Heisenberg's Uncertainty Principle with

[@TomRocksMaths]

Watch part 1 where Michael teaches me about Lie Algebras here: kzbin.info/www/bejne/iancZYp6frqmbK8

[@ready1fire1aim1]

Theory of Everything solution: [Short answer] swap from Newton to Leibniz as our fundamental blueprint of the universe. [Long answer] I contend Gottfried Leibniz was correct about the fundamentals of our contingent universe and he just lacked 2022 verbiage and Hamilton's 4D quaternion algebra. More importantly is that humanity chose Isaac Newton's "real" universe, calculus, gravity, etc. This was a big mistake. We need to correct this problem. Finishing what Leibniz started (with the intention of destroying what Newton started): [Math; Geometry 0D point (Monad)] A point is a 0-dimensional mathematical object which can be specified in -dimensional space using an n-tuple ( , , ..., ) consisting of. coordinates. In dimensions greater than or equal to two, points are sometimes considered synonymous with vectors and so points in n-dimensional space are sometimes called n-vectors. 1D = line, straight; two points; composite substance; matter 《0D (point) is exact location only; zero size; not a 'thing', not a 'part'; Monad》 "He is the invisible Spirit, of whom it is not right to think of him as a god, or something similar. For he is more than a god, since there is nothing above him, for no one lords it over him. For he does not exist in something inferior to him, since everything exists in him. For it is he who establishes himself. He is eternal, since he does not need anything. For he is total perfection. A being can have a relationship with a God but not the Monad as that would be a contradiction." - The Apocryphon of John, 180 AD. Monad (from Greek μονάς monas, "singularity" in turn from μόνος monos, "alone") refers, in cosmogony, to the Supreme Being, divinity or the totality of all things. The concept was reportedly conceived by the Pythagoreans and may refer variously to a single source acting alone, or to an indivisible origin, or to both. The concept was later adopted by other philosophers, such as Gottfried Wilhelm Leibniz, who referred to the monad as an elementary particle. [Quantum] Quark is a type of elementary particle and a fundamental 'constituent' of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. What is another word for quark? fundamental particle, elementary particle. Do quarks take up space? Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up space. How fast do quarks move? the speed of light [In mathematics, a tuple is a finite ordered list (sequence) of elements. An n-tuple is a sequence (or ordered list) of n elements, where n is a non-negative integer. There is only one 0-tuple, referred to as the empty tuple. An n-tuple is defined inductively using the construction of an ordered pair] 1st four dimensions are 0D, 1D, 2D, 3D ✅. 1st four dimensions are not 1D, 2D, 3D, 4D 🚫. Human consciousness, mathematically, is identical to 4D quaternion algebra with w, x, y, z being "real/necessary" (0D, 1D, 2D, 3D) and i, j, k being "imaginary/contingent" (1D xi, 2D yj, 3D zk). 1D-9D 'contingent' universe has "conscious lifeforms" (1D xi, 2D yj, 3D zk)..."turning" 'time'. [In mathematics, a versor is a quaternion of norm one (a unit quaternion). The word is derived from Latin versare = "to turn" with the suffix -or forming a noun from the verb (i.e. versor = "the turner"). It was introduced by William Rowan Hamilton in the context of his quaternion theory.] [Math; 4D quaternion algebra] A quaternion is a 4-tuple, which is a more concise representation than a rotation matrix. Its geo- metric meaning is also more obvious as the rotation axis and angle can be trivially recovered. How do you make a quaternion? You can create an N-by-1 quaternion array by specifying an N-by-3 array of Euler angles in radians or degrees. Use the euler syntax to create a scalar quaternion using a 1-by-3 vector of Euler angles in radians. "Turn" to what, you might ask. 5D is the center of 1D-9D. The breadth (space-time). All 'things' and 'parts' are drawn to the center, the whole. (The Dawn -Book of Cain on the creation of the contingent universe) [Contingent Universe]: 3 sets of 3 dimensions: (1D-3D/4D-6D/7D-9D) The illusory middle set (4D, 5D, 6D) is temporal. Id imagine we create this middle temporal set similar to a dimensional Venn Diagram with polarized lenses that we "turn" by being conscious. Which requires energy. 3D height symmetry/entanglement with 9D absorption is why we are "consumers", we must consume/absorb calories, and sleep, to continue "to turn" 'time' (be alive). 1D-3D spatial set/7D-9D spectral set overlap creating the temporal illusion of 4D-6D set. According to theoretical physicist Carlo Rovelli, time is an illusion: our naive perception of its flow doesn't correspond to physical reality. Indeed, as Rovelli argues in The Order of Time, much more is illusory, including Isaac Newton's picture of a universally ticking clock. Does time exist without space? Time 'is' as space 'is' - part of a reference frame in which in ordered sequence you can touch, throw and eat apples. Time cannot exist without space and the existence of time does require energy. Time, then, has three levels, according to Leibniz: (i) the atemporality or eternality of God; (ii) the continuous immanent becoming-itself of the monad as entelechy; (iii) time as the external framework of a chronology of “nows” The difference between (ii) and (iii) is made clear by the account of the internal principle of change. The real difference between the necessary being of God and the contingent, created finitude of a human being is the difference between (i) and (ii).] 1D, 2D, 3D = spatial composite (line, width, height) 4D, 5D, 6D = temporal illusory (length, breadth, depth) 7D, 8D, 9D = spectra energies (continuous, emission, absorption) Symmetry/entanglement: 1D, 4D, 7D line, length, continuous 2D, 5D, 8D width, breadth, emission 3D, 6D, 9D height, depth, absorption Conclusion: Humanity needs to immediately swap from "Newton" to "Leibniz". Our calculus is incorrect (Leibniz > Newton): What is the difference between Newton and Leibniz calculus? Newton's calculus is about functions. Leibniz's calculus is about relations defined by constraints. In Newton's calculus, there is (what would now be called) a limit built into every operation. In Leibniz's calculus, the limit is a separate operation. Our Universal Constants have convoluted answers. Leibniz's Law of Sufficient Reason fixes this in a day. (FUNDAMENTALS > specifics) Newton: "wait... Leibniz is Humanity's true universal genius?" Leibniz (behind Newton w/🔫): "always have been."

