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/sci/ - Science & Math

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1910831 No.1910831 [Reply] [Original]

Does /sci/ like paradoxes?

Of course /sci/ does.

http://listverse.com/2010/05/28/11-brain-twisting-paradoxes/

>> No.1910873

Reading 9 atm. 10 shouldn't be on that list. sorite's is a faggot

>> No.1910872

"God made me an atheist, who are you question his judgement." ~OC

>> No.1910906

Most of these are stupid.

For example, the one about the Creten who called all cretens liars. Even taking this absurdly literally like all of these instances do, he could be lying like this: perhaps not all cretens are liars, but he is one.

>> No.1910964

#11:valid but pointless
#10: "Heap" isn't meant to be an objective definition, it's an arbitrary term used to describe a large number of, and it's entirely subjective.
#9: is not valid. if there is no such thing as a non-interesting number then the term non interesting number is no longer valid either. The concept doesn't need to exist.
#8:invalid. Time is not atomic; it cannot be divided into instants.
#7:invalid, reason given on page
#6: how is this a paradox?
#5:the paradox is valid, the example is not; judges are perfectly logical, the judge probably made a mistake. Also, if the prisoner expected the hanging not to occur for the reason he gave it could happen at any time and be unexpected.
#4:valid
#3:valid
#2:valid, invalid example
#1:valid but pointless, like #11

>> No.1910995

The statement below is true.

The statement above is false.

>> No.1911238
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1911238

>>1910995

Also, could someone explain Olbers' Paradox in more detail?

>> No.1911255

the thing I dont like about these paradoxes is that they rely on language (the heap is a perfect example) a million grains of sand is a million grains of sand, and 999999 grains is 999999 grains of sand.

all these show is that words are an imperfect tool, whereas mathematics is perfect, and avoids this problems. (ie. the heap of sand paradox in mathematical terms would simplify to 1,000,000 = heap = 999,999 so 1,000,000 = 999,999. clearly this shows there is no such thing as a heap.)

>> No.1911285

>>1911238

the sky should be white. nuff detail?

>> No.1911315

>>1911238

how much splainin' do you need? if there is a star everywhere you look then the whole sky should be white.

>> No.1911327

>>1911255
Our system of mathematics is not perfect. This has been proven many times over. One person who did a lot of work in this area is Kurt Godel.

>> No.1911364

>>1911327

>Our system of mathematics is not perfect

could you elaborate please? non-mathfag here

>> No.1911402
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1911402

>>1911327

explain

>> No.1911426

>>1911327
No. Incomplete =/= Imperfect.

>> No.1911472

>>1911426
No? If you have a perfect piece of paper and you cut it in half you have an incomplete piece of paper. An incomplete piece of paper is NOT a perfect COMPLETE piece of paper.

Our system of mathematics is NOT a perfect complete system.

For the system to be perfect it would have to be complete, so by being incomplete it is imperfect.

>> No.1911483
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1911483

>>1911472

>> No.1911505

>>1911472
>>1911426

Neither of you can prove what you say is true.

>> No.1911530

>>1911472
>It's not perfectly complete HURR
Yet for what it is, it is perfect.

>> No.1911551

>>1911285
>>1911315

Isn't it because of gaps?

And also the way our eyes perceive light, like when a camera shoots a picture at night, you wouldn't see any stars in the picture.

But anyway, it's still confusing to me.

>> No.1911562

>>1911551
If the universe were static and infinite, there would be no gaps. But it's neither.

>> No.1911611

The star one is very simple. Light is not some perfect orb that extends outward from a lightsource; it is physical and made up of physical objects. The father you get from the star the more thinly spread and dispersed light waves get. Eventually it becomes exceedingly unlikely that ANY single light wave from a particular star ever hits earth.

>> No.1911720

>>1911611

Wrong. Its because light can be redshifted to other wawelengths. The whole sky glows.

In microwave.

Also, the universe isnt infinite.

