this is back in the 80's in 6502 assembly language. no namby pamby ffts.

@copper.hat I wrote a 6502 assembler which got upgraded to a 68030 assembler. Part of the reason I got my job at Apple.

oh, cool!

I used it to write 3-D graphics software for the Commodore PET. That was the other part of why I got the job.

awesome machine. prob what propelled me into engineering

I have one in storage. Probably too much dust to work

I also built a 5 channel mixer to write music on the PET

all square wave music. sounded like a calliope

i did not have an assembler (only saw ads for them in byte magasine which meant they were out of reach :-))

my first contact with a real assembler was for the digital fuse project in eindhoven

had to load it by tape.

probably better than the cassette tapes on the PET

essentially an industrial version of same

I finally got a dual 370K floppy for it

and a 40K memory board.

my dad got the bigger commodore for his work, it had a floppy

suped up real good

and, i think., 64k :-)

The Commodore 64. I knew someone with one. I went from PET to Mac

newtons method for interest rate computations.

i liked the pet because i could peek & poke to read values from a connector on the back, so i could do little control experiments

and you could do 'chunky' graphics

they had chars for each of the 16 possible graphics of a 2x2 square.

the memory board had a prom slot on it as well, so I programmed graphics firmware for the PET with that

It also provided 320x240 graphics

wow, so you had a eprom programmer? that was year 4 of college for me

that made the 3-D graphics possible

that is so cool.

My dad was an electronics engineer, I had some neat stuff as a kid.

My uncle was an astronomer as well, so I had telescopes as well

ahh, my dad was an accountant with a penchant for gadgets

i would have died to have known someone who knew electronics

I built all sorts of Heathkit projects

i knew some ham radio folks, but they were just gadgets to them, they were more into contact cards and morse

to get components i had to sent to england, which meant a postal order for uk pounds. took weeks.

so i generally scavenged tvs, radios & the like

Ouch! I just went down to Eagle electronics

i started working in a company called cadence in the south bay and my boss at the time brought me to frys. i was like a teenager in a bordello

i was 30 at the time.

The Fry's near me closed down recently. Most bummed.

myself & my brothers (in ireland) had a minute of mourning for that

i think all frys are shut down now

That is probably so.

nothing equivalent. like when i was growing up.

well ,not quite, jameco, etc.

but being able to wander around was priceless

After nearly 36 years in business as the one-stop-shop and online resource for high-tech professionals across nine states and 31 stores, Fry’s Electronics, Inc. (“Fry’s” or “Company”), has made the difficult decision to shut down its operations and close its business permanently as a result of changes in the retail industry and the challenges posed by the Covid-19 pandemic.

yeah, we saw the writing on the wall for a few years, fry's denied it but we knew it was coming.

i'm having a moment of silence here for frys

One year I went in near Christmas and the line wrapped around the inside of the store. The next year, Amazon had exploded and there was no waiting at Christmas at Fry's

amazon is handy but it killed so many places dear to my heart

yeah

codys books, frys, computer literacy

we did some formal verification consulting for apple a few decades ago

i think it was cook who nixed our being able to put the apple logo on our website.

i am/was a woz fan.

jobs was vile scum imo.

I don't know how long Barnes and Noble will hold out, but we still have one near us

my dad used to do accounts for apple in cork, ireland.

barnes & noble has no tech stuff

Woz was a genius. Jobs was too, but a scary guy.

no math books

@copper.hat the one near us had some for a while. Nothing really advanced, but some fun stuff.

i appreciate job's contribution but there are too many personality things that i cannot deal with (disowning child, etc.)

yeah. No argument here

berkeley still has moes second hand books which sometimes has great deals

I visited one of those when I worked at Apple

cupertino dr?

yep

been there many times.

It is 1 Apple Way, I believe

yup

they have the spaceship as well now.

tough company to do business with

nvidia was much more fun

samsung was more fun

I was there for the big quake. The water pipe above my cube burst and all my CDs were covered in dissolved ceiling tile

better cafe :-)

wow. i was on the 5th floor of cory hall in berkeley

still a student. almost working.

I had left to go to my apt to feed my toucan, and saw all the street lights going wild. I decided to not go back that night.

We moved to the newer building at that point

it was pretty cool aside from the obvious grief it caused

the freeway collapse was awesome to look at.

I missed the quake in LA because I was up there

the Northridge quake

I had just flown up the night before

wow, nice chatting, did not realise the time. need my ugly sleep so i can face my sprint ending meeting tmr

i hate jira

the quake of '88?

how did my life end up here

later

89 i think?

@dc3rd '89 in SF

my wife's cousin's car was pinned by the upper deck, she was luck to be able to crawl out the back window

I remember that...well I was a kid on the Oakland A's bandwagon watching the game when that went down...

she got 10k reimbursement for a 3k car.

other 7k was the trauma relief

that was real money back then.