[@bendaniels7346]

@@ready1fire1aim1 This comment looks like the ones you see under KZbin videos that have copy paste scam links with Bible verses or something

[@ready1fire1aim1]

@@bendaniels7346 glad you didn't read it. Good to know thanks.

[@bendaniels7346]

@@ready1fire1aim1 BRO IT IS LIKE ONE OF THOSE COMMENTS HAHA I just read more of it

[@ready1fire1aim1]

@@bendaniels7346 Monad has significance. I'm not Religious. It plays. Theory of Everything marries Everything together. I read the fundamentals of the Religious sects only. Just want the info. It all lines up. If we swap to Leibniz (updating his 17th century verbiage and including Hamilton's 4D quaternion algebra UPDATED again with 0D, 1D, 2D, 3D ✅ in place of Newton 1D, 2D, 3D, 4D 🚫 empirical evidence nonsense) we have answers for quantum entanglement, can correct the gobbledygook that is String Theory, we can take Simulation Theory and "complete" it (contingent > simulated), gravity would make sense, complete E=mc2 so it doesn't break down with motion, etc. (Also solves Religious stuff).

[@iteerrex8166]

It’s a great pleasure when the student completely follows and even is thinking a step or two ahead.

[@timkohl9831]

What I also like about this is that it dispels the notion that the uncertainty is due to poor experimental procedure, but rather it is actually intrinsic to the system itself.

[@DanWestonX]

It's cool to see this derived so simply and purely algebraically. For some very dumb reason, lower division physics students in the US first see this through its Schrodinger action on the eigenfunctions (as a superposition of spatial sinusoids = delta function in the Fourier domain) and observe the effect of changing the width of a spatial window on the width of the frequency spike. It's much more tedious and leaves the student wondering if the shape of the weighting function could be made more clever, or if it works only in some approximation or limit. The Heisenberg algebra came only two years later. I was envious of my math peers until I heard that they went through the same bad order, wading through real and complex analysis before ever seeing abstract algebra. Time for a reorder of the syllabus, I think!

[@richardneifeld7797]

Very cool! Thank you both, for both lectures. I really like the collaborative format as well as math and physics insights.

