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user147690
00:00
Okay done, I think you should have edit available now
user147690
The math rendering is a little slow when you open a page, and I might be able to fix that, but I am scared to change things since it works and I don't want to break it lmao
I just made my user page so it's probably good :)
And so far the MathJaX is rendering just fine, no speed issues
user147690
Ahh actually where do you live, probably perfect for you haha
user147690
My server is in California I think
haha yes I am in Cali right now :)
Minnesota later
(later means tomorrow XD)
user147690
00:05
Ohh very nice, when does the program start?
Not til Sept but
I have a tutoring job beginning on the 10th
user147690
Oh I saw that, the one where they just expect you to be good?
Haha I have literally no idea what this guy is thinking
Like, I think it'll be fine but
yeah
he's putting a lot of faith in me.
user147690
That's awesome though, who were you teaching? I can't remember if it said in the blog, is he a uni student?
Don't think I did. "He" is the one I've been communicating with; the actual student is his HS daughter.
user147690
00:09
Oh okay, HS students should be fine then to just rock up, as long as you get to see some sort of plan
haha, that's the dream
user147690
My ex-gf tutored some kid in physics and he just rocked up with no plan the first time and it didn't go well - she just tutored him on other stuff from his text-book and said, "Next time, have a plan". Second one went much better :P
eyea..
:P
The weird part for me is that I still don't know why he got her a tutor; it's like, is she doing well, or is he just nervous about college admissions, or is she normally good but floundering in probability?
So I think my first session might also be a bit rocky.
user147690
Yeah that's actually pretty weird that they haven't given you any direction. But my wealthy friends had parents that just liked to have tutors for their kids for seemingly no reason
Annnyway I should probably be trying to figure out a viable architecture to keep the project somewhat self-contained.
on your wiki
user147690
00:12
Yep and I shall head into uni now, I'll be back in 1.5 hrs or so unless someone distracts me :P.

