>Physical measurements can have irrational lengths ok this is just ridiculous. I'm just supposed to accept that a calculated shape has a length that never ends. You will always have some infinitely small opening on its calculated side. But if you actually made a 1x1 square and measured its diagonal length, even at the atomic level the length will end, proving its side length genuinely terminates. You can't have an irrational length and a closed object at the same time - this concept is fully contradictory and makes zero practical sense. Are you also saying that the circumference of a circle is never truly ever closed because Pi is irrational? An opening in a shape no matter how small it is, is still an opening. All shapes will "leak" if they have irrational side lengths which is retarded.
>midwit mistakes the platonic world with the real onemany (finite) such cases
>>17045775>mathematics has nothing to do with reality Then why are we even taught it in school
>>17045776To count potatos for tax purposes.
>>17045771I think computers exposed the necessisty of distinguishing exactness from precison at iteration. Prior to calculators it was alot easier to hand wave over equations, now if they console.log(1.3-1.1) and dont receive 0.2 back but 0.1999999999997 they immediately see the charade. Float point errors make ai non deterministic even when temperature is removed, division in hot path errors have formed the basis of many billions in crypto hacks.New technology, new demands of math
>>17045776because someone too retarded to work with abstractions like irrational numbers won't be able to fare any better with fractions of integers that are in an orders of magnitude of 10^23 (~atoms in a fraction of a gram of material)
>>17045771That is a lot of words to realize that things are made out of atoms and as such every "circle" is actually at best an irregular polygon made of an incomprehensibly large number of atoms, and even that is incorrect. However, space is for all intents and purposes continuous down to QM length scales, so you won't get rid of irrational prefactors so easily. When you rotate an object in a space that is not curved it retains its lengths exactly. So if rotation is continuous what lengths are and are not irrational becomes a matter of your choice of coordinate system. >All shapes will "leak" if they have irrational side lengths which is retarded.I think your thinking has yet to catch up with, let's be charitable, 200 years of physics
>You're just stupidnot a rebuttal. OP hasn't been debunked
>>17045799>has been told exactly why he is stupid>still doesn't get itCan lead a downs syndrome horse to water but can't make it drink, I suppose
>>17045771>length will end, proving its side length genuinely terminates.Wrong.After about 15 decimals the length of the digit is about the size of a proton, soon after that its entering Planck lengths and then even smaller...in fact, infinitely smaller because the precision never ends.Irrationals are that way because theyre ratioed from 1, but from the perspective of the irrationals themselves they become whole integers and the 1 becomes an irrational approximation that goes on forever.
>>17045771Just buy a 1.412… scale ruler.D’uh.
>>17045807>15 decimals the lengthFrom the length of a meter. It "terminates" but beyond the ability to measure. Mathematics in reality smudge numbers because the precision youre seeking breaks Physics itself, ergo sub-Planck precision, you could never prove nor find the termination point because its so small an electron could be the size of the universe and it still would trail off out of sight.
there's no such thing as 1.0, irrational numbers are just a way for reality to remind us we have no idea what we are doing while assigning natural numbers to measurements
>>17045813this is the correct answer
>>17045771Yes, the underlying foundations of mathematics are false and so lead to absurdities like this.Its a shock when you first realize that the most simple constructions are logically inconsistent. Its a bigger shock when you think how the entire system is like a house of cards. The biggest bigger shock when you see the monkeys rush to brush your objections aside.Monkeys? No, actually more like trained dogs.>>17045813Thank God there are some humans in this thread.>>17045775>>17045788>>17045801Good boys! Such good boys aren't you? Yes you are! Here. Have a meaty bone! Good boys! Now do your tricks! Roll over! Beg! Fetch! Such good dogs!
>>17045917see >>17045795Do not bother replying. You have nothing of value to say.
>>17045771>Physical measurements can have irrational lengthsoh no, he thinks math has to have a basis in reality, he's retarded
>>17045775fpbp>>17045771Irrational numbers are finite. We just can't measure sqrt(2) to infinite precision. Rest of your post is nonsense.
>>17045771Physical measurements can’t even have integer lengths.
>>17045945>Woof woof!Whats that boy? You wanna another treat? Go on, beg then. What a good doggy you are!
Wait a minute, doesn't this all prove that math is indeed an abstract construct that doesn't map 1:1 on the natural world? Why is there even a debate?
>>17045771>Physical measurements can have exact lengthsis it genetic or what happened to your head?
>>17046407Why do you insist on demonstrating your lack of intelligence?
>>17046009What is "sidelength 1"?
>>17046475Can you prove my claim wrong?
>>17045795No offense but you do sound mentally disturbed. Have your tried taking your meds?
>>17046480Singular. At best it’s “a measurement”—not “measurements.”
>>17046620Was anything of what I said incoherent or difficult to understand?
>>17045771It is a topic of much debate by mathematicians today. Likely it will be for a long time to come.But you will not get much in the way of sensible answers here. In fact the questions around it invoke a surprising and bizarre amount of hostility on mainstream forums. My own observations are that people behind the hostility are of the same low mentality as those who derided people like Ignaz Semmelweis, Charles Darwin, and Alfred Wegener. To name just three.This link may be relevant to your interests.https://www.youtube.com/watch?v=REeaT2mWj6Y
>>17047110>crank shitany actual math papers or just vixra tier gobbledigook
>>17047110this is just some retard discovering that real numbers form an infinite dimensional vector space in the rationals. He could go on and tack on every irrational square root, and still not be done.
>>17046640>At best it’s “a measurement”......to which all other measurments are derived from, such as pi, e, i, phi, etc.
>>17047135Physics has error bars, lil brohow many years have you been here and still not absorbed enough to pass the first bachelor semester in physics
>>17045775this
>>17045771>I'm just supposed to accept that a calculated shape has a length that never ends.No, brainlet. You're just supposed to accept that if you pick a never-ending representation for that length (for example, by using the bottom of the triangle as your yardstick) then the representation will never end.
