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Log, Aug 12, 2005

Heavy overcast forced us to cancel tonight.

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No one would be happier than I if sciences taught in junior high school included more mathematical examples and rigor but nothing is worse than bad science and false mathematics. Textbook publishers trying to get the lucrative California market came up with some "relevant" mathematics for junior high students which were so bad that I'd like to get on a soap box and shout "NO"! Here is the essential example that set me off:

"Bill saw three red stars and two blue stars last night. Red stars are 6,000 degrees and blue stars are 10,000 degrees. How hot were all the stars together?" The answer that appears in the teachers guide gives 38,000 degrees as the answer.

I can scarcely explain how many fallacies are contained in these few lines of pseudo science and meaningless arithmetic. If the example had been

"Bill saw three glasses of milk and two cups of tea last night. Milk is 40 degrees and tea is 160 degrees. How hot were all the drinks together?" I doubt even the worst science writer would have come up with an answer of a cloud of steam at 440 degrees. Yet this is exactly what the so called science writer did with the stars! Yeeeeeech!

At least with the tea and milk example, it would be possible to combine all the drinks and get a single tepid liquid. If all the drinks were the same size, then hazarding a guess that their combination would be 88 degrees makes some sort of sense. This isn't even remotely the case with the stars.

Here are a few of the worst fallacies in this horrible example.

  1. Red stars have a surface temperature closer to 3500 degrees than

    6000 - but this is meaningless in any case because stars are not uniform in temperature.

    For example our Sun (a true 6000 degree range yellow star!) has an ever increasing

    temperature as you go deeper reaching a central temperature of about 15,000,000.

  2. Some red stars are giants, and some red stars are dwarves.

    Combining stars of unknown masses would yield an unknown temperature. Blue stars are

    giants and sub-giants but even here the masses of these stars vary significantly. Nothing

    in the example indicates that stars have widely differing masses.

  3. Stars produce their own heat from nuclear reactions. These nuclear

    reactions are very sensitive to the mass (and hence the gravity) of the star. Reaction

    rates of stars vary as the fourth power of the mass. Combining 5 stars would result in a

    runaway reaction. If 5 identical stars suddenly became one, they would produce energy at

    rate approximately 625 times as fast as any one of the stars.

  4. Combining the stars isn't like pouring milk into tea. The stars

    would crash into each other under their combined with a huge gravity pull. The resulting

    explosion would be spectacular to say the least. Calculating the temperature by simple

    arithmetic simply isn't possible in this case.

I could go on and on with the fallacies, but you get the general idea. This terrible example of rubbish science and misapplied mathematics has absolutely no meaning. Worse yet, it gives junior high students weird ideas about science and how science uses mathematics. It might not have been so bad, but this was a well known text book company, and these examples raised no objections until the books were in print.

I wonder what that science writer would have made of the following:

"An airplane can cross the Atlantic from New York to London in 6 hours. How long will it take for 6 planes to cross this distance?"

-Les Coleman

Leslie Coleman
Author:
Leslie Coleman
Entry Date:
Aug 12, 2005
Published Under:
Leslie Coleman's Log
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