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Silly Druid

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  5. 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)
  13. 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 )
  14. 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.
  15. 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!
  16. 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
  17. 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!
  18. 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.
  19. 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?
  20. Silly Druid

    On the existence of chairs

    By Silly Druid,


    Philosophy
    What inspired me to write this entry is this video. Before watching it I haven't realized there is so much controversy over a seemingly simple statement that objects like chairs exist. So let me explain what I think about all this.
    First, we need to define what "exist" means. What I mean here is physical existence, as opposed to mathematical existence, which is a different thing. My definition is as follows:
    If something exists physically, it means it's a part of a valid description of reality.
    But what's reality? According to Philip K. Dick, "Reality is that which, when you stop believing in it, doesn't go away." I think it's a pretty good definition, because it captures an important aspect of it: consciousness (there's more about it in my earlier blog entries). Without consciousness there is no reality. Here's my version of the definition:
    Reality is everything that can directly or indirectly interact with consciousness.
    Which means consciousness is also a part of reality, because it can interact with itself or with another consciousness. But wait, aren't there fictional concepts that can affect our consciousness, like these colorful ponies from MLP? Not exactly. They don't exist, so they can't affect us in any way. What can affect us are the depictions of these fictional concepts, which are existing physical objects. For example an episode of MLP that we watch on our screen is something that exists, while the MLP ponies themselves are not.
    Which leaves us with another question, what is "a valid description of reality"? Well, there are many ways we can describe reality. The most basic way (but not very useful in practice), is to take into account the most fundamental elements of it. According to our current knowledge, these are the elementary particles, like quarks, electrons and photons. But we can also think about larger structures built from these fundamental elements, like nucleons, atoms, molecules and so on. When we're not far away from the fundamental level, things (for example specific kinds of molecules) are pretty well defined. But when we move to larger structures like chairs, we need to use fuzzy logic, because there are objects that are "kind of like a chair, but not quite". This way we avoid problems described in the video, like the necessity of defining a boundary line between "chair" and "non-chair", which would mean it's possible to take away one atom from a "chair" to make it a "non-chair". When using fuzzy logic, these problems don't exist, because everything can have a degree of "chairness", and taking away one atom just changes it by a very small amount.
    So what we do is to create a more or less vague conditions of what constitutes as a specific kind of object, like a chair, and check if the reality meets these conditions or not (or meets them to some degree). If we observe that it meets them, then we can say that there's a chair. We can also create more "exotic" kinds of objects like "trogs" and "incars" mentioned in the video, the only difference is that they are less useful in practice than the ones we use, like chairs.
    So the conclusion is, I think chairs exist, as one of many ways to describe reality.
  21. Silly Druid

    How to Solve the Time Loop Paradox

    By Silly Druid,


    Physics
    In principle, physics doesn't forbid traveling back in time. We don't have the technology to do it, but maybe someday we will. But what about the paradoxes it causes? Well, if you go back in time and, for example, land in a distant galaxy where you don't do anything that would contradict what you already know about that place, then there is no problem. The paradox arises when you create a time loop, which means a closed chain of cause and effect.
    Now, if the time loop is consistent, then there is no paradox. Good examples of consistent time loops in fiction are the ones that happen in "Harry Potter and the Prisoner of Azkaban", and in the MLP episode "It's About Time". If every link in the chain fits the previous one, then it's all good. Although there is another apparent paradox, because this kind of loop means that some things can seemingly appear out of nothing. In "It's About Time" it's the information where the time spells are kept. Future Twilight tells it to Past Twilight, but how does Future Twilight know it? Well, when he was Past Twilight, Future Twilight told her. So there is no clear source of this information. But it's not actually a paradox, it doesn't break any laws of logic or physics, so we just have to accept that such things can happen.
    Actually, this kind of time loops happen all the time. There is a phenomenon called "pair creation". It's not only a theoretical concept, it causes an effect that has been measured. Even in vacuum, due to quantum fluctuations, a pair of "virtual particles" can appear. It's a particle and an anti-particle, they appear close to each other, and annihilate after some time. That's the standard description of the process, but, according to Feynman, an anti-particle is a particle moving back through time. If we take that into account, we can describe it as one particle moving on a closed loop through space and time. So, in the micro scale, the consistent time loop happens all the time. And these are the kind of loops where things (namely particles) appear "out of nothing".
    But what will happen if we have the ability to create a macroscopic time loop, and we deliberately try to make it inconsistent? Examples in literature usually include drastic measures, such as killing one of our ancestors. There are many theories what would happen in such case, and I have one as well. Note that I'm not a professional physicist, and it's based on intuition rather than any true knowledge, so it can be complete rubbish. But I think it's interesting enough to share with you here.
    First, let's consider the "orbitals" of electrons in atoms. Only some sizes and shapes of them are allowed, because the quantum mechanics requires that the wave function after "going around" the atom matches the one from the previous "round". Otherwise the wave cancels itself, which sets the probability of such process to zero. I think it's the same in the pair creation process, the virtual particle's wave function after going around the loop in space-time must match itself. And my theory is that it also happens in potential macroscopic time loops. If we try to set up an experiment that allows an inconsistent time loop, then we will observe some large scale quantum effects that will work like a force that prevents us from doing it. It's like the Pauli exclusion principle, where if we try to do something that is improbable in quantum mechanics, like putting two electrons too close to each other, we will get something that works like a repulsive force that prevents it. Actually I suppose that large scale time loops may be very hard to do in practice, because we would have to make sure that every particle involved in the process behaves in a consistent way. So I'm afraid these fictional examples I mentioned will remain fiction for a long time...
    Whoa, that was a long entry! But I hope you liked it, next week we'll talk about extra dimensions!
  22. Silly Druid