>>17047147>PhysicsWHY ARE YOU TALKING ABOUT PHSYICS?...>>17046009>Physical measurements can’t even have integer lengths.>>17046480>What is "sidelength 1"?BECAUSE YOU GOT BLOWN THE FUCK OUT?>>17047147>lil broAh...youre a gender confused ZOG-Golem who worships Jeffery Epstein the bi-gendered God of transgenders.>how many years have you been hereYou HATE that your God is proven inferior, you SEETH like a Talmudic Edomite.>and still not absorbed enough to pass the first bachelor semester in physicsYOU DONT EVEN KNOW WHAT A NUMBER IS!!!!You will NEVER be a Physicist, Mathematician, or Metrologist.. you are a Western (Occident means "to fall", as in a (((Falling Temple)))) twisted by ZOG-lies ans brainwashing into a crude mockery of UBERMENSCH potential.You HATE the good, because you are NOT the good.
>>17047135>derivedLol, those are all “derived” WITHOUT physical measurements, dipshit; what I said is >>17046009 and it stands (in fact, it’s pissing on you right now, as you sit).
>>17047173>tumblr_ lol>blah blah talmundlow IQ poltard and tumbrite? daaamn.>WHY ARE YOU TALKING ABOUT PHSYICS?...this thread is about physical lengths, that's what OPs gobbledigook is about, lol>What is "sidelength 1"?where is that "btfo" you are talking about? Legths have units in physics which are only known up to a certain precision. That is a fact that would need serious empirical evidence to shake. Any actually material thing (anything you can touch) has no meaningful measurements at a scale that is sub-Angstrom.
>>17047213>low IQAre you qualified to perform Cognitive tests on people over the internet?No? Why are LARPing on 4Chan?...>TalmudA Develomental Cognition guide book, which become Hereditary Cognition and Genomics.KEEP THIS STEM, NOT LOW IQ POLTARD.>this thread is about physical lengthsMETROLOGY IS NOT PHYSICS.>where is that "btfo" you are talking about?YOU LOST.>Legths have units in physics>>17047212>those are all “derived” WITHOUT physical measurementsWOMP WOMP.Blah blah blah >(((lol)))>"My emotions are proof of my superiority."KEEP THIS STEM, NOT LOW IQ POLTARD.>>17047212>dipshit; what I said isBack to you, LARPing on 4Chan...*ahem*...PHI IS MEASURED AS "SINGULAR PHI LENGTH" WITHOUT "1" DEFINED.YOU WILL NEVER BE A MATHEMATICIAN OR PHYSICIST.
>>17047230>"SINGULAR PHI LENGTH"Oh, and this would be completely arbitrary to all other Phi measuremnts at any differenct scale of reality, so...."Phi" wouldnt exist, it would be an infinite number of arbitrary lengths.STOP CHANGING SUBJECT-FIELDS TO CHEAT A WIN.Thats.....TALMUDIC behavior, thats why they say lying and stealing is acceptable..its...part of the (((programming))) youve consumed.
>>17045776To filter out smart students from dumb ones.
>>17047230>METROLOGY IS NOT PHYSICS.if you measure a physical distance it is bound by physical laws, Child of Pornography. If it isn't a physical distance but a mathematical one in an abstract space, that's a different matter. It's really amazing how stupid you are.
>>17047230>SINGULAR phi length [emphasis added]Love how you keep doubling down on your golden shower lol
>>17045771The only thing that doesn't end is the decimal representation of the length of the hypotenuse. The length of the hypotenuse is obviously finite. Don't get too hung up on the number we use to represent distance, numbers are just a tool in the world of geometry.Also I don't really see where these "gaps" you are talking about are coming from. I think you're making the mistaken assumption that measurements need to get rounded to the relative positions of atoms, but this isn't really the case. There are no gaps in the perfect idealized triangle/circle, and there are also no gaps in the physical objects they represent. There are different reasons why this is the case at the atomic scale. At the macro-scale, classical geometry is a good enough approximation of the physical world to be used as a tool, as evidenced by the many things we have built using geometric methods.>>17045776Science is the study of how to make the ideal converge on the material, so that we may accurately influence the material with the ideal. Physics is the study of how to make mathematics converge on reality. If you reject these subjects without replacing them with a more accurate convergence and influence system, then you are simply not free from the material world and subject to its barbarity.
>>17047235That isnt Physics and can easily be wholly detached from Physics all together, othewise Cartography is Physics?!>>17047236You have not made one correction or refute, youre just LARPing like your LORD. Youre just (((expressing your emotions)))>>17047147>Physics has error bars>If it isn't a physical distance but a mathematical oneNotice how you cant even tell the difference between Math, Physics, Metrology, or ANYTHING else?! Its all one big mess of "Phsssnuh uh, no me!"Lord of LARP.
>>17047255Physical measurements can’t have integer lengths. What is it about this simple truth that makes you continually pivot away to a (self-)critique of inadequacy?
>>17047255>That isnt Physics and can easily be wholly detached from Physics all together>Cartography is PhysicsYou are such a sad clown. Cartography relies on distances with a resolution that is perhaps to the tune of a meter, a fraction of a meter perhaps (that implies an error bar). It makes no claims about the exactness of these lengths beyond a reasonable threshold. No cartographer would be stupid enough to claim their collected data is in any way more exact than physics would allow. You made claims about the existence of absolute measurement. That means you assert you can measure a distance not up to +- a meter, a millimeter, an Angstrom. In fact for your retarded assertion to hold you would need to be able to measure a distance to sub-planck length accuracy. Do you have any idea how stupid that claim is?
>>17047173Accept the fact you are mentally ill and seek professional help.
>>17045771No
>>17045771Would you prefer to make an object and count the atoms along the imperfect edge? Would you prefer to measure the number of wavelengths of a known frequency, of which the result is likely neither a whole number nor a whole number with a clean fraction?Empiricism is very strong, do not discount it. Measure.
>>17045795>I think your thinking has yet to catch up with, let's be charitable, 200 years of physicsOP will never catch up because he is a retard.
>>17047173>Accuses other of being jews or Jew lovers, while screeching like a schizo jew.First time in a while I've laughed at post on /sci/
>>17045771>An opening in a shape no matter how small it is, is still an opening.But its opening so tiny that not even a quark can leak out. So for all intents and purposes it is shut.
