Activity for Tim Pederick
| Type | On... | Excerpt | Status | Date |
|---|---|---|---|---|
| Comment | Post #288113 |
Even the mathematical part of the question is really about a legal principle—the “balance of probabilities”—much like [another of the asker’s questions](https://math.codidact.com/posts/288101). I doubt there are “official terms” (OP’s request) in mathematics, but there may be in law.
To my underst... (more) |
— | 12 months ago |
| Comment | Post #288101 |
Agreed: this is about what facts a court can establish, not about the calculation of a probability. Mathematically, **yes**, Friend changed Ungrateful’s chance of winning the lottery from very low (the probability that *that* ticket was the winner, multiplied by the probability that Ungrateful would ... (more) |
— | 12 months ago |
| Comment | Post #288090 |
The scenario described is a game played with dice to introduce an element of chance. If that’s not a type of game you’re familiar with, it’s not going to be helpful. (I chose it because it let me stick with the idea of “avoiding injury”, while also having well-defined probabilities.)
Rather than m... (more) |
— | 12 months ago |
| Comment | Post #288087 |
Of course it’s not *sufficient*. My point was only that the question lies somewhere in the intersection of maths and language. It raises some doubt (in contrast to simply saying “Not a math question”), and I chose to give OP the benefit of that doubt.
Other parallels:
① Verizon’s [conflation of... (more) |
— | 12 months ago |
| Comment | Post #288087 |
I disagree. It strikes me as akin to meta-statements like $A\to B$ versus $\left(A\to B\right)\to C$. I think it would *also* be on topic as an English usage question (no need to impute learner status to OP), but that doesn’t invalidate its presence here. (more) |
— | 12 months ago |
| Comment | Post #288081 |
Yes, it does clarify. I’m now more certain that I was reading it correctly: what’s needed here is to draw a distinction between “winning twice” (= “winning Monday’s *and* Tuesday’s draws”) and “winning a second time” (= “winning Tuesday’s draw, given that you won Monday’s”).
This is just one examp... (more) |
— | about 1 year ago |
| Comment | Post #288080 |
① Yes, it is impossible, and I believe that’s Peter’s point. It is intuitively obvious that winning zero times is **not** independent of winning once. So it makes sense that winning *twice* wouldn’t be independent either, or indeed that winning $n$ times isn’t independent of winning $m$ times.
② B... (more) |
— | about 1 year ago |
| Comment | Post #286034 |
“In quaternion algebra, $1$ is not identified with the vector $(1,0,0)$.” I think I’m starting to get it. Or rather, I think I *understand* it, but I still don’t *get* it. My lack of formal quaternion education is probably betraying me here. Why doesn’t the real unit 1 correspond to the 4D vector $(1... (more) |
— | almost 2 years ago |
| Comment | Post #286034 |
@#53398 “But where are you getting triplets in 2D?” From the trivial $(x,y)\mapsto (x,y,0)$.
“…modulo sign (the negation is not orthogonal)…” Ah, see, I was counting the negations, so your three I would’ve called six. But I still don’t see how we get that many! In two dimensions, there’s one (pair... (more) |
— | almost 2 years ago |
| Comment | Post #286034 |
‘I was implying orthogonal when I said it produces 3….’ You’re still beyond me here. What three roots are they? I only count two new ones, plus the two that we had in 2D: $(0,\pm 1,0)$ and $(0,0,\pm 1)$.
‘…an "axial vector" and a "position vector".’ Ah, now we’re back on ground I know—or once knew... (more) |
— | about 2 years ago |
| Comment | Post #286034 |
@#53398 Ah, I see my mistake now. I hadn’t even considered that the normal to a plane would no longer be unique in 4D. But just as there’s only one line orthogonal to a line in 2D, but infinitely many (a whole plane of them) in 3D, it makes sense that the same would happen to the normal(s) to a plane... (more) |
— | about 2 years ago |
| Comment | Post #286034 |
@#53398 And to a couple of your specific points that I didn’t have room for in the above…
“Moving to 3D immediately produces 3 square roots of -1.” Does it? I had thought it produced *infinitely many* roots lying on the circle $x=0,y^2+z^2=1$. And I worried that I’d glossed over that part too quic... (more) |
— | about 2 years ago |
| Comment | Post #286034 |
Let me start by saying that I came at this as someone who learnt complex numbers “properly”, but is entirely self-taught in quaternions out of sheer amateur interest. So I’m far from being an expert, and intended simply to share with the asker a mental model that worked for me.
With that proviso, ... (more) |
— | about 2 years ago |
| Comment | Post #285723 |
Indeed, but as I read it, the author is saying it’s obvious *from the values of $m$ and $n$*, before ever calculating that the side length exceeds $\sqrt{16}$. (more) |
— | over 2 years ago |