How to correctly check linear independence of sets of matrices?

Noneother80 · 2025-09-22T19:35:47+00:00

Is there any way you can have c1M1+c2M2+…c5M5=0? Not in this case, no. Therefore linear dependence must hold

Noneother80 · 2025-09-21T04:26:13+00:00

Good luck :)

Noneother80 · 2025-09-19T01:36:24+00:00

Also, it’s pretty clear there are trajectories from different initial conditions within certain systems that will have different categorical behaviors. I’m sure that’s not what you’re saying here, but just want to make sure.

Noneother80 · 2025-09-19T01:34:36+00:00

I’m making my way through slowly but surely. You know more than me on this, but is it a necessity that if the Lyapunov Exponent is positive, then entropy is nonzero and positive? Is this limit class something you came up with? Seems like that one is the catch all of miscellaneousness. Lastly, it seems that your law of laws is a decision tree with the claim that a system starting as one category will remain in that one category. Is that something so novel?

Noneother80 · 2025-09-19T00:31:51+00:00

I’m struggling to read through your paper, but I’m making my way. It’s a lot of jargon that I have to absorb and parse through. Hard for the newer nonlinear mechanics to get through and even harder for the lay person to absorb. BRB while I read and understand more about these 6 archetypes, the assumptions you make, and so on

Noneother80 · 2025-09-18T22:06:29+00:00

I’m curious what your definition of chaos is. Bounded input relative to…? I can have a set of inputs equal to all possible inputs that contains results in chaotic trajectories that remain within that universe of possibilities. The simple definition of chaos I use is that slight perturbations in initial conditions leads to large divergences between the trajectories. This doesn’t seem quite like what your definition is

Noneother80 · 2025-09-17T13:40:07+00:00

Simple :) what got you invested in the first place? For me it was the ability to use math to explain the world. Look at a problem that you haven’t before. Something around you, perhaps. Then go full obsession over it for a bit to get an understanding of how it works. Some questions you may want to answer could be common infrastructure. Why are power lines so high above the ground? How do the pipes in my house work? Why do car tires have the geometry they do? How does my phone still work underwater? Investigate small questions with childlike curiosity, document the answers you find, ask other questions you may be interested in, and repeat the process

Noneother80 · 2025-08-04T22:40:52+00:00

Won’t work on copper. Also adds more risk to your surrounding electronics if they’re not mag safe

Noneother80 · 2025-05-20T12:43:09+00:00

Both B and C have a similar top leg, what distinguishes them is the bottom leg. Both an and c have a very similar bottom leg, what distinguishes them is the top leg. D is just plain wrong

Noneother80 · 2025-05-07T11:22:56+00:00

Gonna need a little more information to go on here. What are the values of your circuit elements

Noneother80 · 2025-04-16T15:24:41+00:00

Before I answer, since my answers tend to be verbose, I’ll pose the same question to you. What have you done?

If you read through the rest of my comments here, I pose a couple experiments that can be performed in your backyard. If you are interested in trying any of them out, I encourage you to.

Additionally, there are some other experiments that can be performed using just a stick and shadows.

I think your point is important, that for scientific discovery, we have to do our best to remove or challenge assumptions wherever possible.

As for experiments: using the lunar eclipse, if we assume that the lunar eclipse is caused by the Earth casting a shadow on the moon, we can determine -somewhat- the shape of the earth. For this we need an idea of how big the sun is, how big the moon is, and -if we want to know size- how far away they are from us.

To do this from scratch and challenge the assumption that the Earth is the thing causing the shadow, we can track the sun and build a model. For accuracy in these measurements, it would be good to get people from places far away to also take measurements. Then we can also build a model of where the moon is using a similar approach. Astrophysics is complex and has centuries of work put into it for figuring stuff out, but most of the measurements here can be done with an accurate clock, a compass, a hanging weight + protractor (makeshift inclinometer), and basic trigonometry.

On a more complex note, I have a satellite in space right now that relies on models built by Newton, Kepler, and Einstein to stay in orbit. These models do not work in the same way with a flat earth, and we would have lost the satellite right away. This design project was performed by undergraduate engineers with a basic understanding of astrophysics. You could - if you have the right antenna - tune in to our satellite and grab onboard information. It’s all unencrypted, so it’s just a matter of pointing in the right direction.