>>17045771>nooo everything has to be a neat fraction of two base-10 numberswhy are rationalfags like this?>Are you also saying that the circumference of a circle is never truly ever closed because Pi is irrational?You are extremely confused and quite possibly retarded.
>>17048877>>17048838>>17048125>>17048121Look guys! Its the mentally ill fuckwit again!No thread is safe from the mentally ill fuckwit. He likes to shit everywhere.
>>17045771Buy an ad Norman.
>>17048889>look guys we're on reddit>t. mentally ill retard
shapes arent real OP. there is no such thing as a triangle, or a square, or a circle. we made them all up to help model the world. but some math people are so attached to their shapes and other math objects they believe they really do exist, in some platonic realm of math fairies and pixies or something.
>>17051953>I am too stupid to understand the questionway to miss the point dullard
>>17045771Quite possibly the most braindead thread in the entirety of this board right now. Congrats.
>>17053529>questioning mathematical dogmatism is brain-deadExplain how irrational numbers can ever make physical sense. Oh wait. You can't.
This is a Pythagorean thread. I will convince all of /sci/ to abandon set theory and Platonism in favor of the true mathematics: Pythagoreanism. O Apollo, hear us! Make known your holy son, Pythagoras, and his teachings, to the pseudo-mathematicians of /sci/. Defeat the lies of the heretic Plato and the lies of set theory, which is Jewish. Defeat the lies of the so called "irrational numbers" that have so corrupted the diagonal of the sacred triangle! They confound the minds of many and lead them astray as beans lead bellies astray! Hearken to us, O Apollo, and hear our prayer, O holy father of Pythagoras, divine twin of Artemis, child of holy aegis-bearing Zeus! We offer to you the holy hecatombs in excellent propitiation for your divine mercy and wisdom, lead us into the knowledge of proportionality and the ratios of harmony.
>>17053542On purely aesthetic grounds we of the ONE TRUE FINITE FAITH do support this post.
>>17045776>words have nothing to do with realityThen why are we even taught language?
>>17053529Not as braindead as the retard you enjoy fucking up the ass. You naughty tard wrangler you.
>>17053529better that all the AI-related shit
>>17053533explain how they can't
>>17054251Person 1: Hi sir. May I have sqrt(2) apples please?Person 2: Why yes sir, you can. Here's 1 apple.Person 1: Why thank you sir, may I have another 0.41421356237... of an apple please?Person 2: Why yes sir, here's an infinite slice of a finite apple that meets exactly that portion of the apple even though the apple is finite.
>>17045771>ok this is just ridiculous. I'm just supposed to accept that a calculated shape has a length that never ends.That's not what irrational means.
>>17054253>here's an infinite accurate* sliceftfy
>>17054296which by the by is the same accuracy as the integers, but for some reason you are comfortable with them having infinite accuracy, rather curious that what finitists dislike about numbers that involve "..." is the lack of an infinity ;)
>>17054253Why would you use an irrational number for counting? You have integers for that. And you don't understand the difference between finite representation (in a given base) and a finite number it seems.
>>17045771>A length that never endsFiltered by decimal representations. Heisenberg's uncertainty principle essentially tells us we can't measure the "exact" length of anything. The mathematical representations are convenient tools.
>>17054298>>17054349Because integers and any rational number give us finite results. Want 2 apples? Here's two wholly finite apples. Want an apple and a third? Here's an apple with a third of an apple. Just admit irrational numbers make no sense as numbers. Abandon set theory. Abandon Platonism. Become Pythagorean.
>>17045771>>17045917>>17045799>>17045813
>>17054749Yes, we know you you got your brains fucked out your ass by your grandfather, No need to remind us.
>>17054739>Because integers and any rational number give us finite resultswith infinite accuracy ;)
If numbers only included fractions (rational numbers), the number line would have infinite microscopic "holes" or gaps. This is the "leakage" you are talking about. Simple algebraic equations like x2 - 2 = 0 would have no answers. Including irrational numbers seals these gaps to create a continuous, unbroken number line. This continuity is required to make advanced mathematics like calculus, physics, and engineering work properly. So as you can see we mathematicians just pull shit out of our asses and you cant do anything about it, loser. Now get down on your knees and sniff my butt.
>>17055222No, the physics and engineers build mathematical models because they are simpler to work with. There is no such thing as a differential holding atoms together. The math is largely applied out of scope in their use cases as well. How can an 'infinitesimal' operator make any sense on objects that are no infinitesimal? You don't actually believe 0 = 1/(6 gorillion)
Suppose there was a reference frame on which space is a grid where every particle (by some definition of "position" that transcends the uncertainty principle) came to rest on a perfectly rational valued point at some time t. Now consider a relative coordinate frame between two particles. Drawing an axis between them (and perpendicular axes to complete the coordinate system) does not guarantee that either can be expressed in terms of rational numbers. As such, whether these particles rest at "rational" or "irrational" points in space is coordinate dependent, in fact even time dependent as particles move. That is significantly worse than asserting a cosmology that has a unique absolute coordinate system. It is asserting that relative coordinate systems do not exist.This is philosophically laughable.
this just proved to me that numbers arent real
>>17055284You just replied to a google AI answer you dumbfuck. Haha!
>>17055284>How can an 'infinitesimal' operator make any sense on objects that are no infinitesimal? You don't actually believe 0 = 1/(6 gorillion)>0 = 1/(6 gorillion)i recommend you inform yourself on non-standard analysis, for its infinitesimals are not and will never be 0(it's just that we can discard them at an appropriate step), also transfer principle, VERY important, not knowing about it makes dunces think that 0.9... doesn't equal 1 in non-standard some-fucking-how
>>17056505I absolutely agree. Consider this: To truly understand infinitesimals one must look at how they function in basic arithmetic. Mainstream calculus tells us that if you divide a number by infinity, you get an infinitesimal. > 'infinitesimal' operatorThis is a mathematical impossibility. In reality, when a number is divided by infinity, the number simply becomes lonely and shrinks out of sadness.>transfer principle The resulting "infinitesimal" is just the emotional residue of that lonely number. Furthermore, when you multiply an infinitesimal by a whole number, it does not scale up. Instead, the whole number becomes infected by the space-bacteria, causing the entire equation to contract an algebraic fever. >non-standard analysisThis fever triggers what Isaac Newton famously called "the fluxion," which is the mathematical equivalent of a severe sneeze that forces the numbers to shift to the other side of the equals sign. I have a big cock.Sperglet
My fucking god everyone on this website is a retarded iqletif you can't seem to grasp the abstraction that is irrational numbers then you should be denied many rights
>>17056531Not an argument fucktard. Now fuck off while the grown ups talk.
