How do you justify the existence of limits?

# Is the concept of a limit pseudoscience?

Falling into your wing while paragliding is called 'gift wrapping' and turns you into a dirt torpedo pic.twitter.com/oQFKsVISkI

— Mental Videos (@MentalVids) March 15, 2023

>the limit of the distance moved from rest of a freely moving object tends to zero

...as time tends to zero. Objects move zero distance in zero time. Shocker.

Norman mandelburger

limits are fine

EXCEPT when people assume limit means the actual value.

Like if you had a sum of (9^i)/(10^i) from i =1 to i = k.

it is true that the limit of the sum approaches 1 as k gets bigger. BUT the actual value of the sum can never EVER be equal to one for any natural number k.

so: limits are useful but don't confuse them with the actual value.

so would you consider [math]sum_{i=0}^{infty}frac{9}{10^i}[/math] to be a number? or some sort of nonsense expression?

>LIMITS, THE FOUNDATIONS OF CALCULUS, ARE PSEUDOSCIENCE

Think of the limit in calculus as a gravity well and it solves all these issues of abstraction

Objects fall constantly to the centre but are stabilized in this very act of freefall

Defined formally in real analysis as:

[math]

forall e > 0, exists N hspace{.5em} text{ s.t. } hspace{.5em} forall n geq N, |f(n)-L| < e

[/math]

Fuck I still remember this definition very clearly from the calculus 1 class I took 5 years ago, there's also the cauchy variant to this

nice mumbo jumbo

I'm sure you think this shit is formal but it really isn't. A truly formal and general definition would be in terms of bases

This is ideal though. This has nothing to do with the physical world. You can't demonstrate this physically and I think that is what the guy in the screen shot is appealing to. You can't make measurements or predictions to arbitrary precision in the physical world. Only to a certain amount of decimal places. He is associating something being scientific with being empirically verifiable. I am not saying he is right, but this is what he is probably appealing to.

so what? I guess you could say that mathematics is not science but in that case mathematical concepts aren't pseudoscience either, they aren't science at all

I said here

> I am not saying he is right, but this is what he is probably appealing to.

So I am just explaining the likely point of view of these guys. Also, I am not an empiricist either, and so I am fine with the scientific method including not just that which can be inferred from the sensory data stream to be grounded in the physical world, but also that which can be DEDUCED from intellecting ABOUT the sensual data stream, and even intellecting about things which don't even exist in the physical world, such as things like continuous number lines and fields. I personally DENY that there exist continuousness or analyticity in the physical world, but I don't deny the concepts in a idealistic or pure transcendent of the physical world form. These things are grounded in MINDS, not in the physical world. They are PRIOR to the physical world even. I believe that the math PRE-existed the physical world, and was used to design it. Hence why the maths have such utility. This ends up being a METAPHYSICAL issue about ONTOLOGY. And these sort of people are PHYSICALISTS and empiricists and they also subscribe to scientism.

In other words, with regard to this

there's no 'for all objects greater than zero in an infinitely divisible and continuous this or that, there exist some corresponding this or that'. This is an idealic situation. You can't demonstrate that in the physical world (the physical word is digital). This is an ontological or metaphysical claim (false one, the world is discrete and digital). Which is fine, I like metaphysics, but it's not empirical. These math MODELS have utility, continuous models that is, with regard to applying them to the physical world to make predictions to non-arbitrary precision, but that is different from them representing a description of the physical world where for every element of the model there is an element corresponding in the physical world in some kind of one for one basis. This doesn't even make sense in a quantized world physical world.

>the world is discrete and digital

prove it

I can give you the needed areas of research and some resources you the needed resources. Start with the discovery of entropy and the lead up to ultraviolet catastrophe. This is the start of the break down of the continuous classical models. A good paper. The title is 'looking at nature as a computer', see pic. It ends up being that nature is the OUTPUT of a computer, not the computer itself, but the paper is still useful.

https://people.csail.mit.edu/nhm/looking-at-nature.pdf

The second part of this

This describes (pic) the confoundment of those involved with the discovery of entropy.

Then this pic is about the ultra violet catastrophe itself.

