Bret Hart's Method

Sometimes I wish debate was like professional wrestling, particularly the way Bret The Hitman Hart did it.  Debaters always want to make themselves look good and their opponents look bad.  Especially political debates.  But whenever Bret Hart had a professional wrestling match, he seemed determined to make not only himself look good, but his opponent look good as well.  I think even in a fixed sport it takes a lot of confidence to do that.  He brought out the best in his opponent, whether it was Diesel, or Hakushi, or Jean-Pierre LaFitte, or Shawn Michaels.  I can't remember the last time I saw anything like that in a political debate.  

The Mouth of a Liar

The truth coming out of the mouth of a liar is still the truth.

Misleading Evidence - An Important Lesson

It's quite rational to believe that the more evidence a theory has, the more accurate it will be.  And that's probably the case normally.  But there was a wonderful exception to this in a Sherlock Holmes story called, "The Adventure of the Norwood Builder."

In this story, a man was arrested on suspicion of murder.  Lots of evidence pointed him to the crime.  Holmes for some reason wasn't convinced, even though he realized the evidence definitely seemed to confirm the suspect of the murder.  But eventually the police found evidence that seemed beyond dispute.  A bloody fingerprint exactly matching the suspect.

This should have been enough to close the case.  But Holmes instead realized this proved the innocence of the man with the fingerprint.  HOW?

Because Holmes examined the exact spot where the fingerprint was just the day before and KNEW it was not there during his initial examination.  This was while the suspect was already jailed for the suspicion of the murder.  There was no way the suspect could have broken out of jail - and he definitely wouldn't do it in order to place even more evidence against himself.  Holmes realized somebody else had the suspect's fingerprint and put it there.

Even with all these spoilers, I'm still leaving a lot of good stuff out of the story.  Holmes ended up solving the case and clearing the initial suspect.  The real criminal who framed him did it almost perfectly, except he made the one mistake of not knowing when to stop.  That was his undoing.  Otherwise, he would have beaten Holmes.  But he couldn't resist planting the fingerprint later on when he realized what great additional misleading evidence it would be.

So I learned an important lesson here.  Even a ton of evidence leading a certain direction isn't always correct in the direction it's leading.  One additional piece can change the whole course of an investigation.  In other words, sometimes even if you follow a whole lot of strong, available evidence, you can STILL reach the completely wrong conclusion.  

Completion

The book Moby Dick implies that if you fully complete everything you set out to do then your visions are not grand enough. The narrator Ishmael in the chapter on Cetology says, "God keep me from ever completing anything."

The chapter was referring to the Cologne Cathedral in Germany, which was still incomplete at the time of the writing of Moby Dick, but eventually, after over 400 years of remaining in an incomplete state, was finally finished in 1880.

I thought that was an interesting fact.

Why Adding Two Equations To Each Other Works In Solving a System of Linear Equations

 A long time ago, when I was taking algebra in high school, I wondered why you can add two equations to each other to assist you in solving a system of linear equations, but I never really looked into it.

But the other day I thought about it some and I realized why it works.

Say you have two equations:  3x+7y = 4 and 5x-2y = 6.

Now you can add something to both sides of an equation without changing it.  Pretty much whatever you want.  So let's add (5x-2y) to both sides of 3x+7y = 4.

We get 3x+7y + (5x-2y) = 4 + (5x-2y)

BUT the key is, we also KNOW that 5x-2y = 6, so we can just replace (5x-2y) on one side of the equation with 6.

And we get this: 3x+7y + (5x-2y) = 4 + (6)

Which is just adding the two equations together.  (3x+7y = 4) + (5x-2y = 6).

So really when you add two equations together, you're adding the same thing to both sides and then doing a substitution.  And adding the equations directly is just a shortcut.  But a lot of times it's hard to see how the shortcuts work when you don't do them the long way.

And of course it's probably more common to add a multiple of one equation to another rather than to add them together directly, but the idea is still the same.

What is the answer in this example?  I have no clue.  But as Tom Lehrer once said, the important thing is to know what you're doing rather than to get the right answer.  That's probably why a lot of grad school textbooks don't give you the answers to most of the worked problems.

Stumping AI

The best way to stump AI is to ask it really obscure questions.  One time I asked it about a WWF house show that took place at the Summit in Houston in 1997 shortly after Summerslam that year.  I asked it to guess not what the main event of that show actually WAS, but what the main event of the show was initially ADVERTISED to be.  It said Shawn Michaels vs. Undertaker.  Not too bad of a guess because the first time those guys ever faced each other was very close to being around that time.

But the actual answer to that question was Stone Cold vs. Undertaker vs. Bret Hart in a triple threat match.  That was the advertised main event that I saw on a flyer in a store, and I remember being super excited to see it.  But unfortunately, Stone Cold was severely injured at Summerslam and could not perform at the following house show in Houston at all.  So, the main event ended up being Bret Hart vs the Undertaker, which I still enjoyed since I didn't see too many events live.  

What's sad is not only did that match not happen at that event, but it never ended up happening period.  By the time Stone Cold recovered enough from his injury to perform again, Bret Hart left the company and then retired shortly after.

If I asked AI that question again, maybe it learned the answer from me and would get the question right next time.  Or perhaps it would pull up and reference the text I'm writing now and try to use that as an answer.  Who knows.  I imagine it would have to trust my credibility.  But I remember that flyer for that triple threat match plain as day.  Even if everyone forgot it and there's no copies left, that flyer advertising Stone Cold vs. Undertaker vs. Bret Hart in Houston in 1997 really existed.  As Kurt Angle would say, it's true.  It's true.

Easy Proof That the Square Root of a Prime is Irrational

Fun fact I discovered the other day.  I'm surprised I wasn't aware of it before.

Take any whole number.  Divide it by another whole number satisfying the condition that you have a fraction that may be improper but otherwise cannot be reduced.  (The two numbers in the fraction are relatively prime.)  

Multiply this fraction by itself.  If the bottom number of the fraction is larger, squaring the fraction will make the bottom number grow more than the top number, so you can't get a whole number by squaring this fraction.  A similar argument can be made if the top number is larger.  There's no way to get a whole number squaring the fraction in that case either.  

Since you cannot get a whole number by squaring a fraction, you can't have a fraction of this kind by taking the square root of a whole number.  So the only kind of number a square root of a whole number can be is either another whole number, or an irrational.  The square root of a prime cannot be a whole number since it has no whole number factors, so the square root of a prime is irrational.