Zeno's paradoxes - The arrow

[Anonymous No.10871491]

From what I understand, "the racing paradox" concludes that time cannot be composed of infinitely divisible chunks but rather of indivisible pieces. "The arrow paradox" clearly has a problem with the chunk-reality of time but I don't understand how infinitely divisible time intervals resolve the apparent paradox. I then came across this video:

https://www.youtube.com/watch?v=IPNttsu8x24

I don't understand her point that "the flight is not composed of a series of dimensionless moments." How does this make the arrow move? Is her argument correct, is there someone else who explained the paradox better? (I'm reading 'Early Greek Philosophy' by Barnes btw, that's where I came upon the problem and decided to spend more time on it.)

[Anonymous No.10871659]

>>10871491
Instants are not parts of time, for time is not made up of instants any more than a magnitude is made of points.

[Anonymous No.10871669]

don't bother, his paradoxes add nothing new and are just exercises in autistic semantics

[Anonymous No.10871672]

>>10871491
No, the racing paradox is simply an illusion. If you keep the frames of time equal, the race is finished easily. It only seems endless, because you are only adding half of the time that you were adding before.

The arrow paradox is another kind of illusion. He has given the definition of movement as something that requires time, and then asks you to consider it without any change in time.

Zeno's paradoxes are primarily mind-traps (like finger traps), if they seem not to budge, it's because you're pulling in the wrong direction.

Instants are part of time, and we can measure them with calculus.

[Anonymous No.10871679]

>>10871672
I can tell that you've skipped your Zeno lecture

[Anonymous No.10871680]

>>10871491
His paradoxes were good at pointing out the flaws in our time-space models, but we have relativity now.

[Anonymous No.10871765]

>>10871672
>we can measure them with calculus.
WojackWithTinyBrain.jpeg

[Anonymous No.10871806]

>>10871659
But that then leads to the argument that time and space are quantized?

>>10871680
How does relativity explain these paradoxes? Special and general relativity do literally nothing to resolve both paradoxes if you don't quantize space-time, something which is still trying to find its place in modern physics.

[Anonymous No.10871842]

>>10871679
Ahh yes, I see that you know your Zeno well!

[Anonymous No.10871973]

>>10871842
Have a look at the paradox here. See that chap over here? He - Get your hands off my tortoise!

[Anonymous No.10872024]

>>10871491
That's the wrong Zeno, bud.

[Anonymous No.10872042]

>>10871765
>can't measure the area under a curve
>can't track rates of change

[Anonymous No.10872072]

>>10872042
this is what every undergrad says

and it's WRONG

[Anonymous No.10872092]

>>10872042
You aren't measuring anything. You are calculating.

[Anonymous No.10872096]

>>10872072
Have you never taken calculus? If it's wrong, how do we have satellites? The theoretical cannot contradict the practical. To the extent that something is useful, it must be true.

[Anonymous No.10872105]

>>10872096
lol undergrad gonna undergrad

[Anonymous No.10872106]

>>10872092
You're defining movement as a change of position over time, and then asking people to measure movement without time. What's the sound of one hand clapping?

[Anonymous No.10872115]

>>10872105
>am a graduate
>getting criticized by a high schooler
Why do I do this with my life?

[Anonymous No.10872129]

>>10872115
why do you lie on the internet

or even worse, finished compsci/electrical engineering and had no classical education whatsoever

[Anonymous No.10872131]

>>10872042
If the brain is one-dimensional can the left or right dimension ever become predominate?

[Anonymous No.10872137]

Why the fuck are people arguing about calculus and not the topic at hand

[Anonymous No.10872153]

>>10872137
Because it's relevant

[Anonymous No.10872161]

>>10872137
because STEMlords are brainlets

[Anonymous No.10872190]

>>10871806
Paradoxes only exist because models do not accurately depict phenomena. As models become refined, old paradoxes become irrelevant, and new ones eventually take their place. The theories of relativity and quantum physics will do this to Zeno's in time.

[Anonymous No.10872198]

>>10872153
Let me rephrase that; why the fuck are people arguing whether someone is an undergraduate or graduate and don't directly apply their knowledge and interpretation of calculus since it seems relevant? And why is nobody addressing the main question, infinitely divisible versus finite chunks of space/time/space-time?

[Anonymous No.10872205]

>>10872096
Calculus is a useful tool for describing (and predicting) what we perceive.
There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of science and math is to find out how nature is. It only concerns what we can say about nature.

