/sci/ - Science & Math

Explain yourself OP. Your postulate is too vague, be more specific.

>>10785469
No, we just don’t understand it and often assume what isn’t true.

>>10785476
just look at Zeno paradoxes, reality is impossible

>>10785476
>Your postulate is too vague, be more specific.

What if the postulate was that reality was "non-specific"?

>>>/adv/

Yes, thats why there is something rather than nothing. Because the concept of nothing is self contradictory, a thing about nothing is still a thing

Time is "god" or the natural emergent computation taking place to correct this.
Sorta goes like
1. Nothing exists
2. "God" or the concept of concepts "looks" at nothing and "sees" that it is a concept
3. This process occurs outside time as it is the creation of the first timestep, so dont think of those first two as a sequence of events but a map of the situation. Anyways now time exists, a thing has happened
4. Further contradictions as to why this situation makes no sense emerge, in the process defining more reality.

Thats all it is. An endless process of computation exploring every possible physics set etc etc, all because fundementally it actually doesnt make sense. That is the perpetual nature of our reality, a world that exists solely because it should not.

>>10785530
Are you trying to rip my pasta off and not even be arsed to .txt it?
My interpretation is of a 3d storage of data birthed by cataclysmic measurement from a true void.
0 velocity, 0 matter, 0 time, 0 space.
0 = 1 of nothing. Nothing has infinite boundary, infinite measurement, infinite potential.

Boom!

Zero has been defined to exist. 1st dimension born.
What's the next logical course of action?
To go in a random direction till you run into your own ass. 2nd dimension is formed.
Then turn that shit off course and wait to come back for the 3rd so on and forth.
(I think nothing higher than 4d as it's just non frame data. Like signal clipping.)

Forever plotting infinite courses though a infinite 'super absolute solid'.
With that, all courses are accessible at all times.
But it can never hit a boundary. But the transition to the second dimension created a vector.
Because you can't maintain a straight course without 2 frames of reference,
If you're familiar with pi analytics, you'd be aware of it's irrationality and normality.
I believe this would also apply to the superstructure, because of the vectoring.
Nothing is moving, only plotting can/has happen/d. Conceptual data is incorporeal because it's defined within a course.
All courses are connected. So irrationality and normality exists by default on any course by extension.
Time is nonexistent. Only where it's been is known. What lays ahead is unwritten, but effected by previous paths it knows it's coming upon.
It is a collapse witnessing itself.

I believe only one observer needs to witness this. As all pathways = the same as others. The variables are are like a faze change.
Also, you know that thing when you try to get outta someones way, but they move the same way? Yeah, one observer stops that occurrence.

>>10785530
>>10785544
0+0=1

Ah yes, it all makes sense now....

>>10785488
>Zeno paradoxes
They aren't actually paradoxes, just stories that illustrate the counter-intuitive nature of infinite sums.

>>10785582
Not a fan of Bohmian I take it?

Your pic is not contradictory, you just need to understand infinite series.

>>10785582
Think of zero as the empty set. The set exists, and from there, all math is produced.
>>10785637
>infinite series
No such thing. 1 + 1/2 + 1/4.... will never reach 2 because 2 is the LIMIT

>>10785600
you can't sum infinite

>>10785655
>1 + 1/2 + 1/4.... will never reach 2
It's equal to 2 immediately, it's not a process taking time with each you dumbass.

>>10785675
How is it equal to 2? Prove it

>>10785658
It's very easy.

>>10785655
>>10785604
>the universe works solely based on how we describe how it works.

>>10785678
https://en.m.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/16_%2B_%E2%8B%AF
proof on article

>>10785694
It says the “infinite sum” is the limit of the sum. In other words, 2 is the limit. It is not EQUAL to 2.

>>10785678
https://en.wikipedia.org/wiki/Geometric_series#Sum

>>10785698
>It says the “infinite sum” is the limit of the sum.
The limit of the finite sums you moron. Please tell me how many terms are in 1 + 1/2 + 1/4....

>>10785687
Well go on fucktard. Tell me why. Discussion board remember.
Current "Big bang" I find absurd for many reasons.
Loosen up Anon. You're posting Anonymously. No one other than you will know you're wrong if you give a bad attempt. Hell, you benefit from failing anyways. Because you break from this rut of rote and prescription functions.

