00:00 - 14:0014:00 - 00:00

12:20 AM
@leslie I waved in your direction from HiTime in Costa Mesa a few hours ago!

i thought i felt a greeting from that-a-way. i hope you stocked up on good wine.
we saw some shore birds eating fish near huntington beach.

@leslietownes I need to stock up on wine. But good wine is so hard to get here... :(
Weirdly enough, however, there is a guy in town who brews excellent sake, so sake is abundant.
And he sometimes does some interesting things vis-a-vis infusions---the last time I got a couple of bottles, one of them was infused with Navajo tea.

as long as there's something to take the edge off.

@leslietownes I mean, I can usually find drinkable beer.

i don't know that we've had wine in a while. my wife is into those hard seltzers that seem to be everywhere these days. i get the concept but not the execution.

12:29 AM
I drove down to this place a few weeks ago. The wines were fine (better than what I can get in the grocery stores here, but nothing to write home about), but the woman pouring the drinks was a hoot.
She clearly had no idea what wine was or how to talk about it, but was really just excited that her husband(?) was expanding the farm and growing grapes. She referred to the various varietals as "flavors".

ha, that reminds me of iowa.

Her favorite flavor was a "peanut greejio".

there was a nearby winery that had all the flavors. i think they had some kind of pinot grigio as their attempt at wine, but they also had dandelion, cherry, you name it.

I really appreciated the completely unpretentious enthusiasm.
@leslietownes I was too young to drink while living in Iowa (which means that the things I drank were designed to be effective and easy to hide?), but my cousin from the Bay ended up marrying an Iowegian.

i've known more than a few people who work tasting rooms in what i will pretentiously refer to as california's actual wine country, and it's a different experience. just glorified shopping. selling an expensive image to tourists with too much money.
not a lot of good conversation.

12:33 AM
@leslietownes Yup. They memorize a script about the wines, and have no real passion for it.

@leslietownes More gin and vermouth, but six bottles of white.

Though in my various trips through Napa and Sonoma, I have found that some of the very small vineyards / wineries have enthusiastic folk who would like nothing better than to talk about their grapes.
@TedShifrin I think that the last time I went to the store there, the gin choices were Bombay and Hendrick's. :\

smaller places are better, particularly if you can talk to someone who actually is involved with the operation. the bigger places hire people out of 'charm school' or central casting or whatever you want to call it

@leslietownes I mean, the Mondavi's have to sell you a bottle somehow, right?

Hi everyone, I'm very confused by a simple problem. If someone could help, I would really appreciate it.

12:36 AM
i ran out of booze a little over a month ago and haven't replaced it. i'd do well to visit hi time. i'm not getting into my wife's seltzers. they taste like i imagine the stuff you put in a hummingbird feeder tastes.

Here's my work so far:

Holy cow... I have a student who just sent me the third email of the weekend, asking if I am okay because I have not answered the previous two emails. Dude. It is the weekend. I don't reply to work emails over the weekend. LEAVE ME ALONE. :(
@leslietownes The stuff that I put in my hummingbird feeder is 4 parts water, 1 part sugar (by weight)---just a simple syrup.

oof, that's not nice. the pre-pandemic version of that for me would be leaving the office at 6pm, and arriving home at 7:30 with a series of emails: 6:15 "hey can you do x?" 6:35 "hey, can you please do x, this is for something that just came up" 7:00 passive aggressive "never mind i did it anyway"
with the bonus thing being this is not a student who's known me for a few months, but someone i've worked with for years and knows how long my commute takes and when i take it.

@leslietownes Yikes.
I try to make it very clear to my students that I don't work on the weekends if I can avoid it---I offer to meet them for office hours on Saturday morning, but that's it.
I tend to work from about 6-4:30 MTW, and 6-9 on Thursday. There are a ton of meetings on Friday, and then I am spent. Weekends are MINE!
For the record, these emails are from the same student who denies the existence of degree zero polynomials.

of course they are.