$20 would've been considered big money to me back then.......the amount of candy that could buy............

a friend of mine, a structural engineer (he did the steel for the new hk airport) was visiting so we got to visit see some interesting stuff.

Hong Kong?

yup

cool. Never been close to there

last time i visited him there i had the worst food poisoning i have ever had

Sometimes just the change in water can do that

we were drinking a little and we had korean food where you cook the pork on a little brasier thingy.

and i think i might have skipped some of the cooking part

My uncle, who was a Commander in the Navy, had one of those from Japan. I used to love to use it.

anyway, i had tickets for my wife & her family to go to macau, so i sent them off and worked through the hostels supply of tp.

i am a cheap bastard

hate spending $200/night on a rm

awesome, i have no military family that i can talk about :-)

He was the only one. A friend I've had since 2nd grade is in the Navy now, he was the best man at my wedding

He lives in San Diego too

i have/had one military colleague, unfortunately he opened a pipe bomb that was left beside my compter terminal in berkeley

My uncle live there when I was a kid and moved to Virginia to work at the Pentagon. That was when I was at Princeton and I could visit him on holidays.

you are well heeled!

@copper.hat Crap!

totally for john

poor guy. tough as nails.

well good thing you didn't open it

i had finished a topology take home the night before and was exhausted, just came in to pick up my TA check

i would def have opened it if i saw it thewre

Fate is strange

no sh*t

was a bit disappointed at the total and utter lack of concern from the university.

wow......that is an intense story I didn't expect to go there

:-). when you get to 60 you accumulate a lot of stories :-)

yep

i wish i had done more.

there are a lot of us old farts here

I'm seeing this and actually enjoying the stories...I'm like a kid here with googly eyes......

do more :-)

the downside of what i did was giving up a promising professional career and having two kids who say that their dad spent too much time with them.

and consulting now to pay the bills :-)

they say that now.....but wait til they're in their 30's, then they'll start to "get it"

as long as they are happy i am happy

parents should not be a drag

My son will be 29 this year. I hope he "gets it"

I'm not a father, but I do appreciate now in my life those sentiments my father has and the things he's done.

He thinks his parents are "eccentric"

my dad was not around much so i overcompensate

hah! my daughter (20) calls me fossil

it is broadly known that i am not 'normal'.

well I'm sure your children have the foundation of critical thinking to some degree so eventually they'll "get it". I had to develop it myself, took a little longer but such is life

I was hoping my son would see the beauty of math, but alas.

i think my daughter gets it, my son (17) sees more in league...

or valorant

probably he did @robjohn, but the pressure of living up to greatness may have made him choose a different path

but i wish i could think like a mathematician. i am firmly in the engineering train of thought.

my though patterns are too tied to tangible things.

well how different are the two trains of thought? I kind of held them in the same school

@dc3rd I think he is more of an artistic type. Not much for the math or programming life

and it is explained in the next line

i like creative stuff.

math is art @robjohn, should give him Halmos's paper on it as an assignment

proofs are the flip side

@dc3rd I agree completely, but many don't. They mix up math and accounting.

@copper.hat good proofs are art

i agree. but hard to find.

symbol pushing and number crunching proofs are done once and then ignored.

for example, beaten to death i am sure, rudin just destroys proofs.

Being as I'm still somewhat near to the days of my early youth and how I was scared off math, but now after "mature" reflection can see why I was scared off of it.......it has to do with poor teaching of the subject matter at the grade school and high school level

it is so mechanical and drab......

so you get bored and say to hell with this......

As a refresher for people who used to know it, Rudin is pretty good. For a first time, it is not so easy to understand.

i could not get over the amount of rote crap my kids had to deal with

it is good, but not art

no not art

if it was art, it would be good for a first timer, too

yes, i agree.

i am not sure this exactly qualifies, but coxeter is a lovely book with some wonderful approaches

Yea Rudin has left me wounded, but that was because none of my foundations were in place and no math maturity, but somehow my profs still passed me.....probably expected me to drop the pursuit of math.....

real analysis from rudin is like learning to free climb blindfolded

I'm definitely a lot more equipped now to at least comprehend things, but after I finish Ted's course I should be fully loaded

that is a perfect analogy @copper.hat, that is how I felt....

for me, having a friend with whom i could discuss the level of detail i cared about was paramount

he is a probabilist but we still discuss very basic stuff.

you would be surprised at the number of well respected folks who do not have an appreciation for the basics.

personally i liked marsdens real analysis. but that was my 3rd round exposure to analysis.

when I first tried Real Analysis I was prideful/embarassed at being older than the rest of the class so I wasn't the warmest when it came to engaging with class mates. "What could these young whoppershappers teach me?"....I thought.......

every time i think "i know this well" i get a karmic reminder...

that was before I could appreciate how the math realm works.....

some things are still magic to me.

like conformal mappings :-)

and the jordan curve theorem

@copper.hat enjoy when you get the chance to feel good about something you've discovered. You will be slapped down by another problem soon enough.