[@callummilburn8204]

I have followed you both individually so it is great to see you both team up. Especially in these two areas. I have forgotten my physics but did a degree in it years ago. But I remember having commutators but never knowing it was Lie algebra. I am currently embarking on a maths degree out side of my work. Part of me wishes to revisit quantum mechanics, and actually understand the maths more, such as the Lie algebra. This collaboration does this and thank you. It was done in away that could be followed and both presentations linked together enough. Thank you, more please :-)

[@trevorbroadhurst7794]

I'm so glad Dr Tom has learned to write in straight lines.

[@paulkohl9267]

Did not know Dr. Tom Crawford has his own yt-channel. Seen him as a talking head on math topics before. Good pair up. [MP, TC] = i Good.

[@TomRocksMaths]

nice

[@catrionalischka5718]

Great to see you 2 working together! but Tom, I think there is one super, super observation that you should add to your Heisenberg video: - that the Heisenberg exclusion principle applies to two operators precisely when they do not "commute" ie (using your notation) iff [A,B] is non-zero. After all you have gone to the trouble of introducing [A,B]=iC as a generalisation, rather than just talking about position and momentum, so why not hammer home the exact reason the dispersion is strictly positive. And this is really the mathematical motivation to link back to study the Heisenberg Lie algebra. Hope that makes, sense and keep up the good work.

[@twelfthdoc]

Very fun watching both parts. I remember being shown Heisenberg's uncertainty principle when I was doing A Level Chemistry, as it was a good way of explaining electrons, orbitals and spectra. We know roughly where an electron is and roughly what its excitation is, but as soon as we zero in on one metric, we sacrifice the accuracy of measuring the other.

[@dw5chaosfan]

There's an alternative proof in harmonic analysis involving the fact that the fourier transform of the position operator is the momentum operator (in natural units) and a function and that a function and its Fourier transform cannot both be compactly supported (the general uncertainty principle in harmonic analysis). Personally I think this is more "clever", but definitely less elementary and I wouldn't be sure if it involves less machinery.

[@jacopobottoni8597]

I have learnt it like that and the method of this video is much more direct I think.

[@ryanlangman4266]

Do you know of any good sources that go through this proof? I took an intro Fourier Fourier analysis course, but we never went into that. I have heard that before though, and it seems very interesting.

[@scottmiller2591]

Yeah. It really boils down to the fact that the Fourier transform of a Gaussian is another Gaussian, the widths of the two Gaussians are reciprocals, and the product of the widths of the Gaussians is the equivalent to \hbar (times a constant) in the quantum mechanical setting. The Heisenberg uncertainty principle is a MATHEMATICAL, and not just a PHYSICS, relationship, which is often used in signal processing, for instance, to estimate the uncertainty of frequency from the duration of the measurement, where it has nothing to do with \hbar. When this Gaussian is substituted into the form of quantum mechanical operators, and using the relationship between the Fourier transform of d f(x)/dx and \omega F(\omega) the 4 chalkboards of calculations drop out instantly. See en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle - it can be done in 3 lines making the separability assumption, after proving the mathematical form, which can be done in about 3 lines as well.

[@scottmiller2591]

@@ryanlangman4266 See my reply to OP.

[@user-wu8yq1rb9t]

Great subject +Great People It would be so interesting. I'm waiting ....

[@DJsTeLF]

As a physicist my only request is that you put pointy hats on operators, so as to distinguish them from scalars, vectors, matrices, tensors, etc Aside from that tiny thing, it's a wonderful video. Thanks for all your hard work Doc

[@nathanborak2172]

There’s a good way to quickly see the origin of uncertainty without going too deep into the nitty gritty calculation. Remember that operators in QM represent observables, and their eigenvectors represent states of certainty where you are sure to get a measurement outcome equal to the eigenvalue. If the state is instead a linear combination of multiple different eigenvectors, then each eigenvalue represented in the sum of terms is one potential measurement outcome, with the square of the coefficient being its probability. Therefore, states that are linear combinations of multiple different eigenvectors (what physicists call a “superposition”) are states with uncertainty in the measurement outcome. Now, you can show in a couple algebra steps that two operators A and B can be simultaneously diagonlized iff [A,B]=0. Therefore, if they don’t commute, then if the state of the system is in an eigenvector of one of the operators it is *necessarily* in a superposition of the other’s eigenvectors, so if you know A with certainty then B must be uncertain, and vice versa. Uncertainty fundamentally comes from linear algebra, not calculus.