12:46 AM
As you can see, the answer I get by graphing does not agree with the answer I get by calculating $\theta$ by hand.
What am I doing wrong?
If anyone could help, that would be great.

just in terms of units, i'm not sure those equations check out. 13 sin(t) - 3.5 is in km/h and 3.5 is in km. do you need to introduce a new variable to represent the time traveled? even ignoring units, note that "13 cos(t) = 3" all by itself determines a value of t in [0,pi/2] and doesn't even use the other piece of information
maybe T 13 cos(theta) = 3, and T(13 sin(t) - 3.5) = 2?
T being time traveled, theta the angle from just pointing straight across
"and 3.5 is in km" should be "and 2 is in km" above

OK, I'm just reading everything you wrote. Please give me a second.
@leslietownes So 3.5 is actually in 3.5 km/hr, since it's the velocity of the current (problem stated above).

yeah. i think we agree 13 cos(t) is the "x" component of the velocity of the boat in km/h (positive x pointing across the river). after T h you go T*13 sin(T) km, which you want to be 3.

Right, t * 13 cos (t) = 3
Oh, is that my problem?
Oh, jeez, this is so subtle

the "y" component of velocity oughta be 13 sin(t) - 3.5 km/h, but again in T h it'll gop T(13 sin(t) - 3.5) which you want to be 2.
so yeah, maybe solve the first one for T in terms of t, then plug into the second and solve for t

12:58 AM
OK, so then I have:
<t * 13 cos t, t * (13 sin t - 3.5) > = < 3, 2 >
t = 3 / 13 cos t

yeah. i get about 21 minutes of travel time. the angle isn't 'nice' (although i wouldn't expect it to be, with these numbers)

(3 / 13 cos t) * (13 sin t - 3.5) = 2
Plugging that into Desmos, I get
t = 3.667?

does desmos know that the cos t in "3/13 cos t" is in the denominator?

Hm

the way it's typesetting it makes me wonder. maybe add parentheses around 13 cos(t) and see if the answer changes

1:04 AM
Good point
You're right, but now I get an entirely different answer: t = 0.814?
48.84 minutes (0.8*60)?
I'm clearly missing something, hm ...

t is the angle (in radians). the time is 3/(13 cos(t)) (in hours)

You're right, my interpretation was wrong.

i note now that above you had t denoting two things. there should be a T for time spent, and maybe a little t for theta

In degrees, it's 46.63, which perfectly matches the answer.
Yes, yes, it's so easy to trip the interpretation
I just saw t = 0.814 and I thought that was the # hours
But in reality, it's the angle

for extra credit, figure out how to pilot a boat at a constant angle across a flowing river. what do we know about the mechanism of propulsion? i hope we aren't rowing this thing.

1:07 AM
hmm
Stick an engine?
Or that's a rhetorical question

for extra extra credit, account for turbulence effects.

Well, thank you for helping me figure out the problem. I guess the moral of the story here is I should think about units when solving a problem
@leslietownes Yes, I'll find the divergence and flow at (3,2)

can't ignore turbulence. if you think about where e.g. snowmelt begins (in mountains) and where it ends up (at sea level), a lot of rivers would flowing much faster if a lot of that energy didn't somehow dissipate along the way.

@XanderHenderson what store? HiTime has an astounding selection… always dozens of new ones I don’t know.

i'll numerically model this on a supercomputer.
my corner store has everything you need. night train, thunderbird, wild irish rose.
google told me that gallo pulled the original thunderbird some years ago and re-released it as a non-fortified wine. another victim of 'cancel culture' i guess.

1:44 AM
Someone please remind me what's the name of the property that for al $a,b$ in some set exactly one of the three is true: $a<b$, $a=b$, $a>b$
I tried googling trisection but that only gets results about angles, then I tried googling trisomy but that only gets results about chromosomes

trichotomy?

yes thanks

i first went with trireme but i kept getting stuff about the phoenicians

ah yes and troika and the russian chariots

Why for GOD sake graph theory has very little material compared to real analysis, calculus, algebra...!
I keep searching for 1 hour to find a source while for other math courses, it's very easy
What do you think please :/

1:55 AM
@Avra what are you searching for?

