Silly Druid

57 minutes ago, Astralshy said:

I'm crossing my fingers :>

my secret hidden talent 

  Reveal hidden contents

 

is to be round
 

It's not very well hidden though, it's not even in the spoiler

7 hours ago, Trot Shuffle said:

(umm @Silly Druid pssssst I need help with decoding a secret message )

Silky sends us this kind of secret messages quite often, but so far I have failed to decode any of them...

Mint Chocolate

(I know, not very original.)

@ZiggWheelsManning I'm not sure what you mean here...

@Props Valroa Well, the Crystal Heart was Cadance's cutie mark long before the Crystal Empire reappeared, so you can say she was destined to rule it...

My problem with Crystal Ponies is that they seem very passive. They are ruled by foreigners, as King Sombra and Princess Cadance are not Crystal Ponies. And there is not a single Crystal Pony (in the show at least) who would be known for doing anything important. There is more about them in the comics, but in the show they seem like wasted potential to me.

And yes, I like Radiant Hope too, she is one of my favorite characters from the comics. Another interesting character is Princess Amore, who seems to be a distant ancestor of Cadance.

@Sir Hugsalot

Unfortunately, there will be always imperfection in math, not only with not being able to give an exact value to numbers like pi, but even on the deepest level (see "Gödel's incompleteness theorems").

Replacing pi with tau won't help in this situation, it's just more convenient than pi in many cases. We're using pi just because of the tradition that is hard to change, just like the Americans are using their overcomplicated system of measurements, for example.

As for radians, they don't help much either, because they usually make the angle some number multiplied by pi (or tau for that matter), and we can't have the exact value of that... They are the "natural" way of measuring angles though (in a similar way as the natural logarithm is natural), and do make some things simpler, as ChatGPT pointed out.

@Splashee

You asked for it...

@Splashee Here is the answer from ChatGPT:

Quote

Radians are generally considered better than degrees because they are a more natural unit for measuring angles in mathematics and physics.

The main reason for this is that radians are based on the geometry of the circle. A radian is defined as the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. This means that if you have a circle with a radius of 1 unit, an angle of one radian will subtend an arc of length 1 unit along the circumference of the circle.

In contrast, degrees are an arbitrary unit of measurement that do not have any direct relationship to the geometry of the circle. Degrees divide a circle into 360 equal parts, with each degree being equal to 1/360th of a circle. This makes calculations involving angles more cumbersome, as conversion factors are required to convert between degrees and radians.

Another advantage of radians is that they simplify many mathematical formulas involving trigonometric functions, such as sine, cosine, and tangent. In fact, many trigonometric identities and formulas are most naturally expressed in terms of radians.

In summary, while degrees are a useful unit of measurement for everyday angles, radians are the preferred unit for mathematical and scientific calculations involving angles and trigonometry.

I can add to this that, for example, when using radians you can assume that sin x ≈ tan x ≈ x for small x.

@Splashee But if, instead of bits, you use something that can have 3 values, then you don't need to round it in this case. It's not used in practice, but theoretically you can build circuits with three-valued logic.

@Splashee While I can agree that it's hard to imagine (if not impossible) to create a physical object that contains less than one bit of information, when you put that information into the context of reducing the uncertainty about a specific question, then you can say the information gained is less than one bit, like in my example above.

We'll all miss you, Frostbite.

I'm glad I could help. I just wrote a prompt though, the rest is ChatGPT's work.

@Splashee

The sign switch is due to moving the term to the other side of the equation.

S = 1 + 9S

(move 9S to the left side)

S - 9S = 1

-8 S = 1

(divide both sides by -8)

S = -1/8

@RDDash

Such manipulations of divergent infinite sums are normally not allowed and can lead to nonsensical results. It's interesting that your approach leads to the same result in both cases, but I can give you another one that leads to another result:

S = (1+2) + (3+4) + (5+6) + ...

S = 3 + 7 + 11 + ...

but also

S = 1 + (2+3) + (4+5) + (6+7) + ...