>>10785700
>>10785705
It’s perfectly reasonable to say that as n gets larger, or goes to infinity, that the sum approaches 2, but how can you justify the claim that it actually equals 2? Where is the proof/reason/intuition? How can the human mind understand a completion of something infinite?

>>10785714
>>10785698
>ive never taken calculus, btw

>>10785714
>It’s perfectly reasonable to say that as n gets larger, or goes to infinity, that the sum approaches 2, but how can you justify the claim that it actually equals 2?
Because the sum 1+1/2+1/4... does not have terms "approaching infinity," it has infinite terms. The sum of these infinite terms happens to be the limit of the sum of the first n terms, where n is finite.

Don't confuse yourself into thinking that 1+1/2+1/4... has finite terms and therefore can't equal the limit.

>Where is the proof/reason/intuition?
It was already given to you.

>How can the human mind understand a completion of something infinite?
That is part of the beauty of calculus, my underage friend.

If you are too much of a pussy to deal with limits then look here:

x = 1+1/2+1/4...
x/2 = 1/2+1/4+1/8...
x/2 = x-1
x = 2

>>10785469
nawww, looks good to me

>>10785730
>infinite terms can exist
>a sum of infinite terms can be divided by integers
These things haven’t been proven yet. You’re assuming too much. Start from the beginning. Give me your axioms.

>>10785753
>These things haven’t been proven yet.
They have for hundreds of years, you're very late to the party. Maybe when you'll hey older you'll take a calculus course. Until then stop pretending like your ignorance is an argument.

>>10785681
how can you sum a never ending number?

>>10785753
Hes not dividing the infinite sum hes dividing the terms individually going one by one forever.

>>10785767
I took calculus in high school and college, and these things were never proven. You’re supposed to go along with it. This shouldn’t even be a discussion. All of our math should be acceptable as 2 + 2 = 4

>>10785769
That’s assuming such a process can be done. It’s not clear to me that it’s possible or mathematically sound.

>>10785768
>never ending number
You mean like 0.333...?

0.333... = sum from n=1 to inf of 3/10^n = (3/10)/(1-1/10) = 1/3

>>10785774
>I took calculus in high school and college, and these things were never proven.
Then buy up a textbookand look for yourself.

>All of our math should be acceptable as 2 + 2 = 4
It is. You probably understand as little of the foundation of 2+2 = 4 as you do of calculus yet you treat them differently because your intuition tells you to. Your intuition is irrelevant, sweety.

>>10785778
>assuming infinity to prove infinity
every time

>>10785778
I mean an infinite series of numbers

>>10785789
You can’t even explain it yourself. Doesn’t that bother you?

>>10785790
>assuming infinity to prove infinity
What does "assuming infinity" and "proving infinity" mean?

>>10785791
>I mean an infinite series of numbers
That was already explains to you, you take the limit of the finite sums.

>>10785796
It's the difference between Graham's number and infinite I suppose?
We know we can't write Graham's number's with all the matter in the observable universe. But we don't know if we can put down infinite apparently.

>>10785793
You're retarded if you think anyone is going to bother explaining the foundations of calculus to you on 4chan when you can easily look it up for yourself. I'll give you the summary though: when you try to find a term in the sum where the sum is some arbitrary distance from 2, you can prove there is no such term. Thus they are equal.

>>10785805
Don't bother replying to my posts schizo, you're hidden now.

>>10785816
Well fuck you. My reality doesn't need infinite anyways. Just no potential.
Boundary are as far as a vector can deviate.

>>10785658
Calculus btfo'd forever

>>10785826
>xxXSuiseisekiXxx
What brings a person to do the things you do?

>>10785835
I like to stir the pot just to see what falls out of solution.
No real rhyme or reason. I do power play a lot, but it gets results.
Though, I'm classic Autism thinker. So it could be my normal state.
Never pull it IRL. So self soothing I guess?

Scientists and mathematicians have faith in things unseen. The same people who are materialists scientifically will be Platonists mathematically. They like to play pretend.

>>10785852
Almost no one is a Platonist, try again.

>>10785488
I'm not sure if I could beat Zeno in a fistfight... but I'm willing to try.

