Generative Model That Won 2024 Nobel Prize

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  • เผยแพร่เมื่อ 23 พ.ย. 2024

ความคิดเห็น • 203

  • @ArtemKirsanov
    @ArtemKirsanov  3 หลายเดือนก่อน +14

    Join Shortform for awesome book guides and get 5 days of unlimited access! Get 20% off at shortform.com/artem

  • @vastabyss6496
    @vastabyss6496 3 หลายเดือนก่อน +225

    First the Hopfield Network video and now this?! And only a month apart? I cannot thank you enough for the value that you've added to this platform

  • @KevinWang-jc1bx
    @KevinWang-jc1bx 3 หลายเดือนก่อน +64

    AI's not the only one hallucinating, can't believe the rate and quality at which Artem is publishing these videos, thank you so much!

  • @JohlBrown
    @JohlBrown 3 หลายเดือนก่อน +52

    i've never seen a well-worded explanation of temperature (as a casual ML enjoyer) but seeing the sigmoid morph with temperature and the relationship between stochastic and deterministic was such an awesome learning moment, thank you!

  • @holymoly54775
    @holymoly54775 3 หลายเดือนก่อน +11

    Hi Artem,
    I just want to say that in 3 weeks I begin my graduate degree in neuroscience, and it was your channel that inspired me to begin this journey two years ago. Keep up the good work, and I look forward to the inspiration for years to come.

    • @joeybasile545
      @joeybasile545 3 หลายเดือนก่อน

      What classes are you taking right now?

    • @Sam264-n2o
      @Sam264-n2o 3 หลายเดือนก่อน

      @@joeybasile545it’s summer holiday

    • @ArtemKirsanov
      @ArtemKirsanov  3 หลายเดือนก่อน +3

      Wow, congrats!!

    • @SystemsMedicine
      @SystemsMedicine 3 หลายเดือนก่อน +3

      Good Luck. And when things get tough, and they will… endeavor to persevere.

    • @holymoly54775
      @holymoly54775 3 หลายเดือนก่อน

      @@joeybasile545 I haven't started yet, but the program is non-traditional, where instead of registering for classes, there is a dedicated period for lectures everyday that will cover all aspects of neuroscience, followed by lab rotations and research training. Subjects included are neuroanatomy, computational modeling, molecular biology and neurogenetics, vision, audition, and then for the labs, there are courses in EEG, microscopy, and cytochemisty, and this is about half of all the subjects covered. It truly is a comprehensive program, which upon completion will feed me right into a PhD track depending on what areas I have excelled in. My background is in math and computer science, so I am hoping to focus on the computational side of things, but who knows where I will eventually end up!

  • @henrikjohnsson7403
    @henrikjohnsson7403 หลายเดือนก่อน +23

    Quick change of name! For a while, I thought you knew of the Prize in forehand when I scrolled through my list of "saved for later". And watched it now, awesome Work!

  • @theo4884
    @theo4884 3 หลายเดือนก่อน +1

    Watching your "AI & Machine Learning" playlist feels like binge watching my favorite show. Hope you continue them. You are an amazing teacher

  • @ahaskarkarde4163
    @ahaskarkarde4163 หลายเดือนก่อน +14

    With the 2024 Nobel Prize in physics awarded to the pioneering works introducing the Hopfield Network and Boltzmann Machines, your latest videos explaining exactly these topics were just timely enough to help us build a great understanding of such important tools :)

  • @vidal9747
    @vidal9747 3 หลายเดือนก่อน +54

    I never knew my background in Physics would make understanding this topic such a breeze. It is bizarre how in this world areas that look so different can be so close.

  • @huytruonguic
    @huytruonguic 3 หลายเดือนก่อน +5

    I get chills everytime someone tries to explain the differences between data's states and generator's states. The former is surface level while the later is highly abstracted. It says something about the many redundancies of the reality we live in and how there exists a general abstraction (math formalisms for example), or maybe that's just how we observe reality while being part of reality

    • @judehammoud5959
      @judehammoud5959 2 หลายเดือนก่อน +2

      theory of constructed emotion / active inference ;)

    • @EGIMSL
      @EGIMSL 7 วันที่ผ่านมา

      @@judehammoud5959 I would argue a better conceptualization is to consider platonic ideals. Underlying distributions are like the platonic ideals of high dimensional manifolds, but we only every have access to their projections onto our reality.

