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🧵 Untitled Thread

Anonymous No. 16298885

Imagine you want to walk from point A to point B.

To reach point B, you first have to get halfway there. Let's call this halfway point C.

To get from C to B, you have to go halfway again, reaching a new point D.

Each time you move towards B, you always have to cover half the remaining distance.

This process of halving the distance can go on infinitely.

Since there's always another half to travel, it seems like you can never actually reach point B.

This suggests that if you can divide the distance infinitely.

Completing the journey would require infinitely many steps.

Anonymous No. 16299470

>>16298885
Yeah and also, that's just intelectual masturbation because in practice you do very much get to your destination.

Anonymous No. 16299605

>>16298885
non-issue in the real world because it all becomes negligible. both the time and distance intervals becomes so small that they becomes imperceivable and the intervals can't go below their planck limits so there isn't an infinite amount of information for the universe to sort through.
in programming terms: it just werks. sucks to be some loser in the platonic realm though i guess

Anonymous No. 16299618

>>16299470
>>16299605
"it works in practice" does not resolve the paradox of the divisibility of time and space. you're not supposed to take Zeno's paradoxes at face value and refute the conclusion, even if that is what you'd instinctively jump to on first encounter

Anonymous No. 16299620

>>16299618
Distance is not infinitely divisible

Anonymous No. 16299637

>>16299620
yes, and atoms are uncuttable

Anonymous No. 16299638

>>16299637
Retard

Anonymous No. 16299643

>>16298885
>>16299618
Halving the distance also halves the time it takes you to reach that new point. An infinitely small distance would be traversed in an infinitely small amount of time.

Anonymous No. 16299644

>>16299638
my retardation is finite and known, yours on the other hand...

Anonymous No. 16299681

>>16299643
you must be thinking of those as zero or discarding them

Anonymous No. 16299758

>>16298885
>This process of halving the distance can go on infinitely.
>Since there's always another half to travel, it seems like you can never actually reach point B.
Like it already been said, it takes less and less time to reach the next point and since time passes normally you will reach the point B.
But it would be different thing if you said that traveling a distance between points always took X time
>maybe

Anonymous No. 16299781

this is only true if the "you" walking to point B is infinitely small. otherwise "you"'re bounds would eventually contact point B. so your conclusion is baseless, we need more information.

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Anonymous No. 16299891

do mathfags really

Anonymous No. 16299908

>>16298885
>This suggests that if you can divide the distance infinitely.
>Completing the journey would require infinitely many steps.
Wrong, infinitely divisible =/= infinite in length, despite being divisible into infinite parts it still takes a finite amount of steps if it has a destination.

Anonymous No. 16299914

>>16299618
"It just" works does though
In every single way that matters to those living in meat space.

Anonymous No. 16299952

>>16298885
What if, instead of half the distance, you could walk 9/10ths of the distance. Would you ever reach your destination? I.e does 0.999... ever reach 1?

Anonymous No. 16299982

>>16298885
it's easy: you run out of letters to assign to points and then just go the rest of distance in one move.

Anonymous No. 16300124

>>16298885
>what is a convergent series
/sci/ has fallen. Billions must prove.

Anonymous No. 16300167

>>16298885
When you deal with theoretical math you are able to work with concepts such as "infinity", which can naturally break our typical conceptions of reality and its mathematical functions pretty easily (seeing as how infinity, as far as we can tell, is impossible to store or represent in a finite universe). Thus, when we think about this seeming paradox in our logic, it will reasonably confuse and bewilder us. However, all one needs to do to see that this isn't some weird glitch in our empirical methods is acknowledge the fact that our universe has a resolution of sorts (that being the Planck Length), like pixels on a screen. This distance being a limiter for this issue, because if you divide the distance by half "infinitely", you actually end up meeting this limiter, and you are automatically bottlenecked. Thus, the paradox doesn't cause any collapse in the structure of our math or physics, etc., because we are not a universe built upon infinitely small distances or marticles (as far as we know).

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Anonymous No. 16300172

Walking half the distance in the same time means walking twice as fast. Walking 1/4 the distance means walking 4 times as fast. .... Walking 0 distance in infinite time means instant travel. Zeno's paradox breaks down as soon as you go faster than light.

Anonymous No. 16300180

>>16298885
you go to point B2 after point C where B2 is the same distance from A to B, so the the halfway from C to B2 is B. Geez im genius

Anonymous No. 16300191

>>16300167
>our universe has a resolution of sorts...
>...as far as we know
the crux of your problem

Anonymous No. 16300386

>>16299470
>in practice you do very much get to your destination
That's your belief, not the truth. You're deluded.

Anonymous No. 16300405

>>16298885
>what is a convergent series for 100, Alex?

Anonymous No. 16300456

>>16300405
>im just gonna skip the infinite process at some point and jump to the finite sum im approaching

Anonymous No. 16301241

>>16298885
Moving half as far is twice as easy. This proves motionlessness to be impossible because it's infinitely easy to not be still.

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Anonymous No. 16302167

>>16300456
And?

Anonymous No. 16302530

>>16299618
>"it works in practice" does not resolve the paradox of the divisibility of time and space.
Yes it does

Anonymous No. 16302533

>>16298885
What’s the point of intellectual exercise that can be disproven by moving your arm to put another sip of hibiki 21 to your lips?

Anonymous No. 16303902

>>16298885
>To reach point B, you first have to get halfway there. Let's call this halfway point C.
Maybe on the academic bullshit way. In RL there is no halfway. Such as no evolution, big bang, double slit, relativity, nukes or flat earth etc. Your halfway simply do not exist. The prove is simple, If you walk the distance from A to B at speed AtoB 0.1 you reach at time 10.

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Anonymous No. 16303931

>>16303902

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Anonymous No. 16303974

Why yes, it does take an infinite amount of steps. Any distance in continuous space can be represented by a convergent infinite series.

Infinite doesn't mean infinite time or space, that's what you don't understand. It's infinite in the precision with which you can get close to something. That doesn't mean it takes an infinite time or distance, quite the contrary. AB is the sum of this infinite series no matter what.

Infinite series can have finite sums.