I was poking at a game of Mindsweeper as I was trying to wake up, playing the intermediate game, as I mentioned in Levels, without using the flags that mark the bombs. It occurred to me that someone might think it arrogant that I dare to play the game without flags; I only find it mentally stimulating. Some perhaps might think it arrogant that I tell people that I play without flags, as if I were suggesting that I was better or smarter than most people.
I’ve never thought of myself as particularly smarter than others, in general. Oh, there are certainly some people in the world of whom I’ve thought, even I’m smarter than that, but generally I perceive others as being pretty much as smart as I am. I’ve never had the experience which I believe Freeman Dyson recounted. Asked if he ever wondered why he was so smart, he said no, he wondered why everyone else was so stupid. That’s never been my experience. Objectively, I’m aware that the test scores say I’m pretty smart, but subjectively I don’t strike myself as outstanding.
For example, David (whom I’ve mentioned) can tell you the volume of a circular swimming pool in gallons given its dimension in feet. He can do that in his head, in a few seconds, while standing next to the pool. He’s not a mathematician; he’s a theologian. He doesn’t even own a pool, and swimming is not even one of his pastimes, let alone part of his career history. He failed trigonometry in high school. (In fairness, he had to be pretty smart to get into trigonometry in high school; he failed because he didn’t care at the time.)
Yet when I mention playing Minesweeper without the flags, people think I must be smart, smarter at least than they are, because they would never play that game that way.
It doesn’t follow. It’s an easy mistake to make, but it is nonetheless a mistake.
Long ago, right after I emerged from college, I grabbed a job as a security guard while job hunting in a depressed market. I worked at a fiberglass insulation factory on the evening shift for several months. There was there at that time someone whose position might best be described as Maintenance Engineer; if anything broke, he, or someone in his department, fixed it. He did a lot of machinists work, arc welding, mechanical repair. For some reason that I cannot now recall or fathom, I often found myself chatting with him about things that didn’t relate to much of anything. I suppose it must be that he and I shared a certain level of intellectual curiosity, but I don’t at all remember anything we ever discussed. However, I do recall that one day he commented, completely out of any context of which I was aware (although I think at the time he was working on something as we talked) that I should be able to add a column of two-digit numbers in my head. My immediate reaction was that this was not something I could do. I could add any number of single-digit numbers, either given them one at a time or having the luxury of seeing them on paper, but if I were going to add two-digit numbers I would do as I had been taught and add the ones first and then the tens. It would not have occurred to me to do something such as twelve plus thirty-six is forty-eight, plus forty-five is ninety-three, plus fifty-seven is one hundred fifty–it was too difficult.
Yet that sequence I just now invented and stated took me longer to type than it did to calculate. At those rare moments when I am faced with such two-digit numbers (less rare perhaps for me than for many, as I’ve played quite a few games in which modifiers have to be summed to get a target number, dating back to Star Frontiers and continuing with Multiverser) I get some practice at it. I’ve done it for the past quarter century.
The point is not that I’m so smart I can add a column of two-digit numbers in my head. The point is that this was something I did not think I could do primarily because it never occurred to me that it might be done that way. I won’t go so far as to say that anyone can do it; I will say that it’s not so difficult as it sounds, and I’d wager that the vast majority of my readers could do it if they tried, and would get better at it with practice. If you think not, ask yourself this: when you count the change in your pockets, do you add the pennies and nickels and five cents for each quarter first, and then go back to add ten cents for each dime and another twenty for the quarters? I dare say you are adding a column of two-digit numbers then, probably starting with the quarters and working down, possibly just counting them as they come. Those are easier two-digit numbers, perhaps, but it’s the same concept.
This is not about suggesting you practice adding columns of two-digit numbers. That certainly is a useful skill even if you don’t play Multiverser or Star Frontiers or similar games, but it’s not the point. The point is that you are probably quite capable of doing many things which you’ve never attempted, and that you’ve held yourself back from trying them because it has never occurred to you that this is something you can do. One day years ago during a particularly boring Civil Procedure lecture, I entertained myself by calculating the squares of successive integers. When I reached seventeen squared, I suddenly stumbled on the pattern [(x+1)^2-x^2=2x+1, which also equals 2*(x+1)-1, which for consecutive integers yields consecutive odd integers, if anyone cares]. It wasn’t a new breakthrough in mathematics, obviously, but it reflected the facts that by playing with numbers one gets better at numbers, and that Civil Procedure can be an extremely boring subject.
It has long been axiomatic that boys are good with numbers and girls with language. It has been taught and believed that boys struggle with words and girls can’t do math. Then Noam Chomski came along with an entirely revolutionary theory of linguistics: grammar turns out to be highly complex mathematical calculations. That stuff about girls not being able to do math is completely untrue. They do it extremely well. They just get frightened when the see numbers, and largely because we’ve told them that being girls they can’t do that so well.
The fact is that you can do many things with your mind that you’ve never attempted, and you are held back more by your own belief that this is not something you can do than by any real limitation in your ability. Sure, everyone has limits, and it is certainly good to know what yours are; but it is also important to challenge them, to check them, to see whether they are real limitations in your ability or merely your insecurities expressing themselves in self-limitation.
The first time I played Minesweeper without the flags, I lost. It was the beginner level. Now my computer records a record time on that game as Beginner: 5 seconds Dad–No Flags. You can do it. It’s not as hard as you think to think harder.
Next week, something different.
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M. Joseph Young is co-author of Multiverser and Vice President for Development at Valdron Inc. His many contributions to online literature are indexed for convenience, and he looks forward to discussing these things by e-mail or on our Gaming Outpost forums.
