Now, let me explain that I am a programmer and I know how code works and is compiled and so your answer ultimately derives from the following assumptions about magic:
I have a setting where there is an online shop that sells magic script, which sent via email. The magic in this world is activ...
@PVAL-inactive It's going to be army-grade bullet proof armor. I know because simple ceramic scale armor is used by the military. Saw it on tv once in a documentary a while back.
@EricSilva actually that is the perfect target. Most bird lungs have portions in their wings. That's why broken wings are so serious. They can literally suffocate.
It also matters how seriously you take your enemy.
As a specific point of reference, in the battle of Rorke's Drift in the Anglo-Zulu War "just over 150 British and colonial troops successfully defended the garrison against an intense assault by 3,000 to 4,000 Zulu warriors."
I'm sure more advanced tech than military is useful when your enemy has auto and material rifles and rockets, since that's essentially what modern war is.
I'd imagine drones do pretty well at being cost efficient.
I think an honest medieval army would probably be routed pretty quickly by a tiny force with modern weapons, even if they could win by throwing numbers at it
Just because a beetle can do it doesn't make it logically possible for a large animal to do it. I mean, just because an ant can lift crazy multiples of its body mass doesn't mean that a larger animal can do so.
And my point, again, is that if we're insisting on real life comparisons we're not going to get anywhere because dragons are not plausible in real life.
One has to allow some bending of the rules of physics to make this work.
Anyways, if one is willing to allow enough bending that fire-breathing dragons are possible, I think it's plausible to grant them some level of invulnerability against fire.
Eh, that programming analogy cuts both ways. A computer in the real world doesn't have infinite memory or infinite time. So not all programs which are logically possible can actually be executed in a meaningful way.
@Semiclassical true, but if cells are turing machines (my professor once made the analogy when talking about the practicality of encryption beyond just security) then it's just a question of what is within the theoretical bounds of their language (DNA).
@PVAL-inactive the fission has to come from somewhere.
either He would make fission bombs poof into existence or He takes the material from somewhere else. However, both cause a change in entropy and energy, right @Semiclassical?
but how does the lizard not just explode from fission being in its gut?
@Semiclassical I was referring to our current model of physics (which purposefully does not include God as we wish to examine the status-quo He created).
I think that the amount of nuclear fallout that'd be generated in such a bombardment would be enough that the fallout would be spread out even over a much larger world by the atmosphere.
I've been running progressively larger and larger tests
using first order polynomials to crack the Collatz Conjecture is doomed 100% to fail.
we need a different way of expressing numbers uniquely.
it's not new math that we need
it's just a less flaky way of expressing the integers
im thinking of maybe seeing if norms of algebraic integers might be useful here
like maybe taking two sets that span the integers with their norms and using it to get a unique way of representing any integer
(or a non-unique but still somewhat useful way)
i gotta go to the toilet
be back in a bit
user84215
04:22
Although I have little knowledge in mathematics, I am very eager to discuss mathematical subjects. I wonder how you great mathematicians have no tendency even to suggest an idea to create an event in [Discussing Specific Topics](https://chat.stackexchange.com/rooms/62845/discussing-specific-topics) I think answering to the above question is more difficult than solving famous unsolved mathematical problems. I do not know why the Clay Mathematics Institute ignores this problem and pursues the problems like the Riemann Hypothesis and Hodge conjecture.
@aminliverpool what above question? Mine? The Collatz Conjecture is a famous unsolved problem.
and I am currently in the process of thinking of what math would prove it. Rather than try to examine different mathematical systems, I'll work backwards. Just.... determine what I'd need to prove it.
wait a second
that's it!
each time I try to deal with lesser cases, there are cases that split in 2 or 3 or whatever when I multiply times other things
what I need to do is create a form of induction that inducts upon all the infinite splitting cases!