    More on Superdeterminism

    By Silly Druid,


    Physics
    The goal of this entry is to explain my thoughts about superdeterminism in a more detailed way.
    We should start with the double slit experiment: there is a source of particles, two slits, and a screen. The particles can go through either of the slits, and even if we emit a single particle at a time, after many particles there is an interference pattern at the screen, showing that the particle seems to go through both slits at the same time. But if we make a measurement to determine which slit the particle used, it always uses only one of them and there is no interference pattern. So what actually happens here?
    The most obvious explanation would be a simple hidden variables theory, stating that the particle already carries all information needed to determine the results of all possible measurements. So if we don't measure it, it goes through both slits, but if we measure it, it already "knows" which slit it should use. But this explanation is wrong. The Bell Inequality experiments prove it. It's simply not possible.
    Another explanation is the standard quantum mechanics (Copenhagen interpretation). As far as I understand it, it states that if we don't measure it, it's truly undefined which slit the particle (or rather its wave function) uses. It moves through both slits with the probability of 50% each, and it interferes with itself. But when we try to determine which slit was used, the wave function "collapses", so it becomes 0% in one slit and 100% in the other. The problem with this interpretation is that the "collapse" doesn't make much sense as a physical process, because it happens at the same time in all the space occupied by the wave function: if we detect the particle in one slit, the part of the wave function in the other slit instantly becomes 0. This is Einstein's "spooky action at a distance". And we don't even know what "instantly" means, because in special relativity the concept of "at the same time" depends on the frame of reference we use.
    So how does superdeterminism fix these problems? By assuming that the following two things are correlated: the path of the particle (let's call it A), and the way we measure it (B).
    Before watching Sabine Hossenfelder's video, I didn't believe in superdeterminism. Not because the free will nonsense, but because in the sources I've seen it was presented as if the correlation meant there is a common cause (C), that causes both A and B. This makes no sense, because there is no way a physical process would determine both the path of the particle, and our decision how to measure it.
    But now I realized there are other options as well. A correlation can also mean that A causes B, or B causes A.
    "A causes B" makes no sense either, because again there is no way a physical process would make the path of the particle cause our decision how to measure it.
    But "B causes A" is an interesting possibility. If the way we measure a particle affects its path, then we can explain the "problem of measurement" without the need of "wave function collapse". Instead of collapsing, it's already created in a way that depends on what we measure (or don't measure). So if we don't detect which slit the particle uses, the wave function goes through both slits and interferes with itself, and if we do detect it, it goes through one slit. There is no collapse, and it's also consistent with the Bell Inequality results.
    But the measurement is made after we emitted the particle and it has "chosen" its path. Which means backwards causality: the effect (particle choosing its path) happens before the cause (the measurement). The way I see it is when we try to do something with a particle (which means trying to emit it, absorb it, measure it etc.), it creates a "vertex" on the grid of all possible particle interactions, and these vertices have a probability to be connected with each other by "particle paths". I think it's something similar to the "transactional interpretation" of quantum mechanics.
    [EDIT] An important thing is why this backwards causality doesn't cause time paradoxes. It's because it affects only the wave function, which is immeasurable. We can't actually see what happens with the wave function before we measure it. So you can argue that it simply doesn't exist at all. But it should exist, because it's what the Schrödinger equation describes, in other words it's what makes the entire quantum mechanics work. Without it (or some equivalent of it) we don't understand what happens at all. So my understanding of superdeterminism implies backwards causality, but in a way that doesn't allow you to actually send any information back in time.
    As for the tachyons, for those who think they are forbidden in special relativity, it's not true. If we assume a particle has an imaginary mass, it must move faster than light. But now I'm not so sure they are what really happens here, maybe it's something different, like wormholes. (Yes, there is a conjecture, called "ER = EPR", which states that quantum entanglement creates a wormhole between the particles.) What I mean here is that if we successfully combine two theories, it usually predicts something new. For example, when Dirac combined quantum mechanics and special relativity, it predicted the existence of anti-matter, which was experimentally confirmed later. So if we combine superdeterministic quantum mechanics with general relativity, who knows what we will find?
    (Sorry if this entry is too long and messy for you, you can ask questions in the comments so hopefully I can explain some things better.)
  23. Silly Druid