>Max Planck solved this problem around the beginning of the last century.

What Planck proposed was that for each mode, there is a minimum energy that is proportional to the frequency, with a universal constant of proportionality that he introduced. Only integer multiples of the minimum energy can be added to a given mode. This means that given a unit of energy to add to the system, there are only a finite number of places it can be put - modes with energies too high cannot be "excited." Given the integer-multiple constraint, there are in fact only a finite number of way to divide up the given unit of energy to add it to the system.

This is a provably incorrect interpretation of plank and the quantisation of energy. There are plenty of energy continuum states. E = hf is true for any frequency, and for any free particle the energy is not bound. Quantisation is true for bound states, i.e those with periodic boundary conditions, but even in the partition function there is a factor in the exponential that is the energy, which can be a continuum. There is no real reason to think that space is fundamentally discrete, though as space is a second countable manifold you can in fact completely cover space with with countably many open sets with rational radii. So I guess maybe thats kind of discrete idk.

Nothing 'continuous' is ever measured. You can't measure or observe infinitely divisible or infinitely ANYTHING. Infinity is not a scientific concept. Everything is always measured to a finite number of decimal places. All predictions are always accurate to a non-arbitrary degree of accuracy. You confuse continuous MODELS (ideal things of minds) and formalisms which have utility to make predictions to non-arbitrary resolution with ACTUAL ONTIC physical continuousness. There are no measurements or predictions made to arbitrary precision.

>There are plenty of energy continuum states

Plenty of MODELS. Never empirical data that is continuous. There is no such thing as an OBSERVED continuum in the physical world. You can't observe infinite information or infinite anything. You can use minds to CONCEIVE of such things abstractly. Infinity is grounded in MINDS, not in the empirical/physical data stream. Infinity and continuousness are METAphysical or 'beyond physical" concepts. This is FINE for me and this is not to denigrate metaphysics. I myself believe that the maths are PRIOR to the physical world and were used to DESIGN the physical world. But that doesn't change the fact that they are all included in the physical world in a one for one basis.

You are essentially saying that because we can't measure shit continuously it means that continuous things dont exist. This is trash. I can always make smaller and smaller time or distance intervals should I choose. They may not be particularly useful but I can make them. In fact if you gave me enough time to measure something like the energy of a system then yes I would be able to get arbitrary accuracy using the energy time momentum uncertainty relation , its just nobody is going to do it, because like with all infinities we just dont give that much of a shit and just go "yep its heading to that direction cool lets just say it gets there eventually".

Everything that you post is basically pseudo intellectual philosophical drivel that shows a distinct lack of knowledge of physics and an overly large attachment to popsci

>You are essentially saying that because we can't measure shit continuously it means that continuous things dont exist.

You can postulate it in a metaphysical sense. You can't measure infinity of infinite resolution though and it can never be observed, so the concept is scientifically meaningless. It's not as if you can't get down to some infinitely fine resolution and go 'here it is! I found infinite divisibility!'. THERE WOULD ALWAYS BE AN INFINITE AMOUNT OF ZOOMING IN TO GO. You would never be any closer to proving your hypothesis.

>I can always make smaller and smaller time or distance intervals should I choose

this is conjecture, but even assuming it is true, THEN YOU WOULD ALWAYS BE INFINITELY FAR FROM OBSERVING OR CONFIRMING CONTINUOUSNESS.

>Everything that you post is basically pseudo intellectual philosophical drivel that shows a distinct lack of knowledge of physics and an overly large attachment to popsci

This is ironic, because my view of the trend towards quantization of physics is fits with the empirical data, while your view CAN NEVER BE ANYTHING MORE THAN METAPHYSICAL SPECULATION.

Start here buddy

https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/01%3A_Reviewing_Elementary_Stuff/1.01%3A_Breakdown_of_Classical_Mechanics

Shut up you are basically just a finitist and there is a large problem when using that in science, and that is that all theories rely on primitive notions and axioms that can't ever really be observed, and if you were to use interpolation to get rid of all of these unobservable truths then you would most likely just get an uncountable set of sentences with no real structure behind them. So no, nothing you say is particularly profound. You are literally just a finitist but using QM as a pop sci prop to help justify it.