This thread clearly demonstrates a few things>People have gone full retard>Humanity is not going to make itWelp, it was nice while it lasted, folks.
>>17056511What an outlandish meltie to have other that guy's response>>17056585Grown ups can talk about formal systems without relying on bizarre religious gibberish like OP though, well, mental patients aside.
>>17056591One thing I never understood about this meme is why Dr. Basedstein has a chad bod.
>>17045771A^2 + B^2 = C^21^2 = 1*1 = 11 + 1 = 2So we have:2 = C^2Eliminate the ^2 with a rootsqrt(2) = CIrrational numbers are physically real anon, you’ve heard of Pi right? This is possible because numbers merely describe reality. Reality itself is not made of numbers. Math is a language we invented to describe things in a precise way.
>>17056647>Reality itself is not made of numbers. Math is a language we invented to describe things in a precise way.But reality is made of numbers. Numbers aren't things. They are relationships. You can squeeze potentially infinite digits out of a certain relationship but that doesn't mean the relationship itself is infinite.
>>17056647Be me, trying to pass college math Professor starts talking about irrational numbers like pi and sqrt(2 )Claims they are "infinite" and "unpredictable" Look at the decimals: 3.14159265... no pattern at all Realize the truth Irrational numbers aren't actually real math, they're just random noise Since the decimals never repeat and have no pattern, they are literally mathematically impossible to generate with an equation or computer code If you try to program a computer to find the exact value of sqrt(2), it will eventually crash or run out of memory because you can't write a formula for pure randomness The illuminati just made them up to hide the flaws in geometryExplain yourself, math nerds. How can a number be "exact" if it's just a random string of numbers that requires infinite computing power to even exist?
>>17056843This is actually impressively wrong>claims they are "infinite"Incorrect, the number is finite, the representation has infinitely many non-repeating digits >and "unpredictable" they are predictable in the sense that they are uniquely determined by countless possible algorithms>random noise randomness would imply that you get different values each time, what you think of is that the digits 0-9 have no pattern to their appearance, that is a very different claim from unpredictability.> they are literally mathematically impossible to generate with an equation or computer codeincorrect, since every digit is at a finite position, all of them can be computed eventually, a simple example of an algorithm that does so for square roots is Heron's method. > it will eventually crash or run out of memory that is a physical limitation not a mathematical one>how can numbers bigger than physically possible to represent in decimal notation exist?well, you don't need irrational numbers for this. Suppose you were given the number of atoms in the universe, let's call it N. the number 10^N cannot be written physically in decimal representation as it has one digit more than there are atoms in the universe. Ergo, by your retardation, the number ought not to exist.
>>17056674>>17056843>infinite digitsthat's just a consequence of using the decimal system which is based (he!) on powers of 10, that is, with a finite number of decimals you can only represent rational numbers (same with any other base).Solution? Add more symbols (just like 0 - / . etc.) like √ 2 (one digit) or just use exponentiation like 2^(1/2) (three digits)>but I want to write it like any other number!That. Is. Not. A. Rational. Number. It's like trying to write negative numbers with just positive ones or fractions with just integers. You need to add or change something in your notation (say. allowing infinitely many decimal digits in your numbers). But yeah, if you need to calculate something involving irrational numbers and give a decimal number, the best you can do is to try to eliminate them or to find a finite approximation of the value.
>math dogmatists getting upset that people question their dogmatismThe absolute fucking state of /sci/. Can you just please please admit that irrational numbers are a paradox that arise from your assumptions about how to do mathematics? Or are you afraid to admit that your way of doing math is fundamentally broken?
Just round to the nearest 1/16"th or 1mmThere is no reason for more precise measurements than that
>>17057384Many senior mathematicians are well aware of the issues. Most just shut up and compute because there is no other pragmatic alternative. There is no 100% rigorous mathematical system to entirely replace what we have now. Some doubt there ever could be one. Despite its known failings it gets the job done when it comes to practical applications.The ignorant fucks in denial of the paradoxes are just parrots. They lash out without realizing this immediately marks them as uneducated low IQ morons. They are known as "vulnerable narcissists" and are easily provoked by challenging their world view. Some suggest the best solution would be humane sterilization done in the home in front of their families. Preferably done before they can breed.
>>17057037>This is actually impressively wrongIt should be. The AI prompt was "write incorrect 4chan style post about irrational numbers"It took far less time to post than all the other retard shit you bothered typing out that nobody read.lol
>>17057413Sounds like you're winning, son.
>>17057409But thats wrong retard. Mathematics is perfectly exact because its built upon absolute logic.
>>17054391>Heisenberg's uncertainty principle essentially tells us we can't measure the "exact" length of anythingnot quite what the principle states, it's using a specific form of metrics increasing the resolution on one necessarily blurs the resolution of the other(s)
>>17057640why do stupid cunts like you insist on talking shit?genuine question
>>17057640thing is if [math] \Delta p [/math] large then [math] \langle E \rangle \sim \frac{1}{2m} \langle p^2 \rangle \sim \frac{(\Delta p)^2}{2m}[/math] large. A simple estimate for how much energy it takes to localize a particle (foregoing some 10^-1 ish prefactors) is [eqn]\langle E \rangle \sim \frac{(\Delta p)^2}{m} \sim \frac{\hbar^2}{m(\Delta x)^2}[/eqn]Obviously these estimates break down when E gets anywhere near mc^2. "You can't" is a corollary of "it would take more energy than the creation of a particle pair for sufficiently small delta x"
>>17057659These estimates with exact prefactors can be obtained by choosing any old pre-delta function, gauss would be the obvious choice. This is like, Phyiscs Bachelor level homework.