>>10785857
They believe that infinity exists as an idea. We’ve never seen it before or understood it, but yet it exists

>>10785835
Oh, and this notion of 'go away skitzo'. Yeah, that's kinda Irked me. Strangely haven't received it on my key points.
But I see it thrown around here at things that aren't In text books.
And that's saddening considering the URL we're under. For the /sci/ part. Disregarding a topic before discussion could even happen.
But especially the 4chan bit. This is where I and a hoard of others learnt that pre-contrived ideals, notions, and facts don';t me 2 bits of shit.
If you can't front with quantifiable argument against a claim. The claim stands as uncontested. Even it it's against all rationality.
Except for pics or it didn't happen.

What I've been witnessing here is people too afraid to be wrong anonymously.

>>10785866
>They believe that infinity exists as an idea.
The universe appears to be infinite. Also Platonism means that concepts exist as objects in a Platonic realm. Saying that something exists as an idea is not Platonic.

>We’ve never seen it before or understood it, but yet it exists
We understand plenty about it, thanks to math.

Pretty sure Zeno is saying "We know the obvious answer, so something with our formal understanding of infinite series must be wrong. We should work on this."
The interpretation that I've been shown in school, laying outhow stupid Zeno is, is simply perverse.

>>10785876
>The universe appears to be infinite
lmao
>We understand plenty about it, thanks to math.
lmao

>>10785886
Thanks for admitting you lost.

>>10785469
Yes and no.

>>10785892
>infinities can be bigger than other infinities
>that which has no quantity can have a greater quantity than that which has no quantity
Ridiculous

>>10785939
>>infinities can be bigger than other infinities
https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

>>that which has no quantity can have a greater quantity than that which has no quantity
Who are quoting?

>Ridiculous
Wow what an argument! You lose, retard.

>>10785469
No, the foundation of mathematics is just a very useful set of internally consistent abstractions of sense data.

>>10785996
The diagonal argument assumes that you can have infinite decimals, or sequences of digits/elements, which doesn’t seem clear to me.

>>10786239
All these choices, but I get remainder 3 yet again.

>>10786239
>The diagonal argument assumes that you can have infinite decimals, or sequences of digits/elements, which doesn’t seem clear to me.
So 1/3 isn't a number?

>>10785488
learn infinite series, moron

>>10785476
OP just learned the delta epsilon explanation of a limit and he can't handle the subsequent existential truth that stems from it.

>>10786983
Prove that 0.333... is equal to 1/3

>>10787024
Do long division on 1/3 and you'll get 0.333... since the remainder repeats infinitely.

Alternatively you can see that 0.333 = sum from n=1 to inf of 3/10^n = 3/10/(1-3/10) = 1/3

>>10787036
Typo, that should be 0.333 = sum from n=1 to inf of 3/10^n = 3/10/(1-1/10) = 1/3

>>10787036
But the remainder is 1. No matter how many times we divide, the remainder is 1. Prove that you can magically divide it infinite times, doing away with the remainder, and making the sum actually equal 1/3. You can’t.

>>10787055
>But the remainder is 1.
Yes, and each remainder of 1 leads to another 3 decimal.

>No matter how many times we divide, the remainder is 1. Prove that you can magically divide it infinite times,
You just said that no matter how many times we divide the remainder is 1. That means the number of divisions is infinite.

>doing away with the remainder, and making the sum actually equal 1/3. You can’t.
The remainder is never done away with, that would mean the decimals terminate. The sum is 1/3 specifically because they don't terminate.

>>10787024
Epsilon-delta definition.

>>10787064
>You just said that no matter how many times we divide the remainder is 1. That means the number of divisions is infinite.
No it doesn’t. It means if you perform the division process a finite number of times, there’s always a remainder. You’re assuming that you can just do the opposite, and perform an infinite process that does not have s remainder. But you can’t prove that such a thing is possible. At best, you can take it as an axiom, which is an unintuitive one.

>>10787070
>No it doesn’t. It means if you perform the division process a finite number of times, there’s always a remainder.
If something is not finite, it's infinite. Good job.

>You’re assuming that you can just do the opposite, and perform an infinite process that does not have s remainder.
Again, there is always a remainder. You're assuming an endless sequence ends. Why do you keep doing this?

>>10787077
If there is always a remainder, then how does it become equal to 1/3? That would require no remainder, no gap. But how exactly does performing the process an infinite amount of times (which is an unsubstantiated idea) remove the gap between the sum and 1/3? Just admit, you have faith in these infinity fantasies.

