This Sentance Is False!!!

ok, so i have never posted anything on here yet so i hope i am doing this right. but you guys who like these things, you should go to the website www.thisisbroken.com it has some really funny things on it.
lindsey

“This sentence is false” is called Eubulides Paradox. Others include the Liar’s Paradox, “I am lying”, and Socrates’ Paradox, “one thing I know is that I know nothing.”

A related and even more confounding subject is mathematical completeness and consistency. “This statement can not be proven or refuted” can neither be proven nor refuted in any consistent mathematical theory (i.e. a theory without contradictions). Kurt Goedel is the mathematician who formalized this statement, and also proved that a mathematical theory that can prove its own consistency, is necessarily inconsistent.

This is deep stuff and it can take a while to really get it. Douglas R. Hofstadter wrote a book called “Goedel, Escher, Bach: An Eternal Golden Braid” that uses lots of clever example to discuss incompleteness. Good reading if you want to pursue the subject. A puzzle filled approach to Goedel’s theorem is Raymond Smullyan’s “The Lady or the Tiger? And Other Logic Puzzles.” These are fun books, not dry textbooks, so if you are interested in paradoxes you may enjoy them.

One of Smullyan’s books (maybe the one mentioned above) examines Epimenides Paradox in great detail. Epimenides is quotes as having said, “All Cretans are liars…One of their own poets has said so.” He poses logical puzzles set on an island in which half of the inhabitants always tell the truth and half always lie. I actually thought about bringing up these puzzles in another thread, but sometimes discression is the better partof valor.

Ken

I personnally hate those little keychains with stupid bumpersticker-like catchphrases, like “All men are created eaqual, too bad.” They piss me off so in a hypocritical fasion i thought up this keychain:

“Don’t take advice from keychains”

Its somewhat aparadoxal, I think…

Quantum Mechanics. If it doesn’t seem absolutely wrong to you, then you haven’t understood it yet.

I always thought Godels (with an umlaut, of course:) ) theorem stated that it is impossible to create a system of math that does not allow for imaginary numbers, etc.

My favorite non-paradox has to do with perpetual motion. This one is fun to figure out why it doesn’t work. BTW, you can assume you can convert matter and energy with 100% efficiency every time (and vice versa).

You take a block of lead and you drop it off of a skyscraper. Before it hits the ground, you convert it to a single ultra-high energy gamma ray, and reflect the gamma ray back up to the top of the skyscraper, where it is then immediately converted back into a block of lead, and the cycle repeats.

This seems to be in violation of thermodynamics, except for a small part of relativity. If it helps, you could ask: Does a clock on the top of a skyscraper run at the exact same rate as a clock on the bottom? Also, why does all light approaching the event horizon of a black hole become infinitely blueshifted? Finally, what happens to light as it climbs away from a black hole? Does it redshift or blueshift? (By the way, a blueshift in light means that the frequency of the waves increases, and they carry more energy. A redshift is the exact opposite)

A friend of mine went to Canada and saw a sign that said
Caution: Public Notice.

Care to explain that one…?

There is one of those I like that was on a lighter at spencers.“Heaven wont take me and hell is to afraid I’d take over”

It’s true. Public notice all sorts of stuff…

I think the solution is: the ray is coming from the block of lead that is moving away from the top of the skyscraper. Therefore it arrives there redshifted and the energy is decreased correspondingly.

That explains how you do not gain energy. But if you assume 100% efficiency in all steps in a process, perpetual motion (with zero energy gain, just continuation of something) is easily achieved.

Klaas Bil

Imaginary numbers aren’t necessary for a consistent theory. The only numbers used or assumed in Goedel’s theorem are natural numbers (0,1,2 …), which are used to number formulas in the target theory.

You lost me here. You can’t conserve both energy and momentum with this conversion. The block’s momentum equals its energy (E) divided by velocity, but the photon’s momentum is E/c, where c is the speed of light. The block is falling at much less than the speed of light, so momentum isn’t conserved. Conservation of momentum is a fundamental property of physics, so your assumption is invalid.

That’s as far as I got.

Ken

I don’t exist.

It is wrong to be intolerant of people who tolerate intolerance. :astonished:

~Cameron

I think you guys all need to shut-up for a minute. :stuck_out_tongue:

you silly people you… asking questions that lead to no results… PFFF! AS if that ever lead to anything.

Puzzle…

An adventurer exploring mysterious lost jungles is captured by a mysterious lost tribe. Their chief decides he doesn’t like mysterious lost adventurers, so tells the adventurer he is to be put to death one of two ways.

The chief tells the adventurer, “You may make one statement. If it is true, you will be thrown off the highest cliff; if it is false you will be fed to the lions.”

The adventurer uses all his training as a lawyer to thoroughly annoy the local populace by finding the loophole in the arrangement and coming up with a statement that gets him off the hook. What was it?

Phil

How about “I will be fed to the lions?”

The rest of this post intentionally left blank.

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dang john your smart!

I hate biased people. they make me mad and should all be exterminated.

Oh, by the way, “beware the sharp corners on this sign”

you dont see this

Darn, I came up with “I will not be thrown off the highest cliff”.

Yours is simpler. But both answers are right.

juice from concentrate still counts as juice, however, even with this very leanient definition, many “juices” still are not a very high percentage of juice.

:slight_smile:

lets see, self contradictory statements…

…I can’t think of one right now. :astonished:

They may be complying with the labeling laws, by listing the ingredients of the actual juice. 100% fruit juice is probably at least 50% water…