What mathematical procedure are you actually doing with W to arrive at x = W(5) approximates 1.326. (@9:11)? Such a simple straightforward question that people can't seem to answer. And worse, people thinking W(5) is the final answer.

When u multiply two complex numbers and get those matrices... What happened to i? Was not placed into matrix and would of been [ a,-b, bi, ai]. Why not include it? Please respond

Awesome explanation ,U earned a subscriber

I watched several videos on quaternions where they did not define terms, assumed you knew a lot of esoteric information, and basically said that quaternions were confusing and sort of black magic. You series was very complete and each section built on the previous. You explained things a pace and order where you could follow along at a reasonable rate. I give you 6 out of 5 stars for taking an interesting an useful subject and explaining it completely and clearly.

At 13:17 you say that "this thing that I've drawn out here, this relation that I've plotted here, would not be a function, just because we have some x-value here that is going to output two y-values." But there are not two x-values and one y-value. There are two x-values (1 and 2) both of which output one y-value (3). Cf. y=x^2. One x-value outputting two y-values would not be a function.

I wonder what electrical engineers use instead of j for hyperbolic numbers? They use j instead of i since I is used to denote current.

awesome explanation. Now, I can write my own library to write Quaternion utilities....

Excellently presented. Thank you years later my good man.

This is the first video that broke this down in a way that actually made some sense because it didn't try to dumb it down and hide the maths :)

thank you bro, keep going the excellent works 😊😊😊😊

Edgd

I do not understand why v1xv2 = -v2xv1 in the context of the video. Also why did we define the cross prod as the cross prod 7:00

This is exactly what I was looking for

Outstanding clarity and brevity. Thank you.

I saw some of your useful videos, subscribed, and then saw this kind of bullshit in your back catalog. Can you please split the useful (math) videos away from the conspiracy theorist MAGA stuff? I'll stay unsubscribed otherwise.

Why is the first term of the quaternion sans unit vector?

For some reason I was sure that I commutes with everything... It says here that depending on which side you multiply by I, the sign changes.

Very happy to see Newton's book in KZbin.👍

Many thanks for sharing your knowledge 😊

xe^x = -1 => x=W(-1) ≈ -0.31813+1.33723i xe^x = 0 => x=0 xe^x = 0.5 => x=W(0.5) ≈ 0.351734 xe^x = 1 => x=W(1) ≈ 0.567143 xe^x = 2 => x=W(2) ≈ 0.852606 xe^x = 3 => x=W(3) ≈ 1.04991 xe^x = 4 => x=W(4) ≈ 1.20217 xe^x = 5 => x=W(5) ≈ 1.32672

Asymptotes are meridians?

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Great❤

My own personal definition of being that I've found helpful is the act or quality of participating in reality

Well done, Stephen. 🇦🇺 😊

Very help.

when you coming back mate

Incase i have q=(5,1,1,1) then what is q^2 ?

Bruh this one video explains to me a lot of After effects properties and effectors, damn 8 years ago but blew my mind non the less

should the definiton be stricter ie : j^2 =1 _and_ j not equal to +/-1 . ?

first thing i thought of was spacetime diagram when seeing the transformation at the beginning - also reading here the connection with minkowski spacetime - so its a bit surprising how split-complex number isn't more prevalent in the "everyday" - i think the name doesn't help - how about (circular) complex numbers and hyperbolic complex numbers

Wouldn't you have to prove time is linear in order to say infinite regress is impossible.

Nice video but you could have used Desmos to graph W(x). I am also missing application to solve equations like$e^x=3-2x$, or $x^x=2$. Also, the different branches of W(x) are not mentioned ...

I don't understand your argument against conceptualism. When you say that triangularity is necessary, that doesn't mean that it necessairily exists mind-independently, but rather that the features of triangularity necessairily qualify triangles as such. So why can't triangularity exist within finite minds?

The power of a scalar + bivector is magical

Insane how this logical neglection leads to the ratio of the function and it's derivative

Beautiful explanation!

AAAAAh i can finally follow along with e1.dot(e2) == 0 and e1.wedge(e2) == 1 feeling somewhat familiar. Such many symbols :s (yes, this is my second time watching the full series :D)

I think the direction of n^ x v is wrong. It should look the opposite direction. Am I right?

Haines' argument rests on a significant misreading of Van Til. Haines claims that for Van Til there is no common ground between believer and unbeliever. He uses the word common and neutral interchangably, which evidences the misreading, because for Van Til they absolutely are not interchangable. For Van Til, there is no neutral ground, but there absolutely is common ground. The common ground, however, is not neutral. The unbeliever cant escape the fact that he lives in a world created by the Christian God, and he himself is created by and in the image of the Christian God. He is confronted by revelation of the Christian God at every point internal and external, but denies it out of ethical hostility, which is why he is ultimately unable to truly know and explain the way the world is. All of these statements are basic to Van Til's writtings, but Haines seems to have completely ignored this fundamental aspect of Van Til's system. Haines seems to operate with the idea that at heart Van Til is a Kantian and that humans do not have access to the world as it is in itself, but only to phenomena as filtered through an "interprative schema." This leads him to argue that Van Til is stuck in a morass of relativity because there is no way to determine which schema is true. But this could not be further from Van Til's position! He states repeatedly and clearly that all men, believer and unbeliever alike, know that the Christian God exists because of the revelation in nature and in themselves that testifies to this. The problem is not that men cannot access the world as it is in itself; men clearly see that the world as it is in itself is a Christian world. The unbeliever, however, responds by supressing that revelation due to his ethical hostility. Natural theology will not do for the unbeliever because he will distort it such that it does not lead to the Christian God. The core principles must be exposed to show that his attempted system does not accord with the Christian reality that he lives in. There is of course no hint of Kantianism in this view, and a careful and thorough reading of Van Til would show that he ferociously criticized Kant, seeing him as the pinical of autonomous philosophy. However, this seems like another exercise in reading Van Til to attempt to refute him rather than to understand him on his own terms, which is unfortunately all too common. James Anderson has pointed out that this confusion between neutral and common ground is rampant in the critiques of Van Til from the Davenant crowd. I would hope that even those who dont agree with Van Til would do a better job of reading and representing him, as this paper widely misses the mark.

Mathoma? More like a Mathanoma.

0:37 Grammar gripe here - you reversed the words "a" and "an." It should be "Given an x, could a y be found? Given a y, could x be found?" Yes, grammar is important, even in math.

this will be useful to solve imaginary systems in my calculator dat doesnt support imaginary coeficients

What i find anoying is: even if there is an unmoved mover - religios than abuse the 💩 out of that. N keep moving the goal posts. Unmoved mover for sure (like 10¹⁰%) does not condone slavery, stoning ppl to death for either being disobediant to yo parents or for sticking body parts where they dong belong. I.e. yhwh, jesus, allah are NOT it. Period.

Why does the base have to be eulers number? Why can’t it be any other number?

one thing that I'm not sure why is the single reflection itself not a rotation. isn't it already clear that the reflection itself is a rotation. is the double reflection meant to be a general way to say given any to vectors we can rotate another vector about the angle that those two vectors form?

with the SLERP formula, what if θ=π? then the expression is undefined, so what do you do then?

In the actual multivariate normal, x and y can be correlated (linearly dependent) so that instead of all points in a circle being equally likely, it's all points in an ellipse. Does the math still work out in that case?

Well, being is one, beings share in the One being which is God, the essence of things are diverse but there existence is God's existence.

Thank you for your very clearly explained proofs!