[@identityelement7729]

Great explaining!!!

[@DrDeuteron]

L.A. v. calc.... isn't that just wave mechanics vs matrix mechanics?

[@nathanborak2172]

@@DrDeuteron I have usually heard of this distinction as referring to the Schrodinger picture vs the Heisenberg picture, which is not what I'm talking about. My main point is that many qm results that are very clear when phrased in linear algebra are obscured by layers of calculation when phrased as calculus problems. In qm, calculus and wave thinking is just the linear algebra, but done in a particular basis.

[@pedroricardomartinscasella641]

Beautiful, just beautiful

[@TomRocksMaths]

Thank you very much!

[@vijaynarsapur147]

Outstanding explanation...

[@TomRocksMaths]

Glad you liked it

[@i_amscarface_the_legend9744]

Thank u Tom Rocks, i finally understand the Heisenberg's uncertainty Principle ! Beyond the hundered of hours of physics documentary that i have seen, always something not clear about it !

[@RC32Smiths01]

Awesome take on this mathematical and scientific concept! And of course, a cool collaboration!

[@sadmanislam5111]

Great video. Love the topic. You are a great mathematician. Thank you for all your videos

[@TomRocksMaths]

Glad you like them!

[@antoniocorvalan7151]

Amazing collab

[@MrFtriana]

It would be interesting speak about the Feynman's path integral, it's a wonderfull theme and the consequences are pretty awesome. For example, you could derive the Schrödinger equation using the principles of QM, using path integrals and rederive all the operator machinery. It could be great.

[@MrFtriana]

@@corporealcasimir4885 that's right.

[@artophile7777]

​@@corporealcasimir4885 Don't forget Maxwell

[@tomctutor]

Maths is awsome, physics is awsome too, but when you combine both you get; [awsome, awsome] = mindblowing As an aside, Heisenberg had to develop QM maths with infinite matrices, all very cumbersome. It was later that Dirac formalized the system as a complex vector space and invented (or maybe extended _Grassman's_ vector inner products) *_Bra-Ket _* that Tom sneaked onto his blackboard half way through.

[@georgschmidt8574]

Would be great to have someone like Tom as a teacher :)

[@markthebigogre]

The general equation for any two operators A and B is: Var(A)Var(B) >= h^2/4 ||[A,B]||^2 (These are done wrt the wavefunction ofc) But it holds for ANY two operators! :)

[@JoQeZzZ]

ANY two operators that don't commute! There's no issue between position in x and position in y for example.

[@markthebigogre]

@@JoQeZzZ yes then their product is zero. That case is included since the RHS vanishes. :)

[@JoQeZzZ]

@@markthebigogre lol did you just add that or did I look over it

[@farhanahmed2508]

Omg I adore you both

[@TomRocksMaths]

[@drziggyabdelmalak1439]

Dr Tom, loving the growing hair!

[@carlhindman2522]

You guys missed a golden opportunity to "explain" nonrelativistic QM (NRQM) as a consequence of Einsteins STR! When you reverse the order of position measurement and momentum measurement this is the same as reversing the order of a Lorentz boost and a spatial translation, which in Einsteins STR leaves a time displacement. This is the "relativity of simultaneity". If you look at the generators of the Poincare group, the basic symmetry group of STR and take the limit as the speed of light approaches infinity you find that Lorentz contraction and time dilation disappear but the non-commutation of Lorentz boosts (speed shifts) and spatial translations do NOT vanish but turns precisely into the canonical commutation relations of position and momentum definitive of nonrelativistic quantum theory. This was first noted by Jack Kaiser over 40 years ago and has also been independently recovered by Aage Bohr and Ole Ulfbeck, and by J. Anandan as well. It has yet to find its way into, for the most part even the graduate, let alone undergrad curriculum. What this means is that NRQM lives not in Galilean Newtonian space time but in a "contraction" of the space time of STR i.e. the limit just discussed. For the Shroedinger wave function this effect enters only as an irrelevant phase shift which has no effect upon observable probabilities, which perhaps explains why it was unnoticed for so long.

