Skip to content
  • Home Home Home, current page.
  • Moments Moments Moments, current page.

Saved searches

  • Remove
  • In this conversation
    Verified accountProtected Tweets @
Suggested users
  • Verified accountProtected Tweets @
  • Verified accountProtected Tweets @
  • Language: English
    • Bahasa Indonesia
    • Bahasa Melayu
    • Català
    • Čeština
    • Dansk
    • Deutsch
    • English UK
    • Español
    • Filipino
    • Français
    • Hrvatski
    • Italiano
    • Magyar
    • Nederlands
    • Norsk
    • Polski
    • Português
    • Română
    • Slovenčina
    • Suomi
    • Svenska
    • Tiếng Việt
    • Türkçe
    • Ελληνικά
    • Български език
    • Русский
    • Српски
    • Українська мова
    • עִבְרִית
    • العربية
    • فارسی
    • मराठी
    • हिन्दी
    • বাংলা
    • ગુજરાતી
    • தமிழ்
    • ಕನ್ನಡ
    • ภาษาไทย
    • 한국어
    • 日本語
    • 简体中文
    • 繁體中文
  • Have an account? Log in
    Have an account?
    · Forgot password?

    New to Twitter?
    Sign up
arthur_affect's profile
Arthur Chu
Arthur Chu
Arthur Chu
Verified account
@arthur_affect

Tweets

Arthur ChuVerified account

@arthur_affect

Mad genius, comedian, actor, and freelance voiceover artist broadcasting from the distant shores of Lake Erie (he/him)

Broadview Heights, Ohio
arthur-chu.com
Joined August 2009

Tweets

  • © 2021 Twitter
  • About
  • Help Center
  • Terms
  • Privacy policy
  • Cookies
  • Ads info
Dismiss
Previous
Next

Go to a person's profile

Saved searches

  • Remove
  • In this conversation
    Verified accountProtected Tweets @
Suggested users
  • Verified accountProtected Tweets @
  • Verified accountProtected Tweets @

Promote this Tweet

Block

  • Tweet with a location

    You can add location information to your Tweets, such as your city or precise location, from the web and via third-party applications. You always have the option to delete your Tweet location history. Learn more

    Your lists

    Create a new list


    Under 100 characters, optional

    Privacy

    Copy link to Tweet

    Embed this Tweet

    Embed this Video

    Add this Tweet to your website by copying the code below. Learn more

    Add this video to your website by copying the code below. Learn more

    Hmm, there was a problem reaching the server.

    By embedding Twitter content in your website or app, you are agreeing to the Twitter Developer Agreement and Developer Policy.

    Preview

    Why you're seeing this ad

    Log in to Twitter

    · Forgot password?
    Don't have an account? Sign up »

    Sign up for Twitter

    Not on Twitter? Sign up, tune into the things you care about, and get updates as they happen.

    Sign up
    Have an account? Log in »

    Two-way (sending and receiving) short codes:

    Country Code For customers of
    United States 40404 (any)
    Canada 21212 (any)
    United Kingdom 86444 Vodafone, Orange, 3, O2
    Brazil 40404 Nextel, TIM
    Haiti 40404 Digicel, Voila
    Ireland 51210 Vodafone, O2
    India 53000 Bharti Airtel, Videocon, Reliance
    Indonesia 89887 AXIS, 3, Telkomsel, Indosat, XL Axiata
    Italy 4880804 Wind
    3424486444 Vodafone
    » See SMS short codes for other countries

    Confirmation

     

    Welcome home!

    This timeline is where you’ll spend most of your time, getting instant updates about what matters to you.

    Tweets not working for you?

    Hover over the profile pic and click the Following button to unfollow any account.

    Say a lot with a little

    When you see a Tweet you love, tap the heart — it lets the person who wrote it know you shared the love.

    Spread the word

    The fastest way to share someone else’s Tweet with your followers is with a Retweet. Tap the icon to send it instantly.