@SmokenSieEinBitteChebaHitBits. Thank you. For example, maximum bipartite matching and baseball elimination. I am not able to find one single source that explains it step by step without jumping over the place and conclude the solution :(
This is my experience with YouT so far
I am specifically looking just for examples
Examples on youtube draw the graph and then jump to solution immediately without showing intermediate steps even for one iteration !

What algorithm in particular would you like to use cuz there could be 10 or more different onese
@Avra
I mean respond quicker b/c it's like I'm waiting
^_^

bipartite matching for example using using fulkerson
sorry
I am with you
I was fetching the algorithm name
Fulkerson's algorithm e.g.
to solve maxmimum bipartite matching

Usually brilliant is good at explaining things

Yeah I know it :(
This is not though for maximum bipartite matching
This is for simple flow problems
bipartite matching is also simple but I would like one full example that explains it
I found lots of examples on general maximum flow and min cut

2:04 AM
@Avra have you checked and where is Fulkerson's original work on it?

Intuition
Algorithm Pseudo-code
Residual Graphs
Sample Python Implementation
Using the Implementation
Complexity
None is about maximum bipartite matching :(

Those are their paper titles?
@Avra have you seen:

@SmokenSieEinBitteChebaHitBits. Thank you very much, yes this is the issue if you see example
it simply jumps over the solution to final solution without showing steps. At least if they show it for one iteration

I don't see Fulkerson + maximum bipartite matching so perhaps you have new content to add to the site
*a new question
Usually you will get an answer in < 1 day but possibly in < 1 hour

@SmokenSieEinBitteChebaHitBits. Thank you very much! I will do probably today or tomorrow same time. It's already 10 pm here

2:10 AM
K, cool.

You're welcome

What is your major area in math?

No, I study AA abstract algebra, but not in school. I start school in a few days (stats)
But it's for a BA in Math degree through OU (open university)

that's good, you like statistics
statistics is much easier than pure math
and it's fun too!

2:11 AM
I'm not so sure, looking at their early start material. It's kind of overly-easy. I'm used to formal, rigorous books like Lang

At least you can see things and connect them to reality

I can't wait to get to the good stuff though
Yeah, I like that I don't know stats yet

You will like it believe me it's fun

and so I should learn soem stuff

good luck, not taking much of your time

2:12 AM
I was working in graph theory the other day (trying to do subgraph isomorphism search in D (C++-like language)
It's an NP-complete problem
I've scrapped the whole project. Graph searching is not all you need to make a formal system understander

never heard of it

It's just taking two graphs G, H

Graph searching can be done by path finding ?

and finding a monomorphism into H from G
But I want to find all such monomorphisms
But I realized I was approaching the problem I'm trying to code on in the wrong way

yeah good project too, graphs are not hard but theorems get tricky a little bit!!
It has a lots of proofs and leeeemas

2:14 AM
It was a smart move
because
CS
Algorithms are usually graph based just because of the way pointers work
You have chunks of memory "knowing about one another" using an edge in a graph
so a linked list is a path graph

I have not seen any of that in my courser :( it's all proooooooooooooooooooofs

struct Node {
Data data;
Node* nextNode;
}
@Avra you should also be learning how to code
So you can automatically find an application for your graph stuff
I recommend Python
And WingWare IDE
for writing / debugging it in

Right, but when you have multiple things to do other than graph theory, it ends up taking entire day to code a problem!

@Avra you'll be glad you went through the troubles you're going through now, later on
So you do code?

