This is going to be the first post in a series about counter-intuition.
I am still working on some nuts-and-bolts resources for Math Mojo (like addition and multiplication booklets and videos and a teleseminar so people can ask questions as I show an amazing way to teach addition) but sometimes I need to write more about the Mojo than the Math.
Actually, the math is the mojo, but the simple skills as taught in schools are devoid of both. The mojo I’m talking about here is the lessons you can get from understanding math that are beyond simple numbers skills. They are about life-lessons, deeper insights into your mind and how you can think more satisfactorily (for yourself, not for me or your teachers). Which leads me to….
One of the tenets of Math Mojo is Occam’s Razor.
Occam’s Razor is generally seen as “The simplest explanation is generally the best one.” This is true, but the phrasing is dangerous. Another way to put it is, “Make things as simple as possible, but not simpler.” This is often attributed to some hack (um, Einstein LOL?) I think it should be “The simplest explanation that makes sense and does not contradict other known facts is generally the best one.” Of course that is more like what William of Occam meant, but unfortunately it is not how many people think.
The simplest explanation for the Earth’s shape is to say that it is flat. Of course it is. “Everybody knows the world is flat.” That is what “common sense” tells us.
The Sun revolves around the Earth. “Everybody knows that. The Sun comes up and goes down, therefore the Earth stands still and the Sun revolves around it. Just like the moon. Anyone can see that. It’s common sense.”
Of course that’s all bull. But hey, the only reason most people know that that the earth is round(ish) is because they were told that. Not because they understand anything about geometry or astronomy or critical thinking. Many people still didn’t believe it until they saw the first pictures of the Earth from space. Some people still don’t believe it.
We know what “everyone can see,” or what we are told. Well, at least many people do.
When someone uses, “…everybody knows that…” in an argument, it does not necessarily mean that he is wrong, it just means that he is an idiot.
Common sense is generally more “common” than “sense.”
There’s no way to collect or parse all the data, but I’d bet the house (your house, anyway) that 90% of mankind’s problems stem from “what everybody knows.” That’s what happens when people think with their guts. It would be better if they thought with the organ furthest from their butts.
It is sad to see people craving simple solutions for complex questions, without considering that there might be more to something than “what everyone can see.”
This reminds me once again that “intuition” is not what it’s cracked up to be. The flat-earth theory is “intuitive.” The round(ish)-earth fact is counter-intuitive. When you start exploring and developing a feel for counter-intuitiveness, you start getting in touch with your math mojo.
Well, of course you won’t be able to enlighten a person who is dead set on remaining unenlightened. But I’m betting that many readers are more enlightened than I, and that those who aren’t would certainly like to understand more. That’s why I write this blog.
In the next post, we’ll discuss a bit of mathematics that is counter-intuitive, and what we can learn from how people think about it.
Here’s the link for the next post:
Teleseminars are really very helpful and i always look for it on the internet.”*;
i have attended a few teleseminars. They are good, but lack personal interaction.”~’
the great thing about teleseminars is that you learn a lot in the comforts of your home;`,
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