    Superdeterminism

    By Silly Druid,


    Physics
    I just watched a video from Sabine Hossenfelder: https://www.youtube.com/watch?v=ytyjgIyegDI
    She talks about an idea that can fix some problems with our understanding of quantum mechanics. And I have some things to say about it. First, I'm glad I'm not the only one who doesn't believe in all that free will nonsense. Second, I think the idea of superdeterminism has some very interesting implications.
    It states that the path of the particle depends on what you measure. But what she doesn't say in the video is that the measurement takes place after the particle "chooses" its path. Which means we have causality that works backwards in time.
    She also mentions that superdeterminism can be combined with general relativity. So, if we do it, I think it will imply the existence of tachyons, particles that always move faster than light, and can carry information back in time. But their function should be somewhat limited, to avoid time paradoxes. Maybe this will be a part of the long awaited theory of quantum gravity?
  24. Silly Druid

    Adventure Awaits!

    By Silly Druid,


    MLP Fan Works
    Today I'd like to recommend a choose-your-own-adventure series that I really like: d20 Pony. It's a long running series, in an expanded universe based on MLP G4, but with new areas to explore and species to meet. It's a really fun and exciting story with epic adventures and very likable characters (especially the main two: Trailblazer and Moonflower). It's mostly based on OCs, but there are also some canon character appearances.
    It works like this: anyone can post a command saying what the protagonists should do next, then one of the commands is chosen at random and executed, and the next part of the story is revealed, together with a 16-bit style picture. Sometimes there are dice rolls, used to determine if an action succeeds or not (hence the name). As you can see with the current entry, I'm taking part in it too (I'm "nopony" there). It was a part of my inspiration for the "Champions of Celestia" roleplay (the other part are my Tails of Equestria sessions, hosted by @abrony-mouse).
    Even if you're not going to take part in it, I highly recommend that you read it from the beginning, and treat it as an illustrated fanfic. (Warning: Sometimes it gets a bit adult-themed. It's nothing explicit though, just things like a vague description of the situation.)
  25. Silly Druid

    The Dividing Point

    By Silly Druid,


    Mathematics
    It all started with a seemingly simple question I saw somewhere: Is it possible to divide a square into two triangles? You might think you just need to cut it through the diagonal and you're done. But, if you divide something, its every point must belong to one part or the other. So what about the points on the diagonal? To which triangle do they belong? This problem seems to me like something artificial and counterintuitive, and makes me think the rules of geometry should be modified. Normally a point can't be divided into parts, but let's change the rules and assume it can.
    Let's start with a simple 1D object: an interval on the number line. Its ends can be either open or closed. Closed means that the ending point belongs to the interval, and open that it doesn't. But if we can divide a point into two parts, then we can have an interval where an ending point is "at the edge", and only half of it belongs to the interval. It's like taking limits, where we can approach a value from one side or the other, and in some cases we get different results.
    In case of 2 or more dimensions the situation is a bit different, because instead of two parts we can have any number of them. It's like a pie chart - when we zoom in to its central point, the situation around it doesn't change: the area is still divided into several parts, with the same proportions as the entire pie chart. So we only need to apply this division to the central point itself. In case of dividing the square into two triangles, the points at the diagonal belong in half to one triangle, and in half to the other. The two points at the end of the diagonal (in the corners of the square) only belong in 25% to the square, so after making the division they belong in 12.5% to one triangle, and in 12.5% to the other.
    What do you think about my version of geometry, does it make any sense to you? (It's my original idea, if you know something like it that already exists, then let me know in the comments.)
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