Anonymous at Tue, 25 Jun 2024 08:00:32 UTC No. 16252348

In that case, I'll give another example. When coming up with the Dirac equation, there was a point where Dirac realized he needed to take the square root of a vector. Typically these sorts of things get pushed aside as being mathematical abstractions which are simply part of the process, but what does taking the square root of a vector signify in the real world? If the equation can model the real world, then its logical process must reflect something which is as real as the equation is approximal.

Anonymous at Tue, 25 Jun 2024 09:18:12 UTC No. 16252408

Okay, how about this: I just had a thought. When you take a 2D vector, you have a set of coordinates which represents the vertical and horizontal positioning of one of your destination. You also have your origin point. You can look at this as three points of information, since the location of your destination is described by the x and y coordinates, but it can also be looked at as four—vertical, horizontal, origin, destination. Four points makes sense because you are in two-dimensional space. However, when you look at a three-dimensional vector, you simply add a z-axis—a fifth point. There is a missing sixth. I've considered that what is missing is speed. Real three-dimensional space is space-time; time is always relevant. We don't necessarily take it into account, but speed is a relative measurement of time-to-space, and so a truly three-dimensional vector would also have a measurement describing the rate of travel towards the destination point, but I'm not sure whether that is absolutely true and the significance of such a thing. I've only just considered it.

Likewise, since we can, given a line, derive a square, and given a square derive a cube, and give a cube, derive a hypercube, we should also be able to take the root of a 4D cube and get a 3D cube, but I feel like in order to comprehend when this might be useful, the relationship of Square and Cube Roots to the real world must be thoroughly understood.

Thoughts? Insights?

Anonymous at Tue, 25 Jun 2024 10:11:47 UTC No. 16252453

Why do owls have such large ears? It's utterly insane. Large ears assist in the location of sounds due to how soundwaves move over the folds of the ear, helping to determine both direction and distance. How the fuck do owl ears work with random feathers getting in the way? And why are they the only avians with ears? It doesn't make any fucking sense. Owls must be the squares of the avian kingdom.

Anonymous at Tue, 25 Jun 2024 10:16:07 UTC No. 16252458

>>16252453
>see my thread bumped
>"Yes! Someone finally has something insightful to tell me about square and cube roots!"
>see your post
You cannot imagine my disappointment. I'm off to bed now.

Anonymous at Tue, 25 Jun 2024 10:19:21 UTC No. 16252462

>>16252453
Now that my initial disappointment has worn off, I have come to appreciate your post. I love owls. Good post, owl appreciator. Now, off to bed.

Anonymous at Tue, 25 Jun 2024 10:20:41 UTC No. 16252463

What are we supposed to tell you? Your first post indicates you want basic information and your second post leaps into “why are spinors like square roots of vectors” which is an absolutely nontrivial concept even for grad students

Anonymous at Tue, 25 Jun 2024 10:30:14 UTC No. 16252478

squares come from using 1 dimensional information to gain knowledge about objects that are 2 dimensional.
But what if you have a 2 dimensional object and you need to get information about its 1 Dimensional elements.
why does it show up in equations then? because some values give you information about an object that has twice the dimensions of another your are interested in. No one gives a fuck about seconds squared. But we understand seconds very well, so that's the kind of information we want. Which is why when you see a ratio of g and a length, you take a square root. Otherwise what you end up with has no meaning for us. Square roots basically project complicated things onto our own plane of consciousness so that we can ponder them.

Anonymous at Tue, 25 Jun 2024 10:30:57 UTC No. 16252479

>>16252408
A cube that is 2 on its edges has a volume for 8. Each face has an area of 4. The cube root of 8 is 2. Obviously sqrt(2) =/= 2

Anonymous at Tue, 25 Jun 2024 10:50:58 UTC No. 16252510

>>16252463
These are just thoughts I just had. I've only taken up through precalculus. Just tell me everything and anything crucial to the understanding of square and cube roots and their relationship to reality to the degree you are willing. I've never heard any of this discussed in any class or even any math history book I've read. I want to understand them as deeply as I can. How can the student tell the teacher what to teach?

