The false Eureka! moment

Today I had what might be called a mental glitch while walking in the city. I had taken the subway to a certain spot and, upon disembarking, found myself uncertain whether I was on the correct side of the street or not (in order to get where I wanted to be going).

A bird’s eye view of the intersection where I stood would look like this:

Bird's eye view of an intersection

Now, here’s what’s weird. As I stood on street A, looking towards street B, I thought: I must be on the wrong side, based on the angles I’m seeing from my vantage point.

Why did I think this? Not long after having this thought (literally like 5 seconds later), I realized that I was just flat-out wrong; the angles would look the same regardless of whether I were north or south of street B (with me facing the street, the acute angle would be on my left, and the obtuse angle would be on my right). In fact, as it turned out, I actually was already on the correct side. (Fortunately I realized this before wasting my time crossing over.)

And yet, despite the fact that I consider myself someone with relatively good spatial skills, I made this mistake.

It just got me thinking about human thought in general, which is so susceptible to false “A-ha!” moments such as this. How often do you puzzle over a problem, eventually arriving at what feels like a mental breakthrough—Eureka!—only to later realize, Oh wait, that’s actually still not right?

To be 100% honest, it happens to me more often than I’d like. I think the next time I feel like I am making great strides toward solving a difficult problem, I will take a step back and ask myself, Is this like that intersection? Am I really making a breakthrough?

It might save me from crossing over the wrong street, only to have to walk back again.

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One thought on “The false Eureka! moment

  1. Alex says:

    I have had a few of these before. Two in sixth grade. One time I thought I proved that odd perfect numbers do not exist, and found an error in my proof within about five minutes (but I was REALLY excited during those five minutes).
    On Wikipedia not much later, I was looking at the page on super square roots. The super square root of c was the value of x such that x^x = c. For instance the super square root of 256 is 4 because 4^4 = 256. It said on Wikipedia that nobody knew whether the super square root of 2 was rational or irrational (or for any non-perfect super square for that matter). I got out a sheet of paper and proved it was irrational in less than ten minutes. I thought I would be known for proving this, and it turned out there was nothing wrong with my proof (as far as I know today), but Wikipedia lied and it was already known that it was irrational. So I don’t know if this counts as a false Eureka moment or not, but they do suck. Never less, I thought I was a lot smarter than I really was, lol.

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