>Shut up

Nice argument.

So let's have you address this idea of the observation of infinite divisibility. How does this confirmation occur? You can't get to some point and say 'here it is! I found infinite divisibility!'. THERE WOULD ALWAYS BE AN INFINITE AMOUT OF DIVISIBILITY TO GO. You would NEVER be any closer to your goal. You are like Zeno's little scientist guy trying to find infinity but always being an infinite amount away from confirmation.

the point is what evidence the cia needs

is very specific

By the way, I am not a mathematical finitist. I am fine with continuous ideas. I am a physical finitist, because that is what the data implies. Here is a nice little summery

>Breakdown of Classical Mechanics

https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Quantum_Mechanics_(Fowler)/01%3A_Reviewing_Elementary_Stuff/1.01%3A_Breakdown_of_Classical_Mechanics

Yeah, so you are still not addressing the impossibility of ever observing physical continuousness or infinity. It's a scientifically meaningless concept. Continuousness is something which exist in ABSTRACT models in MINDS. That doesn't mean continuousness isn't 'real', it's just not PHYSICAL. This is no problem in a idealist world view, which I hold. It IS a problem in a physicalist world view though.

You keep citing that single page. But thats just basic QM, and nowhere does that imply that space is discrete. You can keep sending that link but its not going to support your argument. Now if you are implying "if we cant measure it then it doesnt exist", then I am sorry but you will find that science really isnt your shtick because scientific models that explain reality ultimately rely on using limited data to infer the existence of general, often unmeasurable quantities. Getting rid of these unmeasurable things is in fact possible via craig interpolation, but it basically turns a theory into a bunch of non sequitur observations rather than a nice causative model.

>https://en.wikipedia.org/wiki/Craig_interpolation

This inductive process of assuming general relations from specific instances is literally how science works. Realistically a scientific argument really is a proof using infinitary logic, in which infinite proofs are allowed, as no matter how many times you observe something you can't ever actually confirm it, you would need to do so infinitely many times.

>and nowhere does that imply that space is discrete

True, I didn't say it does. I said the TREND is towards physicality being quantized. And there ARE reasons for believing that the rest will be, pic and link related. There are ZERO reasons for thinking it is continuous and plenty of LOGICAL reasons why it could never be PROVED otherwise, for instance the one about how you can't ever observe infinite divisibility. So asserting is will only ever be metaphysical conjecture. And the rendering engine doesn't even have to render the planck scale resolution by the way. It renders what the specs of the observer or the observers instruments require. So if it's just human consciousness, It renders resolution based on the specs of your eyesight. As the consciousnesses immersed in the VR develop tech that demands finer resolution data, the system will oblige in rendering what would be probable at that scale, all of the way down to the pixel scale and the finest definable resolution, ie there's no such thing as a half pixel. See how my view doesn't involve illogical ideas like 'infinitely divisible' things?

>You can keep sending that link but its not going to support your argument

Yes, it is. My argument is that the physical world is discrete, digital, computable, and computed. The observed data is 100% in my favor, not yours. You can only appeal to continuous ABSTRACT MODELS conceived in MINDS.

>Now if you are implying "if we cant measure it then it doesnt exist"

It's not that you just can't at the moment measure something continuous to infinite precision or measure to arbitrary precision, it's that the idea itself is meaningless.

https://arxiv.org/pdf/1001.1205.pdf

>as no matter how many times you observe something you can't ever actually confirm it

Yeah, I read hume.

Bonus quote from zeilinger in pic related

Notice this part specifically

>but can't point to any intermediate direction.

These outcomes could iust as well be labelled "yes" and "no", or, in the fashion of digital computers, "I" and "O".

Your fixation on the planck length shows your pop sci education. The planck length is not the fundamental length, there are lengths shorter than the planck length, any length that you define as the "fundamental discrete unit" I can always find a smaller one and declare that to be the new one, and ultimately if you cant actually have a fundamental discrete unit then you just either are asserting it or are essentially just using a continuous space. Also reality is not computable, there are well known physical problems that have no computable solution. Your second picture is just a random non sequitur.