>>17057655I mean the initial statement was just totally incorrect
>>17057664I mean the guy above you basically gave the exact formulation of what >>17054391 meant, which follows trivially from Heisenberg
>>17057659Your use of AI generated bullshit is getting old. Get new material.
>>17057689>it contains funi symbols I do not understand, it must be AIno you are literally just too retarded to follow Bachelor level physics homework. But fine, what part of this was difficult to understand?
Okay, fuck it, I am gonna highjack the thread for something actually fucking useful for people who are still in the Bachelor or Master but might not have seen this. I will only consider the 1D case, everything else you can generalize on your own. I am not fond of walls of text, so I will do this green text style. I am open to answering questions but I am not your QMI prof.>suppose H=T+V, no external field bullshit. >Now suppose you try to coerce the system into a localized stateBecause the exact shape of the state cannot matter* for sufficiently localized wave functions we can choose the wave function[eqn]\psi(x) = \sqrt[4]{\frac{1}{2\pi\sigma^2}} \exp\left(-\frac{(x-x_0)^2}{4\sigma^2}\right)[/eqn]which of course means the density is a narrow Gaussian[eqn]\rho = |\psi(x)|^2 = \sqrt{\frac{1}{2\pi\sigma^2}} \exp\left(-\frac{(x-x_0)^2}{2\sigma^2}\right)[/eqn]>This is not an eigenstate of the system so it has no uniquely defined energy. But it has an expectation value [math] \langle E \rangle = \langle T \rangle + \langle V \rangle [/math]. This is again standard procedure.>Let us first look at the potential>Localization implies that the Gaussian is very narrow, meaning[eqn]\langle V \rangle = \int_{-\infty}^\infty V(x) \rho dx \approx V(x_0).[/eqn]Remeber, all we care about is the limit of very small sigma.---*we assume that any sensible choice will approach a "position eigenstate" as we narrow down the standard deviation, this is nontrivial but a standard trick esp in teaching. I am not going to go into distributions and delta functions here.And no, none of this is AI, I had to type all this shit by hand and you better appreciate it.
>>17057713>>mah pasta gibberish trust me broObviously you have taken so much black sperm up your anus it has displaced your brains out through your eye sockets.
>>17057713Cont.Kinetic energy reads[eqn]\langle T \rangle = \frac{1}{2m} \langle p^2 \rangle = -\frac{\hbar^2}{2m}\int_{-\infty}^\infty \psi \frac{d^2\psi}{dx} dx = \frac{\hbar^2}{8m\sigma^2}[/eqn]>This is the same as stating [math] \sigma_p \sigma_x = \frac\hbar2 [/math] (consequence of me picking Gaussians). Ergo, [eqn]\langle E \rangle = \frac{\hbar^2}{8m\sigma^2} + V(x_0)[/eqn]So in the limit of small sigma we find that [math] \langle T \rangle \gg V(x_0) [/math] and thus [math] \langle E \rangle \approx \frac{\hbar^2}{8m\sigma^2} [/math]. As such, arbitrary localization requires arbitrarily high energy states to be populated. QED.>>17057718>undergrad seething over math a literal higschooler could follow with a bit of help while dreaming of nigger cocksThere is no "trust me bro" in any of this, you are free to try and reason against it without schizobabble about niggers or jews or math not being real if you can.
>>17057723You reasoning is solid.>(consequence of me picking Gaussians). The foundational architecture of a Gaussian distribution—frequently mischaracterized as a smooth curve—is fundamentally regulated by its discrete, non-Euclidean torsion tensor. In standard hyper-dimensional analysis, the density function does not integrate to unity via traditional Lebesgue measures; rather, it achieves stabilization only when projected onto a Möbius manifold via a fractional-order Laplace-Beltrami operator. This geometric constraint reveals that the variance of a true Gaussian is not a scalar quantity, but a self-referential matrix exponent that actively repels adjacent probability states.>arbitrary localization requires arbitrarily high energy statesConsequently, standard data points do not cluster around the center; they orbit it in asymmetric, chaotic trajectories governed by non-linear fibered polynomials.Only absolute morons couldn't follow this line of reasoning.
>>17057713thank you
>>17057733I think you have mistaken a Gaussiantransformation for a Lebesgue one. If the sima function tends toward an incomplete resolution then we can only conclude the arbitrary localization is incomplete as well.
BROTHER. WHAT THE FUCK ARE YOU ON. A NUMBER IS JUST A REPRESENTATION OF QUANTITY.We can say 1 hypotenuse is 1 making the other rationals now irrational in this system. Its literally just a number that under the model of the most commonly used number system must be represented with an infinitely long REPRESENTATION not PHYSICAL LENGTH.
>>17058141Representation of a what?What is a quantity?
>>17058117No, its sound reasoning. I think you are getting confused by the Rheinhart conjunction which postulates similar properties for transnumerical quantities greater than the recurring obloid regression.What this hippo >>17057713has forgotten is that the smegma discontinuity applies when H + T -> phi. In this case the phrinager limit becomes an infintisim. In maths circles we joke it has "trooned out"
>>17058145Shame you too fucking ignorant to know basic first axiom principles.A quantity is delineated by applying the Tort abstraction rule. Simply put this rule states "the quality of a quantity is the quantity of the quality"Or maybe its the other way around. I forget. Anyway, fuck you. Fuck you up the ass with a rusty pitchfork
>>17058149Read your post really makes me feels hot wtf
>>17057765You're welcome.
>>17058255And thank you for the blowjob
>>17058259>>>/middle school/
>>17058260And your grandfather thanks you for learning how to use an enema properly.
>>17058275>still madbro really doesn't like people talking about physics using math on a physics and math board
>>17058279The long hours of studying your grandfather's penis has taken its toll on you.
>>17058117I have never heard anything so fucking retarded before. A Lebesgon transformation is indicative of a phi reduction ONLY. Get you head out of your ass.