>>16252478
I will think about this more, thanks.

>>16252479
Why are you telling me what I already said?

Anonymous at Tue, 25 Jun 2024 10:57:31 UTC No. 16252519

>>16252408
That's interesting, but what if instead of 'speed', though not necessarily completely different, but what if another way to think of the missing ingredient is simply using the proper 'scale' or even 'unit of measurement'?

When you take the ratio of a circle's circumference:area with the radius of 1, we'll see that there is a 2:1, 6.28:3.14.
If we then say r=2, suddenly the ratio begins to skew, and coincidentally interesting or not, at r=2, the ratio is exactly 1:1, 12.57:12.57.
But they're equal ratio at 2 isn't the interesting part, what's actually interesting is that if we keep going for r=3,4,5..., the ratio keeps growing distinctly further apart. If we were to compare the ratio of r=100m vs r=1km, what we would notice is that despite being identical lengths of measurement, the circumference:area ratio for 100m would actually be wildly different to that of r=1km, if you were to simply plug in the numbers 100 and 1.

So even though logically it would make sense to strictly use one unit of measurement, say we either decide to use 100m or .001km, the fact that we are implementing our own "abstractions" for something that is a fundamental natural process in the real world could possibly be completely invalidating what what the data we are observing is truly implying, because we are trying to use km, instead of m, or instead of inches, or even some other unknown abstract method that accurately and precisely conveys the information, regardless of whatever "units of measurement" that we currently use or even fathom. I suppose there is the obvious answer of making a bunch of measurements and trying to use different 'units' until you can effectively match the appropriate 'ratios' that would the match the data you are looking at to correctly find what 'scale' your data appears to be showing you...

>1/2

Anonymous at Tue, 25 Jun 2024 11:05:11 UTC No. 16252529

>>16252519
but for reasons I can't put into words right now, there still seems like there would still be something else missing that would prevent you from accurately calculating the proper scale, even by making sure your data is properly aligned to the correct scale. Maybe this is where your speed could be necessary for scaling calibration, as it could be thought of as another way to abstract 'ratios' in some way that I am not familiar with, beyond typical usages like posted traffic speed limits.

>2/2

Anonymous at Tue, 25 Jun 2024 11:15:04 UTC No. 16252541

>>16252510
It directly contradicts what you said.

Anonymous at Tue, 25 Jun 2024 12:22:11 UTC No. 16252602

>>16252529
Also, I think this approach could lead to possible solutions to being able to magically conjure energy, because why do the Laws of Thermodynamics need to exist? I certainly didn't vote for them.

Let's say we have 3 pokemon energy cards. Actually, let's make that 3 groups of 3 pokemon energy cards.
So we have 9 pokemon energy cards(3+3+3=9).
Toss one 3 of those energy cards away. You can destroy it. You can simply "change the energy into another form of energy"- it's up to you, you're the boss here.
Now, since we took away 3 energy, we're left with 6 (9-3=6).
But, what if we found some neat way that we could somehow take a group of 3 energy, and another group of 3 energy, and then multiply them to get back to... 9 pokemon cards. Maybe they naturally arrange themselves to multiply 3 energy and 3 energy together. Maybe we needed to use 1, or even 2.99 pokemon energy cards to successfully do 3x3=9.

But what I'm trying to get at is... is there *actually* any truly legitimate reason why it's absolutely impossible for us to 3x3=(3+3+3)=3+(3x3)=... indefinitely?

I've been told I have a "tendency to challenge/question authority", which can be borderline(if not outright) "problematic" at times. Allegedly. And maybe this is just the 'defiant rebel' in me talking, but are we *sure* about these immutable Laws of Thermodynamics? I mean, in all fairness they sound aptly name given how they might as well be thought to be as immutably inherent to our life just as much as some of the current Laws we're expected to abide by.
And, yet. People break the 'Law' at such a rate, that it begins to make one ponder just how different some Scientific Laws are from Legislative Laws, or even Social Pleasantries.