>> No.1911760

Blah, blah blah... Let's see:
#11: Bad/incomplete definition of omnipotence
#10: Heap is a subjective term. Besides, even if you define a heap exactly you invalidate P2/turn the whole thing into circular reasoning
#9: I don't get this one... What makes a number "interesting?" Apparently being the first non-interesting number does... Whatever
#8: Bitches don't know 'bout my calculus. Besides motion is change over time; looking and slices of "no time" and seeing no change don't mean squat.
#7: OH NOES TRAVELING THROUGH INFINITE POINTS. Pshhh, that's no paradox; infinite points =/= infinite distance; lrn2 geometry.
#6: This proves examining anything from a purely logical standpoint with no regard for feelings and emotions and subjective "human-ness" will cause you to starve to death. Stupid ass.
#5: I don't know of a clear fallacy to this, but it's kinda like the "They'll attack when we don't expect it, so if we always suspect an attack they can't surprise us!" It's an infinite loop. It's equivalent to "This statement is false."
#4: Ummm, that's actually proof by contradiction that one of the premises is false (either everyone doesn't shave or he doesn't shave all and only those that don't shave themself).
#3: Even if you take it ridiculously literally, lying about all Cretens being liars doesn't mean they all tell the truth.
#2: Hmmmmmmmmm... Okay, that's a good one.
#1: Because an immovable object and an unstoppable force cannot logically exist together, you can't use logic to determine what will happen.

>> No.1911782

>>1911760
>#5: I don't know of a clear fallacy to this, but it's kinda like the "They'll attack when we don't expect it, so if we always suspect an attack they can't surprise us!" It's an infinite loop. It's equivalent to "This statement is false."

There is a clear paradox. Your logical axioms are A and B, however using those axioms you have <span class="math">A \land B \rightarrow \sim A[/spoiler]

Which, in logic land means that you can literally prove anything to be true or false.

However, it turns out this is perfectly realizable in real life. Its a great unsolved paradox, with no consensus. If we suppose that our universe behaves according to the rules of logic then there must be some falacy that is outside the scope of current logic theory, if we suppose that our logic system is closed then we have a universe that behaves illogically and in that case all of science can , in some sense, be thrown out the window.

>> No.1911813

>>1911782

>Its a great unsolved paradox,

Because it have no solution.

A straw vulcan would try to think hard about the best possible outcome for an attack, a normal human would just choose one randomly and the random one due to being random would have a higher chance of sucess.

Sometimes being random is a huueg advantage.

>> No.1911912

There are no paradoxes.Just stupid animals.

>> No.1911936

2 is pretty simple. The winner of the court case and the winner of the bet are both separate wagers. One doesn't supercede the other.

If he won the case, he would have to pay because of the deal, regardless of the court's decision.

If he lost the case he would have to pay because of the court order regardless of what the deal was.

>> No.1911972

Paradox #1 is silly. An omnipotent being can exist in two places at once, separate the realities, and then contradict himself while not contradicting himself. There is no contradiction in omnipotence.

An all mighty being can create a stone even he cannot lift because HE IS THE STONE AND HIMSELF.

Paradox #2. Bounded infinity is the solution. All types of heaps, an infinity, belong under the 'ultimate' heap which is all possible definitions. All fractions are numbers.

>> No.1911998

11. Assumes omnipotence exists, false assumption
10. Semantics, no paradox
9. Claim-->proof-->not a paradox
8. Motion is defined by change over time, so of course it doesn't exist in a single instant. no paradox here
7. Clearly doesn't understand converging limits
6. Not a paradox, not even wrong
5. Prisoner's logic is correct, but he should expect it every day until it doesn't happen to follow through with this logic.
4. Valid idea, but invalid as written.
3. "This statement is false." would suffice.
2. Protagoras can't sue Euathlus because he didn't do anything wrong, would never get to court.
1. Unstoppable force implicitly means there is nothing that can stop it, and vice versa. Such a system cannot exist.
B. "dark sky" could still be due to dimming caused by distances, not a paradox anyway

Final score 1.8/11 (#2 and most of #4)
<span class="math">See~me~after~class!!![/spoiler]

>> No.1912016

>>1911998
I meant #3 and #4 are the only paradoxes (paradoxii :3), not #2.
You can't sue for something that hasn't happened yet, obviously.