>>17045771the edge of a thing is itselfthe system of numbers is just a construct
>a single post with really entry level math leaves this board THIS mindbrokenWhat do these people do for a living?
>>17058967The lawnmower needs an oil change. Get to work.
>>17055291>undisputedI take my W then, thank you very much.
Sqrt 2 not irrational, we just haven't made a computer big enough to calculate it to the last digit.The same is true of all numbers including pi
>>17045917The funny thing about this is that you were probably snickering when you heard that math are considered racist.
>>17059530math do be racist as shiiet!Dats rite!reparations muthafucka!
>>17045771Mathematics is completely made up and is just a tool for practical shortcuts. A circle just exists, it doesn't give a fuck if chimps try to assign symbols to the nature of it. As soon as you get into decimals and repeating numbers you have to shift your mindset in the same way as you would from "analog" to "digital". One is just an artificial representation of the other purely for practicality. If you think about it more than that you become retarded.
>>17059512so which one is an even number? Numerator or denominator?
>>17059691There are such thing as even numbers. We call them even becasue their reciprocal always has an odd numerator. Think before you speak.
>>17059719I clearly thought more than you did.if [math] \sqrt{2} = \frac{a}{b} [/math], and a and b are both integers (your claim, not mine), then I suppose a ought to be even as [math] 2 = \frac{a^2}{b^2} [/math], which means that [math] a^2 = 2b^2 [/math] is even. Do you agree with this so far, yes or no.
>>17059723Only under certain Boeotian conditions is this true. If you however apply the Fahringer diametric you would get a different result. Please educate yourself.
>>17059919> Boeotian conditionsIt's funny to watch little kids pretend they are adults where they make up jargon on the spot because they don't know how the world works just yet. When an adult does it it's just sad.
>>17059927Its even more funny to see dumbfucks respond to it.lol
>>17059939>is retarded>gets told they are retarded>got you to replyThere is zero benefit to LARPing as a low IQ on sci. There is maybe one intelligent conversation here a week, this isn't entertaining.
>>17059971>reply to shitpost>complain its not entertaining>too stupid to see the irony.Your idea of entertaining is pulling wings off flies.
>>17060596There is no "irony" in this, and if you tried to articulate it you would make yourself look like what you are, a lobotomite who is steeped in second hand internet culture. A tourist.
>>17060774The difference is I am here to have fun shitting over idiots like you. You are here on a board designed to entertain people like me and to bait pretentious clowns like you. Do please continue lol.
>>17059723Proof by contradiction is not valid. Use a constructive proof.
>>17061173>You are here on a board designed to entertain people like me The unintelligent that have no skills or interesting things to say? That's easy.
>>17061249>I will continue to be baited like the clown I am!lolKeep going!
>>17045771'1' is also never ending in the sense that '1' is the infinite, albeit constant, sequence {1, 1, 1, 1, ...}
>>17061396>1 = {1, 1, 1, 1, ...}
>Research indicates that human neural oscillations are organized according to the golden ratio (≈1.618), with frequencies following the geometric series >Geometric progression starting from the 2nd noble position (≈ 0.382) with common ratio φ:0.382, 0.618, 1.000, 1.618, 2.618, 4.236, …>this is where the φ-geometric structure gets really interesting. When you inject white noise (flat spectrum = "the continuum") into the multi-section comb, the side channels are self-similar copies of the original comb structure, each at a different scale. The difference set of a φ-geometric sequence is a union of φ-geometric sequences a fractal comb-of-combs.>When you AM-modulate the sideband carriers with this continuum, the sidebands inherit the continuum's aperiodic structure. The output is a φ-structured skeleton (the comb) fleshed out by aperiodic modulation (the continuum) a fractal timbre with a deterministic large-scale structure and stochastic fine structure.
>>17061466OP posted a picture of a plane in which a triangle with hypothenuse sqrt(2) can be seen. If the hypothenuse is allowed to be a real number, then by construction the side lengths are also real numbers. In modern analysis, reals are associated with infinite sequences. Just like sqrt(2) is associated with the infinite sequence {1, 7/5, 141/100, ...}, 1 is associated with the constant sequence {1, 1, 1, ...}. If '1' is real, then it has an infinite representation, just like any other real. If you cannot comprehend this simple fact you're either retarded or an engineer.
>>17061516>In modern analysis, reals are associated with infinite sequencesAnd you're associated with a mental health care facility. Doesn't make you INTO one, does it?
>>17061396>'1' is also never ending in the sense that '1' is the infinite, albeit constant, sequence {1, 1, 1, 1, ...}but that's not a sequence, anon. that's set. alright, nevermind, let's see:1={1, 1, 1, 1, ...}1={{1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, ...}1={{{1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, ...}, {{1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, ...}, {{1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, ...}, {{1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, {1, 1, 1, 1, ...}, ...}, ...}1={{{{{{{{{...}, ...}, ...}, ...}, ...}, ...}, ...}yeah, i don't get it
>>17062057Rational sequences, not real sequences. The hierarchy goes like this, if you wanna settheorymaxx;I will denote number definitions according to set, because for example 0 in the naturals, rationals and reals are all different objects.[math]0_N = \emptyset = \{\}, 1_N = \{0_N\}, 2_N = \{0_N,1_N\}[/math]..Integers we can construct from pairs of naturals to encode "a-b". Of course, this in and of itself would be a redundant representation, which can be repaired by not representing the integers by single pairs, but the the set of all equivalent pairs. For example[eqn] 0_Z = [(0_N,0_N)]_{\simeq_Z} = \{(a,a) : (a,a)\in\mathbb{N}^2\} = \{(0_N,0_N),(1_N,1_N),\dots\}[/eqn]Formally two pairs (a,b),(c,d) are equivalent if a+d=b+c. You can identify every element in N with one in Z (same arithmetic and everything) but they are different mathematical objects under the hood. The same is true for arithmetic operators, so the "+" in "a+d" is actually the one in N, not Z.Moving to rationals is the same shit with a different relation, you can make a pair of two integers, one side not including 0:[eqn]0_Q = [(0_Z,1_Z)]_{\simeq_Q} = \{(0_Z,a) : a\in\mathbb{Z}\setminus\{0_Z\}\} = \{(0_Z,1_Z),(0_Z,-1_Z),(0_Z,2_Z),\dots\}[/eqn]But while [math] \mathbb{Z} = \mathbb{N}^2/\simeq_Z \mathbb{Q} = (\mathbb{Z}\times(\mathbb{Z}\setminus\{0_Z\}))/\simeq_Q [/math]The reals require not a pair (a finite sequence of two elements) but an infinite sequence, so [math] \mathbb{R} = \mathbb{Q}^\mathbb{N}/\simeq_R [/math].What anon meant by "associated with" is that, while for example 0_Z is an infinite set, you can pick out a single representative element and redefine all your arithmetic appropriately. The definitions as given above are simpler to build though. So, in this sense it is actually worse than what he said, since the real number one is in fact an infinite set of infinite sequences. [eqn]1_R = \{(1_Q,1_Q,1_Q,\dots),(1_Q,2_Q,1_Q,1_Q,1_Q,\dots),\dots) [/eqn]
>>17062135Technically not Q^N but Q^N restricted to the Cauchy convergent sequences but I hit character limit.