>>10787024
[math] \displaystyle
p=0.1 \\
\dfrac{1}{1-0.1}=\frac{10}{9} = 1 + \frac{1}{9} \\
\sum_{j=0}^\infty 0.1^j= 1 + \sum_{j=1}^\infty 0.1^j \\
9+1=9+9\sum_{j=1}^\infty 0.1^j \\
1=9\sum_{j=1}^\infty 0.1^j \\
\dfrac{1}{3} = 3 \sum_{j=1}^ \infty 0.1^j = 0.333...
[/math]

>>10787257
>1/9 = 0.111...
Prove it...

>>10785835
Because they're desperate for attention and being called a retard is the only substitute they have for human interactions.
Just stop giving them (You)'s and they go away, like every other retarded namefag who gives it up after a few weeks.

>>10787554
six lines
which line don't you understand?

>>10787554
He just did, retard

>>10785488
reality is indeed impossible, the origin of existence (whether that be the laws that bring it about) will never be explained by anything logical, as they will always demand their own answer

>>10785530
Through which mechanism do they emerge? Which law existed at step 1 or step 2? Why would step 3 occur? Where did that law come from, for things to behave the way you say?

The truth is that no one knows the answer, whether it is us, god, or the universe or anything greater. Reality is insanity and doesn't even know why it exists.

>>10787081
>If there is always a remainder, then how does it become equal to 1/3?
What do you mean? First of all, it's immediately equal to 1/3, it doesn't become equal to 1/3. Second, what does having a constant remainder have to do with being equal to something?

>That would require no remainder, no gap.
You are confused, the remainder only exists during long division. There is no gap between 1/3 and 0.333...

>But how exactly does performing the process an infinite amount of times (which is an unsubstantiated idea) remove the gap between the sum and 1/3?
Because for an arbitrarily small distance x, there is always a finite number of terms in the series for which the difference between that partial sum is smaller than x. There is no possible difference between them, thus they are equal.

>>10785724
That's the thing, you see math as a game and not as something reflective of reality. There is no intuition that shows that infinite should ever complete.

>>10787709
>There is no intuition that shows that infinite should ever complete.
Except for the fact the runner in Zeno's "paradox" does indeed reach the target. There's your intuition.

>>10787709
>intuition
>reality
Choose one retard.

>>10785811
>Hurr durr find the last number in infintiy, bet you cant!!!

Your proof is not convincing. Infinity never ends, so of course there is no final number for distance between it and 2, similarly it never reaches two. Thus the paradox.

>>10787734
>>Hurr durr find the last number in infintiy, bet you cant!!!
Who are you quoting?

>Infinity never ends, so of course there is no final number for distance between it and 2, similarly it never reaches two.
I didn't say there was a final number for distance between 2, I said there is no possible distance between them since any proposed distance is greater than the distance between 2 and a finite number of terms. The finite sums never reach 2, but we're not taking about the finite sums, we're taking about the infinite sum, which is equal to 2 since there is no possible distance between them.

>>10787081
>there is always a remainder
do it the other way then, start with a 1 and systematically cut it up.
Remember, the whole piece is always = 1

[math]
\boxed{0 < p < 1} \\
1 = p + (1-p) ~~~~~~ \overset{1}{ \overbrace{[=====p=====|==(1-p)==]}} \\
\text{divide p using x} ~~~~~~ \overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====x=====|==(p-x)==}]} ~~ + ~~ (1-p)}} \\
\\
\text{solve x and (p-x), when length ratios must be the same} \\
\dfrac{x}{p-x}= \dfrac{p}{1-p} \Rightarrow x- xp = p^2 - xp \Rightarrow \underline{x=p^2} \Rightarrow \underline{(p-x)=p(1-p)} \\
\overset{1}{ \overbrace{ \underset{p}{[ \underbrace{=====p^2=====|==p(1-p)==}]} ~~ + ~~ (1-p)}} \\
\\
\overset{1}{ \overbrace{ \underset{p^2}{[ \underbrace{=====p^3=====|==p^2(1-p)==}]} ~~+ p(1-p)+(1-p)}} \\
\overset{1}{ \overbrace{ \underset{p^3}{[ \underbrace{=====p^4=====|==p^3(1-p)==}]} ~~+ p^2(1-p)+p(1-p)+(1-p)}} \\
(1-p)+p(1-p)+p^2(1-p)+p^3(1-p)+ \cdots =1 ~~~~ \left | ~ \times \frac{1}{1-p} \right . \\
1+p+p^2+p^3+ \cdots = \dfrac{1}{1-p}
[/math]

>>10787716
That does not prove anything about infinity. For all we know reality is discrete, or it is continuous and it behaves in other ways we don't know. Infinity is just a way to cover up the problem and does not align well with other intuitions of reality.