>> No.1912019

#8 All motion happens at a single quanta of speed, which is the speed of light. The only difference is how much mass the object contains. As you move farther away from the object, it travels slower, and as you get closer, it moves faster. There is no true speed, only relationships between objects as in math.

The quanta of speed depends on the objects around it and those observing it.

>> No.1912034

This sentence is false.

The solution: It is both true and false and exhibits quantum logic. (True(AND)False)

>> No.1912038

Does anyone have that comic making fun of engineers? Something about what would happen if you had an identical clone of yourself.

>> No.1912048

4
The barber’s Paradox

The question is incorrect because the rule refers to others and not himself.

>> No.1912058

3
Epimenides’ Paradox

Another example of him being a liar and telling the truth at the same time. (True(AND)False) Both are obviously simultaneously true.

Call it Talse or Frue

>> No.1912070

1
The unstoppable force paradox
Solution: The space around them expands, allowing the object to continue forever while the other does not move, while appearing that both have stopped.

FUCK YA

>> No.1912123

The solution to the turtle paradox is that Archilles reaches the turtle's next position before the turtle does.

>> No.1912130

>>1912048
nice assumption you made there

>>1912070
What are you blithering about?
>“What happens when an irresistible force meets an immovable object?”
>meets
You can't just ignore part of the description.

>> No.1912143

>>1912123
Not really, the "next position" is determined by how long it takes Achilles to reach the turtle's last position, so by the time Achilles reaches the turtles 'next position', the turtle is at its 'next next position'. That's the whole point of the paradox.

But it's all moot, because the time it takes to iterate the infinite sum is finite, thus Achilles overtakes it.

>> No.1912145

>>1912130
If you are to assign every quality to the terms used, not all of them are the same -- specifically the fact that the rules they lay down refer to other men and not himself.

The meeting of two forces is just the interaction of fields. If the fields keep expanding then neither object will ever have to move while space expands forever.

>> No.1912157

>>1912143
Not really, the "next position" is determined by how long it takes Achilles to reach the turtle's last position, so by the time Achilles reaches the turtles 'next position', the turtle is at its 'next next position'. That's the whole point of the paradox.

But it's all moot, because the time it takes to iterate the infinite sum is finite, thus Achilles overtakes it.
----------

They each have constant speed. The amount of time it takes Archilles to reach the next point is cut in half because he is going at a steady rate. The turtle has set 'points' he will be at in intervals according to his fixed speed. Archilles will arrive at the turtle's next point before the turtle will get there.

>> No.1912175

>>1912145
That or the unstoppable object gains dimension, therefore never stopping while stopping.

>> No.1912184

A paradox is how people trolled before the internet. They all involve assuming something that isn't true or taking something more literally than intended. I really don't see why every omnipotent being should have it's omnipotence subject to it's ability to create a stone it can't lift. It can create infinitely large stones, it can lift infinitely heavy things. THAT STILL SOUNDS PRETTY FUCKING OMNIPOTENT.

>> No.1912196

>>1912184
God just needs to BE the rock so that he can decide that he cannot lift it.

>> No.1912208

>>1912157
>Archilles to reach the next point is cut in half
Where do you get half from? It would be the ratio of speeds, which the article states is 1/10.

Again, you're missing the point of the paradox. Anyone who knows the most basic of physics knows the faster object will obviously eventually overtake the slower object. The paradox exists because of the way it's worded. Each iteration occurs when Achilles reaches the point the turtle was at during the last point in time. The turtle is then a finite distance further ahead and the process repeats for an infinite number of steps. This paradox just illustrates the author's lack of understanding of infinity and limits, not anything to do with y=mx+b.

