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12:06 AM
@heather I read that you want to learn quantum computing. What resources have you found about quantum computing?
 
obe
@BernardoMeurer do you know anything about data science?
 
@obe I know some things I believe, why?
 
obe
what's the main difference between that and machine learning?
or are they the same?
 
Hello, I'm (still) having trouble with some homework problems related to quantum mechanics. Can anyone help? I am trying to show that a given psi solves the Schrodinger equation in a given potential (psi 210 and a coulomb potential in this case). The best I can seem to do is to produce an f(r) = E - U.
Is this sufficient?
 
machine learning $\subset$ data science
Machine learning is just a technique for processing data
 
obe
12:10 AM
I thought so
 
that can be used in data science
 
obe
ah okay makes sense
thx
 
No worries
 
well, to learn linear algebra, which was pretty darn important, I used 3Blue1Brown's YouTube videos, which are pretty awesome, plus a textbook I picked up at a used bookstore (I can find it and get the title if you're interested). Then I used the YouTube series Quantum Computing for the Determined, by Michael Neilson, which got me started in my understanding. Throughout, I would try to explain it to other people, like my mom, because that helped me learn.

Then I got a copy of Nielson and Chuang's Quantum Computing and Quantum Information, which I'm still learning from. I've also read a bun
 
@Izzy i dont understand your question. "(psi 210 and a coulomb potential in this case)."
psi 210?
 
12:12 AM
@StevenSagona I don't think the specifics are particularly important. But it is the psi for n = 2, l = 1, m_l = 0
 
Oh, and I've also messed with simulation programs, such as the IBM Quantum Computing Experience and Quirk. I've been working a bit on a program in Python that also aims to simulate an ideal quantum computer (and maybe eventually a non-ideal one).
 
Oh, I misread my notes. I've reduced it to an f(r) = E situation; U is still dependent on r.
as it ought to be.
 
@heather yes
 
@0celo7 okay
 
@heather thanks. I work in experimental quantum information lab yet don't understand how the fancy quantum algorithms work, so I was curious if you found something that's well-explained. That youtube lecture series seems like it's pretty solid for the very early basics, but it looks like that textbook has a lot more content. I might buy it and go through it
 
12:21 AM
@StevenSagona that textbook is (i've been told/have read) basically the bible of quantum computing, so that'd be a good book to get.
 
I'm always doubtful of people calling something "the Bible" of a field
 
@Izzy sorry I really don't understand what exactly the problem is asking for
 
@0celo7 why?
 
@StevenSagona Maybe I can rephrase: I have some wave function Psi, some known energy E, and some known potential U. I am asked to show that Psi satisfies the Schrodinger equation. What I want to know, is what constitutes "satisfying the Schrodinger equation"?
 
12:25 AM
@heather One of the authors of that textbook, Chuang, wrote a somewhat famous paper in my field:
https://arxiv.org/abs/quant-ph/9505011

It's pretty well written so I think the book will be good.
 
"Bible" in the sense of the first well written authoritative book @0celo7
 
Is it enough to eliminate all the derivatives and all Psi, and reduce it to some form of F(r) = C?
 
@StevenSagona as far as I'm aware I think both authors have written fairly famous papers.
 
@heather have you looked at Gilbert Strang's lectures on linear algebra?
 
@skullpetrol i've heard they're good but haven't watched them
 
what is a "K electron"? an electron in the K shell?
 
@Izzy are you familiar with differential equations? If I said a given function "satisfies this differential equation," would you know what I mean?

I think your problem just wants you to show that $H \psi = \frac{\partial \psi}{\partial t} $ by plugging in the particular example you have and showing it's an equality
 
Yes @heather
 
okay, thanks
 
12:37 AM
are x rays and gamma rays carried by photons like visible light because they're part of the electromagnetic spectrum?
 
Thank you for your help. I took a course on differential equations, yes. I understand satisfing in simple cases - i.e. dF/dx = AF would be satisfied by Be^(Cx) where A = BC. My trouble is with the complexity of the Schrodinger equation. DEs were never my strong suit to begin with, and the Schrodinger in spherical coordinates is not trivial. If I am understanding the problem correctly (and what you are saying) I should be able to reduce the Hamiltonian H*psi to some constant C*psi. Is that correct then?
In particular, should I be able to reduce it to E*psi, E being my known energy, with no spatial dependence?
 