S = 1 + 5 + 9 + 13 + ...

now let's add both expressions for S

2S = 1 + (3+5) + (7+9) + (11+13) + ...

2S = 1 + 8 + 16 + 24 + ...

2S = 1 + 8S

-6S = 1

S = -1/6

Also this kind of manipulations were used in the Numberphile video, without explaining properly why they were "allowed" in that case, which makes that video a bad example of popularizing mathematics. (Watch the Mathologer video that I linked in the main post for more information about that.)

@Splashee This doesn't look like a quadratic, the growth from 84 to 482 is way too fast compared to the earlier steps. Unless the x values aren't evenly distributed.

@Splashee Yes. To be clear, it's the area in red here:

When you take the integral, the area below the x axis counts as negative, hence the negative value of the result.

You weren't there from the start, so you missed the part when I turned into a lizard.

@abrony-mouse I like your spark metaphor, it reminds me of Stephen Hawking's question: "What is it that breathes fire into the equations and makes a universe for them to describe?" I believe that thing is consciousness. If the universe described by the equations contains it, it is enough to "self-breathe fire" into them. And a fire starts with a spark...

@Props ValRoa It is true that what we perceive directly are the "photochemical signals interpreted by our brains", but I believe these signals originate from something more than them, something that is "out there". Thanks to these signals, we have some information about that something, and we call it "reality".

I agree with you about consciousness, for me it's the biggest mystery in the universe, because everything else can be more or less described by our scientific knowledge. Of course we don't know everything, but in general we have a pretty good idea what's going on, and we can use the reductionist approach to explain larger things by their smaller parts. Consciousness is different, we have no idea whatsoever how to connect it to anything else. We have some knowledge about how the brain works, but it doesn't explain our subjective experience at all. I believe it must be something more fundamental than just a side effect of processing information in the brain.

33 minutes ago, abrony-mouse said:

I'm gonna say everything that only gains its meaning due to consciousness acting on it 'fictional'. because that is is silly :3

I don't think about it in terms of specific things gaining their meaning due to consciousness, although there are some people who do it, and ask questions like "If a tree falls in a forest and no one is around to hear it, does it make a sound?" or "Is the moon there when nobody looks?"

How I see it is that the entire universe gains its meaning if consciousness is in it, and by entire universe I mean all the spacetime. Many of the comments you and @Brony Number 42 make here are "time-centric", speaking about things that existed before consciousness, or will exist after it. I don't see it like that, as I said time is just another dimension, so you can ask the same kind of questions about distant regions of space. By definition, the universe consists of things that interact with each other, so if at least one of these things exists, all of them exist.

You can say universes without consciousness exist, but, as I noticed in an earlier blog entry, if they didn't exist, nobody would notice any difference. So this kind of existence is pretty pointless to me, that's why I don't consider it real.
 

41 minutes ago, abrony-mouse said:

Chairs are semi-fictional.

I can agree with that. While things like atoms are pretty well-defined, chairs are only vaguely defined, so the description of reality involving them is not 100% rigorous and accurate.

20 minutes ago, Brony Number 42 said:

I don't understand what this means.

If we define a set of properties that a chair should have, and we observe something that meets these properties, then we can say it's a chair.

22 minutes ago, Brony Number 42 said:

I look at the stars and they move while I do not. This is an observation that interacts with my consciousness.

That's true, but it's not clear that it means Earth in the center of the universe.

22 minutes ago, Brony Number 42 said:

Are you saying that a universe without a consciousness cannot exist? If every conscious mind died would the universe stop existing? How is the universe more real after the evolution of consciousness than before? Is something real before a consciousness became aware of it? If you say atoms exist even before they were discovered, then they didn't need any consciousness to exist.

Time is just another dimension, not very different from the spatial dimensions. When thinking about the universe as a whole, we should think about it as the spacetime in its entirety. If it contains consciousness, then I consider it real. If not, it's just an abstract mathematical object. So it exists mathematically, but not physically.