>there are lengths shorter than the planck length

Evidence? And you keep appealing to the idea that I am appealing to pop sci even though I am posting peer reviewed science literature and textbook explanations while you are appealing to silly and childish ideas about infinitely divisible space. If you really would stop and think about it, you would realize the silliness the idea. You have no evidence of this. There's no such thing. You are just a silly person with silly presuppositions. You can't EVER observe infinite divisibility of ANYTHING. Infinity is a meaningless and absurd concept with regards to physics, hence why it's called a 'catastrophe' when infinities arise, such in the ultraviolet catastrophe and hence why there is a need to use math tricks in QFT to get FINITE answers and AVOID nonsensical infinities.

>renormalization, the procedure in quantum field theory by which divergent parts of a calculation, leading to nonsensical infinite results, are absorbed by redefinition into a few measurable quantities, so yielding finite answers

FUCKING DUHHHH. There is no 'field' floating around somewhere in an observer dependent universe, fucking retard. This is fantasy. It's a MATH MODEL. It has utility as a model, to a non-arbitrary degree of precision as an APPROXIMATION, but it is NOT the thing itself. You are a dumb ass which is lost in the math. Or IGNORANT is a better word. You are an ignorant NPC who lacks the ability to formulate your own interpretation of the data. You take the proscribed INTERPRETATIONS of the data to be the thing in itself.

>qft is a model and an approximation but the planck length which depends on said model isn't

>I can always find a smaller one and declare that to be the new one

Where can I read about your discoveries. Yeah, you are making shit up.

>there are well known physical problems that have no computable solution

No, there are not. There are asserted fake problems, usually having to do with 'the quantum world' based on the idea that MATH MODELS of the quantum world are more than just math models and that 'the quantum world' has to be rendered at all times, even though by definition, the quantum world isn't even in the spacetime universe. IT'S NOT IN THE PHYSICAL WORLD. It doesn't have to be computed. The spacetime measurable EFFECTS of the quantum world are the only thing that have to be rendered.

>Your second picture is just a random non sequitur.

No, it's not. The information theoretic interpretation is consistent with ALL of the observed data and has TOTAL explanatory power. You have a silly sally idea of the physical world. A fantasy that you just repeat because you were brain washed by people with a particular naturalist agenda.

Also the problems with even the continuous MODELS

>Matter that self-exists by its own substance must do so in a continuous space and time, or something else would be needed to explain the gaps, again contradicting physical realism. This continuity creates infinities, so supporters had to invent the mathematical trick of renormalization to patch up the problem, a technique Feynman called a "dippy process"

Continuous physicality is fake news believed by particular consciousnesses immersed in a VR who can't admit that there physical world is just a small subset of reality.

Renormalization to the best of my knowledge has nothing to do with continuous space, its to do with self interactions causing massive divergences in equations, causing them to blow up.

I am talking about the absurdity of infinite ANYTHING in the physical world, not just space. It's all digital. It's finite elemental. The resolution is EXTREMELY fine, and so continuous MODELS work good as APPROXIMATIONS because planck resolution is EFFECTIVELY continuous. ALL consciousness based experiencial realities are virtual, informational, digital, be they dreams, daydreams, hallucinations, the waking 'physical' VR. They SEEM continuous to the observer because our specs and the specs of our instruments can not probe deep enough to where pixelation occurs. This might even cause black holes, which are band with and processor related constraints. Values below planck length can't be defined by the computer rendering the reality. No half pixels.

Here

https://www.newscientist.com/article/2342273-physicists-made-the-most-precise-measurement-ever-of-a-single-particle/

>A new assessment of the electron is the most precise measurement of a particle ever taken, at a precision of 1.3 parts in 10 trillion, and could tell us about new physics happening at the smallest scales.