When you make a new chat room, Stack Exchange tries to make sure you're not making a room for a topic that already exists.
When I tried to make my weekly featured post room, the Stack Exchange system had this helpful suggestion:
If anyone can explain how the SE algorithm thought that a room about the F# programming language, in Russian, was the same thing as a room about weekly featured physics posts, please let me know.
@BernardoMeurer
 
@DanielSank Was your room title and description the same it is now? If so, I have no idea
 
Yep, exactly the same.
Apparently SE is just insane.
 
No idea what kind of algorithm runs for detecting duplicate chat room, but apparently it's not as good as the one for related questions in the side bar :P
 
12:50 AM
@Izzy

Yes, that sounds about right. In your case you will likely not have to find a constraint like A = BC (you'll get something like A = A).
Solving for the schrodinger equation for the hydrogen atom and deriving the spherical harmonics is very, very hard - so it's very unlikely they are asking you to do that (but maybe they give you the eigenfunctions and you can simply plug them into the schrodinger equation)
 
@ACuriousMind Yeah. Russian F#? WTF
 
@DanielSank I wrote that algo with the sole purpose of fucking with users
 
@StevenSagona You are correct, we are not deriving spherical harmonics. However spherical harmonics do come up. That was what I was trying to get at in my first comment: the Psi we are given is the Psi(r,/theta,/phi) for quantum numbers n = 2, l = 1, m_l = 0. It's in a coulomb potential, so we also know the potential U(r,/theta,/phi). And we started this section by deriving the energy of an electron in a Coulomb potential, so we know the energy E.
At it's heart, the question is really a simple one: show that given these conditions the Schrodinger equation is satisfied. The simplicity is why I am so frustrated at my inability to make it work. I've been struggling with this for at least 2 hours.
It should just be plug'n'chug, but while I can plug, I can't seem to make it chug :S
2
 
do you know what H is in general?
 
[(-hbar/2m)(del^2) + U] correct?
 
1:00 AM
yeah, so just take the function associated with your state
and do H*state
 
It sounds like I'm on the right track. I've been trying to do that (in fact, I have done it several times over in the last few hours). I can't seem to eliminate the radial component r though. :I
Thanks again for your help.
As long as I'm here, is it correct that the (del^2)*psi term will become 1/r^2(d/dr * r^2 * d/dr + L-hat)*psi = 1/r^2(d/dr * r^2 * d/dr * psi + l(l+1)*psi)?
 
1:33 AM
@BernardoMeurer u there?
@skullpetrol @heather I don't think any book is comprehensive enough to satisfy the definition
The bible is complete, and not in the topological sense
 
@DanielSank check your texts if you havent already
 
The bible is the authoritative reference for all Christian things
ALL
 
2:02 AM
hello..
 
2:31 AM
hi
Have you @0celo7 never heard the word "bible" used as a metaphor?
 
@skillpatrol no
not without some heresy involved of course
I tend to ignore heretics
 
2 hours ago, by skullpetrol
"Bible" in the sense of the first well written authoritative book @0celo7
 
and that's heresy
burn, witch!
 
@0celo7 sort of, but in Catholicism it's a little more complex.
 
Witch = old woman
 
2:41 AM
C programmers of course have the old and new testaments.
Those are of course the first and second editions of The C Programming Language.
@skillpatrol Well ... we did the nose.
 
@DanielSank @skillpatrol @heather My point is that there is no textbook/reference that is as authoritative to its field as the bible is to Christianity.
 
@0celo7 For which every corner sect and denomination has a differing interpretation. Pretty authoritative, that.
 
I got one
The French dictionary
 
Not to mention the political nature of the decisions about what books to include and exclude around the third through fifth centuries.
@Skyler ::chuckles::
 
they have that panel that officially decides on the new words
not like anybody cares though...
 
2:46 AM
@dmckee So the bible is not autoritative and the saying makes even less sense
Either way, I win.
 
You're forgetting context.
Context always wins.
 
@skillpatrol your context does nothing, old woman
 
you forgot the part about being on the Internet with no life
that^ is context
 
what?
 
@0celo7 of course not.
 
2:56 AM
3 hours ago, by skullpetrol
I'm just an "old woman" on the internet with no life.
 