[Anonymous No.10872212]

>>10872198
Oh, because this is 4chan

[Anonymous No.10872230]

>>10872190
I don't mean to be rude but you sound like someone who's read too much pop-sci and believe people like Carl Sagan and Lawrence Krauss when they say that science is the only thing pushing us forward towards a better tomorrow.

I mean I'm a STEMfag myself but I've taken up philosophy on the side solely due to the reason that many scientific endeavors fail to conceptualize and prefer repeating calculations that have been done to death rather than try to explain nature.

Quantum physics is a very shitty field; it's at best an okay approximation of a theory that's yet to take its place with more interpretations than there are people trying to figure out which one is correct. And I have to admit that I see no way General Relativity can explain Zeno's paradoxes for they are not the "paradoxes" that theory is used to resolve (they are actually explainable just by Special Relativity but I guess you meant GR in your post, that's why I'm mentioning it).

[Anonymous No.10872273]

>>10872230
>science is the only thing pushing us forward towards a better tomorrow.
That's... not at all what I'm saying? I have no idea where you got that from. Are you saying that Zeno's paradoxes expose a flaw in something beyond science models? Because it doesn't make much difference, regardless of where a paradox is being found, what I said is the case with them and how they eventually become irrelevant, just change "models" with "worldviews".

[Anonymous No.10872280]

Solvitur ambulando

[Anonymous No.10872282]

>>10872198
because /bantz/ is an indirect form of argumentation. The implication of a proper insult invalidates the argument, but a proper rebuttal reverses it. It's shorthand/ the body language of the internet.

[Anonymous No.10872343]

>>10872273
My apologies for misunderstanding you. Still, saying that the paradoxes will be resolved by QM and GR is not resolving the paradoxes, don't you agree?

[Anonymous No.10872741]

>>10871491
why is this board more interested in non-/lit/ and non-philosophy questions than anything even remotely tied to those two?

[Anonymous No.10872771]

>>10872741
books are boring

[Anonymous No.10872787]

>>10871491
Zeno was like the first brainlet to argue 0.999... =/= 1

His argument is mathematically wrong

[Anonymous No.10872935]

>>10872787
I haven't stumbled upon that information, can you provide source for what you speak of?

[Anonymous No.10872946]

>>10872935
Not that guy, but the arrow in flight paradox demonstrates that between points A and B, because you can point to an infinite number of decimal points in between them, motion shouldn't be possible and the arrow should never be able to reach point B from point A.

[Anonymous No.10872969]

>>10872787
>Mathematical realism

[Anonymous No.10872990]

>>10872946
That literally isn't equivalent to 0.999...=/=1

[Anonymous No.10872996]

>>10872787
mathematically wrong is correct but chemically two hands clapping together do not actually touch, which is one analogy people use for zenos arrow.

[Anonymous No.10874486]

bump

[Anonymous No.10874540]

>>10871491
You know the only point in learning this stuff is to accept the failings of words/reason and that sometimes you just gotta stop trying to rationalize everything.

[Anonymous No.10874639]

>>10872096
What a brainlet post.

[Anonymous No.10874697]

>>10874540
Yeah, why enjoy things?

[Anonymous No.10874798]

>>10874540
It's pretty obvious that one must have a few unprovable axioms in his theory of nature, but Zeno's paradoxes show that two opposing worldviews (namely, dividing space and time into indivisible and infinitely many pieces) will both prove unsatisfactory and I don't believe that the situation is a false dychotomy either. How does one proceed from such a situation?

[Anonymous No.10874829]

>>10874798
>How does one proceed from such a situation?

By accepting that processes with infinite steps can happen in a finite amount of time, just like a finite series can arise from adding together an infinite amount of quantities.

[Anonymous No.10874873]

>>10874829
>a finite series can arise from adding together an infinite amount of quantities.
No, it can't. A finite series is by definition a sum of finite number of elements.

[Anonymous No.10874886]

>>10874873
yeah, I didn't say what I meant to say, I meant a convergent series

but that doesn't mean what I said isn't true
if you add together an infinite amount of quantities, and their values converge, that gives you a finite quantity
you get a few of these finite quantities you get a finite series, ergo a finite series can arise from adding together an infinite amount of quantities.