    Join the conversation

    Add your thoughts about any Tweet with a Reply. Find a topic you’re passionate about, and jump right in.

    Learn the latest

    Get instant insight into what people are talking about now.

    Get more of what you love

    Follow more accounts to get instant updates about topics you care about.

    Find what's happening

    See the latest conversations about any topic instantly.

    Never miss a Moment

    Catch up instantly on the best stories happening as they unfold.

    1. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      (Dug up a more in-depth discussion here http://larryriddle.agnesscott.org/series/rearrang.pdf …) If this were a finite set of numbers, then I would eventually run out of "future numbers" to borrow from, and this trick to make the sum constantly be lower wouldn't work, and the sums would come out the same

      1 reply 0 retweets 12 likes
      Show this thread
    2. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      But it's an *infinite* series, so I *never* run out And so the same set of numbers rearranged converges to 1/2 the original sum This is why doing things an infinite number of times is, again, a filthy lie

      1 reply 0 retweets 14 likes
      Show this thread
    3. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      (Riemann proved you can rearrange this series to converge on ANY sum, at all, or to not converge and instead spit out ∞ or -∞ Which is one of those things mathematicians do that really pisses people off)

      2 replies 1 retweet 22 likes
      Show this thread
    4. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      Anyway There are series that are absolutely convergent, and series that are conditionally convergent, and series that are divergent The series 1-1+1-1+1... doesn't converge, it doesn't "get closer" to anything the longer you do it, it just flips from 1 to 0

      1 reply 1 retweet 11 likes
      Show this thread
    5. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      So does 1-1+1-1+1... equal anything at all? According to the method people used when they started talking about this ("classical summation"), no, absolutely not There is no way to rearrange this series so it converges on anything, it's a divergent series

      1 reply 0 retweets 10 likes
      Show this thread
    6. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      A Norwegian guy named Abel (a deeply weird, extremely smart dude who invented all kinds of new math before he died of TB at the age of 26) was like "Sure you can, it's 1/2" You probably looked at that and said "Yeah it's 1/2", if you thought about it at all

      1 reply 0 retweets 13 likes
      Show this thread
    7. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      The thing is in math you are *completely allowed* to say "Okay the rules say you can't do it but it looks like it should be 1/2 so I'm gonna say it is" You just have to go on to explain to everybody what that *implies* if you decide to do it, which is the hard part

      1 reply 2 retweets 18 likes
      Show this thread
    8. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      I.e. by the delta-epsilon definition of a limit, which is "It has to get closer to the number every time you do the next thing", 1-1+1-1 by definition is not approaching any limit You do it once, it's 1, you do it again, it's 0, then 1, then 0

      1 reply 0 retweets 11 likes
      Show this thread
    9. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      The "distance" between each new sum and the answer 1/2 is exactly the same every time, you *never* get closer A so-called Abelian summation method involves using the idea of *averaging* instead of the idea of *limits*

      1 reply 0 retweets 15 likes
      Show this thread
    10. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      Does that make sense? Should that be allowed? The authorities haven't come to a moral conclusion on the matter, but hey it's fun and cool prizes come out when you do

      2 replies 0 retweets 14 likes
      Show this thread
      Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

      (Philosophically, taking an average of an infinite number of sums is worse than adding numbers together an infinite number of times, because it means you have to "divide by infinity", and that's a big can of worms Which Abel happily opened)

      3:29 AM - 7 Aug 2020
      • 1 Retweet
      • 17 Likes
      • nathan Elliot Fiske Natalie Victor Von Doomscroll bIm McVowels Cheshire Daimon Rodda "Spiritually brandishing a knife" Prime David Ratna
      1 reply 1 retweet 17 likes
        1. New conversation
        2. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          It goes on from there Every new bleeding-edge summation method has more scary problems with it -- or, rather, it lacks certain properties that were assumed under classical summation Abelian summation does not "work" in many ways, but we accept that