[@YourPhysicsSimulator]

What an interesting topic. I love TDSE solutions! I'm gonna watch it for sure! Great guest by the way, love you both ❤️

[@TomRocksMaths]

[@wtt274]

Great video !

[@TomRocksMaths]

Glad you enjoyed it :)

[@euanthomas3423]

You should have finished with " And that's a good place to stop."

[@TomRocksMaths]

lol

[@AliHassan-hb1bn]

To measure a position of a photon at a given moment in time-space you must have another photon that is faster than the one you are measuring.

[@zriteld]

Cool! It is interesting that Schrödinger equation is not used at prove.

[@thomasjakobsen2260]

"I don't understand it, but I accept it now, because I've done some math that I can follow and it tells me this is true"

[@TomRocksMaths]

Amen.

[@gcewing]

Pretty much the attitude you need for all of quantum physics!

[@homerthompson416]

Well Feynman said if you think you understand quantum mechanics, you don't understand quantum mechanics, so I'd venture this is where we all are with this result.

[@topilinkala1594]

@@homerthompson416 But I think Feynman was wrong. We now understand the mathematics of quatum mechanics and IMHO then we do understand qm. My question though is: Do antiparticles travel time backwards? If they do that explains why our universe is mostly non-antiparticles.

[@akirakato1293]

@@topilinkala1594 we still don't understand quantum superposition though, we just know it is what it is by what it cannot be which is everything that's describable using classical physics. we can describe its behavior through wave function but not why it does what it does.

[@sumdumbmick]

my intuition was always the opposite. the uncertainty principle always made more sense to me than everyone's claim that it's weird. if you take a photo of something in motion, it's blurry. you can increase the shutter speed to improve the measurement of the position, but this reduces the accuracy of the measurement of the momentum, and vice versa if you decrease the shutter speed. I'm not sure how anyone would find it unintuitive, since this basic experience is everywhere in daily life. it's how you interact with your crush, how traffic signals work, literally everything. to say that it only manifests at the quantum level is just bizarre. like Michael says, what he showed with Lie Algebras is just a more general case, and it appears everywhere.

[@Ma_X64]

Think about this. The Schrödinger equation is the equation of oscillations of a MATERIAL point in a potential field. In fact, this is just an equation of a pendulum, described from the point of view of Lagrangian mechanics (total, kinetic and potential energy). And if we describe with this equation a set of nearby points, we should get fluctuations in mass density. So why the hell are we talking about probability density when considering electron clouds? And if at this particular point in space the probability density of finding an electron is constant, then what mechanism ensures this constancy?

[@alxna._]

would you be intrested in making a video about the math olympiads eg. a question from the maths olympiad past test (that's challenging)

[@shruggzdastr8-facedclown]

Could this collaboration possibly indicate that we might see Michael ftd. on an episode of Numberphile some time in the future given that Tom has appeared as a guest a lot on Numberphile?

[@shruggzdastr8-facedclown]

Is the Schrodinger equation being explored here the same as in the famous Schrodinger's cat thought experiment paradox or some other QM equation he authored?

[@bocckoka]

uhm... if your potential is not a function of time, then you get the 'simplified' Schrodinger, Hpsi = Epsi, so your energies are the eigenvalues of the Hamiltonian.

[@shuewingtam6210]

At 12:35 expectation equal ......inner product of wavefunction with its conjugate ?

[@JoQeZzZ]

Yes! From statistics we know that the expectation value of some parameter is the sum of that parameter times its probability density function. For example the average value of a fair j-sided die is Σ P(i) . i = Σ 1/j . i for i in {1, 2,.. j} For discrete variables this sum turns into the integral. The magnitude of the wave function squared (Ψ* . Ψ) is the probability density function of a particle, by definition. So that is why ∫ Ψ* . Ψ . A dx is the expectation value. The reason we write is because of the definition of the inner product, the first term gets hermitian transposed, and we want our A not-conjugated.

[@shuewingtam6210]

You missed introduction of ket and bra notation.