@Slereah I found a mathematical paper that sounds like it was written by JD
it denies the singularity theorems, saying that "no mathematical proof exists"
"The orthodox relativists must first prove their assumptions
by rigorous mathematics. Unless they do this, their
analyses are unsubstantiated and cannot be admitted.
Since the orthodox assumptions have in fact already been
rigorously proved entirely false, the theory that the orthodox
have built upon them is also false."
 
Where is "The Evidence"?
 
this paper is actually pretty infuriating
I don't care if this guy is correct or not, he's a total a-hole
 
Question. Why is fire usually associated with plasma?
 
> ∗Owing to the geometry due to Efcleethees, for those ignorant of Greek;
usually and incorrectly Euclid.
Oh dear god
the author was removed from his PhD program
lol
> "I have also had some correspondence with a number of other sheepish relativists of no consequence. Not one offered any science, just the authority of Hawking, Penrose, Einstein, and others. All were rude, stupid and incompetent (precisely what they accused me of being, evidently taking umbrage for my return of the epithets). Other big-shots in black holes and big bangs, such as Thorne, Misner, Israel, Rees, Penrose, Hawking, Ellis, Wald, little-shots such as
> J. Moffat, J. Barrow, S. Carroll, R. d'Inverno, B. Shutz, some tiny-shots not worth a mention, and a few other scribblers of textbooks and popular science, simply ignore correspondence.
 
3:14 AM
Greatest paper I've ever seen: journal.sjdm.org/15/15923a/jdm15923a.pdf
5
 
@Slereah this is gold
> ∗For the geometry due to Efcleethees, usually and abominably rendered as Euclid.
@ACuriousMind Is that how one is supposed to spell it?
This guy seems pretty smart.
 
From which university was he removed from the PhD program?
 
UNSW, I think @Secret 's alma mater.
 
Home of Norman Wildberger.
 
Ah, well. I have better things to do than read crackpot papers
@rob evening
 
rob
3:33 AM
Shush, I'm only virtually here (that is, $p^2 \neq m^2$)
 
@rob ugh, not you too!
It's -+++
 
+++-
 
rob
@0celo7 I'm using a system of units where $\pi = \sqrt{10} = 3 = 1 = -1$
Signs, like factors of $c$, are to be re-inserted at the end of the computation.
 
@rob what
physicists say the strangest things
"temperature is reciprocal imaginary cyclic time"
 
rob
@0celo7 Well, duh.
 
3:42 AM
there's a neat derivation of the Hawking temperature of a black hole by assuming that
 
rob
@0celo7 Cool
 
@rob I can explain more if you're interested and here un-virtually
 
@SirCumference While I am known by my peers as analytic, my mind is too open due to different memories and experience and weirdness mixed together. Therefore I am actually more suceptible to pseudo profound bullshit as there are just way too many ways to interpret meaning from said bullshit's word salad arrangement.
 
rob
::flucturates back to vacuum::
 
E.g. "Hidden meaning transforms unparalleled ab- stract beauty.” means:
Given an abstract entity that has some aesthetic property, knowing it's hidden history, symbolism or in general backstory will transform your view or impression towards it
 
3:49 AM
So...does anyone know why plasma is often associated with fire?
 
Heat.
 
@skillpatrol ...thanks
 
Although I think that'd be a bit broad
 
It's a loose association.
Ask on the main site.
 
3:52 AM
I dunno if that's an actual physics question
 
what terrible formatting
shame on you Dr. Wolf
 
@SirCumference fire is low energy ionised gas, thus similar to plasma, which is also ionised gas?
 
@Secret Fire doesn't require the gas to be ionized
Only very hot flames become plasma
Most candle flames aren't
Not to mention, fire requires oxygen, heat and fuel. Plasma doesn't (except heat)
 
@SirCumference I have a math problem for you
 
@0celo7 It's sunday night, I have work to finish
And in what universe is there a math problem I can solve that you can't?
 
3:56 AM
Plasma is analogous to fire...
 
@skillpatrol How?
One is a chemical reaction, the other is a state of matter
 
@SirCumference I can solve it.
 
Don't they share any common property? @SirCumference
 
@0celo7 I'm busy right now. I also don't know why you'd ask me that if you can solve it.
 
