The fact that humans collectively have survived for centuries does imply that every human has been around for centuries.

Here's a mathematical one:

e = e^1 = e^( (i*2*pi) / (i*2*pi) ) = ( e^(i*2*pi) )^(1/(i*2*pi)) = 1^(1/(i*2*pi)) = 1

Maybe think of it this way... buoyancy is all about the displacement of fluid attempting to find the lowest potential energy state. Since the wheel is fixed on and symmetric about it's axle, any rotation of the wheel doesn't change any of the displacement of the fluids (except for minor turbulent perturbations). So, buoyancy will not cause the wheel to spin since it does not reduce any potential energy.

whoops, I meant to say two posts ago "does NOT imply"

@yebellz: A very elegant explanation - thank you!

This isn't really a fallacy, but it's an interesting puzzle. A spider in one corner of a cubic box wants to find the shortest route to walk to the opposite corner. He can't fly or jump! What route does he take?

@FatherSnitch, the spider moves diagonal across the walls. Simple trig proves that one.

Can he use a string of silk between the opposite corners? If so, then it is a sqrt(3)*L path direct from corner to corner. If he must walk along the inside of the box on the walls, then he should walk diagonally along a face of the cube such that he reaches the edge joining that face to the next at it's mid-way point. Then he should continue along that next face to the corner taking a similar diagonal path. The overall path would be of length sqrt(5)*L, where L is the length of a side of the cube.

Is any one going to address my mathematical fallacy?

More specifically, he would leave his corner and walk to the midpoint of either of the two seams between him and the other corner, then continue from said midpoint of seem to the other corner. In effect, it is a straight line when the box is unfolded.

The spider one was clearly too easy! This one may be no more difficult: what household object casts triangular, circular and rectangular shadows along orthogonal axes?

"The fact that humans collectively have survived for centuries does [not] imply that every human has been around for centuries."

The point isn't to say that the premises don't imply the conclusion... I've already told you that!

"Maybe think of it this way... buoyancy is all about the displacement of fluid attempting to find the lowest potential energy state. Since the wheel is fixed on and symmetric about it's axle, any rotation of the wheel doesn't change any of the displacement of the fluids (except for minor turbulent perturbations). So, buoyancy will not cause the wheel to spin since it does not reduce any potential energy"

That is true, but it doesn't explain the flaw in the reasoning that says that it should rotate indefinitely. Also, the "attempting to find" bit is not really modern physics...you are begging the question, "why doesn't a piece of toast "jump" off the table to find the lowest possible energy state?"

So, what exactly do you want us to say about the "humans and Bob" example?

Still no one has addressed this one:

e = e^1 = e^( (i*2*pi) / (i*2*pi) ) = ( e^(i*2*pi) )^(1/(i*2*pi)) = 1^(1/(i*2*pi)) = 1

The point is to name the logical fallacy, not to see where the error is (that bit is too easy)

It was actually just another example I was giving of the fallacy of division.

@yebells: How do you go from step 3 to 4?

Right, a^(b*c) = (a^b)^c certainly holds for real numbers, but does not necessarily hold for complex numbers.

@Ghost: Oh I see what you mean. The humans/Bob example is quite trivial anyways, but I guess you wanted us to be a little more formal about it. The logical fallacy is in taking that the given "Humans have survived for centuries" implies that all humans have survived for centuries. This is because the given basically says that there exist some humans that were around centuries ago, but it does not imply that all humans have been around centuries ago. Bob is a human, but since our given does not imply that all humans have been around for centuries, we cannot conclude that he has survived for centuries. Is that better?

I thought it had something to do with that pesky complex number in there... But really, I couldn't have figured that out. You didn't have to give it away. The logical fallacy there was... generalization? A false assumption?

This fallacy has a specific scientific phrase attached to it. Give me the phrase.

A doctor examines some patients of his who smoke regularly. He learns that many of them have lung problems and cough a lot, and he sees that many of them also have yellow stains on their fingers. He thus concludes that yellow stains on one's fingers cause lung problems.

"cum hoc ergo propter hoc" would be the name of the fallacy, commonly expressed as correlation does not imply causation.

"@Ghost: Oh I see what you mean. The humans/Bob example is quite trivial anyways, but I guess you wanted us to be a little more formal about it. The logical fallacy is in taking that the given "Humans have survived for centuries" implies that all humans have survived for centuries. This is because the given basically says that there exist some humans that were around centuries ago, but it does not imply that all humans have been around centuries ago. Bob is a human, but since our given does not imply that all humans have been around for centuries, we cannot conclude that he has survived for centuries. Is that better?"

Yeh. I'm a bit of a nerd, so I would be giving the name of the fallacy etc. :P

All doctors are selfish. If yours really did give up all that time for no pay, there must have been some hidden gain we don't know about.


(Note: an informal fallacy)

"I mount a solid iron wheel, the axle of which is embedded in a slot in a dividing wall. On one side of the wall, the iron wheel rests in a tank of water. On the other side, the iron wheel rests in a tank of mercury. Since iron is denser than water, the half that lies in the water tends to sink; the half that lies in the mercury tends to float (mercury being denser than iron). Each half of the iron wheel therefore produces a complementary turning moment which causes the wheel to turn perpetually."

Solution:

Buoyancy is actually the sum of pressures, and only applies under certain conditions. In this case, the rim of the wheel has forces either directly along the radius (so not causing a torque) or else still in the plane of the radius which is perpendicular to the plane of the wheel. Thus there is no torque, once again.

actually, that is only a partial solution. That doesn't explain away axles.

*spokes

New fallacy search:
I'm walking along with a friend in the safest town ever, and we find a dead guy on the sidewalk.
I say to my friend, "He was murdered!"
My friend replies, "No, he wasn't."
"What? He's got knife sticking out his back!"
"So?"
"The back of his skull is bashed in!"
"Maybe he tripped on something and fell down backwards, hitting his head on the curb and falling on a knife."
"THERE ARE BULLET HOLES IN HIS BACK!"
"It still wasn't a murder."
"ARE YOU NUTS!?"
"I'm being rational. There has never been a murder in this town, this town simply doesn't have them. Therefore, this cannot be a murder."
"Despite all appearances? Despite the fact his HANDS ARE MISSING?"
"Yep."

fallacy is that there is a first time for everything.

yep. so blinding obvious too, I suspect my friend did not want to come to terms with reality, so he came up with that line of thought (it would lower property values, I suppose)

It's apriorism. Normally we allow evidence to be the test of our hypothesis, not our hypothesis to be the test of our evidence.