Paradoxes: temporal, logical and otherwise.

[lacktheknack]

Zeno's Paradox

Beautifully concise and seemingly impenetrable.

Except that eventually, the turtle will not have moved far enough that Achilles can run past in one stride. It's overcoming the paradox through sheer literalism.

 

[man-man]

Finite number lines proving infinite number series? You've got more chance dividing by zero.

It's assumed for ease - it's a working theoreum, not a proof.

If they're different numbers, prove it. Show me the maths that demonstrates 0.9 recurring and 1 to be distinct numbers (rather than making irrelevant comparison to dividing by zero) and I'll happily concede the point having learned something new.

I've shown my working, where's yours?

As for

Saying that, integers are completely unreal anyway.

You're just trying to sound smart by being dismissive aren't you. Don't be ashamed, lots of people do it, hell, I'm doing it right now.

You might take issue with the relation between numbers (be they real, integral, irrational or imaginary) and the real world, but 0.9 recurring equalling one is not something with a parallel in the real world, just a question about numbers, so what exactly do you propose to use to talk about said question if numbers are "unreal"?

(That said, f you have a non-numeric proof that 0.9 recurring is distinct from 1, I'd be just as happy to pour scorn on that)

 

[lacktheknack]

The computer will just be like 'You can't do that, eejit.' And ignore you for being an eejit. It's like when people say typing google into google will break the internet. No it won't.

Have you ever heard of sarcasm you stupid fuck?

Ever heard of tact? You'd better edit this before bannification occurs.

 

[gibboss28]

I like this one

 

[AngryMongoose]

You're just trying to sound smart by being dismissive aren't you. Don't be ashamed, lots of people do it, hell, I'm doing it right now.

I think we might have just been trolled. Hell, just look at the guys name.

 

[Maze1125]

Finite number lines proving infinite number series?

That's a meaningless string of words.

0.999... is defined to be a particular infinite series.
That infinite series is geometric and can easily be proven to be equal to 1 using the geometric series theorems.

Here's [http://www.escapistmagazine.com/forums/read/18.85789-Interesting-fact-0-999-1] my old thread on the matter.

 

[krugerrand123]

if there is armor that no bullet can pierce but there is a bullet that can go through anything, what happens when that bullet is shot at that armor.

 

[Adventurer2626]

For my fave paradox, I would have to go with my take on the Time Travel Paradox.

Spoiler: Before I saw DVSAurion's post

Unfortunately it only accounts for willful travel into the past. When a person travels back in time on purpose they have an intention for doing so whether it be stopping an event from occurring or just for the experience. By traveling back in time you at the least fulfill the purpose of traveling to the past. However, you fulfill the purpose before it's conception and so prevent yourself from conceiving the purpose due to its already being completed. With no purpose, you no longer have a need to go back in time and so don't go back in time to complete your now non-existent purpose.

Traveling backwards in time is my favorite.

Asuming that time is linear (and that time travel is possible), traveling back in time is a bit of a mind fuck. Because if you go back in time to do something, there won't be a reason for you to go back in time when you did because there is you already did what you did. So whatever you have done will not happen because it happened. Kinda. Confusing stuff.

This is of course all moot because our perception of time as a linear distance which the universe travels = false. The past does not exist as a separate reality; the present is the same matter that existed in the "past." It's just been moved around. Take a ball and throw it across the room. It's the same ball you had when you threw it. To "travel into the past" you would need a machine strong enough to rearrange ALL of the particles into the universe back to their configuration at the "time" of interest. A) Have fun designing and building said machine and B) good luck creating the extra matter for the machine since it would not be the "past" without the matter used to build the machine.

 

[C95J]

Zeno's Paradox

Beautifully concise and seemingly impenetrable.

I cry bullshit. This is silly. You can quite clearly tell it is bullshit: by panel 5, Achilles is seemingly beside the Tortoise. He can therefore just step over it, BAM, silly paradox destroyed. However far ahead the tortoise starts, this will always be the case. Unless you split silly hairs by saying that the person would get tired eventually yadda yadda yadda.

I feel like you're missing the point, Most paradox don't exist in the real world but on paper they are unassailable.
For example to take this one a bit further, one could argue that it is impossible for an object to move in space. Why? Because within the smallest unit of space imaginable, there is contained an infinit amount of space. Nothing can ever cross an infinit amount of space, hence movement is imposible. I challenge anyone to find a flaw in that logic, and yet we move around without any difficulty at all...........And that's a paradox.
I think so anyway, correct me if i'm wrong.

this guy is right, at first I didn't believe it, then I read a web page about it, and now this new paradox he has said explained it all for me, good logic right there.

