its nearly just an algebra problem.

think one can get a simple formula for how far off it is as an approximation via algebra.

ie compute the formula for error of approximation vs non approximation.

it will depend on all the constants.

It's surprising how many innocent-looking algebra problems are actually pretty hard to compute

"Assuming the values of these constants are such that the maximum value of $x$ is slightly less than $1$..." dont totally follow that. the condition "the max value of $x$ is slightly less than $1$" seems like it would stand alone. it seems to be trying to express some relation between the constants & x

@DavidZ: If all else fails, just scribble "We've found a wonderful proof, but this margin is too small to contain it" in the margin of the paper ;)

A time-honored tradition, that proof style

Hehe, true.... though I think what we have is going to satisfy the reviewer

@vzn well, the idea is just that the maximum value of $x$ could in general be anything, if you don't constrain $A$, $B$, and $C$. But I happen to know that the values of $A$, $B$, and $C$ in this case are such that the maximum value of $x$ is close to $1$. Several previous papers on the topic assumed that the maximum was exactly $1$.

@DavidZ The argument you have already given is satisfactory. As long as you can justify the assumption that $x\leq 1$

Then it immediately follows that you can cross out the $B$ term when $x$ is close to the maximum

On physical grounds, it's obvious. $x$ is a momentum fraction, and it's impossible for a constituent particle to have more momentum than the composite particle that contains it.

(under these conditions)

thats like a conservation of momentum/ energy thing right? (are those two tied? forget)

Yeah

They're all the same law in relativistic systems

there are a lot of 1+epsilons & 1-epsilons in TCS....

@dmckee Let me know if that helps clarify things for how to present it to your students. I know you asked for a system that shows different behavior, but I'm not sure one could exist

@tpg2114 Didn't you solve the problem? I think that I solve it.

@Sofia To which problem are you referring? I'm confused.

@ChrisWhite IPO generates massive problems for us. The compiler either eats itself with an Internal Error or the code generates incorrect answers

Compilers are really bad. For all the "awesomeness" people like to put on Fortran intrinsics because "the compiler will generate super fast instructions for them," almost every time writing our own routines is faster than the intrinsic

@ChrisWhite So fun fact -- Intel and GNU are not IEEE 754 compliant unless you force them to be

And we get wrong answers or numerical instabilities unless we force strict compliance

And C/C++ standards don't even require 754 compliance so they can't even be forced to do it in some cases

I don't know that I agree with that entirely, or maybe I don't understand it. But I can do on my workstation overnight what used to take 200 processors a week to do 10 years ago

And the "calculations" haven't changed, although our implementation is much larger and actually more computationally expensive in terms of flops per cell per step

And what 200 processors can do in a week now was considered far too impractical to do before

But I think the computational complexity of rendering a Clash of Clans village is probably much larger than the orbital dynamics and nuclear problems of yore

Didn't we send people to the moon on a wristwatch? :)

Side note -- I actually read a really fascinating article online about the Apollo guidance computer design/implementation but I can't find it now

klabs.org/history/apollo_11_alarms/eyles_2004/eyles_2004.htm

I think that was it

Double extra fun side note --

ibiblio.org/apollo/listings/Comanche055

Source code listing for the guidance computer!

The problem of DavidZ. Did he solve it?

@Sofia I don't know, I don't know what his problem was about. I was referring to a question dmckee posted on the main site: physics.stackexchange.com/questions/164739/…

@tpg2114 Aaaa! O.K.

018042,000089: 22,3012           03131 11275                    2DEC     .099200                               #  =(.1)COS7.25
018043,000090:
018044,000091: 22,3014           77461 47370                    2DEC     -.012620                              #  =-(.1)SIN7.25
018045,000092:
018046,000093: 22,3016           00000 00000                    2DEC     0          B-28
018047,000094:
018048,000095: 22,3020           00316 30407                    2DEC     .012620                               #  (.1)SIN7.25

At least they documented their magic numbers

Yeah. I also don't like the argument that SI gets rid of fractions of things (usually used by people arguing SI is better for things like cooking/baking)

I think the Imperial vs. SI thing is more rooted in the insistence of a tiny fraction of the world's population to use one particular system, when any choice of such a system is by definition totally arbitrary and is useful only when uniformly used everywhere.

It would be the same beef if everyone used Imperial and just the UK insisted on SI, for example

That said we do have miles on our road signs

The UK's combination of units is just confusing

Indeed.

The thing about roads I think is because changing the signs is deemed dangerous.