Proofs are much much harder, but at least takes less time
code needs lots of time
although little easier

2:18 AM
Both math and code. By Curry-Howard isomorphism, Programs are Proofs and Vise Versa

That is my experience with the course so far
I don't know buddy,,, you seem to be good which is good, in my case, I really think think this course needs 3 times effort compared to calculus
or even real analysis

It's because in real analysis and calculus deal with formulas and with graphs you're dealing with greater "complexity" in the formal sense of the word

My math students friends scolded me for choosing this course!

They think it comes before abstract algebra on level of difficulty !

2:22 AM
Well, graph theory subsumes AA in the sense that graph theory makes use of AA, but not vise versa usually

Agree!
Real analysis, PDE, ODE, etc. are much easier than Graph Thory

Well, once you have your nodes and arrows in order, you will be their better in that area

Do you agree?

To me, PDE / ODE was difficult when I took the course

2:24 AM
No, it was back when I took ODE as an undergrad @ NAU
10 years ago or so

PDE/ODE is nothing compared to graph theory
Lots of materials!
Lots of uns
lots of fun
graph theory no material although it's funny

You're probably smarter than me in math, seeing as you're are farther in school

Even when I ask for instructors online, I did not find any!!!!

You should be talking to your prof as well. They can help give you links / books etc

Most of them go for real, pde, ode, calculus, linear algebra................
Prof does not help at all!!!!!!!!!!
He is very busy with his research
welcome to US

2:26 AM
Try to get involved in their research

Students all busy too and you can barely find someone to help

That is one of the main benefits of nice schools

all work to pay tuition

I spent $1200 and made my dad pay for other have of stats That's all my money :( See, good you have someone to help! Others have no source of income from anywhere 2:28 AM OU is on the cheaper side for tuition, but still too much That is really an aweful, global situation (except a few cool countries) People care more about smart bombs than smart people I think man, if you work for 2 years, then get into school would be great plan! Because the military-industrial complex. Money gets spent on a plane rather than edu @Avra I think so too. I hope I can get focused I'm totally ADHD today at least I studied one math problem in Lang, proof of equivalent property for injective module. And it will probably continue into tomorrow Yeah work and save money for 2 years is good plan. You can then apply for grants Because first 2 years courses are not hard but last 2 years courses are _ I want to get all A's so that I can use that to my benefit for scholarships You can easily get that 2:31 AM I already spent my FAFSA dollars a long time ago, and am still in debt, so loans are a no go First 2 years are all about basic math Nice I should do well then. I just have to go through all this material and do it each day Yeah first 2 years courses have tons of material here and people are very helpful too Even for graph theory I quit smoking everything. So I should change my name but have to wait 8 more days (name change / 30 days only) But problem is writing question on this site for graph theory takes 30 minutes! You can barely ask one question or 2 per day 2:32 AM I've spent upwards of 10 hours on a single question See! @Avra, you'll need to show what you've tried when you post or you'll get downvoted No mercy You could tag the question with reference request as well and ask for links Put in 5 tags (the full amount) So that increases visibility of your question It will thus get answered quicker I really think math exchange is the best website in the world I wish if I knew it before 2:35 AM LOL, yes it must be for me too good LUCK. hopefully I will post question tomorrow. @Avra if you have no luck on MSE try CS.Stackexchange since this is CS-related But don't dual post to both sites You'd have to delete question on MSE then post there Yes Remember to post a link here if you want and ping me I will try. Thanks ;) Stay safe 2:37 AM Will do. You as well! Happy mathing Don't get too mathed out. It's like a drug lol She sounds like Joan Armatrading 2 hours later… 5:07 AM are 'convoluted' and 'convolved' synonyms? or is 'convoluted' more to informally suggest a process was a bit tedious or overly complicated? in everyday use, convoluted is used to mean needlessly complicated and i am not sure that i have ever heard convolved in math, i have sometimes heard people use convolved in the context of the mathematical operation of convolution e.g. f can be convolved with g_t to produce functions h_t with properties ... i'm not sure i've heard convoluted used in the same way in math, perhaps because of the tension with the everyday use 5:25 AM yes i meant convolved re. convolution Yes, "The convolution of f with g" Another is a general construction called the convolution product but was wondering if its safe to assume if someone says 'convoluted' they meant needlessly complicated rather than referring to convolution ahh i see i would say yes Any time you have a semigroup$S$(so including groups) you can take the formal sum over a ring$R$of all elements of$S$such that only a finite number of coefficients are nonzero "convoluted" is not in common use within math although other versions of "convolution"/etc are 5:27 AM the natural product that emerges when you distributively multiply two test terms is called the convolution product i'd like to think that in most usages, context would differentiate between the intended uses even if one had no default rule, but if there's a default, that's my suggestion of what it is The product, the natural addition of formal summs over$R, S$and the set of all such called$R[S]$forms another ring called the semigroup ring, or if with$1$the monoid ring interesting aye i agree there These convolution products show up in other contexts such as Dirichlet series and multiplicative functions I never have personally used the word convolved I always would say convoluted with ahhhh i see 5:29 AM But now I know I should use convolved Makes more sense @antimony do you know about group rings? It's when you replace$S$with a full group hmm its a bit over my head tbh$G$. e.g.$\Bbb{Z}[G] = \{ \sum_{i=1}^n z_i g_i : i= 1... |G|\}$. And$z_i \in \Bbb{Z}$, and$g_i \in G$. These are just formal sums so you don't have to find some realization of them But they do exist because we constructed them and they do form a ring Not over your head in other words ahh i see you're right, that's not so bad :) I'm a tutor I charge$5 / hr or less if you can't afford it

