Logical paradoxes and mindgames

[poxpower]

Ok so I was lookign for porn when I ACCIDENTALY stumbled on this site: http://www.logicalparadoxes.info/

Which contains a couple of paradoxes and mindgames and whatnot, I thought we could have a little fun with them.

Let's start with a first one, the "Theseus Ship" which states that if you replace the pieces of anything one by one, you'll always keep that thing throughout the exchange, even if at the end, you don't have a single piece of the original.
This is like ourselves. I probably don't have any of my original atoms right now. Yet, there is not a single atom that is me. Similarly, if you take all my original atoms, you won't get me. This is going a little bit further than the Theseus ship deal, because that's just a question of 'crossing the line' i.e. 'ok now it's not really his boat anymore' is purely suggestive.

But the fact that I am still me, is not.

So talk about that one, or any of the other ones, or bring new ones you find.

[Peter-II]

The problem of the specious present

This one's always interested me. It's a member of the problem of boundaries (i.e., precisely where is the line drawn between x and y), which seems to be seldom discussed. I've thought about this before, and have come to the conclusion that time is just a name given to how things happen by humans, meaning "time" as such doesn't exist. This would mean that the present is relative to what humans experience as the present. Thus, the present is the shortest amount of time in which a human can experience / notice something.

And by the way, the ship is what the ship is called.

[LazyPint]

Can either of you explain "The Unexpected Hanging"? I understood the rest (insofar as you can understand a paradox) but not that one. Any ideas?

[stafffighter]

It is pure hubris to think that time is an illusion. Simply put there's no need for an illusion. At one point an object is in one place and at another point it occpies a different spece. At one point something dosen't exist, at another it exists and then at yet another it does not.
If time were an illusion to prevent our collapse from not realizing the truth we would be obliterated by the truth we were blind to. However we can be obliterated by the time and place of people and things. . To put it even simpler, we're not so important existance needs to put on a show.

[SirLebowski]

I enjoy Achilles and the Tortoise because it reminded me of a math problem from Geometry.

[LazyPint]

At 3/12/07 05:34 PM, SirLebowski wrote: I enjoy Achilles and the Tortoise because it reminded me of a math problem from Geometry.

That one only applies if he's trying to catch the tortoise itself, surely? If it was just a straightforward race even with the tortoise's head start he would win, right?

Or does the whole problem hinge on them going at constant velocity?

I haven't done maths in ages...

[morefngdbs]

The arrow parodox
The problem I see with this & it may work for all the movement paradox problems is, simply a photograph of an arrow in flight or even a single frame from a motion picture of an arrow in flight .
Only captures the arrow for an instant of time in its flight.
The arrow takes a certain amount of time to go from point a, to point b.
IF we know the amount of time & for my purpose here lets call it 4 seconds.
If a camera is rolling & it captures the image of the arrow, still in the bow, the release and impact, at 24 frames per second there will be 96 still frames of the arrow in flight.
Each photo shows the arrow not moving, but look at each photo & compare it to the next .
It shows the arrow in each sequential frame to be farther from the bow & closer to the target.

SO the conclusion is the arrow is in a different place in each photo

So all a still shot of anything in motion shows is the moment the shutter opens to allow exposure of the subject.
Our eyes are fooled into believing we see motion by playing the recorded image back at a rate of speed that our brain converts to motion.
It all has to do with how our eyes see & how our brains 'read' the information it receives.
It is also why to view slow motion , the camera takes more frames per second.( it records the motion on lets say 1000 frames a second.
So on playback at 24 frames per second instead of a 4 second time frame for the arrow to go from bow to target, it takes over 2 & a half minutes .

So we can blame (if that is the right word) the eye & brain for this paradox.

[poxpower]

At 3/12/07 05:08 PM, Peter-II wrote: The problem of the specious present

I think some guy came up with the minimal amount of time that can exist, a "planck"? I think. Don't remember. Basically, he looked into that very paradox and just went "well if time divides infinitely in the physical world, it don't work :O"
So apparently, in the real world, time can't be cut up indefinately, as far as we know.

But in the "mind games" world, everything can be infinite, apparently :o

And by the way, the ship is what the ship is called.

yeah but you know what it means.

At 3/12/07 05:26 PM, LazyPint wrote: Can either of you explain "The Unexpected Hanging"? I understood the rest (insofar as you can understand a paradox) but not that one. Any ideas?

well the guy thinks he's smart because he figures he won't get hanged, because the judge said "you won't know what day you'll be hanged" i.e. if can't be the LAST day because then the guy would figure out that he was supposed to die on that day. Same with the 6th day, i.e. "if he won't kill me on the 7th for sure, then if I make it to day 6, it means he'll kill me then, but I'll know, so he won't" etc etc
So the guy figures he won't be hanged at all, and he thinks he's in the clear. But then they hang him anyways, which comes as a total surprise to him since he thought he had figured it out.

