Philosophy - #5

Brain-twister # 5 is the "surprise day" paradox. This post is out of order, but I decided to write it quickly since Spiked Math made this comic. Instead of re-writing the deconstruction of logic, I'm just going to cheat and point you to the comments section - the mathematicians explained it better than I could =) They also touch on the "interesting numbers" paradox discussed earlier.

Philosophy - #10 and 9

Both brain-twisters #10 and #9 suffer from an inconsistent definition. Let's take them one at a time, starting with #9.

Take a set of numbers. The "interesting" number is the smallest (in this puzzle). But then, after removing that one, there is still a smallest number. Keep removing the interesting (smallest) number, the argument goes, and you will be left with no "uninteresting" numbers.
But, when you remove the smallest number, you've created a new set! Start again with the initial set; there is a smallest number, but the rest are still uninteresting IN THAT SET. If there are "n" numbers, "n-1" of them are uninteresting. Just stop there. If you remove that number from the set, you've changed the system.

#10 has the same problem. (And actually, I really liked that this problem was included. I used to think along these lines in elementary school when I was home sick for the day. My mom insisted that I go to school unless I had a fever. I used to wonder when the exact minute was that I was officially "sick." And then I'd wonder if I could break it down further - into the exact second, or millisecond, or microsecond that I transitioned from being "well enough to go to school" to "sick enough to stay home." Apparently I was a 6-yr-old philosopher. But I digress.)

Few things in life are in a simple binary state. If someone showed me a millions grains of sand, I'd probably say, "That's a heap of sand!" If someone showed me a single grain of sand, I'd certainly NOT say, "That's a heap of sand!" But this isn't a simple on / off switch. Just as, when I was a child, illness would come on gradually, with an intermediate "take a nap, then see if you're well enough to go to school late" phase, there is a gradient between "heap" and "single grain." Maybe a hundred thousand grains is a "pile." And ten thousand grains is a "lump." There might even be a single-grain difference between what I'd call a "pile" and what I'd call a "lump." But I wouldn't necessarily keep calling a collection of sand a "heap" until I got down to one grain. At some point along that gradient, I'd go into the next label.

Philosophy - #11 and #1

I'm going to start by looking at the first and last brain-twisters. In my opinion, they're kind of the same argument. The contradiction comes from a lack of clarity in the definitions.

If an object is "unmovable," by definition that means that NOTHING can move it. Similarly, if a force is "unstoppable," that means that NOTHING can arrest its motion. Clearly these two things cannot exist in the same universe, so the hypothetical situation doesn't even make sense. It would (almost) be like saying, "What if gravity were both attractive and repulsive?" According to what we know of physics, this can't happen. The question is meaningless.

(For what it's worth, I'm working really hard here not to throw in a discussion of coordinate systems and how motion is always measured relative to something else.)

Similarly, the "omnipotent" being needs a good definition of "omnipotent." What do you mean when you ask the question? Could this omnipotent being increase its own power? In which case the conflict dissolves - the omnipotent being could create a stone it could not (initially) lift, and then increase its power until it could lift the stone. There needs to be a baseline of power against which to measure the "unliftable stone;" but this contradicts the idea of a truly "omnipotent" being. Again, the argument is meaningless without further clarification.

Philosophy

I'm generally not shy about my hatred for philosophy. I think it's because I'm scientifically-minded; I like to test theories, not just debate them. And a lot of times it seems like philosophers argue about semantics and language so abstract that what they're saying has no real meaning. Other times, it seems like philosophers argue about things that could be tested or understood scientifically.

I'm not gonna say that all philosophy is bunk; I understand that philosophy helps exercise logical and critical thinking muscles. However, a lot of times I read a philosophical argument or brainteaser and have to roll my eyes. For example, I recently read this article on "philosophical brainteasers" and they all seem to fall into one of two categories:
1) things that people think are paradoxes because they don't properly understand math and science, or
2) arguments based on contradicting definitions.

Over the next several posts, I'll go through them and explain my thoughts on each of the paradoxes. If there's a lack of science / math understanding, I'll point that out and do my best to correct the misunderstanding. If it's a semantics argument, I'll point that out too.

I realize that a lot of this is going to sound pretty snarky. And like I said, I have respect for philosophy as a means to sharpen logic and critical thinking. But I also hate it when people equate something scientific with something mystical or abstract. (I'm thinking mostly of brain twister #8. I did a facepalm as soon as I read that one. Basic misunderstanding of physics going on there.)

And yeah, it'll probably take a while for me to get through all of them. I'm not exactly regular about posting stufff...

(although as I have zero followers I don't think it's really an issue. If you've stumbled upon my blog, HI! leave a comment so I know my words aren't going into the great black hole of cyberspace.)

Pizza

Well it's Wednesday, which means that it is the Day of Great Decision
here at work.

First, we have to decide whether or not to get a "specialty" pizza (as
opposed to plain). This requires at least 3 people, preferably 4.
Often, there are several people in the "I'll get a specialty pizza if
there are enough people, but I'm not gonna be emphatic about it."
Which of course complicates matters. And then there are the guys who
might have brought lunch, but are willing to chip in for pizza and eat
the lunch they brought on Thursday. But only if the rest of us need
another person.

Then, if it's been decided to get a specialty pizza, we have to decide
which one to get. We've never had a bad pizza, so no one really wants
to choose because there isn't a lot of strong feeling about a "best"
or "worst" to get. (There's a lot of "Does this sound good to
everyone?" "Yup sounds fine." "Or how about this one?" "Also good."
in this round.) If someone who does not normally get specialty pizza
decides to try it, we make that person choose.

FINALLY, it's time for money collection. Pizza slices are $1.50 /
slice (plain) and $2 / slice (specialty). And there's always at least
one person who recently had to go to the ATM and hasn't bought
anything since then so all they have is twenties. So we have the
great "I'll pay for everyone's pizza with my $20 if everyone gives me
what they owe" finagling, with various people trying to trade money
amongst ourselves to get the correct change to give the guy who only
has $20's. My hand to God, one of my coworkers paid in dimes one
week.

And that's the news from your Friendly Neighborhood Engineers.

UPDATE 03/17/11
Bug has illustrated this beautifully. (This has fast become one of my favorite webcomics.)