>>10787719
If you want to use infinite to solve Zeno's paradox, it must follow the other logical laws of the Universe or you must explain why it is exempt. You are claiming that infinite (more specifically of the sort of 1 + 1/2 + 1/4...) exists in reality. The problem is that to assume this to be true, you must also believe that reality exists to infinite precision (is continuously divisible). Until you can show this to be true, and answer the other problems this interpretation introduces, using infinity to solve Zeno's paradox is nothing but a mathematics trick.

>>10787761
You are simply defining it to be equal to two and claiming it as proof.
The finite sum never reaches two, and neither does the infinite sum, if you want the distance between them, it is an infinitesimal. If you claim they don't exist, then I don't know what to tell you.

>>10787818
>The problem is that to assume this to be true, you must also believe that reality exists to infinite precision (is continuously divisible).
If reality is discrete, then Zeno's Paradox doesn't apply

>>10787837
Yeah, it would be a potential solution but we don't know if it's the truth, or if there is something else going on. My point is that "infinity" is only a mathematical solution and does not answer the actual question.

>>10787871
I don't see how it doesn't answer the question. Any arbitrarily small distance is covered in a correspondingly small time interval, their ratio being the average speed over that time. No matter how finely you divide the total distance, as long as the distance steps are nonzero, it's easy to see how it would be traversed.

>>10787898
Because as I stated in my previous post, assuming infinity exists assumes that reality is continuous and infinitely divisible.

If reality were "continuous" and infinitely divisible, then movement should be impossible, no? Because where does the movement begin? It is infinitely divisble, where does the first "movement" take place? it is like trying to reach the end of infinity.

Infinity solves the question in a mathematical framework, under its axioms, but it is not the full story. How do we know the universe is not discrete? If that is the case then there is no infinite, but the question is solved just as well. Do you see what I mean? It is only a potential "solution", but not necessarily the correct one. There are problems with both the continuous and discrete interpretations of reality.

>>10787964
When you ask me to point out a "first movement," you're already presuming discreteness. When a force is exerted on a body at rest, there is movement at all times after the force appears. When looking at an exceedingly small time interval, the movement is exceedingly small. When looking at an instant, there is no movement. I don't see any logical issue here as long as you don't presuppose and require discrete steps in your thinking.

>>10787985
>there is movement at all times after the force appears
To clarify my own post, there is movement in all nonzero time intervals after the force appears.

>>10787985
I'm not assuming discreteness, I'm pointing out a flaw in the idea that reality is continuous, because the point is that there is no "first movement" in the continuous universe and therefore there can be no movement because it can never begin. It goes back infinitely.

There is no need to talk about time intervals like you are doing because it is meaningless to the discussion. The question at hand is whether or not a something infinitely divisible can ever "begin" and the answer is no. It's like asking if time went back infinitely, then how can we be where we are? There is infinite time between us and the infinite past.

>>10787998
And to clarify, I'm not claiming that reality is discrete either as that has its own problems as well. We just don't know enough about reality and likely never will to answer every question.

>>10787998
It begins after t=0. It's completely nonsensical to ask for the first instant at which movement exists, because in a continuous universe, movement doesn't exist in instants. It exists in intervals.

>>10788029
I don't think there is any convincing you so I will leave it at that.

>>10785469
>not even understanding basic calculus

this thread is /x/-tier

>People think they understand calculus because they can do the computations but don't even know what the "=" sign means in infinite series

Zeno's paradox isn't resolved by infinite series you absolute brainlets, 1+1/2+... = 2 is simply stating the paradox again in symbols. Write the equation out in its fundamental epsilon-delta form, for fuck's sake. This is how infinite sums are DEFINED.

