

You can think of an arithmetic as a system of rules like a board game and not think about the underlying space at all. Mathematicians call such systems "formal" which means "I don't care if this stuff really works out, I will apply these rules blindly and hope it makes sense." 8/

The reason numbers feel so right is mathematicians have done all the hard work of figuring our how to make calculations track with reality. They kept modifying and refining the number system until everything worked out. It took centuries of brilliant minds to do this! 9/

At this point, you're probably like "Kareem, are you for real?" You probably think you've never encountered a calculation that felt weird or unnatural. You have! I'll prove it. 10/

One place mathematicians haven't quite figured out how to make things feel as natural is operations around infinity. What is infinity times zero? They just tell you not to do that, right? The reason is because it depends! There is no single answer. 11/

If you take "infinity" to mean a process that's growing very large and "zero" as a process that's shrinking, sometimes the shrinking process overtakes the growing one so 0 ⋅ ∞ = 0. Sometimes it's the other way around 0 ⋅ ∞ = ∞. Sometimes they balance out and 0 ⋅ ∞ = 12.

Because there's no one thing that always happens, we mostly avoid doing arithmetic with infinity. Doesn't that feel like a bit of a con? They don't have a nice set of rules for it, so they tell you not to do it? That's how it is folks. Math isn't as clean as you think it is. 13/

The sense that it all works out nicely is a bit of illusion based on thousands of highly intelligent minds working hard to make sure you know where to step without blowing yourself up. Math is logical but it's not always neat and nice. 14/

My situation is I analyze data all day. I turn reality into numbers. I'm not a mathematician. I don't get to ignore reality. I'm not a layman that can mostly live without playing with math too much. I have to sit on the border between math and reality and make them line up. 15/

So when somebody tells me "2+2=5", I WILL ALWAYS ask them for more details rather than just dismissing them as an idiot because maybe they're talking about chickens and turns out that's how chickens work! /