@SamiBrooker @jcprx @Yash I'll add you as admins if you make a profile on my website
user147690
I'll add you as admins if you make a profile on my website Here
2
user147690
Okay talk soon :)
02:23
@Sami
hey!
i got the e-mail from eric today
and coincidentally i finished my pre-work today
oh! dope :D
the thing is i'm not sure if i can contribute to this project anymore :/
first off, my math maturity is way behind compared to the rest of you
dude same tho
02:25
even when learning linear algebra and combinatorics, i'm still not digesting the information (ie the pdf file eric sent us) well
on the side*
tbh, everything is so abstract for me
aaah me too
which is the point but
anyhow my programming class starts in a few weeks
ooh, what's the class?
so my time will be cut way short from this project
it's an iOS programming course
i'm so excited to start :)
that's rad!
02:27
it is indeed rad
lol
but yeah, i know what you mean. it's a lot to balance
very much so
i would want to give a 100% in this project, but i can't
mmm, totally understandable
i'm still thinking about it
by the end of the week, i'll have a more concrete answer
02:28
how about you? what have you been up to
uggggh i've been overwhelmed by other summer commitments and planning for next year...
ah i see, same here to an extent
i got an offer to be a residential assistant but no one in the housing/residential department at my school is, like, responding to any form of communication?? so i have no idea if i'm still getting the job
ah delayed response. well, they'll have to respond soon enough
hello @EricStucky
02:31
yeah, it's just a matter of responding in a timely enough way that i can buy a plane ticket :P
hiya!
yeah @EricStucky as you can tell from scrolling up, i'm not sure if i can contribute to this project anymore
i'm still going over it
and i'll definitely have a concrete answer by the weekend
mkai
thanks for letting me know :)
np, you said not to apologize, but still, i'm sorry for not communicating for nearly 2 weeks and i have no excuse for that
but yeah, i'm not sure if i could divide my time wisely between programming and researching
they both take up a lot of time
well for me that is lol
i'm a slow coder
very slow
02:36
I'm sorry to see you go but obviously you have to be smart about your time :)
Haha I cna't say I'm any better tho XD
indeed, i'd rather give a 100% than <=50, you know?
coding is kind of a pita
necessary evil :P
pita?
pain in the ass
ohhh
but i'm a masochist
so i enjoy the pita
:)
02:38
XD
even if i decide to leave, can i still stay in the chatroom with you all
i'm still curious about how you guys will progress
this is an interesting topic and even tho my math level is super low, i'm intrigued
user147690
I have added the admin rights for you @Sami
okay... cool.
user147690
For linking internally, you just use [[Page name you want to create|Text you want to show]]
user147690
Sad to lose a member @jcprx
user147690
02:44
Did you see the things I linked above? Maybe they will make you feel a little better about the math. They really help with the definitions in getting the geometric intuition running, or maybe you were already past the polyhedral fans
i did! i saw the links, i am going to confront them
user147690
Oh sorry I meant that for jcrpx
oh whoops okay cool then
user147690
I should have tagged it haha
no worries. i'm not at all sure about tagging etiquette
02:47
Probably also relevant for Sami tho?
user147690
@SamiBrooker Usually you are meant to click the arrows
user147690
@EricStucky Oh yes, I originally was showing it to Sami
click the arrows?
i'll definitely read it @Alex
user147690
@SamiBrooker If you put your mouse over a chat message, on the very right of it
02:48
oops
i don't have a concrete answer yet
and i'm still going over it
i just felt kind of lost for awhile
@AlexClark what???
oh that's
ok
@jcprx if you wanna talk more about your situation/whether or not you wanna stick around, we can talk? i feel like we're kind of in the same or at least similar boats
yeah sure
well first mistake i did was trying to digest all of those pdfs i sent to you all
user147690
Hahahaha
user147690
Yes that's crazy
user147690
I would feel overwhelmed too
02:52
i had a mini-burn out feeling afterwards lol
i definitely shouldn't have done that
oh dude that's totally understandable
user147690
@jcprx Have you answered Eric's initial questions?
i really only answered polyhedrqal fans 1/2(sort of) tropical grassmannian 1
because i could reference from the pdfs i read
user147690
Well that's a good start for sure
polyhedral fans*
but after than i was stuck and i know it was because of my math level
user147690
02:55
If you mouse over your message, on the left there is an arrow for a drop down menu that has edit on it
that*
ah i keep forgetting
user147690
@jcprx I think the math level shouldn't matter much, it seems like stuff most math majors wouldn't have dealt with. I have done essentially no geometry related things at any point
really, because i've never taken anything higher than calc 2 and discrete math
user147690
The only things that have helped me at all were with my confidence, like not being afraid of seeing commutative semi-ring with identity and such
i understood that
user147690
02:57
@jcprx Yes, I have never encountered half-lines, cones, convex hulls, convex sets
user147690
Oh I guess the set theory might be harder, since point-set topology really gets you to appreciate that, so I see what you mean
i understood and comprehended/digested everything on that pdf file until 167/168
user147690
Anyway I think the teams communication probably didn't help. If you realised that we are all really in the same boat, and it is hard for me, you'd probably feel better
i didn't lol
i know you all are math majors
user147690
I felt overwhelmed too, I couldn't find the definitions for anything lmao
03:00
so i thought reading all of this may have been easier
for you all i meant
i feel like this all would've been a really good thing to talk about at the beginning of june lol
that's really good to know :)
user147690
Indeed :P
i know lol
user147690
Eric's probably thinking "I said all this already..."
03:01
I'm kind of curious how you would have liked to see that discussion happen
because I think this problem happened in CRP proper
and I'm trying to give those folks feedback
user147690
I don't think it can be forced unfortunately
user147690
It's sort of a, 'I feel like I suck, I don't want anyone else to know' sort of thing(for me atleast)
well, i dunno, it might've been good to have everyone come on the chat at once and just had, like, just a personal talk?
i mean, then everyone would be a little more comfortable talking to each other and also we could talk about what kind of background we're coming from and stuff like that
idk, i feel like i'd've had an easier time coming in to the chatroom to say that i didn't understand something if i felt like i was talking to, like, people i kind of knew?
user147690
Haha yes true, I agree
user147690
I personally feel a lot better now, and it helps that I found those links I showed above
03:04
definitely!
agreed with all points
i feel much better now knowing everyone's in the same boat somewhat
lol
honestly!
user147690
Hell, I'm probably behind you since life has been distracting me
user147690
My goal is to try to get those questions done by next week
i'll have to go back to my schedule this week to see if i can make time
03:07
yeah i haven't been able to really touch this stuff in about two weeks unfortunately so i'm gonna see what i can figure out over the weekend
@SamiBrooker This seems like an oversight on my part: I have done a few collaborative projects and I have always been really unimpressed by regular large-group meetings; there just isn't enough happening often enough to make them feel warranted. So I missed the value that they have for group formation in the early stages.
i mean, idk, in my mind it's just more of a getting to know people thing
user147690
Yeah when I was doing engineering, the group meetings seemed really important for breaking the ice
to be fair i'm kind of a mushy person and i just like making friends lol
user147690
(admittedly, they usually involved random people drinking together)
03:11
see that's the way to do it
user147690
Hahaha
lol
CRP should do first-week drunk video conference call, got it ;)
user147690
Ahahahahha
brilliant
better yet, make it a weekly thing
03:15
@EricStucky is the pdf with the questions are the only questions we need to answer for the whole project or no?
user147690
Well I am going to dig into some math now, gotta get these questions done + prep for 4 all four classes
@jcprx: That wasn't the intention.
If you could give, like
a really simple answer to #3 on either half
then that would be super nice
really? ah wow, and here am i stressing over answering all lol
hmm if that's the case, i'll reconsider staying on.
user147690
Wait I am confused by your interpretation and mine
user147690
Wait can you clarify 'that wasn't the intention'?
03:18
#3 for both halves are really difficult questions (simple characterization of PFs in high dimension and TG is a PF.)
But neither is where I was intending to focus the project
user147690
Where were you intending to focus the project?
Research problem #3 says that if you take tropical sums of TGs
(Erm maybe #4)
then you get a new PF
and the community knows very little about these objects
They are known in some extremal cases, but all of the interesting fans (living between the TG and the full space $\Bbb R^{n choose 2}$) are completely unknown, iirc.
Sorry, I have to get on an airplane.
I'll be back in 3-4h if you're still here.
user147690
@EricStucky I shall be. Cya then :)
have a nice flight!
safe travels!
 