I miss Mafia
 
3:58 AM
^
Good old days
 
He would have tried to solve it
 
Also when Obliv was around
 
And I would have taught him some cool math along the way
and @obe
 
@skillpatrol Not that I know of. That's why I asked why they're associated so often
@0celo7 He's still around
Heather also wants to learn GR
 
not very much
 
4:00 AM
(removed)
 
There's only so much that intelligence can make up for
You still need to develop the skills for self-study, and that doesn't come easily
5
 
@0celo7 Is intelligence a thing?
 
yes
 
I think passion and perseverance is what someone needs
 
there are certainly people who are stupid
and there are people who are amazing at everything
 
4:02 AM
@0celo7 How can you measure that?
 
^stupid
 
fair...
maybe that guy likes math tho
 
No, he is a (bad) rapper who is addicted to cough syrup despite having multiple children.
He recently got arrested for parking in the handicapped spot at Whole Foods.
Also he had a bunch of pot and guns on him.
 
ok, I see your point. but then is your definition of stupid, "someone who makes bad decisions?"
 
No, that's a subset of the stupid people
I am just saying there are stupid people and smart people
then people like us who are in the middle
so "intelligence" certainly is a thing, but I'm not willing to be more precise than that
 
4:08 AM
I dunno, I think there are people who make good decisions and people who make bad decisions. And in terms of academics, it comes down to how well and quickly people "get things".
Like math, for example
See, that's a really...really bad decision.
 
this book is strange
who spells "riemannian" with a lower case R
or "hausdorff" with a lower case h
 
A nonnative speaker of English?
 
Joseph Wolf
 
What happened to mafia?
 
he deleted his account
I don't know why.
 
4:17 AM
What about Chris White?
 
obe
@0celo7 hey I'm around, but nobody talks to me so I don't come as often xD
 
Hey, wazzup?
 
@obe are you learning analysis?
 
obe
not diligently
for some reason I don't find the same pleasure in learning math or physics anymore as before, dunno what to do with my life.
perhaps i'm doing something wrong
 
do drugs and find yourself
 
obe
4:22 AM
for now I'm just going through my degree and bored af, dunno what to do. i wish I had my old self back
 
@skillpatrol He didn't say why, at least to us, but he requested to have his account deleted. You may read whatever significance you with into the proximity of that event to a dust-up in chat.
 
obe
@0celo7 lungs lol
 
@obe what?
@dmckee Dust-up in chat?
 
obe
remember what happened to me in may?
 
you died?
 
obe
4:23 AM
and that was WITHOUT ever doing drugs or smoking
@0celo7 no, my lung collapsed lol
 
@0celo7 Well, I'm not going to make a public recounting of the details (such of them as I know) because that would re-inflame the issue.
But, yeah.
@obe I'm very sorry to hear that. My wife had a collapsed lung once. Needed chest tubes and days of close care in the hospital.
 
@dmckee Could you please link?
 
@0celo7 Can't recall even exactly when it happened, and I wasn't present in chat at the time so there are no memorable phrases to search on. Sorry.
 
@SirCumference
Jan 11 at 20:37, by Sir Cumference
I miss 0celo...
<3
 
obe
@dmckee well mine was worse than just that
I had to do a big surgery AND
had this big tube in me for like a month
 
4:26 AM
If you @0celo7 want a full account talk to S h o g.
 
obe
it was like a hose lmao
 
@obe My better half needed surgery, too, but they went in endoscopically through the same wholes they used for the chest tubes.
She was about two weeks in the hospital, but the first three and half days were in intensive care.
 
Is she okay now?
 
obe
it really sucks, i hope it never happens to anyone
and for NO REASON it happens
well, a reason but you can't avoid it
 
@skillpatrol It's been about ten years. She had occasional pain from the scars, but otherwise fine.
 
obe
4:28 AM
@dmckee I do too
 
@obe Her's started getting less frequent after about three years. But she is a slow healer.
 
obe
what happened to me was that when I did the surgery and got the big tube removed it collapsed instantly again and I had to get another one, in a different spot.
AND without full anesthesia (was awake)
feeels bad
 
Ok, some chat sleuthing reveals a reference to a "Nazi quote"
 
@obe Yikes!
 
obe
@dmckee though I feel like that whole experience made me a different person than before, and I view life a lot differently now.
lying down for 3 weeks straight staring at a wall can change you xD
5
 
4:35 AM
@SirCumference Still here?
 
But you had internet access, right :P
 
obe
@skillpatrol not fully
I went on facebook a few times but that's it, I only had 300mb of data on my phone.
 