>>10787776
You conveniently leave out p^n in the last equation.
>b-but it goes to zero
Yeah, it gets smaller and smaller but it never becomes zero. PROVE it. This is such a magical step. With any finite version of the sum, you always have the p^n term, and the equation is true, but you’re using some secret axiom that lets you take away p^n and put some ellipses and create an infinite sum. And this is what you call RIGOROUS? You’re in dream world my dude

>>10788229
no u

>>10788093
ok explain then

>>10788239
nothing is going to zero you illiterate retard
the block is ALWAYS =1

it is your job to prove it is ever anything else than 1
protip: you can't

>>10787716
If there are infinite points between me and the wall, and if I can move precisely to the points 1/2^n in succession, with a finite time between each move, then I should never reach the wall. You have to admit that as I get really close to the wall, the time it takes for me to move from 1/2^n to 1/2^2n requires zero time, which is a bit absurd.

>>10788251
The second to last step doesn’t prove anything. It ASSUMES that p^n becomes magically irrelevant and is unneeded in the equation, and that by putting “...” the equation magically becomes true. Again, what axioms of algebra are used to justify such a step? What logic are you using? I cannot see it. This IS a proof, right? So which axiom are you using for that crucial step?

>>10788261
I'm cutting up a 1
not adding little pieces to crawl up to a 1

I already have the 1 in the beginning
lrn2read

>>10788270
In the second to last equation, you leave out p^n, which is convenient, because it isn’t being multiplied by (1 - p). Then you simply divide everything by (1 - p). But if you leave p^n / (1 - p) in the very last equation and place the ellipses in the MIDDLE of the equation, then I will agree. But you’re assuming that you can eliminate the term and create an infinite sequence. But with what axioms are you doing this?

>>10788278
>what axiom
when you cut up a sausage, the pieces still add up to a sausage
this applies with 1 cut
this applies with 2 cut2
this applies with 3 cuts
:
this applies always, even with inf cuts
the sum of the pieces is always one sausage

>>10788278
>what axiom
when you cut up a sausage, the pieces still add up to a sausage
this applies with 1 cut
this applies with 2 cuts
this applies with 3 cuts
:
this applies always, even with inf cuts
the sum of the pieces is always one sausage

>>10788292
But you left one piece of the sausage out: p^n. WITH WHAT AXIOM ARE YOU REMOVING THIS TERM FROM THE EXPRESSION

>>10788296
what is n?

>>10788300
For any finite sequence, there is always some term p^n. You’re assuming that you can first create an infinite sequence, which doesn’t seem to be accurately defined or supported by an axiom, which magically gets rid of the term that has always been necessary for the finite expression, and that somehow the expression can still be equal to 1. How can you justify such a huge leap in logic? You’re literally playing pretend with understanding here. It’s not supported by anything rigorous or intuitive. So what axiom(s) do you use to get rid of p^n and make the sequence infinite?

>>10788315
I don't have n anywhere
see? >>10787776

no problem

>>10788320
Are you purposely being ignorant? In the third step from the bottom, you have p^4. Every other term is being multiplied by (1 - p). You conveniently leave out p^4, or p^n, and magically create an infinite sequence. With what axioms of Algebra are you making this step?

>>10788325
Is cutting a sausage 4 times somehow overwhelming to you?
Did you experience some kind of horrible carpentering accident and now can't count up to 4?

p.s.
the 4 pieces add up to exactly one sausage

>>10788335
I’m still waiting on the axiom that lets you create an infinite sequence and eliminate the p^n term. It’s almost as if you don’t know it and have this weird, dogmatic faith in the whole process.

>>10788325
Is cutting a sausage 4 times somehow overwhelming to you?
Did you experience some kind of horrible carpentering accident and now can't count up to 4?

p.s.
the 5 pieces add up to exactly one sausage

>>10788343
>>10788345

>>10788348
it's a finite or it is a infinite sequence, whatever you want - the pieces always add up to 1

>>10788354
WHAT AXIOM

>>10788367
KETCHUP

I think I solved this. Reality is real. You can keep dividing down the half way point until you get to a Planck Length at the smallest and then one more bit of movement is quantized, pixelated to the next Planck length. It’s like a dot moving across a 4K TV pixel by pixel. Each half way point is an discrete bit so it won’t be half way forever. It shouldn’t take more than 12 half way steps to cross.

