Remember the School House Rock cartoons? I love them, so I happily picked up the whole collection (and some I hadn’t seen) on DVD. For those of you who don’t have the DVD or just have bad memories, you can hear the songs and read the lyrics at the main School House Rock site. I point you to that site because I have a math question for you. There were 11 math songs created in all, and in each song there are lots of numbers mentioned. Take all the numbers from all the songs and multiply them all together. What is the final result? Take your time. I’ll wait for you.

Too hard? OK, I’ll do one song for you. Here are all the numbers from the song about the number two titled, “Elementary, My Dear“:

40, 40, 1, 2, 2, 4, 2, 3, 6, 2, 4, 8, 2, 5, 10, 2, 1, 2, 2, 2, 6, 12, 2, 7, 14, 2, 8, 16, 2, 9, 18, 2, 10, 20, 11, 22, 12, 24, 13, 26, 14, 28, 15, 30, 30, 16, 32, 17, 34, 18, 36, 19, 38, 20, 40, 2, 2, 2, 4, 2, 3, 6, 2, 4, 8, 2, 5, 10, 2, 174, 2, 174, 2, 100, 2, 70, 2, 4, 2, 174, 200, 140, 8, 348, 32, 64, 33, 66, 34, 68, 35, 70, 2, 98, 2, 98, 2, 100, 2, 2, 200, 4, 196, 40, 40

Done the math? Now that’s a very big number! So go do the rest.

 

 

 

 

 

Do you have an answer yet, or does the thought of doing math give you hives? Well, I’ll make it simple for you. If you take all the Multiplication Rock songs and multiply together all the numbers mentioned in the lyrics, the final total is zero. Did everyone get that? Aren’t you glad there is a mathematical principle that says multiplying any number by zero will always make the result zero? OK, show of hands, how many people counted the numbers up in any of the other songs? Come on, confession is good for the soul.

For extra-credit math geekery, I’d like to bring up a related formula called the Drake Equation. This equation calculates the number of non-Earth-based civilizations in the Milky Way Galaxy with whom we may be able to communicate at some point in the future. Here’s the explanation of the equation from Wikipedia:

The Drake equation states that:

N = R^{*} ~ \times ~ f_{p} ~ \times ~ n_{e} ~ \times ~ f_{l} ~ \times ~ f_{i} ~ \times ~ f_{c} ~ \times ~ L

where:

N is the number of civilizations in our galaxy with which we might expect to be able to communicate at any given time

and

R* is the rate of star formation in our galaxy
fp is the fraction of those stars that have planets
ne is average number of planets that can potentially support life per star that has planets
fl is the fraction of the above that actually go on to develop life
fi is the fraction of the above that actually go on to develop intelligent life
fc is the fraction of the above that are willing and able to communicate
L is the expected lifetime of such a civilization for the period that it can communicate across interstellar space.

Whew. That’s a rather complicated formula, and depending on what values you place for the variables, the end number can vary quite a bit. But here’s my complaint regarding this formula: we can only guess at the values of fl, fi, fc, and L because we just don’t know what they are. Essentially, the Drake Equation is scientific-looking fluff that obscures the fact that we’re multiplying by a guess — and just as multiplying by zero makes the answer zero, multiplying by a guess makes the whole answer a guess, whatever the end number may be. It may be an educated guess or just a WAG, but it still remains a guess.

But the Drake Equation is not the only instance of guessing (as opposed to testable theory) in the scientific community. I often read or hear someone talk about the dire effects of man-made global warming, but rarely does anyone explain how these forecasts are made. Climate change forecasts are based on computer models which scientists create in an attempt to simulate future environments. Here is the first paragraph from an article by NASA about global warming model making:

The severity of these environmental changes will be largely dependent on how much the Earth’s surface warms over the next century. As the wide range of estimates for average global surface temperature suggests, researchers haven’t exactly reached a consensus. The reason for the wide range simply comes down to the difficulty inherent in predicting the outcomes of current trends in both human society and the Earth’s climate system.

If you read carefully, you may notice there’s a lot of wiggle-room in that paragraph, and very little hard science. What are climate scientists doing with these models? They are making guesses. Guesses about how much greenhouse gas concentrations will be around in the next 100 years, guesses about what these gases do to the atmosphere, guesses about how the Earth’s ecosystems will react to these changes — there are lots of guesses going on here, folks.

The severity of these environmental changes will be largely dependent on how much the Earth’s surface warms over the next century. As the wide range of estimates for average global surface temperature might suggest, researchers haven’t exactly reached a consensus. The reason for the wide range simply comes down to the difficulty inherent in predicting the outcome of current trends, both in human society and the Earth’s climate system.

Why should I trust these models when they are based on a multitude of guesses? I can suggest one way of proving the efficacy of climate modeling: feed the computer models known data about greenhouse gases in the year 1907 and allow them to calculate climate changes over the next hundred years. If the models can accurately describe the climate changes that actually occurred over the last century, using only the initial environmental data from 1907, I would be much more likely to trust their ability to forecast accurately the climate changes of the next 100 years, using only the initial environmental data from 2007. Or, to put it another way, I will trust that scientists can predict the weather accurately for a date 100 years in the future if they can first demonstrate the ability to predict the weather accurately for a date 100 days in the future. (Hint: most self-respecting meteorologists won’t attempt to forecast weather and temperature changes anywhere past ten days.)

Here’s the final paragraph from the NASA article:

Climate modelers must consider dozens of such factors, boil them down into equation form, and pack them into their models. Not all models are built alike. There is quite a lot of disagreement among Earth scientists as to how much of a role factors such as aerosols and clouds will play in heating the Earth and how they should be incorporated into the models. For instance, NASA climate modelers at GISS have evidence that black carbon aerosol particles (soot) contributes significantly to warming of the lower atmosphere, since they absorb incoming radiation. The IPCC, on the other hand, estimates that black soot plays only a very small role in warming. Each research group or agency builds its models accordingly, and the choices made influence the forecasts derived from the models. Even when modelers do agree on the mechanisms involved, many of these factors have a great deal of uncertainty associated with them.

It’s all guesswork. And just as any number multiplied by zero becomes zero, any number multiplied by guesswork becomes a guess.

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