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

$$5a=5b+5c.$$

Multiplying by 4 and switching the two sides gives

$$4b+4c=4a.$$

Adding these two equations together, we get

$$5a+4b+4c=4a+5b+5c.$$

Subtracting $$9a$$ from both sides, we obtain

$$4b+4c-4a=5b+5c-5a,$$

or

$$4(b+c-a)=5(b+c-a).$$

Dividing both sides by $$b+c-a$$ gives the final result:

$$4=5.$$

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.