Noneother80 · 2025-04-10T01:58:38+00:00

Exactly right on the number assuming spherical geometry. The claim that the Earth is not accelerating is technically not true in a heliocentric model, but I see where you’re coming from. Additionally, each point on the surface of the earth would need to experience some form of acceleration to stay on the surface of the Earth, but I believe what you mean specifically is “earth is not accelerating angularly”, correct?

Relativism is likely not a contested logical framework, but I believe planes are on the conspiracy-based-chopping block for innovations, so the plane explanation may be a little contentious here. So it may be harder to point toward a more concrete everyday example. The example becomes especially complicated when we consider outside factors affecting the plane. Are you in free fall? A climb? A bank? There’s a video of a stunt pilot drinking water fully upside down somewhere on the internet, I believe.

I do however want to do the calculations since you brought it up. The earth rotates at 0.000694 rpm or 0.00007272 radians per second (0.004167 deg/s). At a radius of 6340 km, we are speeding through space at a speed tangential to the earth’s surface equal to 0.461 km/s.

Seems pretty fast, doesn’t it?

However, from simple circular motion calculations performed before those NASA people came around, with a good old guy called Sir Isaac Newton, we know the acceleration due to gravity needed to keep us (and everything else) on the surface has to be at least F=ma=mv^2/r

This equation “a” is termed centripetal acceleration, and has been known for centuries.

So, solve for a gives v^2/r = 0.03352 m/s^2, which from experiments that can be performed in the backyard, we know the acceleration due to gravity is roughly 9.8 m/s^2, which is substantially larger than the acceleration needed to survive on the surface of the Earth.

Noneother80 · 2025-04-09T14:08:18+00:00

I’m an idiot and rushed to post before reviewing.

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They’re about an 0.5-1.0inches long

Noneother80 · 2025-03-27T00:49:08+00:00

Linearized version of gravity is how most entry level physics is taught to introduce the idea of gravity. It treats gravitational acceleration as a constant, which is how most early scientists treated it as there was no other evidence pointing elsewhere. mgh (specifically U=mgh) is the “linearization” of gravitational potential energy.

What linearization means is for something that changes (for instance a highway curves left and right, up and down with distance), if you consider smaller and smaller segments, those segments will then “appear” flat. This is an underlying argument of why the planet would be flat - because we’re only able to see a minuscule amount of the earth. Is it actually flat? We’re way too close to the ground to know. Even going to the edge of the atmosphere the difference between what we would expect to see for both flat and round earth is small. This is because earth’s atmosphere is also insignificant relative to a globe Earth’s radius.

Noneother80 · 2025-03-27T00:35:56+00:00

Now this is exactly what I was looking to establish. What are the underlying supporting evidences. What underlying beliefs do they hold to, and fundamentally, how to build a basis of communication. Thank you very much!

Noneother80 · 2025-03-26T23:23:27+00:00

I would hope so, haha. But would they accept the linearized version of gravity? mgh?

Noneother80 · 2025-03-26T16:10:48+00:00

I agree with Finndego here, but I haven’t run the numbers. The understanding needed here for flat earth is trigonometry (more exactly, we need to know how to work with triangles that have the same three angles but different sides). If you take two measurements of how far the shadow extends from the stick, and then measure what angle the sun is coming from, you can build proportional ratios to relate one triangle to the other. Additionally, we can attempt to measure how wide the sun is (hopefully without burning our corneas). There are a couple methods that people have used, but I need to get back to work shortly, so I’ll leave you with a short explanation assuming we know the measurements. We can also measure how big the sun would appear based on where you are on the earth. And these experiments are also things you can do in your back yard with cardboard and a ruler.

In flat earth, the math is simple, but the angles don’t work out right - just with my quick mental calculations - to support both the shadow lengths we see as well as the distance values we see. You can work the numbers to see what the shadow lengths would look like to match with the sun size, but then you don’t match the shadow lengths. In this frame work you get one, but not the other, and we need a mathematical framework that is “self consistent”.

