I was having a discussion with a lawyer friend of mine. I was trying to illustrate the difference between the advocating done by lawyers and the scientist’s unbiased (or at least, not intentionally biased) search for the truth. One is about cherry-picking facts and arguments to prove a preconceived notion; the other about trying to understand the world around us.<\/p>\n
I told him that anything and the opposite of anything can be proven by cherry-picking facts. Then it occurred to me that it is true even in math. For instance, by cherry-picking facts, I can easily prove that \\(2\\times 2=5\\). Let’s start with three variables, \\(a\\), \\(b\\) and \\(c\\), for which it is true that \\(a=b+c\\). Then, multiplying by 5 gives<\/p>\n
$$5a=5b+5c.$$<\/p>\n
Multiplying by 4 and switching the two sides gives<\/p>\n
$$4b+4c=4a.$$<\/p>\n
Adding these two equations together, we get<\/p>\n
$$5a+4b+4c=4a+5b+5c.$$<\/p>\n
Subtracting \\(9a\\) from both sides, we obtain<\/p>\n
$$4b+4c-4a=5b+5c-5a,$$<\/p>\n
or<\/p>\n
$$4(b+c-a)=5(b+c-a).$$<\/p>\n
Dividing both sides by \\(b+c-a\\) gives the final result:<\/p>\n
$$4=5.$$<\/p>\n
And no, I did not make some simple mistake in my derivation. In fact, I can use computer algebra to obtain the same result, and computers surely don’t lie. Here it is, with Maxima:<\/p>\n