26 minutes ago, Brony Number 42 said:

This talk about fuzzy definitions is not a problem in science but is only a problem in philosophy. An atom is atom and it does what it does. A collection of atoms arranged in a certain way will do what they do regardless of whether or not some primate puts his butt on it and calls it a chair. So what? Fundamentally it all comes down to mathematics. I can define in words what an electron is, and you can argue it. But an electron is a set of quantum numbers that parameterize the solution to an equation. If you ask what it is, then I point to a quantum mechanical solution. It has a mass, charge, and spin.

I agree with everything you said here, and I don't think it contradicts anything I said. This blog entry is about philosophy, not physics. The kind of "problems" we're talking about here don't exist in physics.

@Brony Number 42

Valid means that what we observe about reality meets the criteria we defined for our description of it. As for Earth being the center of the universe, it's not valid in the sense that there are no observational results that confirm it.

I'm not saying nothing existed before consciousness, because every stage of evolution of the universe depends on the previous stage, so it's still what I call indirect interaction with consciousness. And I still think consciousness is important here, because if there is a set of objects that interact with each other, but there is no one to experience them, then it's not "real" to me. It's just a mathematical abstraction.

I think a modified version of your definition is better than mine: Reality is a set of things, including consciousness, that interact with each other.

But I can't agree with the statement that "something exists if it is a member of that set", because in case of complex objects like chairs it creates all sorts of problems described in the video, like the fact that the chair exists but the atoms that constitute it also exist, so we have a redundancy. I think my version with "valid descriptions" avoids these problems.
 

@Sir Done A Lot

If you name a plate a chair and use it consistently for all plates, then you just changed the language, and your description of reality is still valid. But you won't have a word for chair then, so maybe you should name it a plate...

@Splashee Superposition is just like linear algebra. So if there are two "classical" states, A and B, a particle can be in a state that can be described as 0.5 A + 0.5 B (or any other proportions of these two states). The actual math behind this is more complicated, but that's the basic idea. And this "mixed state" can only exist if it's not measured, if it's measured then it becomes pure A or pure B, and coefficients in front of A and B become the probabilities of these results. There are many ways to create quantum superposition, for example if there is an atom that can decay, and we don't measure if it did, it can go into a superposition of decayed and non-decayed state (this is used in the famous "Schrödinger's Cat" thought experiment).

On 2022-03-12 at 5:24 PM, Splashee said:

I know. Planning ahead of time is kinda how the universe works, as time is moving in one direction, changes are being made after they have been decided on... (this is from your previous blog entry):

The measurement begins when Alice and Bob have agreed on the experiment ahead of time, not when the measurement happens. The experiment is very loosely defined here. If the world works in a way that particles can change their behavior instantly knowing a change was made, then that particle would already know the instant Alice and Bob agreed that the measurement would take place at a later time. I don't see a backwards-in-time causality here.

Fooling the particle has proven to not work, as it magically knows the result for every action truthfully expected of it.

But how an agreement between two people could affect the path of a particle? This doesn't make any sense, it's like a big conspiracy theory, where an all-powerful being knows everything about all planned experiments and adjusts particle paths accordingly. This version of superdeterminism just doesn't work for me, that's why I prefer the backwards causality version.

Another problem with this approach is that they only determine when Bob adjusts the experiment, but not how. He can do it randomly, which means that the decision is truly made after the emission of the photon. Of course this brings up the discussion what "randomly" means, and if true randomness exists or not. Theoretically a coin flip isn't random, but for all practical purposes we can treat it as random. And the idea that the photon somehow "knows" the result of a future coin flip doesn't make any sense to me either, it's that big conspiracy theory again.

So for me, what can truly affect the path of the particle is the measurement itself, which happens after the particle is emitted, hence the backwards causality.
 

Some more answers for you (better late than never):

About doing the double slit experiment in practice: It's true that the picture I posted is just the normal intensity laser light. I don't think you can truly "see" the low intensity version, where the photons are emitted one at a time, and you can use detectors to prevent the interference from happening. To do it, you need to measure the place on the screen where the photons hit, and after many photons you can graph the results to see the interference pattern (or lack thereof). For what I know, it's not just a thought experiment, and it definitely has been done in real life, in many variations. I don't know any YouTube video showing that someone actually does it, perhaps you can find it if you look for it (I didn't).