[Anonymous No.10874902]

>>10874886
>if you add together an infinite amount of quantities, and their values converge, that gives you a finite quantity
Wrong, 1+1/2+1/3+1/4+... converges.

[Anonymous No.10874906]

>>10874902
diverges*, I'm autistic, sorry.

[Anonymous No.10874912]

>>10874906
oh no mr semantics got me again

[Anonymous No.10874919]

>>10874912
But it is what you said, is it not? Adding infinitely many quantities whose values converge, you get a finite quantity.

And I have no idea why everyone here is so sure that convergent infinite series resolve the paradoxes; they literally deal with the ambiguity and paradoxical nature of the fabric of space-time yet nobody addresses that?

[Anonymous No.10874924]

Time is quantised, lads. And so is space.

https://en.wikipedia.org/wiki/Planck_time

[Anonymous No.10874927]

>>10874919
>But it is what you said, is it not?
no, I said "that gives you a finite quantity" which can happen when the series converges
I did not say that it always does, and I assume you know what I meant

[Anonymous No.10874931]

>>10874924
Explain "the rows paradox" then.

[Anonymous No.10874933]

>>10874924
you haven't even read that wiki article, brainlet

that's just a theoretical really short amount, beyond which our theories can't say much

[Anonymous No.10874955]

>>10874931
The "rows paradox" is only a paradox if you buy the assumption that passing two Bs should take longer than passing one A. There's literally no reason to buy into this, because it doesn't make sense.

>>10874933
You're right, I haven't read the wiki article but I do have a degree in physics and I've studied quantum physics. It's all still up for debate, and obviously we can't (yet) know the exact Planck time.

However, for me, the discrete energy levels - proven beyond all reasonable doubt - in electron shells and the rest of it, down to quantum field theories, implies a fundamental discreteness of the very small.

[Anonymous No.10874978]

>>10874955
>implies a fundamental discreteness of the very small.
braindead statement

at the moment things imply that at very short distances spacetime is neither continuous nor discrete

[Anonymous No.10874994]

>>10874978
>at the moment things imply that at very short distances spacetime is neither continuous nor discrete

What is it then? Because the only theory of physics that works at very short distances is quantum physics, and that gets shit done by "quantising" what classical physics assumed was purely continuous.

I'll even accept the answer "both" continuous and discrete but not "neither"

[Anonymous No.10875003]

>>10874955
>a paradox isn't a paradox because it doesn't make sense to me

Btw, the exactness of the Planck scales, be they time or distance, is not important per se. I believe that everything is fundamentally quantized as well but you still run into problems if you describe nature in that way.

[Anonymous No.10875013]

>>10871669
Imagine actually believing this

[Anonymous No.10875016]

>>10874994
string theory suggests it

it seems your understanding of physics stopped at about 50 years ago

[Anonymous No.10875022]

>>10875003
>Btw, the exactness of the Planck scales, be they time or distance, is not important per se
Yeah, fair enough.

>a paradox isn't a paradox because it doesn't make sense to me
Hey, Zeno wasn't some god who never made mistakes. He came up with some interesting and clever paradoxes that make you think. But the assumption Zeno makes in the rows paradox actually doesn't make sense.

See pic related. The Cs are moving faster relative to the Bs than the stationary As. How does Zeno's assumption that passing two Bs will take longer than passing one A seem like a reasonable thing to assume? It's a nonsensical assumption that's only made in order to set up the paradox.

[Anonymous No.10875035]

>>10875016
>string theory suggests it
Hoo boy, here we go.

String theory suggests what exactly?
What string theory are you talking about?
But it doesn't matter because no string theory is yet a proper scientific theory. Quantum physics, the quantised nature of the very small, has been proven in the lab. String theories have no experimental proof.

At this point it's just maths. Maths that could describe nature but also could be bullshit.

[Anonymous No.10875038]

>>10875013
tell me, what grand insight has Xeno's autism brought you? nothing

[Anonymous No.10875044]

>>10875038
Reality is representation
Becoming is illusory
God isn't real

[Anonymous No.10875047]

>>10871672
>>10872042
>Instants are part of time, and we can measure them with calculus.
Calculus is only articulation here, not refutation. It allows us to more clearly describe how we perceive something that doesn't make sense, but it is in no way negating Zeno's claims that it really doesn't make sense.

>if they seem not to budge, it's because you're pulling in the wrong direction.
basically what you're saying is "if Zeno's paradoxes seem not to budge, it's because you're not ignoring them properly!"