  • @copywright5635
    @copywright5635 3 หลายเดือนก่อน +13

    Always happy to watch your uploads. The Boltzmann distribution is something that I think is often misunderstood. So thank you for this video!

  • @guillaumeleguludec8454
    @guillaumeleguludec8454 3 หลายเดือนก่อน +1

    Wow you really nicely explained what Boltzmann machines are and where they come from, and the animation in super pretty ! Thank you Mr Kirsanov

  • @scottmiller2591
    @scottmiller2591 3 หลายเดือนก่อน +1

    This video was one of the bright spots of my day. It was well-crafted, reminded me of my work on ladder RBMs long, long ago, and got me thinking about how modern machines could build on these methods, and vice versa.

  • @AshifKhan-sn6jx
    @AshifKhan-sn6jx 3 หลายเดือนก่อน +1

    Okay, you taught me about boltzman distribution better than my school physics teacher and it wasn't even the main point of what you were trying to do

  • @imaltenhause4499
    @imaltenhause4499 3 หลายเดือนก่อน +14

    Fantastic video. A small typo however at 08:41. There you denote -ln[p]/epsilon = T. It should be: -epsilon/ln[p] = T.

    • @ArtemKirsanov
      @ArtemKirsanov  3 หลายเดือนก่อน +2

      Thanks! Good catch!

    • @raajchatterjee3901
      @raajchatterjee3901 หลายเดือนก่อน +1

      Is this the relationship that relates temperature with differentials of energy and entropy?

  • @etunimenisukunimeni1302
    @etunimenisukunimeni1302 3 หลายเดือนก่อน +3

    You have a knack to explain things in an understandable way without dumbing them down too much, thanks! Finally I know what the temperature setting actually does in a neural network, funny how analoguous it is to physical temperature :)

  • @vladimirputin7443
    @vladimirputin7443 3 หลายเดือนก่อน +1

    This guy is awesome. I can't explain how much more intelligent I feel after watching your video. Thank you so much for taking out time to educate people like us.

  • @joonaskuusisto2767
    @joonaskuusisto2767 3 หลายเดือนก่อน +1

    This is incredible stuff once again. You have pretty much covered everything I’m interested in neuroscience with insight I never possesed. I researched brain criticality and modeling but now on a boring day job. Glad we have people like you!

  • @innerthrill
    @innerthrill 22 วันที่ผ่านมา

    These are the first neural networks I learned. Fascinating and deep connections to statistical mechanics/thermal physics. Best class I ever took in uni.

  • @kahvefincanim234
    @kahvefincanim234 3 หลายเดือนก่อน

    It is really great to visually explain such complex and valuable information in such an understandable way!

  • @giuliomatteucci5352
    @giuliomatteucci5352 หลายเดือนก่อน

    Great video! Amazing visualizations and clarity of explanation!

  • @mezu-e
    @mezu-e หลายเดือนก่อน +5

    My sleep-deprived layperson brain is so engrossed in the high level concepts that I got hung up on 32 × 32 = 1024

  • @clayre839
    @clayre839 3 หลายเดือนก่อน +31

    The trouble with true creativity is intention. It's easy for humans to recognize things that we ourselves can produce and extrapolate patterns and impose experience and emotion on them but fundamentally if Randomness is the only thing driving the adaptation rather than transitive expression it is no more creative than a wind chime. You can think of it as the training data representing the tuning of each resonator and though we might FIND beauty in the emergent patterns, it is no more creative than its design and tuning, both requiring explicit human intervention. These models fed their own results very quickly deform into incomprehensible static

    • @clayre839
      @clayre839 3 หลายเดือนก่อน +17

      To add to this; the false equivalency and under emphasis of the human involvement in tuning is a large proponent of the demonstrably harmful supposition of replacing humans with machines; ignoring the value judgment that is imposed at every level of refinement. I deplore you to refrain from such false equivalencies as it's currently being used in attempts to undermine just about every creative field from engineering to writing to graphic design and would better be described as a sampling tool. These misconceptions have real world implications that are doing demonstrable societal harm. Take for example that even now I am fighting with the predictive text elements attempting to re orchestrate my unorthodox sentence structure and subsequently undermining the intent of my writing; that such a machine would have no insight into. It cannot understand meaning outside of Association and lacks any capability of truly understanding the emergent contradictions of language. So please stop describing these slot machines as creatives when its success is fundamentally built on confirmation bias.