About hitting the wall between slits: If I understand this correctly, for the purposes of this experiment we just ignore the particles that hit the wall, only those that hit the screen interest us.

@Splashee What I meant is that they plan the experiment beforehand (which includes agreeing on the time when Alice is going to send the photon), so Bob knows when to do the random adjustment without the need to get any signal from Alice.

@Splashee

Quote

Also, sending a photon and adjusting the experiment while the photon is mid flight?????

Isn't light the fastest information? Send a photon, then, tell the experiment to change (using something faster than light obviously since ->), before the photon reaches the experiment. And now, suddenly "future events were changing the present".

You don't actually need to send any information. I'll explain it using the most popular names in this kind of examples, Alice and Bob.

So Alice sends a photon, and then, while the photon is in mid flight, Bob, who controls the detectors, adjusts the experiment randomly. And that adjustment seems to affect the entire trajectory of the photon, from the moment when Alice sent it.

Of course what comes earlier or later is relative, but let's say that Alice and Bob are at rest in relation to each other, so they have a common frame of reference.

(I haven't seen the videos you posted yet, I'm going to do it tomorrow and give you more answers.)

I edited the entry by adding a very important paragraph about things I forgot earlier, see the part that starts with [EDIT].

On 2022-03-02 at 1:12 AM, Splashee said:

Anyone actually have proof of this? I know it is true, but it would be cool to see it! It is the opposite of how the world actually works, so it would be cool to see.

The double slit experiment was done many times in real life, this image (taken from Wikipedia) is an example how the results look.

On 2022-03-02 at 1:12 AM, Splashee said:

If you are the measurement, wouldn't the interference pattern disappear? What does measurement mean in this case? I have heard explanations about using a machine that, when simply removing the plug from the electric wall socket, will get the interference pattern back. I take it as electricity must exist for the experiment to count as an experiment.

What does a measurement mean is a very good question. Basically, in quantum mechanics, it's impossible to achieve some information about a particle without affecting it in some way. So any attempt of detection which slit the particle uses must involve some interaction with said particle, although in some cases this interaction is indirect: if we try to detect it in one slit and we find out that it isn't there, it's enough to affect the wave function because we know it must go through the other slit.

The difference between the standard interpretation and superdeterminism is that in the standard interpretation a measurement only affects the wave function forward in time, so before the measurement it looks like it goes through both slits, and when we measure it in one of the slits, it suddenly changes everywhere to a form that goes through one slit. In superdeterminism it also affects the wave function back in time, so if we measure it in one of the slits, it goes through one slit from the start.

On 2022-03-02 at 1:12 AM, Splashee said:

By using clever math to discard rules for probabilities. This is where I don't even follow. That's why I don't have a Nobel Prize.

TBH I don't know how the Bell Inequality works either. I just take it for granted that it proves what it proves.

On 2022-03-02 at 1:12 AM, Splashee said:

What if it isn't the particle that interfere with itself, but the measurement changing the state of the way the particle takes? This is again tied to my top question. There is no proof of the measurement ever changing where the particle ends up behind the slit. There are two slits, and it assumes that one particle somehow made it through both slits, 50% in one, and 50% in the other, and 0% in between the slits, or outside the "play-area". It is ridiculous vague what the double slit experiment actually proves, other than creating an interference pattern when many particles have been accumulated on the wall behind it.

As far as I know, this kind of interference pattern can only appear because a particle (or, more precisely, its wave function) interferes with itself. Maybe there is another possible explanation, but I haven't heard of any.

One more thing: The reason I mentioned tachyons in the first place is because I heard of the idea (the actual research paper is here if you're brave enough to read it; I didn't do it), stating that if we allow "superluminal observers" (i.e. frames of reference that move faster than light relative to each other) in special relativity, the resulting theory recreates the basic laws of quantum mechanics. Speculating about such ideas (without the need to actually do the math) is fun indeed