That is what I find out

and brouwers fixed pt theorem

I knew I didn't know the material well, I also just thought I could force it in my head by brute force......the "never give up and push to the limit" mindset...

is brouwers fixed pt similar to Poincare's?

@robjohn very naively when i started out i thought i could master enough mathematics to be able to take a good run at anything.

@dc3rd no, it is a very geometrically appealing fixed point theorem.

@copper.hat I thought that when I started out, too

well.......I don't like this dose of reality I'm reading.....

@dc3rd a continuous map from a compact convex set into itself has a fixed point.

as this is the pair of rose tinted lenses I have on now....

@dc3rd math can be beautiful, but it can also be hard.

@dc3rd it is like mountain climbing.

that adds to the beauty when that hard thing becomes more understandable

I'm definitely a masochist and glutton for punishment @robjohn, my contemporaries and friends are in their careers and I made the choice to pursue math instead...

I think it is that addiction to the hard things becoming understandable that keeps me drawn in and pulls me in more and more......

@dc3rd That is very addictive

keeps me going

years later i am still trying to make a dent in fritz john's pde book

I had started it out with it supposing to be a "quick fix" for some finance analysis I wanted to do.......and then I started asking too many "why's".....

the key is focus.

i keep telling myself that

squirrel

why do they use this formula here? where did the idea to use this analytical technique come from? I don't believe this idea works, prove it to me.........,,,black hole for sure...

I remember two things I thought magical and I needed to understand them: the Euler-Maclaurin Sum formula and the Soddy-Gosset theorem.

lol..........my friend uses the squirrel analogy all the time in just that form...

from when I was an undergrad

@robjohn we are at vastly different levels :-)

ok, i am going to retire to my nightly anodyne, netflix

good night folks.

gn!

gnall

Is there a term for a graph that is almost symetric but has it's sign flipped on one side?

I think what I mean to say is symetric around the origin

@AndrewMicallef odd function

If g(x) =f(x-1) . Then , can we sa y

That f(2x-1) =g(2x)?

yes

@Astyx Ohk. Thnx. One more thing , if I say g(x+1/2) , then what would that be equal to in terms of f?

Divided by 2 is whole over x+1

You want $g(y)$ with $y=x+1/2$

Yes

I want to find its value in terms of f

@Astyx It’s like , why do we say if we multiply x with 2 in g(x). I would get f(2x-1). Why not f(2x-2).

you can view $g(x)=f(x-1)$ in terms of composition of functions. namely, let $h(x)=x-1$. then one has $g(x)=f(h(x))$, i.e., $g=f\circ h$

and if you do a different function inside $f$, then that's your $h$ instead

i'm usually too lazy to write that all out, but it's important because underpins the chain rule in calculus

that second condition is quite a restriction. that's like, maybe 15 choices of each?

Only?

IT's the minimum value

rather than come up with a smart way to do it i'd just feed it into a computer. which is also a smart way to do it. at least if you're asking it to do something reasonably finite and not sum a divergent series.

How can I put it in wolfram?

2^14 = 16384 is already greater than 10,000. so yeah, very cabined set of possibilities.

oh, hrm, i don't know how to fool wolfram into doing it. you can sometimes trick wolfram into being programmable but i would prefer to use an actual programming language.

my high school calculus teacher, who might have been the only teacher trained to do what he did for a living, had a funny story about setting a computer to sum a series that he didn't realize was divergent, back in the days where computer time was expensive and it probably interfered with a weekend's worth of other projects.

that's how you could do it in the haskell interpreter. it's looking for nondecreasing tuples [a,b,c] only

How many are there

38 nondecreasing tuples, 86 total

you get that by putting "length" in front of the list in the interpreter

there's enough of a pattern to that list that i bet there's a smart theorem lurking in there somewhere. but i'm happy with the list of tuples

thank you for reminding me that i'd installed haskell on this machine. i think that was day 1 of computer setup. then i never used it until today.

stackexchange sent me the 'mentioned' audio for my last message being posted one hour ago. i don't know why. my heart raced.

@leslietownes I wrote something in our private chat. Not a math related thing.

oh is that it. that makes more sense. thank you.

i spent the last hour managing my cat. she's obstreperous.

