Are polynomials actually wrong? Dimensional analysis makes it obvious that you cannot compare, let alone add or subtract, cubic meters, square meters, and meters. So how can a polynomial mixing up volume, area and length make sense?
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Remove yourself from the gene pool
Why would his DNA be in the pool? Was he in it? Why is that an issue?
Dimensional Analysis is whack, man...
b-b-but t-the b-buckingh-ham p-ppie theorem
Want to fart link with me. Go after 3.
3..
2..
1..
Go now.
Actually you're right.
The coefficients of the polynomial have units to make it work out
how can you have -0,935 of something?
False equality.
x^3 is not volume. V is volume, measured in X^3. just because V is measured in x^3 does not make x^3 equal to volume.
Etc for x^2 and A, and x and L.
Even for c. You can count chickens, but chickens aren't numbers.
>but chickens aren't numbers.
*cough*
I worked out how to connect to my abstraction frame machine is to focus on these parts of my body that tell, and it puts you in a realm of abstraction if you notice. And there's a secret code for your frame to fall into this state. You gain it upon installation. I might be able to contact you with directions to my stomach that I'll talk from.
Absolute meltdown here lmao.
X^3 IS volume of a cube by definition. Give an example where x^3 will not be the volume of a cube whose side is x
(x meter)^3 = x^3 meter^3 is volume
(x)^3 is multiplication
cope again
Doesn't really matter. You could choose any other unit and x^3 would still be a volume in that vector space. For example, consider generalized position and momentum coordinates then, Liouville's theorem states that the volume occupied by the phase of the system is preserved on time evolution. In this case generalized position and momentum can have any units or could be unit less. They still occupy a volume in pj,qj vector space
The sizes are just wrong in the pic
Every cube should have total area of −0,817
Every square should have total area of −0,874
Which means that the squares should be much larger, 1 square would need to fit more than 1 area of a cube
I already know everything. The cure. The method of contact. But I can't think through, my through is blocked. I can't read my own thoughts or hear it so I make no movement in correlation. To my intelligence. Which is nil where nil is still a facet, incomplete. I can't articulate or select precisely the vocabulary I want either.
I'm making moves on my theory of psychological stance, before I was following my dreams wrongly too much. It definitely makes a imprint on my passive motion through space time. Perhaps there is a way to do this. Obviously there's no point in trying to think about it. So I just gotta land on the correct answer through guesswork and re application.
Space time is the negative nature of space. How it is there, but how it is there is a result of some greater machine like a vacuum, and the nature of it being there is creating 'time' where it exists.
Ought we focus on hyperspace-time or Zero Space time because space is not all there is and time is not inclusive of just the experience of space but all and thus there is an element of a higher proportion involved such as hyper or zero, including all objects on a mental level.
Both space time and hyperspace time are things.
the coefficients always have the correct units to balance out the variables' units.
if they don't you are doing it wrong
This.
Just by looking at units you can even cook up what the form of the quadratic and cubic formula should be without manipulating the equation at all.
Why doesn't Wildberger talk about this?
what, OPs personal misunderstandings?
also math != physics
What if we phrase it this way:
> Find me the side length of a cube so that three times its volume minus twice its cross sectional area plus three times said side length plus seven equals zero
Seems like a perfectly reasonable (albeit very difficult without polynomials) task.
>three times its volume minus twice its cross sectional area plus three times said side length plus seven equals zero
>let me just subtract 3m and 2m2 from 3m3
At the end of the day, all these things are just numbers which you can manipulate. If I asked you to find me a square where the side length is equal to its area, you wouldn't complain that the side length is in meters and the area in meters squared. A solution to the problem obviously exists. This is no different.
It's alright since the thing you plug in for x is the same kind of dimension.
Are you moronic? The polynomial coefficients fix the units, example
ax^2 + bx^2 + c + d = 0
a: 1 (no unit)
b: meter
c: meter^2
d: meter^3
I'm assuming you're this
guy. In which case you said twice it's cross section, not 2m times it's cross section, three times side length not 3m2 times length etc or whatever units is chosen
If it is a question of comparing numerical relationships (math) then it does not matter, because there are no units. If it is physics, the units are accounted for in the coefficients.
>Dimensional analysis
Works well to make sure you are doing calculations with units correctly; a quick way to detect certain mistakes. Should not be used to "reconstruct" equations because certain unitless functions (like exponentials) cannot be detected in this manner.
>physics != math
Math is a language. Physics is the rules by which matter, energy, and space operate. These are the only two actual subjects in known existence. All other subjects are a subset or combination of the two.
>Bonus
Maybe math is a subset of physics. If Plank's constant were large enough objects would become indistinct from one another. In that case simple things like 1+1=2 would lose meaning and the entirety of mathematics would need to be rewritten.
>Math is a language.
*Is* and the *representative of*.
Fascinating.
>In that case simple things like 1+1=2 would lose meaning and the entirety of mathematics would need to be rewritten.
Frickin, this, and why Norman Wildberger rants about "Problems in the Foundations of Mathematics" like some ancient Greek ecentric.
Trying to conflate x, the number with a bunch of solid shapes and calling that arithmetic. You need to go back and study peano's axioms of arithmetic.
"the value of the cube volume of a quantity times three, minus the value of the square area of side length of said quantity times two, ..."
there, wasn't that easy?
you FRICKING ABOMINATION TO MANKIND, YOU FRICKING BABOON ANIMAL have a nice day IMMEDIATELY.
1/3x + 1/3x + 1/3x = 1
3/3x = 1
x = 1/1
x = .9999999999
each one of those geometric shapes is actually just a collection of points.
lines, squares, and cubes are not infinitely divisible.
Only in a finite field
all fields are finite, good try moron
Quantum fields are not.
quantum literally means discrete dumbass
False. Quantum is Greek and means mysterious physics that has something to do with consciousness.
it means discrete, quantum mechanics is discrete mechanics
>spectrum of the position and momentum operators is continuous
Consider yourself fact-checked.
look the definition for taylor series
[math]f(x) = sum_{n=0}^{infty} frac{1}{n!} frac{d^nf}{dx^n}bigg_{x = x_0} [x - x_0]^n[/math]
the function has units of [thing]. the derivative introduces units of [thing * x^-n] and is multiplied by the part raised to a power that has units of [x^n], so the series ends up having units of [thing].
He's right
The only polynomials that show up in physics are data trend descriptions
homie, pretty much anything called a Law is just the first order term in a taylor expansion of the real physics
Name one example
x is unitless, not in units of length. It is more valid if you make each term into a line.
>So how can a polynomial mixing up volume, area and length make sense?
It doesn't, because it's got nothing to do with dimensions. You can't have less than zero volume, or area, or length. You're attributing physical space to numbers when it makes no sense to do so.
they're all on R one though so the dimensions are the same.