More reflections on infinity as Chapter 5 of the book is just reached: Unreachability is not a unique trait of infinity. Dedekind finite sets can be indefinitely reduced in cardinality but the process will not complete in finite steps
@Secret that seems like a lot of inspirational rhetoric statements make sure you come up with a huge number of symbols never used before to accompany those new vague definitions, this will off put those sticklers that expect silly things like algebraic insight and allow you too keep the unreachability status quo needed to be a viral sensation consistently
@Adam Ted will not allow this. It is one of the reasons I also post less here
Also:
The nature of voracious emptiness and how its insatiability when directed correctly, can be used to drive endless motivation Emptiness, fundamentally speaking, is something which can never be filled in regardless of how hard you try. It is generally considered to be a highly negative trait, because it uses the same mechanism as the carrot and stick. What is less known, however, is that certain kinds of emptiness, at least in the short term, can be used to lure ourselves to continue to do important but annoying things.
People have so badly misunderstood the nature of good and evil.
You have not experienced the violent, brutal means that good sometimes use to achieve its goals
You have not experienced the experienced, calculating and mindless motivating means evil does things
Good and evil, ultimately two sides of the same coin. They only differ because of moral systems
While moral systems are relative, at least for us the entire human society, we do have a commonly agree standards, and hence, we have a sense of what is good and evil
Good is something you do not worry about it going in excess, evil is the opposite
In the end, it is all down to dosage, just like a poison can save lives at the correct dose
Having said all of that, manipulating cans of evil takes intense training and skills. It is more dangerous than the madness of infinity, or the excruciating death of hydrofluoric acid
It is not for the weak willed, nor for the faint of heart
and I, being just a normal human being, have no authority over evil
Sympathy is the liar. It only cares about what feels good It does not care what the person really is Empathy dives deep and learn the truth of the person, and respect them as they are
If $f:\Omega\to \Bbb C$ is a holomorphic map, and $\Omega$ is a simply connected domain, with $\gamma:I\to \Omega$ a closed loop. Is the following correct?
@RyanUnger the metric they consider seems pretty simplistic; near the singular stratum it looks like a cone on a principal bundle with bundle group acting on fibers by isometries
but maybe this has applications in equivariant setups. idk why positive scalar curvature metrics are a natural question here
@TedShifrin Consulted a doctor, who said it's probably just lung infection of some sort (which makes sense, because I have massive sinus and congestion right now and the fever went away). I do a test tomorrow anyway.
@TedShifrin There's no real definition of entropy as a function on the state space of the system, there's just the Carnot-like argument which proves that $\delta q/T$ is closed.
Only by assuming it's Euclidean you get a function, the antiderivative of the closed hence exact form.
My interest in the cohomology business is different and less colorful though: it seems the goal of classical thermodynamics is to come up with a good definition of temperature of your system. If $M$ is the state space, you can say it's a function $T : M \to \Bbb R$ (this is basically the statement of the 0th law). But then you want to measure this somehow, and which is what Carnot's theorem (a corollary of the 2nd law) grants you: if you have an engine which takes $Q_H$ amount of heat from a reservoir of higher temperature $T_H$ and rejects $Q_L$ amount of heat from a reservoir of lower tem…
This is basically saying that $\varphi$ is a 1-cocycle, which I'd like to call the "efficiency cocycle". And their claim is the efficiency cocycle is a 1-coboundary.
There's some hidden claim that the first cohomology group of the "temperature state space" is zero here, but maybe I am sounding like John Baez now
Found my source for it and the sensible statement: If two Hermitian operators commute, then both can be written as continuous functions of some other Hermitian operator
I want to generalize a stronger Goldbach's conjecture a little bit because that might help solve it.
I was thinking:
For all $n \geq 2$, every sufficiently large positive integer $x \geq b_n$ is the average of $n$ distinct primes?
Clearly this implies Goldbach's conjecture.
So, was wo...
Hi, um.. so I'm trying to adapt an answer to a problem I have, but frankly I haven't had math in a long time and I'm struggling, if anyone doesn't mind helping me out.
My scenario is this: I have a roll that goes from 1-7. I want to know how long it takes (how many rolls on average) to get a 5 or higher.
no, no: you have a 1/7 chance to roll each number. You care about rolling 5, 6, or 7 --- so 1/7 chance to roll 5, 1/7 chance to roll 6, and 1/7 chance to roll 7
so there's a 1/7 + 1/7 + 1/7 = 3/7 chance to roll 5, 6, or 7
I want to generalize a stronger Goldbach's conjecture a little bit because that might help solve it.
I was thinking:
For all $n \geq 2$, every sufficiently large positive integer $x \geq b_n$ is the average of $n$ distinct primes?
Clearly this implies Goldbach's conjecture.
So, was wo...