          1 reply 0 retweets 11 likes
          Show this thread
        3. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          It "works" in other ways and that's okay Cesaro summation and Abelian summation are two methods that give you 1/2 for a "mildly divergent" series like Grandi's series (1-1+1-1)

          1 reply 0 retweets 8 likes
          Show this thread
        4. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Abelian summation is slightly more "powerful" and can also handle weirder cases like 1-2+3-4+5, which according to him = 1/4

          1 reply 0 retweets 7 likes
          Show this thread
        5. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          If that bothers you -- "The number keeps *increasing* in absolute value, how can I go up to 2 then down to -2 then up to 3 then down to -3 and then at the very end of it get 1/4?!" -- well, you're in good company, Abel summation is said to have brought mathematicians to blows

          2 replies 0 retweets 14 likes
          Show this thread
        6. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          You see at every step we're leaving a little more of "common sense" math as a child would learn in grade school behind, we're redefining the meaning of the symbols "+", "..." and especially "=" a little more to say something else And that's fine

          1 reply 1 retweet 11 likes
          Show this thread
        7. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          And that's how we get to the real weirdness, where "1+2+3+4...=-1/12" This is a sum that does not "work" at all with Abel's summation method, it contains no "oscillation" (the switching from + to -) that was the secret sauce to make the 1-1+1 and the 1-2+3 stuff work

          1 reply 1 retweet 8 likes
          Show this thread
        8. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          *Any* answer that's actually a number is going to be wildly counterintuitive But asking "Okay, but what happens if you try it" is how math works The dude who tried it was Ramanujan, a real weirdo whose life story is tremendously inspiring, and who was kind of an awesome troll

          1 reply 0 retweets 20 likes
          Show this thread
        9. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          The method Ramanujan used to prove "1+2+3+4...=-1/12" is summarized in this famous YouTube people, which made a lot of people very angry and was widely considered a bad movehttps://www.youtube.com/watch?v=w-I6XTVZXww&t=303s …

          2 replies 1 retweet 18 likes
          Show this thread
        10. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          It's important to note that this method, stated in the form the guy gives in this video, is wrong He's doing multiple things you're just not allowed to do Ramanujan liked that kind of shit

          1 reply 0 retweets 10 likes
          Show this thread
        11. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          I.e. if you naively just assume everything he's doing -- adding infinite series to each other, multiplying a finite term across an infinite series, etc. -- is allowed in every circumstance, you get contradictions

          1 reply 0 retweets 10 likes
          Show this thread
        12. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Trying to build a summation method this way for a diverging series 1+2+3+4... does not work, the way 1+2+3+4... diverges makes it neither "linear" nor "stable" I.e. if I stick an extra zero in there ("0+1+2+3+4..."), I can use his method to prove 1=0

          1 reply 0 retweets 9 likes
          Show this thread
        13. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          And 1=0 is generally frowned upon, people don't like it, it's dogs and cats living together As a great philosopher once said "If SOMETHING is the SAME THING as NOTHING then YOU COULD HAVE ANYTHING You can't just have anything, you've got to keep the riffraff out"

          1 reply 1 retweet 15 likes
          Show this thread
        14. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          And yet it's not *arbitrary* Ramanujan's "dirty trick" isn't just bullshit, I can't actually use it to prove anything I want If you do the specific thing he's doing the way he's doing it, consistently, every time, you get consistent answers

          1 reply 0 retweets 10 likes
          Show this thread
        15. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Whatever the hell he's doing, even if it isn't "adding up numbers" in any recognizable way as we normally do it, it is a *real thing* and it always gives you the answer "-1/12"

          1 reply 0 retweets 11 likes
          Show this thread
        16. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Ramanujan famously told Hardy in his letter about this "Please read to the end of the page before sending me to the insane asylum", and Hardy let himself get infected with the brainworms before calling the authorities in time to stop it, and now here we are today

          1 reply 0 retweets 14 likes
          Show this thread
        17. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Formalizing the method Ramanujan used here -- explicitly stating what rules actually define the things Ramanujan was doing so you can't just do anything and get 1=0 -- created the method known as "Ramanujan summation"