[Anonymous No.10875048]

>>10875044
so Xeno is equivalent to taking a few doses of shrooms and fucking your brain up forever? got it

[Anonymous No.10875055]

>>10875048
No because one comes from reason and the other doesn't. I never touched psychedelics in my life by the way.

[Anonymous No.10875062]

>>10875055
how come you sound like your average stoner then

maybe it's just that all escapism leads down the same path

[Anonymous No.10875064]

time is just a convenient concept used to measure motion. it doesn't exist

[Anonymous No.10875071]

>>10875064
>time is just a convenient concept used to measure motion. it doesn't exist

If time doesn't exist why are you getting older?

[Anonymous No.10875072]

>>10875064
motion is just a convenient concept to measure time, it doesn't exist

[Anonymous No.10875073]

>>10875062
Did I trigger you in some way

[Anonymous No.10875090]

>>10875071
it's almost as though the cells which make up my body interact with the environment

[Anonymous No.10875099]

>>10871491
At any instant, in the thought experiment, all things are completely stopped but there is some vector which captures extra information and carries it to any next instant. As a result, space and time are worthless constructs of this simplified model.

[Anonymous No.10875106]

>>10875099
>there is some vector which captures extra information and carries it to any next instant.

you are a worthless construct of your simplified brain

[Anonymous No.10875109]

>>10875090
>it's almost as though the cells which make up my body interact with the environment
It's almost as if they interact with the environment over time, you mean

[Anonymous No.10875125]

>>10875109
time is defined by the interaction of matter, not the other way around, you blithering retard

go ahead and tell me how you would measure time in a vacuum, i'll wait

[Anonymous No.10875141]

>>10871973

Gentlemen, this is temporality manifest. Te-ta and farewell.

[Anonymous No.10875146]

>>10875125
I'm so SO sorry but for me to explain how I'd do that would take time. That's something I don't have - according to you.

[Anonymous No.10875152]

>>10875146
glad you admitted you got owned and have no reply other than this mediocre attempt at wit

[Anonymous No.10875161]

>>10875106
Nice attempt at a shit post.

[Anonymous No.10875389]

>>10875125
So if nothing interacts, time doesn't flow, is what you're saying?

[Anonymous No.10875699]

>>10871680
>>10871806
brainlet here. I think I got it.
What relativity presents to us that solves the Arrow, is Lorentz contraction.
This solves the Arrow because Zeno thinks, essentially, that there is nothing we can find IN the object that could determine whether or not it is in motion. He believes motion can only be determined with external references.
With Lorentz contraction, however, we can determine that an object at motion time is shorter along it's direction of motion.
> Anything occupying a place just its own size is at rest.
Objects in motion don't occupy a space their own size, if we define their size to be the space that they occupy at rest.

[Anonymous No.10875785]

>>10875699
zeno's paradoxes are not meant to be solved by post Newtonian physics, or even Newtonian physics themselves

[Anonymous No.10875791]

>>10875699
You can always shift to their frame of reference and they will always occupy the same space.

[Anonymous No.10875802]

>>10875785
non-argument
>>10875791
If Zeno's god-observer can stop time, surely it can choose its frame of reference to be the most appropriate one for analysis.

[Anonymous No.10875917]

>>10875802
Are you saying that different observers don't see the same physical phenomena? There is no such thing as a preferred frame of reference.

[Anonymous No.10875918]

>>10875047
Idiot. All paradoxes are a misdirect. Consider Achilles and the Tortoise. We are given the speed of the tortoise in relationship to Achilles speed. When Achilles reaches the halfway point, the tortoise will have moved half that distance. This will happen again and again and again. But by highlighting this process, you have been tricked into looking at irrelevant points. Achilles does not slow down. He runs at a constant speed. Speed is measured by distance over time. That is what it is. When Zeno proposes that the tortoise has moved half the previous distance away from where Achilles now stands, he has tricked you by using a smaller section of time than he used in the "moment" before. A paradox is simply a chinese figner trap for the mind. You are pulling at the wrong pieces. If you take someone moving at a constant speed, and measure the distance traveled in increasingly shorter intervals, of course they will have traveled less than in the larger interval. Zeno's paradox does not reveal a flaw in our concept of either motion or time, but rather sets the mind to try and resolve a fractal equation.

