Roger Penrose Agrees with Me: 2+2 may not = 4!
July 28, 2008 1 Comment
One of the sections of “The Universe – Solved!” that generated a bit of controversy was my assertion that there is really nothing that we can know with conviction to be true. An exerpt:
“2+2=4? Not in Base 3, where 2+2=11. In Base 10 (or any base >4), 2+2=4 by convention, but only in an abstract way, and not necessarily always true in the real world. If you add 2 puddles of water to 2 puddles of water, you still have 2 (albeit larger) puddles of water. For a more conventional example, a 2-mile straight line laid end-to-end with another 2-mile straight line will not add up to exactly 4 miles in length due to relativity and the curvature of space-time in all locales. Therefore, 2+2=4 can not be universally true.”
In addition, You have no way of knowing whether the convention that 2+2=4 is only true in the false reality that we think we are in, but not in the real one. Again, from the book: “So, maybe all we can know for sure is what is happening to us at this exact instant. Then again, how do we know that we aren’t in a dream right now??? So, the set of things that are 100% true is simply the null set!”
Some readers have argued with these assertions.
So, imagine my pleasure when I read the following quote in the July 26 – August 1 issue of New Scientist magazine by esteemed mathematician and physicist Roger Penrose: “”Do we know for certain that 2 plus 2 equals 4? Of course we don’t. Maybe every time everybody in the whole world has ever done that calculation and reasoned it through, they’ve made a mistake. Maybe it isn’t 4, it’s really 5. There is a very, very small chance that this has happened.” His argument is based on the logic of reason, which was different than my argument, but the result was the same nonetheless.
Thank you, Roger, for your enlightened point of view. I would gladly send you a free autographed book. Please send me your address.