Recently I’ve had a few political conversations on the internet. Although they were with different people and on different topics, I noticed a striking similarity.
The first conversation went something like this:
Him: The deficit is evidence that we spend too much money!
Me: Actually, the deficit is the difference between two variables: spending and revenue.
Him: But if we just spent less, the deficit would be less!
Me: Well, if the government took in more revenue, the deficit would also be less.
Him: No, Obama’s deficit spending is the problem. It’s out of control.
Me: The fact that you put the word “spending” into the phrase “deficit spending” doesn’t change the fact that the deficit is not only a spending issue.
Him: Of course it is! Just think about it: if the government didn’t spend any money, there would be no deficit! Therefore, the deficit is a spending problem!
Me: No, just because spending matters to the deficit doesn’t mean that it’s the only thing that matters. If the government increased its revenue enough, there would also be no deficit.
Him: But if you just tax people more, that doesn’t solve the spending problem!
Me: Why do you think there is a “spending problem”?
Him: Well, just look at the deficit!
And so on and so forth.
It’s a kind of “infinite loop” conversation that is maddening. Maddening on both sides, I’m sure: I’m sure that, just as much as I thought that he was being irrational and making no sense, he thought the same of me. So, like most internet conversations of this type, it eventually just faded away.
But, within a short period of time, another conversation emerged along these lines:
Him: Small business owners succeed on their own! It’s their hard work and effort that leads to their success, and the government can’t take credit away from them!
Me: Well, small businesses takes advantage of all kinds of opportunities provided by our culture. They use roads to get their products delivered, they use banks to get loans, their employees often are educated at public schools. Everyone has help from somewhere.
Him: You can get all of the help and assistance from the outside that you want, and if you don’t work hard, you won’t succeed!
Me: OK… but just because your hard work is necessary to succeed, doesn’t mean that you didn’t also get help from the outside.
Him: When I built my company, I didn’t get any help. There wouldn’t be any company without the 8 years of hard work I put into it.
Me: Sure, but you also live in a society, an entire culture, that you make use of. You learn things, you use telephones and the internet, you don’t have to hire a private company to put out fires in your office building because you know the Fire Department is there, you use the post office. You use all of these things that help you. So you didn’t do it on your own.
Him: Of course I did! Anyone has access to those things, but not everyone has a company of their own! To have a successful company, you need your own drive and skill!
Me: Of course, but just because your own hard work matters to success doesn’t mean that it’s the only thing that matters. If you were a poverty-stricken child in Somalia and had no opportunities to start a business, it wouldn’t matter how hard-working you were.
Him: That isn’t the same, because their society isn’t built around the principle of this kind of success.
Me: You mean their society doesn’t help them succeed at business?
Him: Hey! Nobody helped me with my business! I did it on my own!
And so on and so forth.
In both cases, it seemed like the same pattern was at work. I was saying “The thing that you are talking about is a function of two variables, not just one.” The response that I was getting was: “No, I think just one of those variables matters!”
What was more frustrating, for me, was listening to the kind of reasoning being used by the person with whom I was speaking. In both cases, the argument just seemed obviously ridiculous. This is how it seemed to me:
Me: The thing you are talking about, Z, is a function of two variables, F(X,Y). You cannot define Z without referring to both X and Y.
Him: But look how important X is! Without X, there would be no Z! Therefore, X is the only thing that matters!
Me: Just because X is necessary to define Z doesn’t mean it’s sufficient to define Z. You need Y as well.
Him: That’s not true, because… just look how important X is!
At some point, I just couldn’t even comprehend how someone’s mind might work that way.
Is it really possible that these conservatives don’t understand the concept of functions with more than one variable? Has our soundbite culture deteriorated people’s reasoning skills so badly that they literally can’t hold in their heads the idea that some outcome might be the result of more than one input?
Not so fast!
Luckily, I have some very smart conservative friends, and at least one of them is as nerdy and math-oriented as I am. He was able to argue the case, and it was something like this:
Him: So what percentage of credit am I allowed to have for starting my own business?
Me: I don’t think it’s a matter of “percent” … it’s not a zero-sum game. It’s not like each “point” of credit you give to the people who built the roads you use for free somehow takes away a “point” of credit that you get for your hard work.
Him: I just think that although people can get help from the outside, the influence of that help is vanishingly small compared to the influence of your own effort and skill. To use your language of the multi-variable function, let’s say X is my effort/time/money, Y represents things I don’t control (family circumstances, teachers in elementary school), and Z is things like living in the US and other things that all Americans get. The function for success as I see it is X^3 + Y^2 + Z > 1000. So for large values of X (which is required for success unless Y is really really large, a la Rockefeller and Kennedy children), X dominates. Not that the other factors aren’t important, just that X matters most and dominates for large values.
Me: Interesting. But I don’t think the factors are additive. I think they multiply. Let me explain why I think that: If any factor is literally ZERO, then the end result is zero. If you literally have NO resources, NO opportunity, whether in the sense of family OR government assistance, then you don’t succeed because you never have a chance to make use of your skills. Similarly, if you have literally ZERO effort and skill, then you don’t succeed, because you can’t do anything with the advantages that life gives you (even if you are a Rockefeller child). However, if either of these factors is even SLIGHTLY above zero (even if only a small amount), then it can be overcome by having VERY large amounts of the other. So, a person with minimal skill can succeed if he was born with the proverbial “silver spoon” in his mouth, and the come-from-nothing street-urchin can work his way up as long as he is given some kind of chance to be noticed.
That’s my intuition. I’d say the equation is more like X*Y*Z > 1000. Or at least, perhaps, something like X*(Y+Z+Y*Z) > 1000, since you might argue that government assistance isn’t needed if you have enough family support, and vice-versa.
Him: I wasn’t really thinking of anything more than a big exponent versus a smaller one, but yeah, multiplicative, versus additive, makes sense. But I still think the external factors can’t weigh as much, so you would need the exponents or the magnitude of the numbers is different. My own experience (poor state, poor family, average genes) is that hard work and desire of the main actor dominates.
Me: I’ll concede that. But here’s my thing: even if you have exponents, if your “success” formula is multiplicative, then if the external resources (Y+Z) are zero, you can’t succeed. In a situation where (Y+Z) is zero, the total will always be zero. Even if your formula is so heavily weighted that it’s X^100 * (Y+Z) > 1000, then you still need to have SOME external resources to succeed.
I think this is what President Obama meant, when he said “You didn’t do it by yourself.” I think he meant: if (Y+Z) = 0, then the total is 0, no matter what X is.
This was the conversation I was looking for! I actually never got a response to my last hypothesis about Obama’s “you didn’t do it by yourself” statement, so I’m not sure if he would agree or disagree. But nonetheless, I was very happy to have the conversation carried this far. I think it’s far more interesting to take a thoughtful and analytical claim like “the factors of success are multiplicative instead of additive” or “individual work accounts for more of the variance in success than external factors” and put it under the microscope and examine it in detail, instead of going around in these merry-go-round conversations like the first two that I described.
In case you ever had any doubts: this is yet another reason that knowing math is important.