Plus lots of people still use Imperial units in common parlance

Unrelated: This might be a dumb question, but is, uh, the non-insulting use of fuck a valid or an invalid offensive flag?

Define the "non-insulting use of fuck"

Either you're insulted or not, I don't see the distinction

As in "used for emphasis"

You mean, when it's not directed at someone in particular?

@ACuriousMind Unless you guys would like to find out from this discussion, you want want to use f**k :)

Like wtf

Yeah, don't get me wrong, I don't care what people use in everyday life.

I would just be annoyed if I tried to have a conversation with an engineer who didn't understand SI units.

I mean, a work-related conversation.

The US is a small portion of the overall population, but we do have 25% of the total worldwide economic output. It's not that we're a small player in things globally

@MarkMitchison My problem -- I "understand" SI units but I can't relate to them

I have no idea what air pressure is at STP in psia. But ask me to draw a X cm line and I will have positively no idea

@tpg2114 Fair enough. I guess I have the advantage of growing up in the UK, which is one of the few places in the world where people have a good intuitive grasp of both.

1 atm = 14.7 psi :)

I only know that from scuba diving to be fair...

@ChrisWhite Quite. I use (many different systems of) units where $\hbar =1$.

I also dislike how many units there are for pressure

None of them come out with useful numbers for milk volume

Bars, torrs... I mean come on

@ACuriousMind I would agree with @ChrisWhite that "wtf" isn't offensive. I mean, to even know what it stands for you already have to be conversant with the word

@MarkMitchison Apparently Rolls Royce has its own system of units which combine imperial and SI wackily. Like uses BTU, degrees kelvin, pounds, meters for example

@tpg2114 Ha, that sounds like fun.

And they do it so if somebody ever steals their data/performance metrics/expressions used in design, it will be batshit confusing

@ChrisWhite Yeah, cgs system for bar. But mmHg? mmH2O? 1 Torr = 1/760 atm. That's just ridiculous

Actually in my opinion it is good for physicists to be totally comfortable with all sorts of units. Unless you always deal with the same system then you need to change them frequently. It just makes sense to do interdisciplinary stuff in a single framework. Given that the majority runs with SI on that front, it makes sense to go with that.

The atmospheric science people might use the most hybrid unit systems. At least in the US

@SabreTooth Awww.

@MarkMitchison Alright, thanks. ;) I had to ask because someone flagged (among other "f***ing comments") one that consisted only of wtf.

@ACuriousMind wtf has a bad word in it? I thought it meant "well, that's fun!"

wtf

Also -- while talking about the history of computers this morning, I decided I"m really glad chat rooms have advanced over time.

Anybody remember the good 'ole AOL days?

a/s/l/pic???

Except I don't think teenagers use those anymore cause they are old people language

^this

They have new ones I don't understand.

I think I'm older than you

I know we're pretty close, but I think I edge you out

"When I was a kid, we had wireless phones that had a plug going into the wall!"

No joke -- I grew up in a gross little steel mill town surrounded by coal mines in the mountains in Pennsylvania. My first phone number had letters in it -- HAZ-8230 -- and we could only use rotary phones

We had the oldschool block phones with the rotary dial on it. Eventually we did get a wireless handset, but we had to set it to rotary instead of tone

They were kinda fun, and you could dial quick on them once you knew how

Doing things like punching in a credit card number was painful

OH! I also remember having to unplug all the phones in the house when I wanted to play Warcraft (the original) online with my friend because I didn't want somebody to pick up the phone and kick me offline

I could only check my email once a week because it was too expensive to dial in...

@tpg2114 I haven't taken the time to dissect and internalize the argument, yet, but it looks good.

I agree that I confusing the two properties seems more surprising than treating them as different but a couple of them were really going that way for a while.

You distinction between storage and transmission is essentially the "new verbal tack" I had in mind and I believe that it helped.

@dmckee I remember in my turbulence class it was drilled into us repeatedly that things like viscosity were a property of the fluid, but turbulence was a property of the flow

In any case, thanks for the effort.

No problem. Sorry I didn't notice it when you posted it earlier today. Hopefully it isn't too late to maybe help

I knew that I could count on the community here.

Thermo was my worst subject in school. Undergrad and graduate, so teaching it is serving as quite a leaning experience for me.

And that derivation is straight out of that reference if you want to go back to a source material for it. It is on like... page 16 or 17

@tpg2114 I may very well just print it out and give it to them.

Thermo was my worst. Until I saw it from the statistical mechanics side and then it suddenly made much, much more sense

Why does NIST have peanut butter?