    • @vinniepeterss
      @vinniepeterss 3 หลายเดือนก่อน

      😮

    • @conduit242
      @conduit242 3 หลายเดือนก่อน +3

      Hilariously, your writing style is awkward and unnecessarily formal rather than creative. One would think computers would be just fine with such a style.

    • @clayre839
      @clayre839 3 หลายเดือนก่อน +6

      @@conduit242 for real, it's hard enough being autistic without my computer trying to fuck with me. We're both on the outside hear you'd think we'd be working together 🤣 but it's not the formality it's the variance that tends to fuck with predictive text. the tone was just to have assert a sincere formality to it. Like the larger issue of mechanization in Creative fields is a serious problem, full stop; and I think it's important the language we choose when we're talking about it

    • @unclicked4690
      @unclicked4690 2 หลายเดือนก่อน +3

      I love the wind chime analogy, that's a really cool conceptual analogy.
      I disagree with the basic premise that creativity requires intention, for example I'd say evolution is very creative but has no underlying "intention".
      It's also very well understood that human consciousness (and creativity) are fundamentally built on bias, indeed one can only learn if there is a bias to exploit. A very simple example of this is w.r.t identifying similarity of objects, we say a red cup is more similar to a blue cup than it is to a chair, however this requires a bias towards human every-day items.
      What I mean is that if we had to put a number on the similarity of blue cup and red cup, we could say they are 90% similar, while a chair is only 10%. Soon you run into trouble with this method, because how do you quantify how different a chair and a cup are from the ocean? what about a crimson cup? what about bacteria? what about a black hole? What about a cermanic red cup?
      What you see is that you need ever increasing detail, and you metric of similarity simply explodes or collapses to non-sense.
      Humans exploit bias to be able to think, to be able to logically classify items and objects and produce creative solutions.

  • @victormanuel8767
    @victormanuel8767 2 หลายเดือนก่อน

    Fantastic. Absolutely phenomenal work here.

  • @JonRichie294
    @JonRichie294 3 หลายเดือนก่อน +1

    This is insane! I love your videos on this channel! I’m just waiting for your channel to exponentially boom to a million subscribers.

  • @owenpawling3956
    @owenpawling3956 3 หลายเดือนก่อน +5

    So glad for another upload! You have no idea how fast I clicked!

  • @ItsGlizda
    @ItsGlizda 3 หลายเดือนก่อน +1

    I recently stumbled upon your channel, and it's absolutely fascinating! It ignites my curiosity and explains things in a way that awakens my inner child. Keep up the fantastic work!

    • @ArtemKirsanov
      @ArtemKirsanov  3 หลายเดือนก่อน

      Wow, thank you so much!

  • @English-bh1ng
    @English-bh1ng 3 หลายเดือนก่อน

    I eventually grasped the notion of RBM. Thx

  • @iamdaddy962
    @iamdaddy962 3 หลายเดือนก่อน

    happy to see you in the US!! Hope you thrive here

  • @pandusonu
    @pandusonu หลายเดือนก่อน +31

    Good time to rename this video to "The generative model that won nobel prize in physics 2024"

    • @ArtemKirsanov
      @ArtemKirsanov  หลายเดือนก่อน +9

      ahaha, good point!

  • @AyushVerma-ui7re
    @AyushVerma-ui7re 3 หลายเดือนก่อน +1

    beautiful explanation.

  • @이상원-t3h7i
    @이상원-t3h7i หลายเดือนก่อน

    Wonderful animations and impeccable explannations. Thank you so much.

  • @RBRB-hb4mu
    @RBRB-hb4mu หลายเดือนก่อน

    Great content, dark background and graphics !! Keep it coming

  • @BinghaoWang-k5b
    @BinghaoWang-k5b หลายเดือนก่อน

    amazing, detailed and easy to understand. thank you so much

  • @EvanMildenberger
    @EvanMildenberger หลายเดือนก่อน

    22:42 it seems like the contrastive Hebbian is about rewarding true positives while also punishing false positives to allow more generalization without necessarily over fitting. 😎

  • @syrachify
    @syrachify 2 หลายเดือนก่อน

    Awesome video! I love this channel! I have a question, which I hope someone will clarify for me: if Boltzmann Machines are unsupervised, how do we know what data is meaningful (like number digits) and what data is just noise, so that we sculpt valleys around the meaningful patterns in the energy landscape? Similarly, in the weight update rule: updating iteratively works on maximizing the probability of the training data, equivalent to minimizing the energy of patterns, but the rule itself assumes we have to know beforehand what the patterns are (because of data - model). Can anyone help with an answer?