For instance, I suspect that all numbers m $2^n + 1 < m < 2^{n+1}$ map directly to $2^n$.
showing every number maps a finite distance away would solve it
@Daminark what is interesting is that an + 27 where n is arbitrary might be impossible to prove in general.
(aside from following from the conjecture of course)
@Daminark Of course it might just be that the right combination of cases trivializes it. It might be that divisibility by 5 matters in the long run. 7 is coming up as a recurring number in this whole thing.
@Typhon you can't. the parity is lost in this representation.
2 hours later…
user84215
08:59
@Daminark @Typhon The "above question" refers to my question, "I wonder how you great mathematicians have no tendency even to suggest an idea to create an event in Discussing Specific Topics"
@aminliverpool I don't really see how that room differs from this one
user84215
@TobiasKildetoft In this room, people may ask their homework problems, but that room has been created for discussing a specific topic that its subject would be determined by others before beginning.
Because I think it is not good that only a room owner can create an event for the room, I have created the room, Discussing Specific Topics . In this room, people can discuss the topics they have specified before. Each topic lasts in this room for at most one day; It depends on its popularity among others. Its duration also can be specified before beginning.
@aminliverpool I see (this was not very clear from the room description). I am usually up for discussing anything related to algebra, but I don't have any good ideas for topics to discuss right now
I'm trying to perform an analysis of a recursion. I'll provide a bit of background and then the actual question later.
Let $\left\{ \omega_j \right\}_{j\in\mathbb{N}} = \left\{ \arctan \left(2^{-j}\right) \right\}_{j\in\mathbb{N}}$, let $\theta \in \left[-\sum_{j=0}^{+\infty} \omega_j, \sum_{j=...
Being trigonalizable implies that the matrix has an eigenvector. Some set of matrices being simultaneously so implies that they have a common eigenvector.
So he does show that we have an eigenvector $e_1\in W$ that generates an $M$-stable line, and he takes $V/Ke_1$, to give us an $n-1$-dimensional space, where any commuting set $M'\subset M(n-1,K)$ is trigonalizable by induction.
I just need to show that I can restrict my elements of $M\subset M(n,K)$ to $M(n-1,K)$, utilize my induction, and then bring their action back to $V$?
For $x \in \Omega \subset \mathbb{R}^n, v \in \mathbb{R}^n, t \in \mathbb{R}, f: \mathbb{R}^n \to \mathbb{R}$, how does the $f(x+tv)$ looks like? Is that a line?
@TobiasKildetoft oh it is in the definition of the partial derivative of $f$ in $x$ towards $v$: $\partial_vf(x) = \lim_{t \to 0, t \ne 0} \frac{f(x+tv) - f(x)}{t}$.
e.g. $f(x+h)$ for $f=x$ in $\mathbb{R}$ ist visually clear, but $f(x+tv)$ in $ \mathbb{R}^n$ not really
@user462339 yeah, the set for a fixed $x,v$, but variable $t$
Hi I tried to calculate the center of mass of a half circle with respect to the radius to avoid using x, y coordinates directly...See here on Wolfram Alpha: https://www.wolframalpha.com/input/?i=(2%2Fpi)+integrate+r%5E2+dy+dr,+y%3D0..pi,+r%3D0..1 (I used y as $\phi$) Unfortunately the result is wrong. Isn't it possible to calculate the center of mass with respect to the radius. Such that I can calculate: $S_x = S_r*S_{phi}$?
Now, let me explain that I am a programmer and I know how code works and is compiled and so your answer ultimately derives from the following assumptions about magic:
I have a setting where there is an online shop that sells magic script, which sent via email. The magic in this world is activ...
I'm trying to perform an analysis of a recursion. I'll provide a bit of background and then the actual question later.
Let $\left\{ \omega_j \right\}_{j\in\mathbb{N}} = \left\{ \arctan \left(2^{-j}\right) \right\}_{j\in\mathbb{N}}$, let $\theta \in \left[-\sum_{j=0}^{+\infty} \omega_j, \sum_{j=...
