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Silly Druid

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  11. Silly Druid
    This time it's a silly song about spring. Translation by Google, with my corrections. Sorry for bad video quality.
    They say true art will defend itself. But not from me.
    (Verse 1:)
    Spring is coming
    You can hear a bird chirping
    It's a pretty song
    But it's so silly
    A stork has arrived
    And it's digging in a puddle
    I don't mind it
    It only gets sillier from here
    (Chorus:)
    Aa aaaa It's spring already
    Aa aaaa Longer days
    Aa aaaa Flowers grow
    Aa aaaa Silly, isn't it?
    (Verse 2:)
    Rivers are thawing
    Ice floes are flowing into the sea
    Not the worst verse
    But there's no rhyme
    Trees have buds
    There are chicks in eggs
    Nature is like this verse
    Underdeveloped
    (Chorus)
    (Verse 3:)
    The sun is shining brighter
    Smoke is drifting in the field
    It makes no sense at all
    But it rhymes
    Nature wakes up
    It's green everywhere
    There's nothing to be afraid of
    The chorus will come again
    (Chorus)
    (Verse 4:)
    Spring comes after winter
    According to folk proverbs
    I don't have health anymore
    For these idiocies
    The song ends
    There's almost no snow
    Write stupid lyrics
    Even I can
    (Chorus)
  19. Silly Druid

    Translating Polish songs #2

    By Silly Druid,


    Culture
    I already did one of these, so why not do it again? This time we have a pretty funny one:
    If you want to be strong, join us
    Become a real aquarist
    There are already three hundred or four hundred of us
    Including two majors and one bishop
    Eight dentists with the rank of ministers
    Aquarium Club
    We have a two-color stamp
    And a post office box at the main post office
    We have already received several letters
    With the note "Aquarium Club"
    We have an aquarium with a fish swimming in it
    Any member can touch it
    And feed it daphnia
    Be an aquarist
    The water is changed once a month
    Then attendance is mandatory
    Continuous readiness 24 hours a day
    Rubber clothing is required
    As for the main guidelines
    We have an aquarium manifesto
    It contains practically everything
    Be an aquarist
    And one more thing: If you ever
    Would like to leave our ranks
    Get involved with a group of other hobbyists
    Don't count on aquarists' mercy
    Translated by Google, with some corrections from me. I omitted the "yabba-dabba-doo" parts, because they don't require translation )
  20. Silly Druid
    I've written about these things in this blog before, but now I'd like to summarize my thoughts about how I understand the quantum mechanics and how I see the nature of the universe in general. It seems nobody understood my previous post, and probably nobody will understand this one either, but that's OK, I'm writing these primarily for myself, to gather and organize my thoughts.
    In the standard interpretation of quantum mechanics, there is a thing called "wave function collapse", which doesn't make any sense in my opinion. It's supposed to happen "instantaneously", but what does that even mean? In Special Relativity there is no such thing as things happening in different places at the same time, because "at the same time" has no well defined meaning, it depends on the observer. There are situations where for one observer event A happens before event B, and for another observer event A happens after event B. For example, when, according to the wave function, a particle can be in two places, and we measure it in one of the places, the part of the wave function that is in the other place immediately gets information that the particle isn't there, and is updated accordingly. So if we make a measurement there, we know we won't detect the particle. The problem with this approach is that, as I mentioned before, for a different observer the measurements can take place in the opposite order, so the flow of information happens in the opposite direction. This is what Einstein called "spooky action at a distance", and it makes quantum mechanics in this interpretation non-local (btw this can't be used to transfer any actual information between the two places, but that's a different story).
    So let me tell you what I think about all this. As I wrote in this blog before, when it comes to fundamental laws of physics, both directions of time should work the same way. Which means that the wave function should propagate in both directions - not only forward in time from the place where the particle was emitted, but also backward in time from the place where it (or lack of it) was measured. This way it contains only the information that is consistent with all events that happened in the past and will happen in the future. There's no need to collapse the wave function, and we avoid the "spooky action" and non-locality. What we get in return is retrocausality, which means that events happening now can be caused not only by things that happened in the past, but also by things that will happen in the future. In the above example, there is a connection between both measurements and the event where the particle is emitted that goes locally along all possible paths of the particle, and all 3 events are determined in a way that makes them consistent with each other. Note that with this approach the wave function can still be a superposition of different histories of the particle, if all of them are consistent with all the events happening before and after, which, for example, explains the interference pattern in the double slit experiment.
    So, if I'm right, what does it tell us about the universe as a whole? Well, the way I see it it's a complex four (or more) dimensional object that consists of a huge number of events, interconnected in a consistent way. And time is not a fundamental property of it. It's an emergent property that is important only in large scales (larger than single particles), and originates from the boundary conditions that (for whatever reason) are imposed on the universe, by making one "end" of it have high density and low entropy (aka the Big Bang). This creates a "trend" that goes through the entire universe and makes it expand and the entropy grow. Why are the boundary conditions like this? I have no idea. The only thing that comes to my mind is the anthropic principle, which doesn't really explain it, it simply states that it must be like this because otherwise we wouldn't exist.
  21. Silly Druid