It's not a paradox in the REAL world, so maybe that's what confused you, because in the real world, it would all depend on how that prisoner thinks, but in theory, we assume that he's always thinking the most logical thing.

[Elfer]

The Theseus Ship is not a logical paradox, as can be seen on any given episode of Pimp My Ride.

[MortifiedPenguins]

Are you smoking again?

How about this, you exist, you influence your enviroment and you have among you people that love and respect you.

[poxpower]

At 3/12/07 07:08 PM, MortifiedPenguins wrote: How about this, you exist, you influence your enviroment and you have among you people that love and respect you.

Thanks, Plato.

[MortifiedPenguins]

At 3/12/07 07:16 PM, poxpower wrote:

At 3/12/07 07:08 PM, MortifiedPenguins wrote:

Thanks, Plato.

Well, I mean your arguing things that have little impact on reality, society, life or even of interest.

Who cares if the individual atoms that created you are no longer there, your the same person as you have always been.

The body is just a shell to the mind and memory.

[stafffighter]

At 3/12/07 07:22 PM, MortifiedPenguins wrote:

The body is just a shell to the mind and memory.

The atoms that makes the material of storage and process for the mind and memory change like all others.

[MortifiedPenguins]

At 3/12/07 07:25 PM, stafffighter wrote:

At 3/12/07 07:22 PM, MortifiedPenguins wrote:

The atoms that makes the material of storage and process for the mind and memory change like all others.

But do the memories. Once something happens, it can't be undone and it can only be forgotten.

[xscoot]

These paradoxes seem pretty good, but I have found a way to disprove all that I have read. Just ask me to disprove one and I will.

[poxpower]

At 3/12/07 08:01 PM, xscoot wrote: These paradoxes seem pretty good, but I have found a way to disprove all that I have read. Just ask me to disprove one and I will.

ok well explain the first one I talked about in this thread.
What truly constitutes human conscience?

[Peter-II]

At 3/12/07 05:32 PM, stafffighter wrote: It is pure hubris to think that time is an illusion. Simply put there's no need for an illusion. At one point an object is in one place and at another point it occpies a different spece. At one point something dosen't exist, at another it exists and then at yet another it does not.
If time were an illusion to prevent our collapse from not realizing the truth we would be obliterated by the truth we were blind to. However we can be obliterated by the time and place of people and things.

Were you responding to me? If so, I never said that time was an illusion, but rather a description of how things happen. So this would mean that time is relative to whatever a human can experience.

Still, if we take modern developments into account such as rapid movement of particles which we of course can't notice, then the present would last as long as the smallest amount of time which is necessary for something to happen.

To put it even simpler, we're not so important existance needs to put on a show.

Of course not.

[Elfer]

At 3/12/07 06:01 PM, poxpower wrote: I think some guy came up with the minimal amount of time that can exist, a "planck"? I think. Don't remember. Basically, he looked into that very paradox and just went "well if time divides infinitely in the physical world, it don't work :O"

That's not the minimal amount that can exist, just the minimal amount that can be talked about while still having any meaning as a measurement, because we measure stuff by bouncing photons off it, but you can only put so much energy into a photon before it creates a black hole when it hits something, which would swallow the photon and make it impossible to get the measurement.

Anything smaller than a Planck time has no meaning in terms of observation, but it might mean something in terms of interaction.

[poxpower]

At 3/13/07 07:18 PM, Elfer wrote:
Anything smaller than a Planck time has no meaning in terms of observation, but it might mean something in terms of interaction.

If something has no effect, and cannot be observed in any way, how does it exist?
In concept, time is infinitely divisible, of course, but in concept, I can grow a pair of giant testicles on my forehead and sail the milky way.
It's POSSIBLE, but not observed, or feasible within this reality... So maybe time cannot be divided infinitely in this reality either.

I can't say for sure, but, like I said: if something has no effect, it doesn't exist.

[stafffighter]

At 3/13/07 07:41 PM, poxpower wrote:

I can't say for sure, but, like I said: if something has no effect, it doesn't exist.

Well that would mean that ina sense time does not exist. Because while day and night and the lengths of each do occur in nature the system of numbers and dates exists soley for our benifit.