    • @REDPUMPERNICKEL
      @REDPUMPERNICKEL หลายเดือนก่อน

      I suspect the evolved culture
      into which we all were born
      was perhaps entirely responsible
      for impressing meaning onto
      the buzzing blooming confusion of our earliest months
      as growing neural networks. ish

  • @anywallsocket
    @anywallsocket 3 หลายเดือนก่อน

    My 2nd physics class adjunct prof told me his fave subject was statistical physics, now I get it 🙏

  • @VaradMahashabde
    @VaradMahashabde 3 หลายเดือนก่อน

    Best explainers, hands down

  • @darkyz543
    @darkyz543 3 หลายเดือนก่อน

    Marvelous. Thank you. I almost forgotten how delicious mathematic is.

  • @Jacob-ji1ec
    @Jacob-ji1ec 3 หลายเดือนก่อน +2

    This video is amazing man 🔥

  • @BiswajitBhattacharjee-up8vv
    @BiswajitBhattacharjee-up8vv หลายเดือนก่อน

    It is highly intuitive that the average kinetic energy in Boltzmman machine realise as scaling probabilistic triggering and the shape of that sigmoid curve an anti Fermi level statistics , appears as pattern synthesis.
    No doubt your excellent presentation and clear demonstration make you giant of learning channel on NOBEL DECISION .
    Good channel, thank you.

  • @catcatcatcatcatcatcatcatcatca
    @catcatcatcatcatcatcatcatcatca 3 หลายเดือนก่อน +1

    0:23 oh god. Reading that chatGPT answer hurts. That is equivalent to asking for a pasta recipe and seeing the answer starting with
    1) start a greasefire in the kettle
    2) for eight to ten minutes, pour water on it

  • @jiananwang2681
    @jiananwang2681 หลายเดือนก่อน

    Nice animation and love the first generative models!

  • @sirinath
    @sirinath 3 หลายเดือนก่อน +2

    Can you do a course on Markov / Semi Markov / Hidden Markov / Semi Hidden Markov models please.

  • @anywallsocket
    @anywallsocket 3 หลายเดือนก่อน

    What you could do for visualization is plot a distribution of x for the digits above them like a mountain that looks like an 8 is different from that of a 2 etc

  • @ced1401
    @ced1401 2 หลายเดือนก่อน

    Great video. There's a small typo around 9:15. ln(1/p)/epsilon would rather be 1/T.

  • @rxphi5382
    @rxphi5382 3 หลายเดือนก่อน

    I like the passion I feel from you in your videos! I just wanted to inform you that there is am small typo at 15:06 in the bottom right corner

  • @faturita
    @faturita 5 วันที่ผ่านมา

    Super great explanation !

  • @haroldhamburgler
    @haroldhamburgler 3 หลายเดือนก่อน

    I've learn today, as many times before. Always finish the video before leaving an angry comment.

  • @domwilson-rx4ky
    @domwilson-rx4ky 21 วันที่ผ่านมา

    I’m heavy into physics.
    I recall reading up on something how it’s possible to be moving very fast and never age.
    I believe if we do speed up our pc to be able to process data chips that allows these physics to happen within a pc…. I wonder … just what can happen .

  • @enriquesolarte1164
    @enriquesolarte1164 3 หลายเดือนก่อน +1

    Great videos

  • @louisdupont2126
    @louisdupont2126 3 หลายเดือนก่อน

    Man your videos are just awesome, and I finally understood the boltzman formula xD

  • @-mwolf
    @-mwolf 3 หลายเดือนก่อน +2

    the 3b1b of neuroscience an ML, thx for the videos!

  • @gracealive5191
    @gracealive5191 5 วันที่ผ่านมา

    Thank you❤such an extraordinary presentation with relations and simplicity

  • @Darkev77
    @Darkev77 2 หลายเดือนก่อน +1

    Given our current understanding of Quantum Mechanics and energy levels being quantized, is the statement @8:08 true (is it constant with the same amount)?