 

[Lesd3vil]

Here's an interesting one for you.

Just over every 1,000 miles west from where you are, the time is an hour earlier than it is where you start; Therefore, surely if you travel around 1,050 mph west, the time will steadily get earlier as you go. Logically speaking, if you keep going for 25,000 miles, you'd arrive where you started just before you set off...

 

[smashmaniac64]

Sorry i just had to

dammit ninja'd >_<

 

[Maze1125]

Here's an interesting one for you.

Just over every 1,000 miles west from where you are, the time is an hour earlier than it is where you start; Therefore, surely if you travel around 1,050 mph west, the time will steadily get earlier as you go. Logically speaking, if you keep going for 25,000 miles, you'd arrive where you started just before you set off...

That's where the international date line comes in. Once you pass that, going west, you jump ahead a day.

 

[The_root_of_all_evil]

Right...first a qualifier. I've done this stuff at degree level. I do know what I'm talking about.

Yes they do. As you go into infinite detail, your number gets infinitely close. If somethign is infinitely close to something, the distance is zero.

Ok, you can't define infinitely close as 0 without creating a paradox. It's close to 0, but it's not equal to 0.

Except that eventually, the turtle will not have moved far enough that Achilles can run past in one stride. It's overcoming the paradox through sheer literalism.

That's the point of the paradox. It's the same as the proof that Bumblebees can't fly. Mathematics breaks down because it can only measure finite space. Infinite space - whether large or small - breaks mathematics.
Achilles strides aren't being measured here. It's the distance he travels, rather than the amount of distance he can travel.

If they're different numbers, prove it.

Easily. 0.99999 recurring < 1.

Show me the maths that demonstrates 0.9 recurring and 1 to be distinct numbers (rather than making irrelevant comparison to dividing by zero) and I'll happily concede the point having learned something new.

Ah, now here's the rub. Mathematics (Statistical/Mechanical) says they are. Mathematics (Pure) says they are indistinguishable. Difference is slight but there. Mathematics own rules defy itself on that. (And many other points)

I've shown my working, where's yours?

X/X >< 1 for values of X=0

You're just trying to sound smart by being dismissive aren't you.

Nope, I actually studied this for four years. Smart doesn't come into it.

but 0.9 recurring equalling one is not something with a parallel in the real world, just a question about numbers, so what exactly do you propose to use to talk about said question if numbers are "unreal"?

1 doesn't exist either. You can't have 1 of anything unless you specifically define it as the singular object of something I've just designated.

If I have two apples, and I take a bite out of one - I still have two apples : despite them having nothing in common apart from their names.

Finite measurement versus Infinite divergence.

We created the numberline (and numbers in general) to simplify images, not to measure accurately - mainly because, as Einstein said, there's no way to have a fixed point in space - so all measurement is useless.

(That said, f you have a non-numeric proof that 0.9 recurring is distinct from 1, I'd be just as happy to pour scorn on that)

Pouring scorn isn't really what we're here for I thought, but if you insist:

A proof that has been put forward for 1 = 0.999, as follows:

x = 0.999...

10x = 9.999...

10x &#8722; x = 9.999... &#8722; 0.999...

9x = 9

x = 1

In the 4th line of the proof we see that from the RHS: 9.999...-0.999... = 9. This is not the case. While it is true that the number of 9s after the decimal point is infinite, it is neither sufficient or trivial to assume this step. For example:

Take an infinitely long integer consisting exclusively of 9s, call this number A. Take second infinitely long integer also consisting exclusively of 9s and call this number B.

A - B = 0

If and only if the number of digits in A and B are the same. Since x has been multiplied by 10, its infinite number of 9s after the decimal point is one less than in x by definition. It is not sufficient either to say that there are an infinite number of 9s after the decimal place therefore it does not matter, irrespective of whether the repetition is finite or not, the number of digits does need to be the same, and as Mathematicians know, not all infinities are the same. Therefore the 4th line should say:

9x = 9 - d

Where d is an infinitesimally small number which is strictly non-zero but limited by zero.

The radix system, which most people use, due to the usual Euclidian way of measurement sets .9 recurring equal to 1, but only because the radix system doesn't represent numbers uniquely. It terminates at a set finite point on the assumption that an infinitely small differential will have no finite difference the two values - however, it will have an infinite difference which is not accounted for. That's what comes from numerical methods.

