February 24, 2010

When 2 + 2 = 5

Filed under: Main — admin @ 12:01 am

The joke goes that 2 + 2 = 5 for sufficiently large values of 2. It’s not really a joke, though; you’re computer can prove it for you.

I remember reading Orwell’s book Nineteen Eighty-Four . A while back, I was in a theatrical production of Nineteen Eighty-Four . I know the story well.

In the book, the antagonist O’Brien convinces the hapless Winston Smith that 2 + 2 = 5 because the Party says so.

In the end the Party would announce that two and two made five, and you would have to believe it.

This is where I could draw an analogy to American politics and where political parties dictate similar, nonsensical dogma and their unquestioning followers not only accept it, but defend it without doing their own research. Scary, but that was exactly the point of Orwell’s book.

Meanwhile, back on your computer.

Fire up Excel or any other spreadsheet program.

Are there any other spreadsheet programs? Oh, yeah. There’s the one that comes with iWorks by Apple. I’ve used it, but haven’t used it so much that I can recall its name off the top of my head.

After starting Excel, type 2 in one cell and then type 2 in another. In a third cell, type a formula that adds the contents of the other two cells. This figure shows you how I set things up:

When you press Enter, the third cell shows 4 as the result, which is what you’d expect, what they taught you in grammar school, and what mathematicians might even agree to.

Now modify the values to look like this:

That’s 2.4 plus 2.4 in the two cells. Excel instantly calculates the sum as 4.8 in the final cell; there is no need to re-type the formula.

Again, the result is based on simple math and most people accept it. The world can continue spinning on its access.

When I select all three cells, however, and click the Decrease Decimal button (), it modifies the way Excel displays the cell contents. You see this result:

The values of 2.4 are rounded down to 2. The result of 4.8 is rounded up to 5. Effectively, you get 2 plus 2 equals 5.

Obviously this method of getting five of something wouldn’t work when counting sheep. It would work when counting change, though. $2.40 plus $2.40 equals $4.80, which would be considered $5.00 as far as the IRS is concerned.

My point, for both mathematics and politics, is that it really helps to know all the information when you’re trying to interpret the results. The non-thinking partisans will attack you regardless. But for your own self, discover the truth.

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