@tpg2114 Yeah, the statistical approach helped me, too, but a third of these kids haven't even had modern physics, so I have to go very easy on the QM.

@KyleKanos Standard sandwiches?

Maybe

@dmckee I never had any QM. My only experience with it was from the gas dynamics perspective

@tpg2114 I'll look into that. Probably too late for this semester but for next time...

@dmckee Definitely check out the book, Introduction to Physical Gas Dynamics. I found it to be really good. We didn't go through all of it, just the "important" parts from an aerospace perspective

But I found it to be really approachable and easy to read.

@KyleKanos I don't know if I can recommend it just yet since I'm still downloading some of the books, but if your kids are nerdy like you, check out: humblebundle.com/books

I bought it for a friend. But I'm downloading things now to see if they are any good

Wait, I'm a nerd?

I put in $15, that's worth it for the EFF even if only 1 is worthwhile.

You sit in a physics chat room discussing computer programming and FF7 speedrunning... I'd say that qualifies

I also didn't say it was a bad thing

I was going for humor, but seriousness works too

Grading labs kinda sucks.

Writing them does too

These students are in what we call Physics 200 which is supposed to be 2 semesters of algebra-based physics compacted and dumbed down into 1 semester

But a different faculty stepped in and made it, Physics for Future Presidents

So they don't actually learn any physics

wtf

But they still have to do physics labs

@ACuriousMind You're right, that is fun ;)

They don't know what a vector is

Absolutely :)

And I have to teach them vectors for lab tomorrow

Fortunately, they can follow directions fairly well

@KyleKanos I don't get the effusive praise for that book.

If that's what passes for science knowledge among the political class we're doomed.

Doomed, I tell 'ya.

I haven't read it so I cannot comment on it

But the professor teaching it thinks it's interesting

He knows it's not "really correct," but gives a "good introduction" to the ideas of physics to the students (in terms of what political policy should be)

I only read about a third of it before deciding my time was more valuable that that.

But it seemed to me like the author simply asserts the results immediately before the thing he wants people to believe and allow it to be seen that the result is the result.

Well, duh!

But they're still taking his word for things, just the things one step back.

Grrrrrr!

@KyleKanos What's your vector Victor?

We learned what a vector was in... 11th grade? The high school physics 1 class

@tpg2114 What's your clearance, Clarence?

@KyleKanos Even my Physics for poets students no what a vector is: "a measurement with both size and direction".

They can't do any actual math with them, but they know that they have to match in both categories to be equal.

@dmckee Kinda like how the Big Bang didn't happen?

Yeah, these guys are special. They're agricultural and food science majors.

Didn't read that paper and only skimmed yesterday's chat about it, so ... I'll have to take your word on that.

@dmckee I didn't read it. My understanding is just what people summarized for me in chat on Monday (and then again on the question)

@KyleKanos When I was a TA, I had a guy bring me an intercollegiate competition excuse form. He was going to miss some class because he was representing the school in ...

Basically their conclusion holds if their assumptions hold but they make no effort to show the assumptions hold and just state them as fact

a Meat and Carcass Evaluation Competition.

....how does one even evaluate such things?

Cow colleges are a hoot.

I've had students discuss cow & horse competitions where they had to "dress" them

But no one's asked for time off for that

I also make a game out of lab: how long does it take them to ask about my personal life

Current record for longest without asking is 12 weeks into a 13 week lab

A quote from the book on geeky stuff to build with your kids:

A sock cthulhu would be cool

It's actually really awesome looking

I had a stuffed cthulhu at one point in my life

Not sure where it's ended up

@KyleKanos As I understand it, the main procedures are to look, poke and sniff. But there is talk of bringing in some actual instruments any day now.

Let me see if I can get a screenshot for you

@KyleKanos Probably returned to Ry'leh

Sock Cthulhu

@dmckee Which I guess isn't much different from any sort of comparison competition

@ACuriousMind It's possible. Other options include my nephew having it or my wife having thrown it out

This book also has a design for what they call the "Mean Ass Jingle Bear" where you build a small electric shocking device inside a teddy bear. The section ends with:

Honest? As in, "I've done it before, it's not worth it"!?!?

That totally sounds like advice from personal experience

I like this book. There's actually some pretty cool stuff to build in it

Never heard of it...

Only Berkley physics series book I'm familiar with is the E&M II one (which just happened to be lying around the "ApJ room")

Wait...is that Purcell?

