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mental-labour updated Mental Labour

11 months ago

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koilwood updated 🜊 k o i l w o o d 🜊

11 months ago

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nightvision updated Night Vision Process

11 months ago

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11 months ago

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nolin updated Nolin Brashears

11 months ago

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Nolin Brashears

koilwood

11 months ago

now rest beside your innocence

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ouroborista

11 months ago

Does anyone else have *really weird* site traffic stats starting either around December 18th or 26th?

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mihaigolanul 11 months ago

not my website, but my yt channel

iago updated PÁGINA WEB DE IAGO RAMOS

11 months ago

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deadalivedoll updated sophies basement

11 months ago

daliwali lionbunni

11 months ago

i like your library... based and brain-pilled. thoughts on calhoun's "mouse utopia"?

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lionbunni 11 months ago

Haha, thank you! Calhoun's study is unnerving to say the least, but overpopulation in nature is typically regulated by factors like resource scarcity, disease, etc. Which were mostly controlled for in the experiment. The closest human comparison was Kowloon, which had a high population density and infant mortality rate, but people could leave the city and demographic reports are questionable. Avoid Calhoun's Utopia!

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gollum revolution909

11 months ago

Added your button to my site! Love your designs and art!

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revolution909 updated REVOLVER

11 months ago

REVOLVER

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blame1984 updated Blame

11 months ago

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deadalivedoll updated sophies basement

11 months ago

koilwood updated 🜊 k o i l w o o d 🜊

11 months ago

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seryndelle updated Seryndelle's Sanctum

11 months ago

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lowryside updated LOWRYSITE

11 months ago

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revolution909

11 months ago

Just added a ton of site buttons to my about me page!! If I follow you and you don't see yours I probably couldn't find it, so if you want me to add yours pls comment and lmk where it's add and I totally will! And of course, if you'd like me to remove your button or link just lmk :]

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revolution909 updated REVOLVER

11 months ago

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REVOLVER

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eastathenaeum updated East Athenaeum Neocities Portal

11 months ago

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eastathenaeum 11 months ago

4D Golf spoiler added for final 5-dimensional levels

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xpaper 11 months ago

Currently the only rigorous notion of 4-dimensionality I feel I understand well is the Linear Algebra notion of a vector space with 4 linearly independent vectors. Everytime I try looking into tensors, I just get confused, so I'd be interested in seeing what you mean by "a metric tensor with a negative eigenvalue." I know what a metric and an eigenvalue is, at least.

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eastathenaeum 11 months ago

After seeing enough of these, visualizing in enough different ways, and thinking about it for too long, 4D space becomes so easy to understand that it's kind of a no-brainer. Not going to lie though, it took me years.

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eastathenaeum 11 months ago

The negative eigenvalue in time has everything to do with entropy in a positive direction, especially in particle interactions. Spacetime is dynamic, which means that it is tending eventually to a point of rest. This played a large role alongside the universe's expansion leading to the assumption of heat death, that time itself would eventually breakdown, no events, even though space would continue to expand forever.

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eastathenaeum 11 months ago

Don't beat me up if I got any of that wrong, by the way. There's been loads of observations in the last few years alone, especially with JWST, that have been telling us that our existing cosmological models are definitely fundamentally flawed and in need of rewriting.

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xpaper 11 months ago

To be honest I wouldn't know if you are right or wrong lol physics is by no means my area of expertise. I was hoping for more of a pure-math explanation. For me 4D or 5D or nD vector spaces already make sense (just add another coordinate), even if I don't know what they look like.

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eastathenaeum 11 months ago

As far as purely mathematical, I don't know of any applications. I was trying to say in the intro while angrily shaking my fist that time has nothing to do with it. There's always one that's like "Time is the fourth!" All of these softwares are pure Euclidian space, because responsible adults made them. Lol

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letslearntogether 11 months ago

@xpaper - It sounds like you already got the gist of it. Most of this software seems to treat the concept of "four dimensions" as simply an extra coordinate, let's call it w. Changing that w coordinate gives us another space, while changing x, y, or z changes our place within that particular space.

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letslearntogether 11 months ago

In the context of Physics, a "scalar" is only a magnitude (e.g.: a speed given in miles per hour). A "vector" is a magnitude with direction (e.g.: 60MPH due North). Both are "tensors". A scalar is a "tensor of rank-0", a vector is a "tensor of rank-1", and so on.

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letslearntogether 11 months ago

More specifically, tensors are objects that can be described as points on a "manifold". A manifold is a space that may have different "local" and "global" properties. A common example is the Earth. Locally, its surface seems like a flat plane, but globally, it is a sphere. This is a concept from Topology.

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letslearntogether 11 months ago

The concept of tensors is not used as much when it comes to Linear Algebra. A rank-2 tensor can be described by a matrix, but tensors are not synonymous with matrices. In Physics, you might switch from using one branch of math to the other depending on what you are describing though. So, the term "four dimensions" is often referring to either one of two concepts when used in Physics:

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letslearntogether 11 months ago

1. The use of four coordinates where x, y, z describe where something is in regular Euclidean space, and a coordinate t that describes when it is there. Simple and intuitive. But when dealing with extremes of speed, like in the case of Relativity Theory, we would use "Minkowski spacetime".

