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.
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
Multiplying by 4 and switching the two sides gives
Adding these two equations together, we get
Subtracting \(9a\) from both sides, we obtain
Dividing both sides by \(b+c-a\) gives the final result:
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:
(%i1) eq1:5*a=5*b+5*c$ (%i2) eq2:4*b+4*c=4*a$ (%i3) eq3:eq1+eq2$ (%i4) eq4:eq3-9*a$ (%i5) eq5:factor(eq4)$ (%i6) eq6:eq5/(b+c-a); (%o6) 4 = 5
All I had to do to make this happen was to ignore an inconvenient little fact, which is precisely what lawyers (not to mention politicians) do all the time. Surely, if I can prove that \(2\times 2=5\), I can prove anything. So can lawyers and they know it.