Interesting. Didn't realize it was (Amazon confirms)

It's the red copy, not the blue one

@ChrisWhite I prefer the contents of whiskey bottles entering my mouth, not the other way around

The burning TP would be pretty cool though

I really want to build a cloud chamber some time

@ChrisWhite The first time I read that I interpreted "TP" as "theoretical physics" and everything up to the dashes still made perfect sense.

In other news, it's 28 degrees but feels like 12 because we have ridiculous wind outside right now

It was 61 yesterday. Hit 67 on Monday

Yeah, gotta love the South when it comes to weather like that

After moving to the south, I'm not all that interested in moving back up north

@KyleKanos It's way, way, way better than the end of Jan last year when this happened:

@ChrisWhite Oh. I was talking about C...

Yeah, I remember the shut-down

My two older kids loved the snow for about 10 minutes

That photo was taken 28 hours after the snow fell

Then they wanted it gone

And that traffic hadn't moved

And which direction did the Mayor clear so that he could get to the Weather Channel?

Heh, the blocked one actually

The Weather Channel is about... 4 miles in the direction of travel there

It was something crazy. Like 500,000 cars stranded

The 65 mile loop of 285 was jammed completely the whole way around

My 25 minute drive took 4 hours and I was on the very short end of the time spectrum.

That sucks

Amazing that it was that bad

It was seriously nuts.

It's actually really, really scary. I mean, they knew the storm was coming days in advance. They claim they only knew hours, but whatever.

I don't even remember what it was like around here. I just know I didn't go to school for a day or two

Imagine if there was a real disaster. Earthquake, terror attack, whatever. Something unexpected

Nobody would be able to leave the city. It would be completely impossible.

Ooooh, or more recent

The pin-hole camera that shut down 14 lanes of the interstate for the entire rush hour:

11alive.com/story/news/local/downtown/2015/02/02/…

Took me 2 hours to get home that day

Yeah, I would grab my bike and go. Shoot between the cars

Especially here. The transit system is so horrendous

@ChrisWhite My favorite order-of-magnitude example is from the same book I referred to dmckee for gas dynamics. They estimate how many molecules of Caesar's dying "Et tu Brute?" breath we have in our lungs

> ... a man is known to breathe out about 400 c.c. of air at each breath, so that a single breath of air must contain about 10^22 molecules. The whole atmosphere of Earth consists of about 10^44 molecules. Thus one molecule bears the same relation to a breath of air as the latter does to the whole atmosphere of the Earth.

> If we assume that the last breath of, say, Julius Caesar has by now become thoroughly scattered through the atmosphere, then the chances are that each of us inhales one molecule of it with every breath we take. A man's lungs hold about 2000 c.c. of air, so that the chances are that in the lungs of each of us are about five molecules from the last breath of Julius Caesar

From Introduction to Gas Dynamics

And it's actually a quote from an earlier book: Jeans, 1940. "An Introduction to the Kinetic Theory of Gases"

I've heard that kinetic theory book is good

But I haven't picked it up

Of course it was reissued in 2009 by Cambridge. Just in time to keep the copyright from expiring

69 years into the 70 year copyright. Otherwise we could probably buy it from Dover for $10

I think the reason old books about topics are so good sometimes -- They are not nearly as "specific" and rely more on trying to describe the observations and physics of the problem from an intuitive sense

When I took turbulence, we used a book by Tenekes and Lumly from 1972 and a book by Pope from 2000

Both are really great books on turbulence, but Pope focused a lot on the structure functions, and modeling, and the derivations of the equations

T&L focused more on describing the phenomenon, explaining in words what was happening physically

And using things like scaling arguments or order-of-magnitude to explain what mattered and why

That's why I like the gas dynamics book. They really go out of their way to explain what is happening and why. Not just throw a bunch of equations and citations at you because they need to cram 30 years of really specific research into a book

@ChrisWhite Sounds like my experience with detonations. This book is the basis for all modern theory but he says in the book "Yeah, we have no idea what is going on and we don't see that changing"

And all the modern works say "We base it on this and yeah, we still don't know what's going on but we took 200 pages in various journal papers to say we don't know"

People use Rybicki & Lightman for radiation processes. Still not sure why, it's not that good because they swap variables and unit systems each chapter

I don't really understand the radiation bit too much. I vaguely recall talking about Einstein coefficients but it was at the end of the semester and we were all scrambling to learn the rest of the material

It was kind of an after thought

The intentionally make it confusing, which is just bothersome

I need to stop going into work at 5am. It feels like it's ridiculously late and it's not even 11pm yet

That is early

Yeah. I keep trying to adjust my life schedule so it's consistent. But the morning time adjusted, my bed time has not