Orthogonal Vectors

Disclaimer: This post is not actually about math.

In physics, vectors that are orthogonal have absolutely no effect on each other. A force acting on an object in the y direction will have no impact on that object in the x direction. (Why? NO ONE KNOWS.)

In math, it’s just as clear: Standalone ideas have no effect on each other at all.

I couldn't find an interesting picture, so I went with the most boring picture I could find. Note the Comic Sans and the 2003 publication date.

I couldn’t find any interesting pictures, so I went with the most boring picture I could find. Note the use of Comic Sans and the 2003 publication date.

So why can’t this same principle be applied to ethical problems? Just like with physics problems,  the individual parts that make up a problem should have no effect on each other.

The Heinz Dilemma

Let’s start with the classic example used in Kohlberg’s theory of moral development:

Heinz’s wife was dying from a particular type of cancer. Doctors said a new drug might save her. The drug had been discovered by a local chemist and the Heinz tried desperately to buy some, but the chemist was charging ten times the money it cost to make the drug and this was much more than the Heinz could afford.

Heinz could only raise half the money, even after help from family and friends. He explained to the chemist that his wife was dying and asked if he could have the drug cheaper or pay the rest of the money later. The chemist refused saying that he had discovered the drug and was going to make money from it. The husband was desperate to save his wife, so later that night he broke into the chemist’s and stole the drug.

-from http://www.simplypsychology.org/kohlberg.html

The question is, should Heinz have stolen the drug?

Split it up.


Is stealing bad? Yes.

Really bad? Well, going to jail bad. And that’s only if you get caught.

Conclusion: If you steal, you get the medicine and might go to jail.

His wife dying:

Is his wife dying bad? Yes.

Really bad? Yes. (In the sense that virtually everything else in life is reversible.)

Is there anything he can do to help? Yes. Steal the medicine.

Conclusion: His wife dying is really bad, and he can steal the medicine to save her life.

Putting the two vectors together, this is what you get:

Either he steals the medicine and gets caught and goes to jail, or he doesn’t steal the medicine and his wife dies. It’s balancing jail time with his wife’s death. Going to jail is clearly the lesser of two evils here, so the man should steal the medicine and go to jail.

Pretty straightforward right?

A follow up situation:

A policeman on guard sees the man steal the medicine. Should he report him or not?

Before you start being all sympathetic, remember that his wife is dying is on an orthogonal vector to the man going to jail. They should have no impact on each other. If you do something, you pay the consequences. 

So should the policeman report the man? Yes. And the man should steal the drug knowing that he might get caught.

The argument shouldn’t be “I know he stole something, but his wife was dying.” It should be “I know he stole something, and his wife was dying.”  There is no correlation between these two .

When we first did this exercise in my psychology class, my teacher said that in the highest stage of morality, the man should have stolen the drug and then turned himself him. My conclusion was that he should steal the drug knowing that he would get caught. Not quite there, but I’m still proud of myself for getting where I did.

Charlie Hebdo

Now to apply this to current events.

Is killing 12 people bad? Yes. (Same logic– it’s irreversible)

Even if there’s a reason? Yes

Was the reason bad? Not really.

Is offending a specific group of people bad? Sure.

Is free speech good? Sure.

Are they mutually exclusive? (aka can you have free speech without offending people?) Most likely not.

Did the event catch people’s attention? Yes.

In a good way? No.

Did it prove a point? Yes.

Was it the intended point of the attackers? Probably not.

I could keep going about this, (Don’t get me started on Je Suis Charlie), but even just adding up all these vectors, what do you get?

It depends on the magnitude of each individual vector, but you’ll always end up with a multi-dimensional vector. In other words, something complicated. 

I know that’s not a satisfying answer. How are you supposed to feel about this?  Is this just going to be another one “I’m too much of an intellectual to have an opinion about this so I’ll just not say anything.” conclusions?

Yes. And I’m not going to apologize for it. Even as I was writing everything, I had to resist the urge to find a news article that would just tell me what I was supposed to believe about the entire incident. If you’re looking for that, go to your news site of choice.


As always, complicated problems are easier to solve when you look at them through a mathematical perspective, but that’s not always reasonable. Hypothetical situations and faraway current events are easy to analyze, but what about something more personal?

In the case of the Heinz dilemma, a common follow up question is: “Would/Should Heinz have done the same if the sick person was a stranger?” Or what if I was the guy selling the drug? Would I see Heinz’s actions as ethical? In the case of Charlie Hebdo, what if I were French? A Muslim? What if I personally knew one of the editors that was killed? Would that change my views? Heck yeah.

You mean math doesn’t work for everything? Bummer

Once you introduce the personal element, you also could argue that all the vectors aren’t orthogonal. For instance, is the fact that 12 people were killed really not correlated with catching media attention and sparking a social movement? It becomes less clear.

Sometimes I wish that I could treat all the people I know as vectors and keep everyone in their own dimension. It’d make things so much easier to manage. But that’s not how the world works. Inevitably, everyone’s vectors collide into each other at various angles, thanks to something called human nature. How can you be completely objective when your human nature vector keeps crashing into everything unexpectedly?

But frankly, even though it might pay off in the long run to be objective,  I feel like I need the slightest shred of irrationality to justify my existence as a living being. Our tiny deviations from ideal behavior are what define human nature. Otherwise, we’re all just robots following a set of arbitrary rules. Living is a form of art. And just like other forms of art, it’s a virtue to follow the rules, but the real living happens when you break the rules.

Often I think my defiance is just delusional, self-glorifying bullshit that artists have always told themselves to compensate for their poverty and powerlessness. But sometimes I think it’s the only thing that has preserved me intact, and that what has been preserved is not just haughty caprice but in fact the meaning of my life. So this is what I told Mao: In lieu of loving the world twice as hard, I care, in the end, about expressing my obdurate singularity at any cost. I love this hard and unyielding part of myself more than any other reward the world has to offer a newly brightened and ingratiating demeanor, and I will bear any costs associated with it.

Paper Tigers

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