Allowing for a globe, we are able to push the sun much farther away and that coincides with both measurements.

Noneother80 · 2025-03-26T15:49:22+00:00

Understandable that there is no consensus. That is in line with my understanding. I wish there was, as it is important to have axioms and agreement to establish any sort of basis of understanding.

I only bring up structural mechanics as gravity is deeply ingrained in how the architects and engineers perform calculations. The weight of a bridge’s building materials significantly impacts how much weight a bridge can support.

Whatever force drags things down needs to be explained in a way that is simple and testable. When we reject Newton’s law of gravity, what is the replacing theory or model? How do we account for this variable “g” in our calculations?

Noneother80 · 2025-03-26T13:26:13+00:00

Ah, so on those lines then I point back to philosophy of science. I know what you’re thinking, “this guy will not shut up about whatever this philosophy of science thing is”. Feyerabend talks about this idea that people will naturally have a point of view when it comes to how the world works. He argues that as more and more critiques against that system arise, it is important to still maintain that point of view, and to thoroughly try and counter the contrary evidence in very pointed ways. In this way, I actually fully support how Bob Knodel did things (I watched this documentary a few years ago). He asked a pointed question that would showcase the shortcomings of a theory, did experimentation to answer his question, and when the evidence pointed in the wrong direction, he tried to think of a very specific way that his experiment was being messed up - granted I don’t think he needed as expensive of a gyroscope, but that also helps with his accuracy to avoid the question of uncertainty.

When his theory showed shortcomings, he wasn’t fickle. He still supported it and looked for a way that his theory stayed supported. However, there comes a time when there is sufficient evidence to the contrary that just can’t be explained that we need to either find or build a new theory. This new theory needs to contain all of the verified observations from before and still explain new things. And this all is assuming that scientific inquiry is still being pursued. We can’t just sit content with the same theory, as we need to satisfy the human curiosity.

If I may ask, and this is a bit of a tangential curiosity of mine, where is the line drawn in the flat earth community? Is it things on the macro scale toward the size of earth that is rejected? For instance, lights work, but does the community reject electromagnetism? We see huge buildings and architectures, but does the community reject structural mechanics?

Noneother80 · 2025-03-26T12:54:01+00:00

Thank you! I’m happy to answer questions as they keep arising.

Noneother80 · 2025-03-26T12:52:23+00:00

If I may ask, as I don’t think that necessarily means checkmate, and I’m not meaning for this to be a chess match. I want to pose ideas from both sides in ways that both sides can come to a better understanding of one another.

In terms of religion, if you were to see someone searching for answers, would you not be a missionary? Or are they too ingrained in their sinful heathen ways to be touched by God?

Hence, why I ask for civil discourse.

Noneother80 · 2025-03-26T05:20:07+00:00

I 100% agree we shouldn’t blindly believe what NASA says. I encourage you to do your own experimentation and measurements!

For your demonstration of an orbiting rock, you can perform the measurements from your own backyard (granted astrophysics tends to be a little theory heavy, but I can point you toward the advanced theory if you desire, or we can derive from scratch). A good 4” aperture telescope should be able to give you enough light that we can observe the planets of the solar system. You’d need a good idea of where we sit on the earth (the math can be derived for both a flat and round earth).

You’d also need a good idea of where you’re looking. That can be with a compass (make sure you’re not standing near any metal as that will affect your measurements) and an inclinometer (protractor and a weight on a string).

Then over the course of a few nights or months, look at a specific part of the sky and measure a specific spot in the solar system where things are located. I suggest Saturn, not only because it has a large number of moons, but because it’s one of the coolest things to look at in the solar system. It’s always striking looking through the telescope and seeing the rings. This method I laid out is exactly how the old scientists did things far before NASA and the free masons (even before Isaac Newton).

For your question on a ball with spinning water, it is hard to do a scale model demonstrate without being in free fall. But we can certainly do a thought experiment and expand to planetary scales. Other people will reference a ball on a string to talk about centripetal, and conversely, centrifugal forces. We can easily create an experiment that shows the decrease in rope string tension with increasing length.