Or in Physics speak : Measure with a micrometer, mark with chalk, cut with an axe.

Finite number lines proving infinite number series?

That's a meaningless string of words.

No it isn't. "Deadbody Freezerbox Telephone" is.

 

[Carboncrown]

I think OP's pic is overthinking, the rope is sraight. I doesn't become any longer, just because it looks that way if you look into the portal. It's space being bent, not the rope.

Turtles all the way down.

Or - the Unmoved Mover. Aristotle's philosophy on how the world was set into motion. Goes like this:

1.There exists movement in the world.
2.Things that move were set into motion by something else.
3.If everything that moves were caused to move by something else, there would be an infinite chain of causes. This can't happen.
4.Thus, there must have been something that caused the first movement.
5.From 3, this first cause cannot itself have been moved.
6.From 4, there must be an unmoved mover.

The question is - can there be?

ah good old prime mover, always nice to give the religous folk a fighting chance

*cough*Hawking*cough*

 

[HK_01]

*snip*

Somehow, I'm tempted to trust everyone else on this one rather than one person claiming to have done this at degree level (whatever degree that might be). Nothing against you, but you just can't trust people on internet forums, therefore I'm going to believe what I was taught in school, can read on Wikipedia, etc until you actually prove something. Maybe I'm just too stupid to comprehend (most likely, acutally), but I don't get your "proof", while I have no problem understanding the proof of .9 recurring equaling 1.

As for the turtle paradox, you're just constantly measuring increasingly small units, that's how it works. If you keep the units of distance and time the same, no paradox!

 

[Anchupom]

On the Achilles paradox, it is sound logically though of course it is not practically.

Take example:
Usain bolt sprints at a speed of 10m/s
I walk at 1m/s.

I walk away from Usain for 10 seconds, he starts sprinting toward me.
In the one second it takes him to cover the ten metres I already walked, I have walked another one metre.

It then takes him a tenth of a second to make up that metre, but I have travelled another tenth of a metre beyond that.

He travels that tenth of a metre in one hundredth of a second, and I've moved forward a thousandth of metre beyond that.

Mathematically speaking, this can recur infinitely.

Of course, if Usain Bolt sprinted towards you, he would overtake you in seconds.
Mathematically, it can't happen. Yet you know it does.
Ergo, it's a paradox.

Terminators, too.
If they succeed in killing John/Sarah Connor, they are most likely never to be created with that purpose, so they were never sent to kill him, so he survives, so they ARE constructed, yadda yadda yadda.
Or alternatively, if they weren't sent back, would they need to be? First movie, someone was sent back to protect Sarah from a Terminator. If that terminator was never sent back, neither would John's father, meaning they wouldn't need to be sent.

My personal favourite paradox is wondering if you are self-aware. At first, it seems like more of a stupid question, but it opens your thought to the "Matrix" way of thinking. Is this the purest level of reality (or in this case cognitive awareness)? As soon as you do that, you are heightening your self awareness and proving there is another layer.
Lather, rinse, repeat until head explodes.
Also, on the subject of the matrix, is it a piece of fiction, or the truth disguised as fiction to stop us from breaking down our fabricated reality?


I like this topic.

 

[Gooseboy]

Anyone said the whole Divide by 0 thing?
Not exactly a paradox but if you have a calculator it is fun to see it's reaction.

 

[Marsell]

God is to Humans,
What color is to blind people.
Well OK thats not much of a paradox.

 

[The_root_of_all_evil]

*snip*

Somehow, I'm tempted to trust everyone else on this one rather than one person claiming to have done this at degree level (whatever degree that might be).

But you'll trust wikipedia? C'mon man...

Nothing against you, but you just can't trust people on internet forums

No offence taken. I know I'm telling the truth (Bsc Hons. Software Engineeering btw), but you don't. Seriously though, don't believe Wiki or School though, they'll tell you there's such a thing as a solid and not something that's 99% free space held together by VdW forces.

Maybe I'm just too stupid to comprehend (most likely, acutally), but I don't get your "proof", while I have no problem understanding the proof of .9 recurring equaling 1.

Nothing to do with smartness, but I'll try another disproof anyway.

Ok. Let's say .9 recurring = 1

That means that the .0 recurring 1 = 0

That means 10 times .0 recurring 1 = 0

That means X times .0 recurring 1 = 0

Now 1 + N times .0 recurring 1 = 2 (Basic addition)

So 1 + 0 = 2

So 1=2

QED

 

[Jason Danger Keyes]

Pinocchio: "My nose will now grow"