i am not in immediate need, but would like to grab your details if you don't mind :)

5:32 AM
Nice
fruitfulapproach ((((gmail))))

lovely thanks you!

Just send me an email whenever
I'm also in school and have tutors lol
But I tutor in AA (abstract algebra) mainly

great thanks alot
ahah yes, the endless chain of learning - it is a good thing after all

I also tutor Python programming - 8 year expert here

do you take python projects?
(assuming you would want to work on the math-heavy submodules, rather than a whole project)
[not homework/school projects, mostly opensource btw]

5:37 AM
? what do you mean by take them
I work on Abstract Spacecraft right now an open source project of mine in PyQt5.
I'll make a screencast of it real quick

<3 pyqt
by take i mean, a bit of paid work. wouldn't be a wage, more like expert role to solve specific problems

Yes. I'm a self-employed contractor actually with no work atm
I can show you some previous work if you want
I can solve many issues with a custom algorithm. E.g. I came up with several smallest grammar algorithms however that problem is NP-complete so in python as you can expect the time to process one 500 char string went to too large to handle in a few minutes
I came up with one using a groupoid approach though I have yet to code
however making a universal formal system analyzer backend in C++ or D and a PyQt5 front end that is visual seems to be more important to the world than solving just one specific algorithm elegantly

lovely :) great

I kind of gave up on this Abstract Spacecraft

@SmokenSieEinBitteChebaHitBits can I ask a question

5:42 AM
project for technical reasons the other day, but I'm back on it again

yes the main interest would be a combination of numerical optimisation but also being mindful of computational optimisation where applicable
lovely! sounds very cool

Yes, I can work on that with you though you'd have to specify some things at a coding level since I don't understand PDE's 100% lol

ahh ok gotcha

I understand why they're used and all the application areas, but I don't know any of the vocab
@Euler2 sure, what's up
I know some ODE, but couldn't reconstruct the theory by heart (yet)

@SmokenSieEinBitteChebaHitBits what exactly is abstract spacecraft? I haven't looked at the source code till now

5:44 AM
Let me make a screencast guys
back in 3 mins

ahh thats fine i think, we're not looking at making any new formula or theories, just optimising existing problems

I mean screen capture

(which are mostly well documented)