[Anonymous No.10875930]

>>10875918
The Achilles and Tortoise and The Dichotomy paradoxes can both be resolved by treating them as finite values obtained by infinite sums of ever decreasing values; The Arrow and The Rows lead to contradictory conclusions.

[Anonymous No.10875931]

>>10872996
fuck off you sperg. What is touch if not the physical phenomenon we experience from our hands when they approach other material?

[Anonymous No.10875961]

>>10875930
I've already resolved the arrow. He gives a definition for motion that requires the passage of time, and then asks you to consider an object, which he calls moving, without granting it a span of time. It is not a valid question. It is not that reality is unresolvable, but rather that illogical statements are illogical. The rows paradox is even more ridiculous. The bodies are granted a speed not in relationship to each other, but in relationship to the field. He then tries to say that the movement is impossible because their movement related to each other is not the same as their movement related to the field. Absolute absurdity.

[Anonymous No.10875978]

>>10875961
What the fuck no.
>then asks you to consider an object, which he calls moving, without granting it a span of time
You do consider it in a span of time and you're left with the choice if that span of time is "now" (an infinitely small chunk of time) or a finite chunk; an interval if you will.

>The bodies are granted a speed not in relationship to each other, but in relationship to the field
What is this supposed to mean? They move at same velocities in opposite directions relative to an observer at rest.

You're calling them illogical and absurd yet you don't seem to understand them.

[Anonymous No.10875998]

>>10875917
> Are you saying that different observers don't see the same physical phenomena?
clarify, please.
> There is no such thing as a preferred frame of reference.
the preferred, or most appropriate frame of reference to analyze a human arrow is rest with respect to the surface of the earth

[Anonymous No.10876021]

>>10871491
Stop believing in time.

[Anonymous No.10876032]

>>10875998
Crash course in Relativity. Two postulates:
1) The laws of physics are the same in all inertial frames of reference.
2) The speed of light in vacuum has the same value in all inertial frames of reference.

In layman's terms, all observers must agree on what happens, whether they are stationary or riding a rocket going at near light speed. Hence, there is no preferred or "most appropriate" frame of reference to analyze the arrow - you specified the surface of the Earth. Why not the surface of the Moon? The center of the Milky Way?

[Anonymous No.10876048]

>>10876032
because you can't measure the arrow and determine if it is Lorentz contracted if your measuring stick is also contracted by the same amount. is that right?

in either case, do you agree that, in this way, relativity solves Zeno's Arrow?

[Anonymous No.10876059]

>>10876048
Why would the measuring stick be contracted?

[Anonymous No.10876088]

>>10875389
imagine a universe in which all matter is perfectly static. how do you measure the passage of time? does such a concept even make sense in that scenario?

[Anonymous No.10876099]

>>10876088
If you get to build a hypothetical universe, I get to bring along a hypothetical clock that would work.

[Anonymous No.10876105]

>>10876088
Don't listen to him >>10876099.
A perfectly static universe would be one where:
1) NO interaction between matter exists or
2) where nothing exists

I can't think of any way of measuring time in either scenario right now but I'll think it through and report back.

[Anonymous No.10876247]

>>10875978
1. Please tell me how a span of time can be an instant. A span of time is defined by two distinct end points and all the instants within. An instant is a single point. Carry over this principle to a non-time measurement. Let's abstract it: let us say that we are measuring movement along a single axis. A span would be the distance traveled between one point on the axis, and a second point on that axis. A single instant, a single point, has no distance.. You therefore cannot ask what is the distance of a single point on the axis. It is defined as having no distance. Returning to Zeno, he defines speed in a conventional, two axes manner: the distance travel in a given interval of time. He then asks us to consider an object at a single instant on this journey. Of course in that single instance no distance is traveled, because no time has passed. Something at rest would be something that has no physical movement during an interval of time. Since he demands that no interval of time has passed, then we cannot speak of distance travel, for traveling a distance requires an interval of time, which he has denied us from considering.

2. Precisely. The movement is given as related a stationary observer, with both groups moving within the same field of space, which is also motionless. To determine their speed, which is distance traveled during an interval of time, we must first establish what to what we are comparing this movement. He grants in the beginning of the paradox that the distance traveled is measured in relationship to the static field, or if it makes it clearer to you, the static observer. The two groups are traveling the same amount of distance relative to the ground, or the observer, during the same interval, and so are said to have the same speed. But then, after this is established he tries to claim it is contradictory that their speed relative to each other is not the same as their speed relative to the observer. This is an invalid observation. If the observer is motionless and Group B is in motion, then the relative speed of Group C as measured against the observer cannot be the same as its relative speed as measured against Group B. Group B and the observer do not share an equal relationship to Group C. He is demanding two things that are inherently unlike to be the same. Of course it will not resolve.