Second solution to Zeno’s paradox regarding the arrow in flight. The idea that you can capture the image of a flying arrow so that you can’t tell if it’s moving seems wrong.

First off movement of the arrow must be relative to the observer to even be considered moving at all. The last thing is if you know the precise length of the arrow before it’s fired, when you snap a picture of it you can tell how fast it’s moving by it’s length contraction due to relativity. So we can find information from a snap shot about speed. The mind blower for me is if you can take a super fast snapshot and measure the length contraction and you can pinpoint the arrowhead top, you can know both position and speed?

>>10788369
Space isn't cut up into Planck-sized cubes.
Pick a point, any point, and you can't calculate what happens within a Planck distance of it (uncontrollable infinities creep into the equations) .
But you can choose a new point a 1/10 of a Planck distance to the left and successfully do calculations about what happens around it.
Space isn't a grid like a TV screen.

Why are autists so bothered by the concept of "infinite?" This seems to come up a lot. I don't understand why they want so badly to get rid of it, even to the point of making insane suggestions like there should be a largest natural number because the universe will end eventually, as though numbers are somehow meant to be defined in terms of how many symbols biological organisms can write down before dying.
Using infinity as a concept works. We get plenty of mileage out of it. Insofar as it doesn't work you can explore ways to more rigorously pin down how you want to engage with it. There's no need to go nuclear on infinity and try to banish it altogether.

>>10788369
>Planck Length is the smallest unit of distance
Nope.

>>10788407
The concept wasn’t created rigorously in mathematics. It’s all metamatematical assumption. It leads to paradoxes and gaps in understanding.

>>10788416
Do you have a specific example of a gap in understanding caused by the concept of infinity?

>>10788423
We’re dealing with objects we don’t understand. The notion of an infinite set is already outside of our comprehension, and leads to paradoxes. Add 10 balls to box A, and take one ball out, and add it to box B. Repeat the process “to infinity.” How many balls are in each box? If you say infinite, you’re wrong. I numbered the balls and made sure to take out ball “1” after the first dump, ball “2” after the second dumb, and so on. Therefore, all numbers are in box B, and there are zero in box A, even though there should be 9 times more balls in box A, from a finite perspective. And if you measure the difference between the number of balls between the boxes as you make increasingly more dumps, then that number grows to infinity. This is a huge paradox and reveals our horrible understanding of such a concept.

>>10785544
Miss me with that schizo shit

>>10785582
No, arithmatic isnt an appropriate ruleset in that environment, it will be run into eventually as a part of any reality, but the rules have to emerge first

>>10787698
Same mechanism "producing" qualia as you view this

>>10787835
>You are simply defining it to be equal to two and claiming it as proof.
You are simply ignoring ther proofs I gave you.

>The finite sum never reaches two, and neither does the infinite sum,
So what is the difference between them? I already showed you that there is no difference. Your baseless assertion doesn't counter anything.

>>10787818
>If you want to use infinite to solve Zeno's paradox, it must follow the other logical laws of the Universe
It does, your faulty intuition is not logical, let alone a law if the universe.

>You are claiming that infinite (more specifically of the sort of 1 + 1/2 + 1/4...) exists in reality.
No, I'm claiming that if it does exist then it's 2. If it doesn't exist then the premise of the "paradox" is false since it describes an unreal situation.

>>10788431
The limit of the sequence of sets for Ross–Littlewood is the empty set.
The cardinality is 10n - n = 9n which would converge to aleph-zero (infinity), but taking cardinality isn't a continuous operation so you don't get to use the limit to calculate it. Instead of taking the limit of S(n) as n approaches aleph-zero you would take S(ω) which is 0 and does not contradict the limit of the sequence of sets being the empty set.

>>10788229
>Zeno's paradox isn't resolved by infinite series you absolute brainlets
t. brainlet

>>10788661
>Instead of taking the limit of S(n) as n approaches aleph-zero you would take S(ω) which is 0 and does not contradict the limit of the sequence of sets being the empty set.
^This. In ordinal arithmetic 10ω - ω would equal 0.
>>10788431
>I numbered the balls and made sure to take out ball “1” after the first dump, ball “2” after the second dumb, and so on.
>There should be 9 times more balls in box A, from a finite perspective
If this were true you would be able to name one of the numbered balls that would still be there.