2 hours later…
user147690
05:23
Stupid question: A face of a convex polyhedral cone, lets say in $\Bbb R^3$, refers to any of the flat regions created by the straight lines joining two half lines from the origin, right?
user147690
Of course the top is unbounded, so this isn't a tetrahedron, but I mean, the other '''faces''' of the "tetrahedron" are called the faces on the convex polyhedral cone right?

http://imgur.com/H9JAz24
user147690
I.e. the red region
whoa um
ok
hmm
user147690
I mean it soudns right, but I can't find a solid definition xD
yeahhhh i'm having a hard time reading some of this stuff
user147690
05:38
Hmm faces are defined differently by dimension - never encountered that before
05:50
ok wait, sorry if this is hella dumb, but is a polyhedral cone just, like, an ngonal pyramid where n is the number of halflines, and like, the tip is at the origin?
okay i think we are on the same page wrt faces?
user147690
@SamiBrooker You mean in $\Bbb R^3$?
sure! yes.
sorry i forget that that needs to be specified
user147690
Well from what I understand, a cone is a set of half lines, as well as every point between any of these points. I.e. If we have only two half lines from the origin in $\Bbb R^3$, then we have three cases 1) they are in the exact same direction, and we get just the half line, 2) They are in exact opposite directions, and we get a full line, 3) They are facing at some less than 180 degree angle from some perspective, and we get a pizza slice 'plane'
oh shit, yeah, you're right
i don't know why i'm thinking there's only one case and it's the one i drew on my whiteboard, i'm so sorry
user147690
Haha no worries at all!
user147690
06:02
I drew like 30 pictures last night
user147690
I started in R^2 which helped heaps
user147690
Then I haven't got a nice mental picture yet of n-halflines in R^3 yet since I got caught up in the face definition haha
ahhh yes in $\Bbb R^2$ it's just, like...
hm
user147690
And in R^2 if you have n-lines, and the sum of all of the angle differences is less than 180, you just get a pizza slice with the edges being the greatest angle different
user147690
If that makes sense
06:05
yes!
user147690
And if the total angle difference is greater than 180 you get all of R^2
whooooa okay i hadn't thought about that umm
user147690
Then you have the single half-line case and the full line again
hm
ahhh right okay
user147690
I wrote up some of my really early thoughts (that may be embarrasing for me) here:

www.alexpclark.com/index.php?title=Some_thoughts_on_polyhedral_cones

The titles are pretty accurate lol
user147690
06:08
I don't know why linking isn't working properly for me
nothing at all to be embarrassed about!!!
user147690
Hopefully @EricStucky can come and clear up the faces definition thing for me xD
06:36
in 3 space, is the convex hull of two halflines going in opposite directions--like, they're both starting at the origin, they go off in space in the opposite directions--is their convex hull the plane they lie in?
sorry if that's atrociously worded
user147690
Like two halflines that look like a single line together?
user147690
I think their convex hull is the same as just the set containing all points on the two half lines
user147690
I.e. the convex hull changes nothing
ohhh... hm.
user147690
06:37
Like if they were lying almost colinear, you would get the 'pizza slice' of all points between them
user147690
But if they are colinear, the convex hull should just be the line
okay, what was the case in r^2 where the convex hull ended up being the entire plane?
you said that earlier, right?
lemme scroll back
user147690
Yep, I think in that case we need three lines
user147690
Say three lines that divide the axis into three
06:39
wait, sorry, are we looking at two or three dimensions?
user147690
R^2 is two dimensions
right
just making sure we hadn't moved out of that
user147690
Okay haha sorry I should say it
no worries!
oh wait okay that makes sense
so okay, three coplanar lines in 3d
user147690
That's good, since I can't draw with this sketch pad haha
06:43
but like, they have to basically follow the same rules as for three lines in 2d that we just said
the whole plane
shit sorry i'm not saying entire sentences auggggh
user147690
No I know what you mean
ok dope!
user147690
In $\Bbb R^3$ yep, three coplanar half-lines will follow the same cases
right on. ok.
oops sorry
yes, half-lines, nothing but half-lines here
user147690
That was me too haha
06:45
i was gonna say, y'know, getting sloppy because it's kinda late at night
but what, it's like, afternoon for you?
user147690
4:45pm xD
user147690
Like 1am there?
nahhh 11:45
user147690
This stuff is actually really awesome
what, cones?
user147690
06:46
yeah haha
it's pretty fun
user147690
I have never really liked geometry, so I knew none(although I am taking differential geometry next sem)

But I am really getting into this
hahaha
i have kind of always sucked at geometry but it was sort of, y'know, either pick up on the geometrical interpretations of things or just never understand anything ever
user147690
@EricStucky If you would prefer, I imagine I would be capable of creating another wiki off of my server, strictly for official purposes(that would run side by side on the same domain, like alexpclark.com/crpx/index)
user147690
Otherwise in terms of making it disjoint you could just ammend crpx onto the start of everything(I'm just thinking about your 'keep the project somewhat self-contained' comment)
09:01
@Alex: I think my plan was roughly that we would put everything into a CRP category, which would have basically the definitions pages that we generate (like your polyhedral cones page), our user pages, pages for commentary about articles, and then 3 misc. pages (home, results, wishlist). Hopefully that keeps it relatively small?
Sorry for being an hour+ late; bus took a long time XD
Re: math discussion. Seems that you have the right idea about faces, but using this definition they're... awkward, afaik. The definition of a cone I am familiar with is the intersection of half-spaces bounded by hyperplanes, in which case the definition of a face is just "well, also intersect with one of the hyperplanes".
I think the following definition works: a polygonal cone is a convex hull of finitely many lines, so choose a minimal subset of those lines which generates the cone. Now a face is just the convex hull of some subset of those lines.
One thing that is wrapped up in these definitions which I'm not sure you got from that picture is: faces do not have to have codimension one. By that I mean, not only are the "triangular" boundaries faces, but actually the lines themselves are faces as well, as is the set containing the origin.
line -> half-line :/
Hmm actually I'm not seeing where you're drawing your thoughts on polyhedral fans from. Maybe from a paper on polytopes? It seems like you're going through a lot of work to define the groundwork for cones again. But in the PF definition we take cones as a prior concept, and you already have a good definition.
 
12 hours later…
21:15
@Sami: are you following mathed-potatoes?
21:25
@all: Yash has let me know that he will not be continuing with us. If you could kindly leave him out of your tags from now on, that would be great :)
 
2 hours later…
22:58
@EricStucky i am not following mathed-potatoes, why, what's up?

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