[Anonymous No.10876270]

>>10876105
This is false. You can't think of a way to measure time, because you have defined time as something that relies upon the movement of particles. If you define something as requiring a certain characteristic, then you cannot present a hypothetical world in which that characteristic does not exist as evidence for why the defined thing requires that characteristic. In this imaginary world where all matter is static, you have not denied the possibility of time, but simply a human device for measuring. You have not demonstrated that time requires movement, but rather that humans, limited beings, cannot currently notice time without the movement of matter.

[Anonymous No.10877321]

>>10876247
https://www.youtube.com/watch?v=aoKAmWiYM_Q&t=0s

>>10876270
That's why I said I'll think it through ffs, it's not really an elementary question if it's still being asked about.

[Anonymous No.10877371]

>>10872787
>>10872946
wow Aristotle came up with the same argument way back in the day, and didn't have to resort to mathematical hand-waving in the process

too bad it was a weak argument and a weak argument now

anyways, for the brainlets here: Zeno's paradoxes are about FINISHING the journey, not about "hurr wtf are infinitesimals lmao."

Let's do this in reverse, to make it clearer:
Let's say that there are an infinite number of gods trying to prevent you from making a journey. The first god plans to throw up an unpenetrable barrier when you get half way. The second plans to throw up an unpenetrable barrier when you get a quarter of the way. The third: when you get 1/8. And so on. Now the "I peaked when I got a B in high school calc" answer is that you can't move at all (e.g. distance travelled is 0), because of you know limits and shit. But then means that no barriers have been erected, and nothing is stopping you from moving! And now we have a paradox that's the EXACT SAME as Zeno's.

[Anonymous No.10877376]

>>10874886
>if you add together an infinite amount of quantities, and their values converge, that gives you a finite quantity
Zeno's paradox isn't that infinite series can't converge - they're more that you can actually add up an infinite series. Think you can? Try it and get back to me.

[Anonymous No.10877383]

>>10877371
Can't wait for that one anon who's gonna say "lucky for us there's not an infinite number of gods trying to prevent us from making a journey". Good thinking btw.

[Anonymous No.10877385]

>stand at point A
>shoot arrow to point B
>arrow hits point B
UHHHHHHH, ZENO?!?!?!?!?

[Anonymous No.10877399]

>>10877383
it's kind of funny how these "omfg super logical" types that think that calculus solved Zeno probably also think that the omnipotence "paradox" is a legit problem for theism

[Anonymous No.10877540]

I'm not saying modern quantum physics can solve Zeno's paradoxes, but there is a sense of relief that quantification of time and space offers one possible explanation

[Anonymous No.10877574]

*runs past the tortoise*

pssht, nothing personnel zeno ;)

[Anonymous No.10878137]

>>10877371
Your comparison is not the same at all. In your example, you have caused the speed of travel to be reduced for every half of the remaining distance traveled. You have also reduced the infinitesimal to zero, which cannot be accepted and said that there is a distance small enough that the Gods will no longer prevent movement. This is all to say that no increment can measure smaller than itself. You are trying to show the limits of reason, but instead are simply showing the limits of measurement.

In Zeno's paradox, the speeds of travel remain constant.

All of these paradoxes are tricks of relativism. You are saying "compare these two things. Now consider this different comparison. They are not the same, so the first comparison is invalid." Unless someone argues that all relationships must be perfectly identical, these paradoxes are a charade.

[Anonymous No.10878364]

>>10878137
>You have also reduced the infinitesimal to zero, which cannot be accepted and said that there is a distance small enough that the Gods will no longer prevent movement
Q is dense in R, and theres no largest value of 2^n BRAINLET

[Anonymous No.10878370]

>>10878364
tl;dr: no matter how little you travel, there will always be a barrier up

[Anonymous No.10879038]

>>10875044
Too assumptive. These are not insights, they are vague ideas justified (grammatical construction does not make those things legitimate and well-made concepts). Xeno being an irrelevant means to an end.