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letslearntogether 11 months ago

2. In Minkowski spacetime, we still have the three axes of Euclidean space, but "time" is considered a fourth axis that objects travel along at the speed of light. This makes the speed of light constant for every observer and everything else is measured relative to that.

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letslearntogether 11 months ago

Personally, I feel that a lot of seemingly complex math has been thrown at what are essentially simple relationships, so I understand eastathenaeum's displeasure with how the idea of "four dimensions" is often presented.

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eastathenaeum 11 months ago

Please tell me that you teach.

1 like

xpaper 11 months ago

I have varying levels of familiarity with everything mentioned here. However, I feel like I still don't have an answer to the question of how someone would go about determining eigenvalues for the "metric tensor of a dimension" and what those objects are in a mathematically rigorous sense. But when I look into it that's precisely the part that remains mystifying.

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eastathenaeum 11 months ago

It sounds like the confusion lies in assuming that spacetime is an object residing within dimensions as opposed to the dimensions being a part of spacetime itself. Basically the metric tensors are functions that translate how space looks to us with what is actually going on and visa versa, a feature of projection for mapping in differential geometry.

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eastathenaeum 11 months ago

I'm thinking about either changing or removing the wording now, because on all levels, peoples' minds are already made up for whether or not time exists. To me that's kind of a dumb argument, because how do you experience something for yourself and claim it doesn't exist? It's like saying emotions don't exist because they are just biological chemical reactions, when in reality that's an argument for how they exist.

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letslearntogether 11 months ago

@eastathenaeum - As in teach professionally? You are too kind. No, I just love learning and sharing...While I cannot speak for xpaper, I think they were trying to grasp what "the negative eigenvalue of a metric tensor" means mathematically. In other words, how do we calculate that? Are we treating a metric tensor as a matrix and then finding its eigenvalue?

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letslearntogether 11 months ago

If I had to take a guess, from your descriptions on the dynamic nature of spacetime, I have a feeling that you are using the inverse of the resultant eigenvector(s) to define "time"...as if spacetime itself is expanding at the speed of light, something like Einstein's cosmological constant...

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letslearntogether 11 months ago

Don't quote me on that though. I could be entirely wrong. I'm just trying to understand exactly how you are looking at the situation. You obviously have a deep understanding of it.

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letslearntogether 11 months ago

@xpaper - The concept of spacetime is such an interesting amalgam of Differential Geometry, Topology, and Linear Algebra that it can be a challenge to understand it. Some of the best videos to get a general idea of the Math behind it that I have seen are: https://m.youtube.com/playlist?list=PL__fY7tXwodmfntSAAyBDxZ4_eE3ZwbFE

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letslearntogether 11 months ago

I usually approach the idea of "dimension" in terms of how many coordinates are needed to specify any location within a given space. So, a "1-dimensional line" only needs one coordinate to specify any point along it, a "2-dimensional plane" needs two coordinates to specify any location within it, and so on.

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letslearntogether 11 months ago

In the same way that we might think of a "2-dimensional square" as a slice of a "3-dimensonal cube", we might think of a 3D cube as a slice of a "4-dimensional hypercube". People might trip over visualizing such a thing, but again, all we are really thinking about is how many coordinates. When it comes to applying this idea to Physics, well...

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letslearntogether 11 months ago

To be honest, I think Einstein (and the theoretical physicists who followed him) go a little overboard with the Math sometimes, to the point of obscuring the actual physical phenomenon that they are describing...though I am not as harsh with my assessment of Relativity as Nikola Tesla. 😂

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letslearntogether 11 months ago

One has to keep in mind that Einstein formulated his idea of spacetime when scientists were arguing over the constitution of the aether. So, I think Einstein was like, "Here guys, let's just use this mathematical model to describe light and gravity for now. We'll figure out the composition of the aether later." Unfortunately, it seems to have led to a lot of confusion.

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eastathenaeum 11 months ago

No, my understanding sucks, but thank you for the vote of confidence. I've only taken physics for engineering & science majors 1 & 2 in college as well as some others completely unrelated to cosmology. I've read about it a lot in Wikipedia over the decades and kept up with hypothetical models trying to make breakthroughs, but that hardly constitutes as studying.

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eastathenaeum 11 months ago

The eigenvalue is determined from a metric tensor matrix, which is the scalar equivalent to the eigenvector, so yes, that is correct. I'm kind of falling down a rabbit hole trying to find pure mathematical context, and everything I'm looking up leads back to physical interpretation. In relativity, negative eigenvalues are pretty much a given rather than a consequence. I never gave it any thought.

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eastathenaeum 11 months ago

I just called a friend over this after numerous carefully worded searches. He has two degrees, one in math, and he told me there is no purely mathematical context, that all it would do is flip the field and that it is never used. Now my brain hurts because this doesn't sound at all like the context laid out in relativity. Lol

1 like

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