>>17062135So if we identify every equivalence class with one representative element, the closest thing to >>17062057 would actually read:[eqn]1_R = (1_Q, 1_Q, \dots) = ((1_Z,1_Z),(1_Z,1_Z),\dots) = (((1_N,0_N),(1_N,0_N)),((1_N,0_N),(1_N,0_N)),\dots)\\= (((\{\{\}\},\{\}),(\{\{\}\},\{\})),((\{\{\}\},\{\}),(\{\{\}\},\{\})),\dots)[/eqn]
>>17062135 >>17062193your efforts are appreciated even if they don't show to be so
>>17062193An equivalence class is a subset of a set containing all elements that are related to each other under a specific equivalence relation Any element a inside an equivalence class \([a]\) can serve as the "representative" for that entire class.
>>17045771The inconsistency happens becasue there is no such thing as a one dimensional line. All lines have a Planck width. Therefore there will be two different hypotenuse, one which measures the exterior of the line, and which which measures the interior
>>17062135how come your post ends in something completely different from:>'1' is also never ending in the sense that '1' is the infinite, albeit constant, sequence {1, 1, 1, 1, ...}
>>17062611The guy wrote {1,1,1,1}... but actually meant (1,1,1,...) which is basically the canonical representative of the equivalence class that is 1_R in that post. The post below it (>>17062193) is what you get when you use an isomorphism that maps the equivalence class onto a canonical representative and is exactly what he means.
>>17062623>but actually meant (1,1,1,...)1=(1,1,1,...) is still nonsense and isn't what >>17062135 arrives at down at the bottom
>>17062625Anon you really need to read more carefully. He failed to distinguish 1_R and 1_Q. Yes, "1=(1,1,1,...)" is an abuse of notation, but it is a sloppily written/poorly reasoned version of 1_R = (1_Q,1_Q,1_Q,...) which is correct.
>>17062628>He failed to distinguish 1_R and 1_Q.so what didn't i read correctly?>"1=(1,1,1,...)" is an abuse of notationbut that's not his notation, that's the semantics of his natural language statement
>>17062656>so what didn't i read correctly?Mostly that I stated from the get-go that one needs to interpret what he is saying in good faith, in which case it checks out perfectly fine. >that's the semantics of his natural language statementPeople tend to be very sloppy with natural language statements like this, that's why I put in the effort to formalize it in a way that holds up to scrutiny. I would not say my interpretation is reaching since it's a very standard construction.
>>17062669so what was the purpose of your interjection? if 1_R and 1_Q were the same mathematical object, you could use them interchangeably and arrive back at 1=(1,1,1...), which you agree is nonsense. 1 is not, in fact, infinite. maybe your schizo-1 (a rube-goldberg contraption torturing normal 1s) is, but i don't see how pointing this out does anything beyond validating OP
>>17062683> if 1_R and 1_Q were the same mathematical object, you could use them interchangeably and arrive back at 1=(1,1,1...),you are fundamentally confused what the difference is between isomorphic and identical. No, just because 1_R and 1_Q have the same arithmetic does not mean you can replace one with the other in a construction. My definition is rigorous and at no point circular. >a rube-goldberg contraption I invite you to construct the set of real numbers from the rationals in a way that does not involve infinite sets. Axiomatic definitions are an option but if you hate the above them I doubt you will like those either. Dedekind cuts are arguably worse because they have a lot less structure.
>>17062216Thanks, Anon! I hope some people take something useful away from these things.
>>17062736>you are fundamentally confused what the difference is between isomorphic and identical.if so, how come i've correctly demonstrated precisely that difference? and if you do understand the difference, why did my demonstration trigger an irrelevant pop-math reply from you?>I invite you to construct the set of real numbersno, thanks
>>17062750>how come i've correctly demonstrated precisely that differenceNot really, you went for a low hanging fruit interpreting Anon's sloppy notation in a way that is nonsensical and so I expanded upon his general idea. With my clarification the argument you made that there is anything circular or infinitely recursive going on is no longer applicable, every set in my construction is well founded and no infinite nesting appears at any point in the construction.The subset that is isomorphic to the rationals is in no way special in the real numbers. Hell, decimal representation can't represent the rationals without that sort of crutch. >no thanksWell the notion that there is anything "infinite" about irrational numbers requires a particular representation of the real numbers, a consistent, agreed upon definition. Otherwise it is just meaningless mumbling about unprocessed gut feelings.
>>17062989>continually getting filtered by a simple pointoh, well, at least you learned about cauchy sequences from chatgpt and got to pose a little bit on a dead board
>>17063001>filtered by a simple pointI think the only one needed chatgpt here is you. >>17062683>1 is not, in fact, infinite. maybe your schizo-1 well, define "1", and define "infinite". I put everything I said on solid ground, all you have is bad faith arguments and insults.