[poxpower]

At 3/13/07 07:51 PM, stafffighter wrote:

Well that would mean that ina sense time does not exist. Because while day and night and the lengths of each do occur in nature the system of numbers and dates exists soley for our benifit.

Well that depends on what time actually is and how it relates to other things...

I mean, is time just a measure of change? So like, if nothing changes, does that mean time has stopped? Or does time keep going to record that "nothing changed in the last 10 minutes" or something?
And if time stops, how long does it stop for?
:P

[stafffighter]

At 3/13/07 08:51 PM, poxpower wrote:

Well that depends on what time actually is and how it relates to other things..

It's 8:54. That means 6 minutes until House.

I mean, is time just a measure of change? So like, if nothing changes, does that mean time has stopped? Or does time keep going to record that "nothing changed in the last 10 minutes" or something?

Time happens wether you measure it or not. Things happen. It's the very nature of things. Without things and the happening of things to said things there is no existance to speak of

And if time stops, how long does it stop for?

P

Forever. Lack of molecular motion makes everything go boom

[Torso-Zombie]

The Barber is a simple one. He just hasn't ever been shaved by anyone.

[Altarus]

well?

[lapis]

At 3/14/07 04:48 AM, Altarus wrote: well?

kyaaaa

[Gunter45]

At 3/14/07 05:12 AM, lapis wrote:

At 3/14/07 04:48 AM, Altarus wrote: well?

kyaaaa

Yeah, seeing as how (-1)^-1 is just i, you really have to be stringent with it. There isn't as much leeway to monkey around with it as your formula suggests. For instance, you can't break an imaginary number up into seperate fractions. Really, the only way to work with it is to find an i^2. Of course, that's only what I'm taught in calculus, I'm not sure what's going on with number theory, I could be wrong.

[Altarus]

At 3/14/07 05:12 AM, lapis wrote:

At 3/14/07 04:48 AM, Altarus wrote: well?

kyaaaa

Hmm.. yeah. Dang, you are fast too. The funny thing is that lots of websites contain that paradox such as this one I found:

http://www.mathwords.com/s/square_root_rules.
htm

Even some school books seem to suggest it and a variant using logirithms are possible.

At 3/14/07 05:17 AM, Gunter45 wrote: Of course, that's only what I'm taught in calculus, I'm not sure what's going on with number theory, I could be wrong.

the complex numbers is just the set of ordered pairs of real numbers

..which is a MUCH better explanation than that other site which says "well it just isnt defined that way." It actually explains why those rules are false.

I am gonna post another math paradox if this thread is still alive when I get back..

[lapis]

At 3/14/07 05:44 AM, Altarus wrote: Dang, you are fast too.

Not that hard.

..which is a MUCH better explanation than that other site which says "well it just isnt defined that way." It actually explains why those rules are false.

Haha, well it's basically the same thing. If you regard a complex number as a mere 2-dimensional vector then you can't multiply (a,b) and (c,d) using the standard definition because of a dimension conflict so you define a set of operations such as the multiplication, division and power...taking or whatever they're called in English and conclude that you can write (-1)^(1/2) this way as (0,1) because (0,1)*(0,1) then equals (-1,0). However, even though it's a convenient way to obtain an expression for sqrt(-1) and a set of rules to work with the thing, (a/b)^(1/2) = ((a)^(1/2))/((b)^(1/2)) won't hold when a*b<0 under these definitions while it does when a is non-negative and b is positive.

You can't apply all standard rules for real numbers to complex numbers because of the definition of the complex number so "it's not defined that way" is a proper answer, but I personally don't really think that the real number pair explanation as given in your link really makes clear why the formula above doesn't hold, although it does explain why a complex number can't always be treated like a real number (then again, so does a simple "sqrt(-1) doesn't exist in the real world so be careful when you use it").

[morefngdbs]

At 3/13/07 09:03 PM, Torso-Zombie wrote: The Barber is a simple one. He just hasn't ever been shaved by anyone.

;
The answer The Barber doesn't shave is one possibilty.
Another is the Barber suffers from severe alopecia, because of this the Barber doesn't need to be shaved.

[poxpower]

At 3/14/07 01:03 PM, morefngdbs wrote:

The answer The Barber doesn't shave is one possibilty.
Another is the Barber suffers from severe alopecia, because of this the Barber doesn't need to be shaved.

look the point is not to find a stupid loophole like 'he's 5 years old' or some shit.

He has a beard that must be cut.
There is no answer, the statement is simply FALSE. It's not true that there is a barber who cuts everyone's beard as long as they don't do it themselves. Not possible.