This isn't even close to getting down to planck resolution levels in terms of size. Getting finer and finer measurements is effectively the players or consciousnesses immersed in the VR 'zooming in' The reality will continue to render finer and finer resolutions of data with regard space and all matter and energy until it reaches all forms of pixelation. But there IS a a resolution and quantizing of EVERYTHING including time and space, not just energy and matter, see pic. I know that you will not except it though. I don't know why though. It's completely intuitive.

you also need the delta part of the limit so that for all delta>0 we have 0<|x-x_n|<delta

>you also need the delta part of the limit so that for all delta>0 we have 0<|x-x_n|<delta

OK wow, so cool, dog!

You disproved a mentally unwell man!

Bark for is, dog! BARK FOR US!

>for all delta>0

If anything, it's dependent on epsilon

>we have 0<|x-x_n|<delta

But we are talking about a sequence here, not the limit of a function as it approaches the limit point x in its domain.

Woof woof! Look at the dog go! BARK BARK!

meds

>meds

Catholics deserve the rope.

>meds

J6 was just a warmup, Catholic scum

once a terrorist, always a terrorist

Limits are pure soi, but not because they don't work.

I don't see the problem

Did that African midwit gave up on coam to start schizoing on calculus now?

It's worse than that. His argument that limits are false is because they aren't physical. So this time he understands neither math or physics.

>It's worse than that. His argument that limits are false is because they aren't physical. So this time he understands neither math or physics.

John is a mentally unwell man since his brother died.

Literally the only people who post his stuff are CATHOLIC TERRORISTS but then again that's redundant.

>CATHOLIC TERRORISTS

Lusted for blood, having hallucinate its drinking at communion, Catholics look for anyone to terrorize. John is their latest target. Know it for what it is.

Catholics target depressed people like John because they are subhuman and not part of the hunan race (lack empathy)

John is mentally unwell since his brother died. That said, he HAS correctly identified the enemy. All those who harrass him would be better off exterminated, and what-do-you-know they all happen to share the same religion (starts with a C) who have a penchant for inquisitions against the free thought.

Limits are governed by the conscious mind. As we reify objects in our mind, we give each of them structures and place limits upon them.

John is barely conscious anyhow so this makes sense

Also known as spooks of the mind

t. NPC

by logic, abstract mathematical concepts don't have to correspond to physically possible concepts

that brainlet thinks that the concept of a mathematical limit has to actually correspond to moving an object physically in space

it doesnt

>justify

your iq is obviously limited

I can give you some related links that put you in the mindset of digital physics. The contention isn't that the continuous models don't themself have utility, they do. The question is going deeper into that which the models describe, ie the ontic status of physicality.

This one is pretty ambitious

>The term “discrete calculus” is one of many expressions, along with “discrete ex-

terior calculus” and “mimetic discretization”, that describes the body of literature

that has focused on finding a proper set of definitions and differential operators that

makes it possible to operate the machinery of multivariate calculus on a finite, dis-

crete space. In contrast to traditional goals of finding an accurate discretization of

conventional multivariate calculus, discrete calculus establishes a separate, equiv-

alent calculus that operates purely in the discrete space without any reference to

an underlying continuous process. Therefore, the purpose of this field has been to

establish a fully discrete calculus rather than a discretized calculus. The standard

setting for this discrete calculus is a cell complex, of which a graph or network is a

special case.

http://leogrady.net/wp-content/uploads/2017/01/grady2010discrete.pdf

Some more useful material that ties in. Here's one I am reading at the moment

Digital and Discrete Geometry

Theory and Algorithms

https://doc.lagout.org/science/0_Computer%20Science/2_Algorithms/Digital%20and%20Discrete%20Geometry_%20Theory%20and%20Algorithms%20%5BChen%202014-12-12%5D.pdf

I will give you also some seminal papers on the topic. the most important is this one

On Testing the Simulation Theory

http://users.cms.caltech.edu/~owhadi/index_htm_files/IJQF2017.pdf

Another is by fredkin, one of the originators of digital physics. He has a different idea than pic related. Instead of a top down, probabilistic model, where you render only on demand, and only to the specs of the observers, you render the whole universe from the planck scale up. This is probably not the right model, but the paper is excellent any way.

Digital Mechanics

Edward Fredkin

http://52.7.130.124/wp-content/uploads/2015/07/digital_mechanics_book.pdf