          1 reply 0 retweets 12 likes
          Show this thread
        18. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Which ended up being a special case of the regularization of the Riemann zeta function, a form of analytic continuation (which is a phrase for "doing things you're not allowed to do") Which the guys who made the above video go into detail about herehttps://www.youtube.com/watch?v=E-d9mgo8FGk …

          2 replies 0 retweets 11 likes
          Show this thread
        19. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          I fully admit I do not really understand what they are talking about, and that my brain plasticity at my age is already probably too low to ever actually feel like I have the energy to really get into it But it's a real thing, and it works

          1 reply 0 retweets 9 likes
          Show this thread
        20. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          It doesn't map onto the real world in a familiar way very well, at all But it wasn't meant to Counting things up infinitely isn't something you can do in the real world AT ALL either, remember?

          1 reply 0 retweets 10 likes
          Show this thread
        21. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          And yet, bizarrely, this result is meaningful in an applied context It comes up in quantum physics, where the real physical world gets extremely weird and we need to use weird math to talk about it

          3 replies 1 retweet 11 likes
          Show this thread
        22. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          It's part of the mathematical description of the Casimir effect, which has been experimentally verifiedhttps://en.wikipedia.org/wiki/Casimir_effect …

          1 reply 1 retweet 9 likes
          Show this thread
        23. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          The extremely broad metaphor the guy gives us for trying to imagine this is -- the actual positive numbers that we add up in 1+2+3+4... can't give us a real sum The number keeps getting bigger, it leads us only toward ∞, and ∞ isn't a number, so the sum just doesn't exist

          1 reply 0 retweets 8 likes
          Show this thread
        24. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Analytic continuation is about saying "Okay, so if you take out everything that you're not allowed to do that absolutely by the rules cannot give you an answer, can you find something about it that *does* give you an answer"

          2 replies 0 retweets 11 likes
          Show this thread
        25. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Paradoxical Zen koan shit Like Death in Discworld saying that the universe by definition is everything that exists and everywhere is inside it so you can't be outside it and standing outside it is a contradiction in terms But if you could, then from the outside it'd be blue

          1 reply 1 retweet 19 likes
          Show this thread
        26. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          -1/12 is a "residue", it's a "leftover piece" of 1+2+3+4..., the one bit that can be made to act like a number

          1 reply 1 retweet 7 likes
          Show this thread
        27. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          And that, in its way, is connected to the paradoxical thing the Casimir effect is, this thing where in a total vacuum where nothing should be exerting any force on anything, two metal plates very close together will attract each other

          2 replies 1 retweet 9 likes
          Show this thread
        28. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          I.e. -- getting really sloppy and vague from my layman's POV again, in real life in quantum physics a "vacuum" is actually filled with "virtual particles", which kinda almost do exist but then don't

          3 replies 1 retweet 9 likes
          Show this thread
        29. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          The vacuum energy is adding up all the particles that *could* be interacting with those metal plates, an *infinite number* of ways those plates could be pushing against each other and exerting force via an electromagnetic field

          1 reply 1 retweet 5 likes
          Show this thread
        30. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          But infinite force can't exist, doesn't mean anything, and what this actually adds up to instead is the "residue", the -1/12, i.e. a very small negative number -- a force that goes the opposite direction and attracts things together, but only at a very small distance

          1 reply 0 retweets 4 likes
          Show this thread
        31. Arthur Chu‏Verified account @arthur_affect 7 Aug 2020

          Yes, actual physicists, I don't know what I'm talking about The point here is just me dreaming of one of the many things in heaven and earth I hadn't previously had in my philosophy

          1 reply 0 retweets 9 likes
          Show this thread
        32. Show replies

      Loading seems to be taking a while.

      Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.

        Promoted Tweet

        false

        • © 2021 Twitter
        • About
        • Help Center
        • Terms
        • Privacy policy
        • Cookies
        • Ads info