    Entangled in Time

    By Silly Druid,


    Physics
    Let's talk about quantum entanglement. At first glance it looks like a very strange phenomenon, where the properties (like spin) of two particles coming from the same source can be measured in different points of space and time, and the results of these measurements are correlated, while still being fundamentally random. If you make a spacetime diagram of it, you get something like this:

    Now, I want you to think about it in a different way, similar to what I've already posted in this blog about creation and annihilation of pairs of virtual particles, where in my interpretation it's just one particle going in a circle in spacetime.
    There is no meaningful definition of the "direction of a particle in time", the history of a particle in spacetime is just a line, with no specific direction attached to it, like described in this video by Sabine Hossenfelder. And the fundamental laws of physics work the same way in both directions of time, the difference between past and future that we perceive is based only on large-scale phenomenons, like entropy and expansion of the universe.
    So, for a single particle, we should accept the possibility that its "world line" can "bend" not only in space, but in time too. This way we can interpret the above diagram as one particle "bouncing in time" at the "source" point. With that interpretation, the quantum entanglement becomes less mysterious: of course the measurements are correlated, because it's the same particle!
  22. Silly Druid

    Why Tau is better than Pi

    By Silly Druid,


    Mathematics
    I'm writing this on Pi Day, but I think pi makes no sense as a fundamental mathematical constant, and it's used only because of force of habit.
    The circle is defined as the set of points on the plane with a given distance to the center. That distance is the radius. So the "circle constant" should be defined using the radius, not diameter. It has been proposed that this constant would be denoted by the Greek letter tau. Tau is equal to 2*pi.
    The full angle (360 degrees) in radians is one tau instead of two pi, which is a more simple and natural way of doing things.
    Also Euler's identity is in my opinion even more beautiful when using tau instead of pi:
    e^(i*tau) = 1
  23. Silly Druid
    I've read about this in an old book about Bridge (the card game). The example below is a modified version of the one used in that book.
    There are 3 people (including you) sitting by the table, and every one of them gets a card. There are 2 black cards and one red card, and for some reason you want to know who has the red card. The cards are lying on the table, face down. So, how much information do you need to know who has the red card?
    By definition, the amount of information (in bits) is log2 of the number of possibilities. For example, a byte has 256 possible values, which means it contains log2 (256) = 8 bits of information. In this case, you have 3 possibilities (you know one of the 3 people has the red card), which means you need log2 (3) ≈ 1.585 bits of information.
    Now, you reveal your card and see that it's black. How much information did you gain? Well, about the card itself you gained one bit, because it could be black or red. But about the question "who has the red card" you had 3 possibilities and now you have 2 (one of the two other people has the red card), which means now you need log2 (2) = 1 bit of information. So the information gained is 1.585 - 1 = 0.585 bits. So getting a smaller amount of information than one bit is indeed possible!
  24. Silly Druid

    -1/12

    By Silly Druid,


    Mathematics
    Some time ago there was some controversy across the Internet whether 1+2+3+4+... = -1/12 or not. Here's what I think about this:
    Clearly, this sum diverges to infinity, so you can't assign any finite value to it, using the standard math rules. But there is a way to associate this value with this sum, which uses some advanced concepts that I don't fully understand, like analytic continuation, Riemann zeta function, and Ramanujan summation.
    So I did something different. First, I took the formula for partial sums: S(n) = n * (n -1) / 2, and treated is as a function of all real numbers: f(x) = x * (x -1) / 2. It's a quadratic function, with a graph that looks like this:

    Between -1 and 0 the value is negative. I wanted to know the area between the x axis and function in that interval, so I took the integral. And guess what? The result is -1/12. Coincidence? I think not.
    Later I watched this video, and it confirmed my suspicions that something interesting is going on here. It's in the last minute of the video.
  25. Silly Druid
    Here is my (probably pretty bad) attempt at translating the lyrics to English:
    When I weaved my braids into winter days
    Blue ribbons smiled at you like two sisters
    And the gloves, which I kept losing so you would look for them
    Always had for you ten nuts hidden in their fingers
    And into the footprints on the road
    Which I made gliding through the snow
    I threw summer's fruits
    For you to follow me
    Today I don't have braids anymore
    The wind took the ribbons
    I don't wear gloves
    I don't gather nuts at all
    And there are no footprints
    Because it rarely snows here
    I save the fruits for worse days
    And you're still following me
    How can you just love me like that?
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