Besides, the 'next position' was already defined in the description a specific way, you can't just use the same vocabulary in your explanation and expect people to know that you mean something entirely different.

>> No.1912214

Lets reformulate the postulate more concretely.

Can God square a circle using only a straight edge and compas?

>> No.1912215
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1912215

>>1912058
>>1912070
>>1912175
sure is time-cube in here

>> No.1912239

>>1912208
I see. Then the real answer is that, at the end of time, they will both finish exactly simultaneously.

>> No.1912240

>>1912215
Space has to be created somehow.

>> No.1912241

>>1912239
nnnno... The infinite sum ends up with a finite time because it converges.

>> No.1912257

>>1912215
Someday you will move beyond binary propositional lattices. Did you know there is just more than binary, 0 and 1, propositions?

>> No.1912260

>>1912241
Which is only possible at the bound of an infinity. The bound of time.

>> No.1912265

>>1912241
FUCK YOU

>> No.1912317 [DELETED] 

>>1912260
<span class="math">\displaystyle\sum_{n=1}^\infty\frac{1}{2^n}=\big(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\c
dots\big)=1[/spoiler]

In this case, we have:
<span class="math">\Delta t=\displaystyle\sum_{n=1}^\infty\frac{1}{10^n}=\big(\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{
1}{10000}+\cdots\big)=.111\ldots[/spoiler] which is finite.
QED

>> No.1912323

>>1912260
<span class="math">\displaystyle\sum_{n=1}^\infty\frac{1}{2^n}=\big(\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+{}
\cdots\big)=1[/spoiler]

In this case, we have:
<span class="math">\Delta t=\displaystyle\sum_{n=1}^\infty\frac{1}{10^n}=\big(\frac{1}{10}+\frac{1}{100}+\frac{1}{1000}+\frac{
1}{10000}+\cdots\big)=.111\ldots[/spoiler] which is finite.
QED

>> No.1912356

>>1912323
1=0

>> No.1912370

>>1912323
No, but really, what you said is so much less confusing than words.

>> No.1912550

#11 An omnipotent being can change the laws of nature.
#10 You can't apply subjectivity to objective measure.
#9 If there aren't any non-interesting numbers, it's a pointless concept. It's an oxymoron.
#8 Time is not atomic.
#7 Distance is quantum. The tortoise is not in constant motion; Achilles' motion does not wait for the tortoises' motion to complete before moving.
#6 Not a paradox.
#5 There's a logical fallacy here, but I can't name it. It assumes itself so it's incorrect.
#4 Seems valid, but it's probable that the premise is flawed. Occam's Razor, etc etc
#3 The opposite of "all Cretans are liars" is not "all Cretans are truthful." It is "not all Cretans are liars." Which allows Epimenides to be correct.
#2 Both are separate claims, neither supersedes the other, arbitrary choice.
#1 Space expands, thus giving the illusion of stopping, while, in reality the object keeps moving while the other stops moving.

>> No.1912600

>>1910831

ITT: paradoxes for the uneducated individual.

>> No.1912691

I'll lump them into broad groups:

Infinitesimals, derivatives: 7,8
word games: 1,9,10
this sentence is false: 2,3,4,11
bad logic: 5,6
lack of scientific understanding: B

5: if you are going to be hanged one of the next two days, you can't make any predictions. If you aren't hung that day, you will know you are hung the next. I guess this actually falls under "this sentence is false", but is sufficiently complex that it should be noted.
6: the donkey makes some arbitrary decision, since either way is equal, just going one way makes prefect sense.
B: there are clouds of dust which obscure stars, redshift, non-infinite universe, finite power of universe, so on and so on.

>> No.1912740

>>1912691
That or the light has already reached this point and died.

>> No.1912787

So wait... are we INSIDE or OUTSIDE the big bang?