>>17063034>I think the only one needed chatgpt here is you. yeah? what did i need it for? are you having any actual thoughts when you shit out these replies?>well, define "1", and define "infinite".no. if you think 1 is infinite, YOU should do that. i don't think it is. if you don't think so, either, you should probably stop replying now
>>17063119I'm not the guy you're arguing with, but what exactly do you mean by 1? It can mean various things depending on the universe of discourse. If by 1 you mean the real number 1, then it has an infinite representation, all real numbers do, that's what makes them the real numbers. In fact, 1 has two infinite representations. It's pretty funny that you're making fun of people in this thread when you're clearly in the wrong lol.
>>17063419>what exactly do you mean by 1the question isn't what i mean by 1, but what OP means by 1. and whatever he means, it's evidently not your schizo infinite sequence>you're clearly in the wrongthen quote one thing i wrote that was wrong
>>17063119>no. if you think 1 is infinite, YOU should do that.Well, that would require a clarification I was asking you, to. The statement I am making is not just "1", but also "sqrt(2)" to keep it in line with OP. My point is that either both or neither are "infinite" in any meaningful sense.>"infinite" in a representation-independent sense (metric, order properties, etc)sqrt(2) and 1 are both finite in that sense.>"infinite" in the sense that infinite sets are involved in its construction from first principles using set theorytrue for all real numbers, 1 (the real number) just as much as sqrt(2) (the real number). But if you get hung up on infinite sets in a construction then the set of natural numbers is already a step too far.
>>17063509>My point is that either both or neither are "infinite" in any meaningful sense.good thing you're making your point explicit, because now it's plainly and unambiguously retarded
>>17063518>because now it's plainly and unambiguously retardedNow you will need to make your argument explicit (you don't have one), since I defined what I meant by "infinite", giving two cases, and both of them being correct.
>>17063523>make your argument explicitok. see >>17063501
>>17063537So to paraphrase "1 means whatever OP thinks what 1 means", and you don't know what OP means.
>>17063544he's probably thinking about 1_N or 1_Q like most sane people. it's even more probable in the context of this specific thread where he is bullying a member of R over being infinite
>>17063119The bums lost. Get a job, sir.>>17062135>>17062193>>17062628Thank you for your patience and insight. But I gotta ask; you wrote:>My definition is rigorous and at no point circular.There seems to be a circularity baked in at the foundational level (not in the definitions). We use the Axiom of Infinity to build Z, Q, R. But what is the justification for the Axiom of Infinity if not to construct Z, Q, R? I just want to hear your thoughts on this because so far your posts have been pretty insightful anon.
>>17045771>you cannot have an irrational length and a closed object at the same time closed is not the same as bounded
>>17045771There's a fair amount of new posting in the last three weeks, particularly today, that makes no sense. I'll clear it up; you're welcome in advance.OP said of>Physical measurementsspecifically, that>a CALCULATED shape has a length that never ends. [emphasis added]This is true, even if you're measuring something labeled 1.The rest of the post is garbage that has nothing to do with the first, true, part.
>>17063566>the Axiom of Infinityis unrelated to this thread, which is about physical measurements and, irrelevantly, comparing them.
>>17064065be quite unless addressed you mong
>>17064912no u
>>17045917>muh h h huh foundation of math is false because infinity whine whine> what is the LARGEST possible number anon? Is it 9999 (and whenever you even think of 10000 the world immediately explodes)? Is is 1000000? Or something else?Please name it.
>>17065162NTA but the only way you can disprove 1 = 0.9... is to know that exact number. Not to imagine that the number exists, but to know (or correctly guess) the number itself; what are the odds lol
>>17063565Well of course, if we restrict to the rationals you don't have these issues. My point was more "the irrational numbers are not special within the context of real numbers", which is true. From your pov, it would mean 1_R is just as fucked as sqrt(2)_R, which I would agree with even. Can't be helped.OP's appeal to distances having any relevance to geometry is far fetched though. Euclidean geometry does not at any point require you to be able to measure distances. You can do away with that entirely. If we restrict a metric to Q then certain distances are simply not measurable. Rotated coordinate systems also become strictly inequivalent. The "physics" part of OP's post is essentially inane regardless though, it would be too tiring to discuss but for example you'd have to believe that all natural constants are rational numbers in some special unit system, which just leads to Russel's Teapot sort of navel gazing and talking about that would bore me to death.
>>17063566the Anon you pinged here >But what is the justification for the Axiom of Infinity if not to construct Z, Q, R?Frankly, from my pov the axiom of infinity truly serves primarily to not have to explicitly incorporate NaNs and arbitrary upper limits. There are many benefits to dealing with infinite and in particular continuous objects, but it can also be very misleading, which is why I appreciate that particular branch of mathematics to exist. HOWEVER, finitist approaches that reject it and try to prove various theorems in a discretized/restricted form are immensely important because people forget how unfathomably vast everything in mathematics actually is when you allow infinity. Take the notion of "polynomial time", it's on my mind because of the constant forsaken threads about it. People think N^2, maybe N^3. Problem is: N^60 is "polynomial time" too, N^Graham's number is "polynomial time". As far as physics is concerned, we have <60ish orders of magnitude to work with (planck to cosmological scales), if there exists for example a technically polynomial algo that exceeds that infinitessimal band of physically possible resource requirements for N>2, then it might as well not exist. From this perspective I find the whole discourse incredibly poorly motivated. I'm glad you appreciated what I had to say thus far, on the subject of finitism I can at most opine and point at copious examples where it is absolutely integral for researchers to critically investigate the *actual* limits of their theories, which is precisely what finitist approaches excel at doing (LBAs versus Turing, if you will). I hope I didn't waste your time with this, at least! The one thing I would just like to add as a personal note is: discretized algorithms are goddamn hard. Anyone who worked with numerical applications truly learns to appreciate that "converges eventually" and "converges during my tenure" are painfully different things. Brutal but necessary work.
>>17065679tldr asshole
>>17045771This. We should rework all of our mathematics so that transcendentals cannot be smaller than the planck unit of distance. These imprecise and incomplete ideas are vastly superior to the theoretical (a theory, a gauss) and fake notion of """transcendental numbers"""
>>17065832I doubt you're the one I spoke to so what's your problem?