Maybe the Universe sees no need for having 'balanced equations' in the grand scheme of things.
Who do we take it up with if the Universe doesn't have a balanced checkbook?
Do we call the Physics Dept? The IRS? Do we put the big U on notice with Retractionwatch? idk

Anonymous at Tue, 25 Jun 2024 12:24:52 UTC No. 16252607

>>16252519
>>16252529
I'm going to think about this further, but for now I really should go to bed. I hope this thread keeps going in the meantime.

>>16252541
No, not really. Read the first line more closely.

I was simply thinking cube roots gave the area of a side. Not that the square root of x was x. If a cube root of a given cube is simply equal to the square root of its side, that doesn't really change the nature of the investigation—which is to know how cube and square roots function in their various forms in the real world. Even so, thanks for reminding me that the solution to a cube root is simply the length of a side of a side, rather than its area.

Anonymous at Tue, 25 Jun 2024 12:53:47 UTC No. 16252642

>>16252607
You can take the square root/cube root of any number. The square root of a cube root does not necessarily map to the cube as you have stated.
However, it does map to a dimensionless unit cube. curt(1 = 1, sqrt(1 = 1, Area of cube face = 1

Anonymous at Wed, 26 Jun 2024 04:33:56 UTC No. 16254231

bump

Anonymous at Wed, 26 Jun 2024 11:26:50 UTC No. 16254578

>>16252285
>a square root of the surface of a square will give you the side length of that square
FTFY, it wasn't clearly worded.

>therefore a cube root will give you the surface area of one side of a cube
A cube root of what? The volume of the cube? No: the cube root of a cubic volume of 8 is 2, for example, and the area of one of its sides is 4, not 2.
Therefore, cubic root of a cubic volume also gives you the edge length of the cube, which is the side of any of it's squared faces.
Maybe you meant something else?

Anonymous at Thu, 27 Jun 2024 03:00:40 UTC No. 16255922

>>16254578
Read the thread before posting. It has already been covered.

Anonymous at Thu, 27 Jun 2024 03:01:44 UTC No. 16255925

>>16252642
I didn't state that. If you would actually read, I brought up an instance where it is used with a circle and a vector and asked why. You people are too lazy. Read!

Anonymous at Thu, 27 Jun 2024 04:34:07 UTC No. 16256040

>>16255925
That may be what you are saying now, however in OP you are clearly looking for this sort of information. To be perfectly clear on the matter, there is a square root/cube root of any real number. The square root of a cube root does not necessarily map to any object you have described. However, there is a special case for the unit cube where the square root of the cube root does apply.

Anonymous at Thu, 27 Jun 2024 05:02:56 UTC No. 16256055

>>16252453
Those are not ears dumbass read a book about owls. Sorry I can't help with the math shit.

Anonymous at Thu, 27 Jun 2024 06:06:27 UTC No. 16256164

>>16252285
An application of square roots is obtaining the hypotenuse of a triangle, or rather the dimensions of its sides according to its diagonal in square spaces. I guess anything that relates to acceleration will use that as well on similar principle. I remember perfect cubes was possible for up to a certain number or something like that. I have no idea what else could square roots or cubes intuitively work for, and the rest of powers are pretty much abstractations to me.

Anonymous at Thu, 27 Jun 2024 06:33:18 UTC No. 16256208

>>16256055
Read Guardians of Ga'Hoole

Anonymous at Thu, 27 Jun 2024 06:34:24 UTC No. 16256212

>>16255922
>Read the thread before posting. It has already been covered.
alright, my apologies. I won't bother though, its not that interesting, I just wanted to point out the apparent error there.
Have a good discussion, everyone.
Cheers

Anonymous at Thu, 27 Jun 2024 22:20:14 UTC No. 16257343

>>16252285
perhaps euclid can help

Anonymous at Thu, 27 Jun 2024 22:25:49 UTC No. 16257355

wrong picture