Reasonableness - More Value-Based Than Fact-Based

We have no scientific way to measure how reasonable something is, so even though it sounds strange, we must conclude that reasonableness is more rooted in value than in fact.  Sometimes I think reasonableness is a preference for facts, but even a preference for facts would be considered a value and not a fact itself.

Why do people prefer logic to emotion?  Probably because it's closer to truth.  But why do they like truth?  Probably for an emotional reason.

A Strange Creature Marco Polo Described

In reading The Adventures of Marco Polo, I got to a chapter where the title character spoke of a special kind of lion that helped the Grand Khan hunt, and the lion had white, black, and red stripes all over it.  Strange indeed.  But actually, it was an animal we learn about in grade school now.  A tiger.  Hard to believe at one point few people in the European world knew what one was and had to resort to these strange descriptions.  He had an interesting description for yaks as well, but not as interesting as this.

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.