Math and Logic Errors

[HereBeforeCoachK]

QUE? Society does not exit.

It did in Old Phi Kap's equation...upon which I based my equation. And BTW, the logic of my equation is sound whether society exists...

[OldPhiKap]

It did in Old Phi Kap's equation...upon which I based my equation. And BTW, the logic of my equation is sound whether society exists...

To be fair, my logic is very non-Euclidean.

[tteettimes]

To be fair, my logic is very non-Euclidean.

Apparently mine is excludian

[Jeffrey]

(Boy, this kind of logic will give you Brain Damage).

It's just another brick in the wall.

[swood1000]

UNC sucks.
Vacuums suck.

UNC is a vacuum.


Intellectually, true. Literally, not really.

Cats have fur.
Dogs have fur.
∴ Cats are dogs.

[RPS]

That's an unfair coin, right there.

Probably. But it is no more or less likely than any other combination of 1,000 tosses.

[RPS]

Not to derail things, but does anyone else feel he deserves more minutes?

K won't ever extend his bench.

[Bostondevil]

Probably. But it is no more or less likely than any other combination of 1,000 tosses.

No - it's much less likely than all but one other combinations (all heads or all tails being equally likely). It has the same probability of any other exact sequence of 1,000 tosses. But even then, I wonder if "time to first toss that turns up tails" could be modeled with a poisson distribution. Surely after a thousand tosses that turn up heads, any statistician looking at the problem would begin to suspect an unfair coin. I wonder what the break point is - how many heads in a row does it take for a statistician to start questioning the fairness of the coin? If something important to two opposing side depended on the outcome, I would discard the coin long before 1,000 tosses, that's for sure. So - in theory your conjecture is true - in practice, we would never get there.

[crimsondevil]

No - it's much less likely than all but one other combinations (all heads or all tails being equally likely). It has the same probability of any other exact sequence of 1,000 tosses. But even then, I wonder if "time to first toss that turns up tails" could be modeled with a poisson distribution. Surely after a thousand tosses that turn up heads, any statistician looking at the problem would begin to suspect an unfair coin. I wonder what the break point is - how many heads in a row does it take for a statistician to start questioning the fairness of the coin? If something important to two opposing side depended on the outcome, I would discard the coin long before 1,000 tosses, that's for sure. So - in theory your conjecture is true - in practice, we would never get there.

Well, let's see - the probability for 5 heads is about 3%, so that passes the p < 0.05 threshold. At 7 heads, you're at 0.7%, so that's below p < 0.01 - two asterisks in a scientific article(!) Depends how many coins you plan to test, though...

[crimsondevil]

The "exception that proves the rule" phrase is nearly always misused. People use it as a cliche to trivialize a counterexample. Guess what? The counterexample doesn't just disappear in a puff of smoke.

The proper usage of the phrase is in noting that a specific exception that one has made is an indication that a rule exists; one wouldn't have to make an exception if one didn't first have the rule. The proof is not of the truth of the content of a rule but rather its existence.

Example: The medical hardship redshirt option (or whatever the proper term is) so long as the player has played fewer than a certain percentage of games that season. It is an exception that, by its existence, shows the existence of a rule that normally eliminates the redshirt option once someone plays any minutes at all.

There are circumstances in which a general rule might not be formally or explicitly stated and therefore the exception is useful to infer its existence.

Yes, exactly. The phrase makes no sense the way it's almost always used.

[RPS]

No - it's much less likely than all but one other combinations (all heads or all tails being equally likely). It has the same probability of any other exact sequence of 1,000 tosses.

That's what I thought I said, but your iteration is better.

But even then, I wonder if "time to first toss that turns up tails" could be modeled with a poisson distribution. Surely after a thousand tosses that turn up heads, any statistician looking at the problem would begin to suspect an unfair coin. I wonder what the break point is - how many heads in a row does it take for a statistician to start questioning the fairness of the coin? If something important to two opposing side depended on the outcome, I would discard the coin long before 1,000 tosses, that's for sure. So - in theory your conjecture is true - in practice, we would never get there.

The opening scene in Tom Stoppard's play (later a movie -- see below), Rosencrantz and Guildenstern Are Dead, deals with this conundrum (and more).

[OldPhiKap]

That's what I thought I said, but your iteration is better.

The opening scene in Tom Stoppard's play (later a movie -- see below), Rosencrantz and Guildenstern Are Dead, deals with this conundrum (and more).

I absolutely LOVE that movie. Except for Richard Dreyfuss, who has always irked me in some indescribable subconscious way.

[RPS]

I absolutely LOVE that movie. Except for Richard Dreyfuss, who has always irked me in some indescribable subconscious way.

I love it too. I also love the play, which works especially well at a Shakespeare festival in rotation with Hamlet and with overlapping casts.