Intense pain is terrible.
But at least you're still alive :-)
 
obe
yeah some ppl die from it.
 
@skillpatrol That's one scary way of pacifying :-P
@obe Is your treatment still going on ? Is it better now ?
 
obe
4:43 AM
it's all behind me now xD
recovery was about 3 months.
 
@0celo7 Now I am
@0celo7 Oye, that's gonna haunt me
But to be real here, everyone's leaving
or at least it seems that way
 
@SirCumference I have sent Mafia an email.
 
cool
 
I had to undergo endoscopy a few times due to some lung/digestive problems when I was 9 year old. The experience was so traumatic that I remember it clearly even after 10 years. I definitely can understand that tubes in your lungs would be way worse. :/ Anyway, I hope you don't face such health problems in the future. :) All the best!
 
@SirCumference Chris, Mafia, Obliv
 
4:48 AM
Consider 12 face diagonal of a cubical block . How many pairs of them are skew lines .
 
@0celo7 Back then, @obe and you were gone too
 
Chris and Mafia left because of site-related incidents.
 
According to me it should be 24
 
It was pretty barron
 
But the answer given as 30
 
obe
4:49 AM
@anonymous thx, you too
 
@obe Huh? Your health ok?
 
obe
more or less yea
 
What's up?
 
obe
we're talking about something from last year
 
obe
4:50 AM
idk if you remember but my lung collapsed in the spring
 
actually, i didn't hear
dang, sorry
 
obe
May 30 '16 at 1:59, by 3075
Bad news guys I'm in the hospital because my left lung collapsed. :'(
 
@obe Huh, must've missed that
 
@DavidZ Thanks for the clarification, didnt know it was a Nazi symbol too, Swastika also happens to be a religious symbol of Hindus. — Oswald Dec 19 '16 at 4:48
Ah, the age-old troll
@SirCumference are you...not at all curious how I have his email?
 
@0celo7 I assumed you exchanged it with him
 
obe
4:53 AM
@0celo7 haxxx
 
@SirCumference no
 
@0celo7 So then how
 
@SirCumference mods have access to emails
@obe close
 
@0celo7 So who gave you it?
@0celo7 It's a good thing I use an obsolete email
 
@SirCumference let's hope Mafia doesn't
 
obe
5:00 AM
@SirCumference why?
 
@obe So no one gets my contact info
 
obe
...
dude why do you think you're the centre of the universe?
nobody cares about your e-mail
 
@obe I kind of want to leave no trace of the dumbass things I say
 
obe
then don't say them :p
 
David Z has added an event to this room's schedule.
3
 
5:04 AM
@0celo7 Not to send messages to them though
 
@DavidZ good thing I'm not a mod
 
That's not always true.
 
obe
pce
 
pce?
 
5:19 AM
@obe Uh, do you still have that logo?
 
@JohnRennie I'm just saying I like pink floyd more than led zeppelin :-)
 
5:43 AM
And I never liked the beatles.
As far as distinguishing one from the other ill quote billy joel: it's all rock and roll to me.
 
@ACuriousMind ::algebraic bat signal:: I have a vector space $V$ with basis $\{X_i\}$. I have two algebraic curvature tensors $R,S$ on $V$. If $(z^i),(y^j)$ are $n$-tuples with $y^i X^i\wedge z^j X_j\ne 0$, then $R_{ijkl}z^iy^jz^ky^l=S_{ijkl}z^iy^jz^ky^l$. Supposedly, "by analyticity", one can lift the condition on the $n$-tuples but I don't see what they mean by that.
the LHS and RHS are polynomials, sure, hence real analytic in $\Bbb R^n$
but what does that do for me?
Should one show that the power series of $(R_{ijkl}-S_{ijkl})z^iy^jz^ky^l$ vanishes to all orders?
 
screw it spacing sucks here
@0celo7 does that help
 
6:00 AM
maybe
*real analytic in $\Bbb R^{2n}$
 
Since this is an algebraic bat signal perhaps (AC) / M would be more appropriate.
And yes @Secret that expression makes no sense if M = 0 in the set of real numbers :-)
 
I thought it was supposed to be a group quotient
 
Just elementary algebra.
My dear Watson :-)
Yeah, I should have used lower case letters.
 