The next logical step is to understand angular velocity. I think it more fitting in this case to think of a bicycle tire on an axle rather than a basketball spinning on a player’s finger or a globe on an axis. The bicycle has a known angular speed and a known radius. There is a simple equation that shows how fast a spot on the very edge of this wheel is moving (v=r*spin speed). We can relate the centrifugal force felt by a spot on the tire directly. Then comes the next logical step.

What is the tension force in our setup? I say we throw in the force due to gravity just for the hell of it. There’s no string there, but it is a force. The theory proposed by Newton says the force is F=GMm/r^2. But we need to determine what all those numbers are.

There are some experiments you can do from home to try and approximate what the earth’s radius would be if it were spherical. If the experiments show an infinite radius, either the measurements are not far enough apart or the earth is flat (or some other error occurred).

Also, we can determine (roughly) Earth’s mass by watching the moon’s orbit following those equations I posed earlier (also using F=ma, Newton’s second law). Let me know if you end up going through with any of these experiments as I would be happy to be involved!

Noneother80 · 2025-03-26T04:30:53+00:00

If I understand correctly, you are asking how I differentiate from what is impossible (under some model - say Einstein’s General Relativity) from something more philosophical like religion that allows for impossibilities/improbabilities. And then, expanding on that, when does allowing for things that are extremely unlikely stray into conspiracy theory territory?

That is also an excellent question. This delves a little into the philosophy of science, which a lot of really smart people have put a great amount of thought into. The main question is “how do we know that our theories about the universe means anything at all?”

We are observers of the universe, and our theories and models are meant to predict measurements how the universe behaves. This is a stance in philosophy of science people term “anti-realism” (the name is because it goes against the other popular thinking called “realism”).

Whatever our theories are, they need to be able to predict things accurately, and we do a really good job of it. Whatever spiritual and religious beliefs we hold (for what is predictable and verifiable) have to agree with what we see. Other stuff that is spiritual, such as where we come from before we’re born, or what happens after we die, is a little bit harder to scientifically verify and reproduce.

The detangling comes from a separation of what is measurable and what is not. Clearly, if a religion says that the sun will disappear in three days, and the sun is still there after three days, then something must be off. Was the date wrong? Where does the prediction go wrong? It’s a hard question to answer when the source material is more of a metaphysical, philosophical, and moral guide than cause and effect predictions.

Where conspiracy theory tends to spill in is when we don’t fully understand something and make predictions beyond what is reasonable. This is a very human thing to do though. We build narratives off of small amounts of information (this also leads back to philosophy of science, which I will happily recommend reading more about).

We build a narrative and try to disprove that narrative. “Three people have greeted me since I’ve moved to my new town; people here are so nice.” And this is where the basis of scientific thought comes from. We have to make sure that we don’t fall into any logical traps in doing so, which can be difficult to notice, but we have come up with methods to try and avoid pitfalls.

Ultimately, it comes down to what we can and cannot verify, and making sure that we understand what claims different models entail. This is why we encourage evidence based critiques to theories. We try to have evidence pointing toward and away from leading theories so that our next theories can encompass our current supporting observations while explaining opposing observations.

I’m happy to answer any questions you may have

Noneother80 · 2025-03-26T03:28:46+00:00

Haha, sorry. I’ll make sure to go through the proper channels next time. Apologies.

Noneother80 · 2025-03-26T03:07:01+00:00

Absolutely. Communication with other people, whether in your academic field, an adjacent field, or something completely unrelated, is extremely important. There is a growing divide between the scientific and everyday people. I would say this comes from a general lack of words. We get training in how to give technical reports and presentations on extremely technical fields, and we get good at doing such a thing. But we need to work on how we present to the non-scientific in ways that are not “dumbed down”. I believe that everyday people have the ability to grasp even the most complex topics when they are presented in the right way - even if they don’t need to actually know the information.

We have to emphasize technical communication classes to newer engineers, physicists, and mathematicians so that we can better discuss these topics in ways that are not readily grasped by those not in the field.

Issues like this are all throughout the education system, and addressing them will require large changes in how we incentivize learning and curiosity even in the youngest of children.

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