The most obvious thing is that you assume the scientific calorie and the colloquial "calorie" are the same thing. The latter is actually a kilocalorie, so you lose 37 calories while gaining 10,000 calories, for a net gain of 9,963 calories.

Yup - it's an ambiguity or equivocation.

I'll take advantage of the fact that TBroadley hasn't providing a new fallacy by providing one of my own:

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.

Assume an ideal system, i.e. no friction, no leakage between tanks etc.

Is the definition of the calorie really well known outside the circles of middle aged dieting women? I was thinking along the lines that it assumes the ice cream taking heat from the body forces the body to do more work to replace it. A lot of the time the body is working hard to get rid of excess heat and the addition of some coolant may well reduce the amount of work the body has to do to maintain a constant temperature.

Lets talk for a bit about the universe.

If you were to build a telescope in the UK and point it straight up it is possible to observe via their redshift that almost galaxies lying in that direction are moving away from the Earth. If you were to do the same in Australia, Canada, China, Russia, Argentina, or indeed any other country in the world, you will observe the same thing. Combine this with the knowledge that all matter in the universe originated in the big bang and it is clear that the Earth must therefore be either at, or at least close to, the very centre of the universe.

@Octavious, your answer is incorrect, see TBroadley's.

Although it is true that the body does generate excess heat at least some of the time, the argument is *always* wrong.

The fallacy in yours Octavious is simply an assumed, incorrect premise: that to have all objects moving away from you means that you are near the centre of an explosion.

The perpetual motion machine is strangely convincing :P

So, just to be clear on the original, it's wrong because you used a different calorie to the one you defined?

The two uses of calorie mean different things, and the use is ambiguous.

No wonder dieting middle aged women look so confused! They should use joules like everyone else! :p

@FatherSnitch - the wheel can neither sink or fall as it is mounted on the axle, fixed to the wall.

I have no fallacy. I am tired and wish not to think.

@FatherSnitch: How could there be no friction if the wheel is embedded in a slot? The wheel would run against the end of the slot

frictionless surface- it is an idealised system, but it would be possible to imagine using teflon to reduce friction to the point where the supposed acceleration is greater than the friction.

The failures of perpetual motion machines are not ignoring friction, but rather thinking that there could be a perpetual acceleration. They are perpetual motion rather than perpetual acceleration machines precisely because of the frictions involved.

Welsh speakers are disappearing. Dafydd Williams is a Welsh speaker, therefore Dafydd Williams is disappearing

Note: this one is only worth doing as a *name the fallacy*- the error is obvious.

On an side note, is floating even possible without friction?

buoyancy is not equivalent to friction.

Strongly related, surely?

not really, tbh.

Consider a block of wood floating in the water. If you push it in direction x it will move that way and be slowed by friction with the water. Try to imagine how the wood can interact with the water in such a way that friction is zero. It can't be done

It is impossible for a stationary fluid of even pressure as described to prevent an object from moving, it can only slow it down.

re: Welsh speakers: Hasty generalization/specification is what I'd call that. What say you?

@FatherSnitch: It slipped my mind to post a new one.

Hmm... all I can think of is that the friction of the wheel in the mercury is higher than the friction in the water, and so would slow down the wheel even though the forces acting on them reinforce themselves. Is this close?

@Fathersnitch - and fellow answerers - the fallacy is the wheel is not falling or floating - it is resting on an axle. it would only be given a force to spin if is were truly falling - but the force of gravity is being opposed by the axle, and the water/mercury is irrelevant. There is no unopposed force in the system.

Also - you could do away with the friction element with a magnetically levitated axle.

If so, here is another fallacy, this time mathematical:

x=y
x^2=xy
x^2-y^2=xy-y^2
(x+y)(x-y)=y(x-y)
x+y=y
2y=y
2=1

@Tbroadley: I forget which step, but at some point you divide by 0.

It's at (x+y)(x-y)=y(x-y). You can't factor out zero.

Yep. Between step 4 and 5, I divide by x-y. Since x=y, this must equal 0.

"re: Welsh speakers: Hasty generalization/specification is what I'd call that. What say you?"

It's the fallacy of division. Just because something is happening to the class of things A doesn't mean that it is happening to the individual members of the class.

Humans have survived for centuries, Bob is a human, therefore Bob has survived for centuries.