  • @nessiecz2006
    @nessiecz2006 3 หลายเดือนก่อน

    I was worried i was missing something at 8:43 . Nevertheless, great vid, gonna continue watching now:) Thank you for making these explanations
    PS: appreciate the 3b1b music and style;)

  • @CopperKettle
    @CopperKettle หลายเดือนก่อน

    Thank you, this is very interesting. Keep up the good work.

  • @yacinebel-hadj6559
    @yacinebel-hadj6559 หลายเดือนก่อน

    Thanks amazing work I love this topic :)

  • @justanotherytaccount1968
    @justanotherytaccount1968 3 หลายเดือนก่อน

    Awesome video, thanks!
    Could the stochastic “hallucination” phase be related to hippocampal replay training cortical networks (“hidden” layer) during sleep?

  • @vidal9747
    @vidal9747 3 หลายเดือนก่อน

    Our brains activate neurons based on probabilities. Those are created by particles that follow laws pretty close to what is explored in thermodynamics and statistical mechanics. There is nothing more fitting than creating models that tend to mimic those aspects. Our computers are absolutely better than humans for problems we already know the equations. Because we know the uncertainty of every number in a computer. But for new problems, a probabilistic approach is very good.

  • @robmorgan1214
    @robmorgan1214 หลายเดือนก่อน

    Your video was great. Very clear explanation. Would have liked you to discuss training algos like grad descent or sim annealing. Next video?
    Giving the physics nobel prize for this is the equivalent of giving a nobel prize to someone for failing statmech. This is just an ad hoc application of an incorrect statistical distribution due to incorrect choice of algebra but compensating for the problems this introduces by throwing extra dimensions and parameters at the problem... it's basically the same flawed thought process that brought us string theory. Too bad anyone left in the academy that knew this is emeritus AF. ...smh.

  • @giuseppepapari7419
    @giuseppepapari7419 3 หลายเดือนก่อน +2

    9:05 I guess you meant -ln p / epsilon = 1/T. But that is minor, I like the video

    • @nessiecz2006
      @nessiecz2006 3 หลายเดือนก่อน

      ive been searching for this comment, was wondering if im missing something. Thank you kind stranger

  • @SystemsMedicine
    @SystemsMedicine 3 หลายเดือนก่อน

    Sweet Vid… Rock On!

  • @Krienfresh
    @Krienfresh หลายเดือนก่อน

    Just came across to this. Top tier content

  • @guyguy12385
    @guyguy12385 3 หลายเดือนก่อน +1

    yea you are absolutely goated

  • @WillyDarko
    @WillyDarko หลายเดือนก่อน

    Insanely high quality content

  • @leonardorazzai840
    @leonardorazzai840 3 หลายเดือนก่อน

    Wow, so fascinating 😍

  • @Pedritox0953
    @Pedritox0953 2 หลายเดือนก่อน

    Great video!

  • @vinniepeterss
    @vinniepeterss 3 หลายเดือนก่อน

    great video

  • @memegazer
    @memegazer หลายเดือนก่อน

    Tbf fair we have automous driving, we have cars that can pilot themselves without incident.
    And that was achieved well before generative art models came along.
    The issue is not a self driving car, it is a self driving car in an environment heavily populated with people that are driving, walking, and people changing the environment as well as natural pheonomea chaing it spountansiously at nearly every moment.
    A much more difficult problem to solve than a vehical piloting itself without incident once those factors have been controled for as much as possible.

  • @ArbaouiBillel
    @ArbaouiBillel 3 หลายเดือนก่อน

    Amazing keep going 👍🏼

  • @JuergenAschenbrenner
    @JuergenAschenbrenner 3 หลายเดือนก่อน

    great stuff, keep up Your good work

  • @dylanmenzies3973
    @dylanmenzies3973 หลายเดือนก่อน

    Good work.

  • @InquilineKea
    @InquilineKea 3 หลายเดือนก่อน

    What temperature optimizes for the highest range of perplexity values?

  • @Tethloach1
    @Tethloach1 27 วันที่ผ่านมา

    Thank you I learned something

  • @daleanfer7449
    @daleanfer7449 3 หลายเดือนก่อน

    great content❤❤❤

  • @ralvarezb78
    @ralvarezb78 หลายเดือนก่อน

    14:00 This is strongly related to simulated annealing optimizacion method

  • @lorenzovannini82
    @lorenzovannini82 หลายเดือนก่อน

    Thank you

  • @IoannisNousias
    @IoannisNousias 3 หลายเดือนก่อน

    How do you create your animations? This is awesome.