[@sschmachtel8963]

Amazing. Truely. And given you assume that the assumptions are True or make Sense then the Uncertainty principle follows. Due to you accepting the assumptions . Never would have been able to guess that this is basically not due to Quantum mechanics , but merely due to properties assumed in Quantum mechanics to be true. Quite amazing for physics or in general measurement of such alike properties... ! Kind of cannot be wrong if your assumptions are right. Who would have thought that?? Heisenberg uncertainty principle mathematically proven to be correct given the assumptions. Great stuff!!! And so different than most of the other stuff in physics which is about models that strictly speaking cannot be proven to be right. :-o

[@flavioxy]

Man our derivation in 3rd semester was so much shorter :D

[@tomgilbert4848]

jesse

[@kappasphere]

12:29 Why does this still need to be normalized? I thought |ψ|² was the probability density, so integrating that over the entire volume should just yield 1.

[@AliHassan-hb1bn]

You guys are measuring the immeasurable. You can't devide time-space into time and space because they are inter-coiled, ie they are inseparable. It needs mental lab not physical lab to understand.

[@julianking6513]

This is when Walter White became a Mathematics teacher instead of a chemistry teacher

[@sh6700]

Is this a true derivation, considering the ih in the Schrödinger Equation is from the assumption of Heisenberg’s Uncertainty Principle, (assumption of wave functions being linear combos of sines and cosines, and use of complex exponentials as representation thereof) as is the ih in the momentum operator, and even the assumption of probabilistic properties when calculating the dispersion, expectation values, etc.? Seems somewhat circular. Granted, I’m no expert so I could be mistaken.

[@gcewing]

Planck's constant doesn't come from assumption of the uncertainty principle. It comes from the relationship between energy and momentum in special relativity, together with the experimental observation that light energy comes in quanta proportional to wavelength, which implies that momentum is related to wavelength, with h being the constant of proportionality. That's the reason h appears in the momentum operator, and thus finds its way into the Schroedinger equation.

[@sh6700]

@@gcewing I was more referring to the presence of i in ih, which I was under the impression came from the complex exponential, which is there because of the concept that the wave function is just that: a combination of sine and cosine waves, which is represented in the complex exponential. This idea that it is the combination of oscillating waves seems to inherently assume an indeterminacy of quantum states.

[@gcewing]

@@sh6700 No, it comes from the hypothesis that the relationship between momentum and wavelength that was discovered for photons applies to all particles, and thus all particles behave (at least in some ways) like waves. The complex exponential is just an obvious way to represent waves. And once you have the idea of a particle being a wave, with momentum equalling wavelength, the fact that it can't have both a definiite position and a definite momentum becomes kind of obvious. The wave can either be bunched up in one place with a sharply defined position, or spread out with a sharply defined wavelength, but not both.

[@sh6700]

@@gcewing Ohhhh. That makes a lot more sense. Thanks for clearing things up.

[@shruggzdastr8-facedclown]

Are the i- and j-variables seen in the working-out of this equation to be interpreted as quaternion in nature; if so, is there a k-variable as well?

[@gamerdio2503]

i and j are just indices representing the different coordinate axes. In 3 dimensions, both i and j range from the integers 1 to 3. p_1 would be momentum in the x direction, p_2 would be y direction, and p_3 would be z direction, for example.

[@shruggzdastr8-facedclown]

@@gamerdio2503: Thnx for the thorough explanation!

[@steelbrotherhoodof2359]

according to murphys law. the heisenberg uncertainty or coidence. happens when you least expect it. thus means. constantly all the time.

[@steelbrotherhoodof2359]

for noobs. uncertainty is the rule. wverything constant , the expected and normal is gone. means statisticly. you can expected uncertain things all the time. makes it the new normal. thus makes un-certain, for certain. call thay evolution of the odd one out. everythig odd. except the (old) normal.

[@LeRainbow]

It's weird to me that the explanations are based on mathematical rather than logical derivations ... but right.

[@eosrose6126]

I m horrible at math, but it is somehow intriguing

[@TomRocksMaths]

as long as you're having fun :)

[@eosrose6126]

@@TomRocksMaths i do, a lot 😊. I just wish my general understanding would be better.

[@LeRainbow]

Heisenberg's uncertainty principle: your reality is based on the present.

[@TheUrns]

25:46 why does the discriminant have to be negative? Or why are there no real roots?

[@TomRocksMaths]

The quadratic in t is equal to the norm squared which is a positive object. This means the quadratic must also always be positive for all values of t. Therefore it does not cross the x-axis and as such has no real roots, meaning the discriminant is negative.

