Order of Operations
Please excuse my dear Aunt Sally.
Most of us remember the mathematical order of operations from middle school by one silly acronym or another. In this case, it’s the standardized process for calculating a mathematical expression.
4 + 8 / 2 * (12 - 4 * 2) = ?
I’ll give you a chance to remember how to do this. Work it out for yourself, then scroll down.
x
x
x
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x
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x
The answer is 20. How did I get there? Skip the explanation if you’re not interested, as it’s not strictly necessary for the rest of this blog post.
Explanation
Parentheses first. So let’s look at (12 - 4 * 2).
Exponent next. But there are no exponents here.
Multiplication and division come next, and all else being equal, are done left to right. We’ve got 4*2 = 8, so we’re now looking at (12 - 8) within our parentheses, which is of course 4.
Okay, now we have 4 + 8 / 2 * 4.
Again, multiplication and division are done left to right. So we do 8/2 first, which is 4. That leaves 4 + 4 * 4.
Multiplication before addition, so now it’s 4 + 16.
Finally addition, which gives us 20.
Whew.
Disorder in Art
Now, it doesn’t HAVE to be that way. We could have decided the order of operations was subtraction, exponents, multiplication, division, addition, parentheses or “Sally, excuse my dear Aunt, please.”
If we did that, the answer would be 68. And that’s not necessarily wrong. Mathematical expressions, after all, are simply conventions we’ve agreed to. But the point is, we’ve agreed to them. And it’s in that agreement that all mathematicians can communicate, which is critical in science.
But in art? Not so much.
- A guitarist’s pedal board is subject to the order of operations. Placing the wah pedal before the overdrive before the reverb will give you a dramatically different sound than placing the reverb first, overdrive next, and wah last. Neither is better. Merely different.
- A painting is subject to the order of operations. Painting black before pink will render a very different result and process than the reverse. Again: different, but not better.
- Relationships are subject to the order of operations. You can move in before marriage, or wait until after marriage to begin living together.
- Do you eat before going grocery shopping, or after?
- Do you make your ‘ask’ or request first in an email, and close with a personal note? Or open with a personal note and close with a request?
- Get your emails out of the way before starting your ‘real’ work, or the opposite?
- Should you get experience in your field first, then go for a formal degree? Or study for four years before gaining any real-world experience?
Most of our work, most of the time, is closer to art than science. The order in which we engage with our various tasks, responsibilities, hobbies, and desires makes a big difference. There’s no “right” order to do any of these things, but it would be foolish to ignore how impactful the order is.
Rule of Thumb
If there’s a task that would prevent you doing the rest of the list, or prevent everything else from working properly, do that first. For everything else, ask yourself what you’re trying to achieve, and if switching the order of operations will help you get there.
And if you’re in a rut, try arbitrarily changing up your life’s order of operations. Sometimes change for change’s sake is precisely what’s needed.
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