    • @ArtemKirsanov
      @ArtemKirsanov  3 หลายเดือนก่อน +1

      After Effects + Python + Blender :)
      I have a video about it that might help: th-cam.com/video/yaa13eehgzo/w-d-xo.htmlsi=EcoTIRW9Qhnnb9xS

  • @notu483
    @notu483 3 หลายเดือนก่อน

    13:14 Softmax wasn’t mentioned?

  • @not_amanullah
    @not_amanullah 3 หลายเดือนก่อน

    Thanks ❤️

  • @davidfmendiola2009
    @davidfmendiola2009 3 หลายเดือนก่อน

    🙂¡Gracias!

  • @MlNECRAFT69
    @MlNECRAFT69 3 หลายเดือนก่อน

    lol the new title made me watch it again on accident😊

  • @ozachar
    @ozachar หลายเดือนก่อน

    A physicist comment: if I understand your presentation correctly, the original Hopfield algorithm is the zero temperature limit of the Boltzmann Machine.
    The hidden levels, I would guess, are just an efficiency enhancement. i.e., there would be a large enough No-hidden-layers network of equivalent performance to any network with hidden layers. Most likely someone proved such theorem already.

    • @REDPUMPERNICKEL
      @REDPUMPERNICKEL หลายเดือนก่อน

      This hypnotic video rendered me briefly unconscious several times
      so I'll have to watch again but
      the impression I got from this first viewing, in regard to hidden-layers,
      was that they maintain memories in a kind of holographic way that
      might not be available in a no-hidden-layers network.

  • @ronnysanjaya6823
    @ronnysanjaya6823 2 หลายเดือนก่อน

    Yes many thanks.

  • @luke.perkin.inventor
    @luke.perkin.inventor 3 หลายเดือนก่อน +1

    At 2x speed it sounded like you said "what sparked this sh*t" 😂

  • @Noconstitutionfordemocrats1
    @Noconstitutionfordemocrats1 27 วันที่ผ่านมา +1

    AI is even winning our awards.

  • @faisalsheikh7846
    @faisalsheikh7846 3 หลายเดือนก่อน

    Wonderful❤

  • @luisluiscunha
    @luisluiscunha หลายเดือนก่อน

    And that Hinton said was the wrong path and now only a historical curiosity. Good for him he used the name of a Physic to baptize these models.

  • @SeattleShelby
    @SeattleShelby 2 หลายเดือนก่อน

    As a Boltzmann Brain in a fever dream, I found this video very insightful into my waking nightmare.

  • @SaúlAlejandroVillaradosFlores
    @SaúlAlejandroVillaradosFlores หลายเดือนก่อน

    I fn Love ur channel buddie

  • @peterpetrofff
    @peterpetrofff 2 หลายเดือนก่อน

    20:47 spelling error. Thank you

  • @gunaysoni6792
    @gunaysoni6792 3 หลายเดือนก่อน

    I was expecting a Brilliant Sponsorship 😂

  • @littlecat677
    @littlecat677 21 วันที่ผ่านมา

    As a (struggling) physics majored student, I feel uncomfortable at given so much explanation on why partition function is written that way

  • @Rockamoley
    @Rockamoley 2 หลายเดือนก่อน

    This is a good video, but the history given in the first few minutes is completely hallucinated. Associative memories are as old as van Neumann architectures, and thinking like humans has always been the first goal of researchers. Calculating exact trajectories was a useful stepping stone.

  • @Тима-щ2ю
    @Тима-щ2ю หลายเดือนก่อน

    Here after nobel prize winners announcement)

  • @paichethan
    @paichethan 29 วันที่ผ่านมา

    Videos are great. My attention span is just 10 minutes.

  • @crazyedo9979
    @crazyedo9979 3 หลายเดือนก่อน

    Dr. Chandra. Will I dream?😁

  • @maths.visualization
    @maths.visualization 3 หลายเดือนก่อน

    Can You Share Video Code?

  • @tamasszili4511
    @tamasszili4511 หลายเดือนก่อน +2

    The math doesn't add up at 8:48. If -ln[p]/ε = T, then e^(ln[p] * ΔE / ε) = e^(ln[p] / ε * ΔE) = e^(-(-ln[p] / ε) * ΔE) = e^(-T * ΔE), and not e^(-ΔE / T)