[@TheUrns]

@@TomRocksMaths this might be a dumb question but cant the norm also be zero?

[@TomRocksMaths]

The norm can also be zero which is why the inequality for the discriminant is less than or equal to (as opposed to being strict).

[@TheUrns]

@@TomRocksMaths thank you!

[@philcooper279]

The quantum world and macro world, are two different realities, rather like British politics.

[@byronwatkins2565]

In fact, we cannot "know them both in the real world" either. No measurement tool has unlimited precision. Estimate the precision in velocity that would be needed to determine the momentum of ~1 gram to the precision of hbar/1 mm. (I'll even give you hbar/1 micron, but smaller than that is the nanometer/quantum scale.) In math we might imagine doing so "by construction," but the real world is not ideal.

[@gcewing]

That's true, but the uncertainty principle puts a fundamental limit on measurement that's due to the nature of the thing being measured. It has nothing to do with the precision of the measuring device.

[@pranavjosep2119]

Walter Whites uncertainty principle

[@JamesWylde]

The blackboard is really a turn off. You've been on Numberphile, you've seen 3B1B, way better channels with animated explanations.

[@drdca8263]

Animations take a lot of work?

[@Untoldanimations]

what a completely unreasonable expectation to have of someone. maths is taught on blackboard. when you go to college you don’t go into a cinema and watch animations

[@bendaniels7346]

SAY MY NAME. Heisenberg

[@racquelsabesaje4562]

math

[@b4byf4c3455451n]

I have a different Interpretation [..] Endrit Vuka

[@morrispearl9981]

My solution is that the answer is the same for each digit, there are a total of 1000 numbers from 000 to 999, so a total of 3,000 digits, so the answer must be 3,000 / 10 or 300. (If the "0" are blanks, it would not make any difference)

[@wafikiri_]

Your solution to.... what? I'm afraid you've replied to the wrong video.

[@steelbrotherhoodof2359]

uncertaincy and coincedence and the intrepretation of a lower physic class by mass the consiouss intrepretation to find connection there where, could be, on a very narrow linear sequencial way. depending on the perception of your group. some species of humans form a collective or a multi organisme. too form part of a bigger. blablabla and bla

[@f5673-t1h]

Spoilers: Answer below (not in-depth, as that will probably be the content of the video) . . . . . . . A tenth of the time in each place, and there are 1000 3-digit numbers. So 100+100+100 = 300.

[@abebuckingham8198]

I started with 111 has 3, now I count the combinations with two such as 112,211,121, or 011=11, we have 9 possible combinations and three possible positions for a total of 27 which we double because there are two 1s in each for a total of to 54. For numbers with a single 1 we have three positions and 9^2 possible combinations to go with it so 3*9^2=243. This totals to 3 + 54 + 243=300.

[@TomRocksMaths]

nicely done both!

[@rebimpskitzo8489]

Um this guy Heisenberg is making a principle out of uncertainty. I don't think we should be listening to him. The other guy that likes to put his pet cats in boxes sounds much more credible.

[@Jkauppa]

bs, dont be uncertain, even if people lie about all the time

[@JesusChristlovesyou_friend]

Brothers and Sisters, God loves us so much that He sent His Son Jesus Christ for us to save us from our sins, and he bled and died on a cross for us to redeem us from death, and to gain life everlasting, for those who put their trust in him. And what's more, he has risen, and is willing to call you to repentance (correction) and as his witness, by his grace indeed. "For it is by grace you are saved, through faith". Jesus loves you, God cares for you! Therefore, repent and believe the gospel.

[@ready1fire1aim1]

Theory of Everything solution: Swap from Newton "real/necessary" universe over to Leibniz "contingent/not-necessary" universe as our fundamental blueprint of the universe. This includes Leibniz calculus vs Newton calculus. All of it. Leibniz rocks. Newton can kick rocks. Gottfried Leibniz "contingent/not-necessary" universe just lacked 2022 quantum physics verbiage (just match up definitions) and Hamilton's 4D quaternion algebra (created 200 years after Leibniz died). Lastly, the first number is NOT 1. It's 0. First four numbers are 0, 1, 2, 3 ✅. First four dimensions are 0D, 1D, 2D, 3D ✅.