@leslietownes Thanks!

i don't want to evangelize for haskell too much but it's a really good way of doing exploratory number theory. almost anything you can write in set notation, it can compute. obviously it gets hard if you push it in that direction, but it's surprising how much can be done without any thought as to how a computer would process it.

i miss lisp

@Semiclassical thanks

i like lisp, but i really like haskell.

i like the consistency of lisp notation.

i had to use ocaml for a project when i was a postdoc. it was OK but not the paradise that haskell would have been. the funding thing mandated ocaml. i think prince william or someone mandated that we use it.

@dc3rd FYI, the Brouwer Fixed Point Theorem is in chapter 8 (proved with Stokes’s Thm).

@TedShifrin managed to solve that problem from yesterday in the end :)

Can I uniformly approximate a continuous function on a compact convex set with smooth functions?

Not just me :-)

Fantastic, @Flows. Sorry I was not of much help.

@copper Does Stone-Weierstrass work?

that seems like it ought to be doable. says the guy who has not thought for more than 15 seconds about it.

You were :) @TedShifrin !

my instinct would be to convolve with something.

@leslie I love those convolution arguments, but how does it work on a weird convex set?

that's what i'm worried about, if it gets you outside of there.

@TedShifrin I am wondering about that.

I guess you extend the function by 0 and do it on $\Bbb R^n$?

So where is convexity relephant?

The proof of Brouwer I ground through was a mess of simplices.

i'm still worried that you can't guarantee the convolved thing stays within the domain of the original function.

i identify with that. i'm a mess of simplices.

I was wondering if Stokes & approximation was a simpler route (at least moving the complication to Stokes).

Oh, that's Lefschetz, not Brouwer.

kakutani. schauder.

pick your poison.

Brouwer is basic homology (retraction to boundary).

Lefschetz is small simplices. I love that proof.

What do you mean about staying within the domain, leslie?

I like fixed point stuff.

when you convolve you blend with neighboring regions. i don't know how to limit that if someone says 'this has to be in a compact convex set.'

i have not thought long enough on it to form an opinion, but i worry about it. i'm anxious.

Just restrict the domain of our smoothed extension?

it's definitely me worrying about ghosts. i just wonder.

i shoudn't project my anxiety onto the channel.

Ah, I need convex smooth approximations. Now I remember.

Oh. Different.

hello

A few decades of rot in process...

For what, copper?

Hi, Simone

Hi Ted

i asked a question once about filling in continuous data for a discrete set of specified points that were consistent with having a convex approximant or even an approximant that matched higher-level derivative signs. it completely dropped into the void. then again under my current account, same thing.

don't ask the internet about convexity. that's what i learned.

@TedShifrin Proving the Brouwer fp theorem using smooth approximations.

I am a Rockafellar fan.

Nah, Stone-Weierstrass works fine. This is even an exercise in Guillemin & Pollack. You map the ball into a slightly larger ball and then shrink down .

Is positional notation an interesting mathematical idea?

i don't know. there is a broad question about the nature of notation to the things we try to express, and a narrower question about the meaning of position. i have strong opinions about prefix, infix, postfix notation. but only in a context of an overriding system of notation.

i think inches and feet are dumb, but i think in them. proposals to displace my understanding of that will be looked at skeptically.

Why was the US so anti-metric? I don't even know.

Because Napoleon was a great proponent of the metric system, that tends to spoil things XD

so much of my primary school life was spent converting shillings per acres into pounds per rood. the old notation for pounds, shillings & pence was LSD.

decimalisation in 1971 was a blessing for school kids.

some odd units have some reasonable justification, like nautical miles :-)

Say I have functions $f_h$ which weakly converges to $f $ in $L^1( [0,T] \times \bR^d)$. Also assume I have a sequence of partitions $[t_n,t_{n+1}$ of $[0,T]$ whose length is $h$. How obvious is the convergence of $$ h \sum_n \int_{t_{n}}^{t_{n+1}}\int_{\mathbb{R}^d} f_h(t,x) \phi(t_{n},x) dxdt $$ to $$ \sum_n \int_{t_{n}}^{t_{n+1}}\int_{\mathbb{R}^d} f(t,x) \phi(t,x) dxdt $$ where $\phi$ is a compactly supported smooth function.

Why is the $h$ there outside?

copper.hat thomas koerner's "the pleasures of counting" includes numerous unit conversions of that sort.

i think relating to the buying of carpet.

goofy stuff. i can't judge because i live in america, where we mostly do goofy stuff.

@leslietownes looks like a nice read...

Not to mention unchristian Christian stuff.

it's a really good book. i have given it to the children of several of my friends.

@TedShifrin because my calculations got me there xd I must have messed up. dw about it !

we're goofy!

what do the Americans make of Andrew Yang?

i don't normally speak for 320 million people, but, many of us like the general idea, although we have doubts about the execution.

i'm fairly certain that all coronavirus vaccines are bill gates microchips, but that's another subject entirely.

my wife has a microchip. what should i do?