6:25 AM
Did you enjoy Chicago? @0celo7
 
@skullpetrol the traffic was awful. There was this latina who just drove at a snails pace. Finally, he honked his horn and all he could say was "Chica, go!"
 
6:41 AM
@skullpetrol I don't see why that signal nor ACM is algebraic
 
@Secret ACM=ACuriousMind
Its his signal
 
It was a joke pal @Secret I just thought I'd add some more algebra to it :-)
 
7:10 AM
@0celo7 link to paper
 
@JohnRennie Hello. Need some help with thermo here (physics.stackexchange.com/questions/313367/…) ! Any ideas about the question ? :)
 
@anonymous the word diathermic just means conducts heat
On one side you have gas at 100K and on the other side you have gas at 400K. The pressure on both sides is the same because the wall slides freely so it moves to equalise the pressures.
So what happens is that the 400K side heats the 100K side. The 400K side cools and cotracts and the 100K side warms and expands. So the sliding wall moves to the right.
 
@JohnRennie One question: How do you know that the initial pressure is same on both sides ? Or did you assume it ?
 
The question says the wall is freely sliding. If the pressures were different the force would be greater on one side of the wall than the other, and the wall would slide to make the high pressure side expand and the low pressure side contract.
So with a freely sliding wall the pressures on both side are always equal.
 
@JohnRennie "freely sliding wall". Oh that's the catch! Got it :D
You're great :) Thanks a lot!
 
7:24 AM
@anonymous if you're happy with that I'd be tempted to delete the question as it's pretty homeworky ...
 
@JohnRennie Lol :P I deleted just a second before you said it :)
Yeah, it was a bit homeworky.
But I couldn't find a better place to ask ;)
(And you weren't online while I was writing the question!)
 
7:58 AM
@ACuriousMind did you see the paper by Klemm et al? It's probably good (I think Klemm is good)
 
@anonymous what is your country?
 
8:26 AM
Hey guys, what is the power law for signal strength of a phased array
 
Ooh, there might be a new Tool album on the way. Maynard Keenan has allegedly started work on the vocals for it.
 
@Danu which paper is this?
 
8:44 AM
I have a question.While reporting the mean time of pendulum oscillation with error.How should be the error range?The one which inludes all the data or the one which shows of the data?
The data I ve:90,91,92,95
 
@Kenshin Indian expatriate in Kuwait.
Why?
 
just wondering
 
8:59 AM
Probably not your type of thing :P
 
sup sup
 
9:18 AM
[Random] Mythology: A "cryptology" where the encryption is lossy, imperfect, partially true and above all, heavily symbolic and metaphorical that makes decoding very difficult without knowing nearly a century of context
 
 
1 hour later…
10:35 AM
"Those readers familiar with the theory of the perceptual qualities associated with the right and left hemispheres of the brain will quickly relate the mythological form of knowing in terms of a direct participation in the wholeness of nature with the spiritual right hemispheric perception. The logical and analytical left hemisphere is clearly the one dominant in the scientific mode of perception. "
Nope, left right brain is outdated. Both brain halves work together for abstract and art like reasonings
"Another possibility is that the core myths of world mythology are much older than we suppose and have been handed down in a continuous stream as a verbal but non-written tradition perhaps from the earliest beginnings of human awareness. We have records and artifacts dating back only about 5 - 6000 years, a period which is brief by comparison with the time span of sentient man on Earth. "
Tradition is also a method in leaving messsages to future generations
"Joseph Campbell saw the symbols of myth as universal archetypes, as did psychologist Carl Jung, which appear again and again in dreams and are the inspiration for religion and art. He interpreted the heroic story of the Monomyth as a metaphor representing the inner psychological transformations and spiritual potentialities awaiting every man on his journey through life."
If the supernatural does not exists, spirituality still make sense as the quest to improve the understanding of oneself or a group related to you. In such sense it is similar to introspection, but is carried out via some ritualistic acts
It might be possible all these similarities might be reflecting a characteristic way on how our thinking is wired. One way to test this hypothesis is to ask what animals and plant perceive and feel, or in the far future if ever possible, aliens
"In the holistic mode of ancient thought, however, both perspectives are valid ... of their features, he might partake of divinity himself and control his own destiny. "
not necessary. Coincidence turns out to be common, and there are also patterns that has no meaning. For the careful esoterist, one has to be mindful of such complications
 

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