For @Euler2 then I'll make one. I don't want to show what's already on YT b/c that's kind of last week & not up to date
@Euler2
@antimony yes. That is the best way to code - already known about algorithms. I work with those for the most part. It's usually the only thing that is custom is the critical part of the code like for this it would be subgraph isomorphism searching because of the unusual string mapping that respects variables that I would like and that networkx doesn't know about / can't use.

ok

5:56 AM
@Euler2 see, you can nest nodes. You represent those graphically as just a node and an edge pointing to a parent node while the edge is labeled with the keyword label for "parent"

that looks nice, pretty nice

Also I support that arrows domain / codomain can be an arrow as well (think of a natural transformation notation in cat theory texts)
So that is also different from networkx support
though you can simulate this on a basic multigraph that is directed by having the arrows be nodes themselves and so any arrow can connect to them
except two special keyworded edges go to the source / destination "nodes" which can be arrow or node.
So I have a lot of design decisions to make. Do you code Python and possibly want to help work on it?
Or C++ or D?

I code both in python and c++, but I don't think I would be able to get enough time
I would try

The reason for subgraph isomorphism is the language is naturally graph theoretical (it's physically nodes linked by pointers)
Let's do it then
Are you available right now?
We could Zoom or something
well my email is above

I am sorry, but no
I was working on some stuff

6:00 AM
Nice, what are you mathing on?

just a simple math parser (small project, I thought I would expand it to a CAS) I think the lexer is completed

Nice. I was thinking of taking another approach
Terms or labels on nodes /arrows would be CAS expressions
And tie into a CAS in between real CAS's and the more abstract proof-assistants
Because I'm trying to get AS to prove things (that's the goal)
But CAS's are the fastest computationally
e.g. Lean takes 30x what C++ takes to render a photoreal ray traced image
For reasons I don't know yet but I do know b/c I asked them on Zulip, and they said, the library is searched linearly any time something is needed to be "looked up" (I think by the library_search" module)
So for instance looking up the arguments of a function you type out for the purpose of static type checking, etc
Or mathematically speaking, given a set of let statements, what lemmas can be applied that reside at some part of the library
And so the library has to be searched. They said they have the thing in a list!
A list!
As if it were just like the type theory that describes the Calculus of Constructions that it employs
I thought as coder you're supposed to follow the algorithm recipe but also code it in a smarter way than what is literally stated
For example using O(log N) search structures where possible
It could be that searching math is just a hard problem, but IDK
@Euler2 do you have a link to the code?
or is it not on github / bb yet?
An older, Django + Neo4j based project in which I try to embed Quiver CD editor into my site with Graph DB storage of the CD's (commutative diagrams). The point was similar to the newer software: apply graph transformations in order to prove something.

2 hours later…
8:37 AM
A convoluted discussion about convolution, convolving colloquial and mathematical usages.

9:35 AM
Given: $a_{n} =\frac{1}{2}\left( n-2-3\left\lfloor \frac{n-1}{3}\right\rfloor \right)\left( n-3-3\left\lfloor \frac{n-1}{3}\right\rfloor \right)$
I want to find limit points of the sequence $(a_n)$
I observe that $(a_n)$ is a sequence of integers ( (odd) (even)/2 etc.) and is bounded also. So $(a_n)$ must have a convergent subsequence.
And every convergent integer sequence is eventually constant.
It is easy to see that the subsequence $a_{3k+1}$ has limit equal to 1.
But how do I find all limit points of the sequence $(a_n)$?
Is this correct?: Since every convergent sequence of integers must eventually be constant. For every convergent subsequence of $(a_n)$, n must cancel out. If $n$ is not cancelled out then the subsequence will be unbounded hence not convergent. So 1 is the only limit point of $(a_n)$?

9:56 AM
I got it now. :)

3 hours later…
1:00 PM
@TedShifrin The only grocery store within 30 miles is a Safeway.

1:28 PM
It's been a long day without you, my friend
And I'll tell you all about it when I see you again
We've come a long way from where we began
Oh, I'll tell you all about it when I see you again
When I see you again

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