#and wikipedia and stack exchange and some more stuff?

[sevenfactorial]

Hi! Can you tell some uni or colleges math resources?

Can you be more specific? Like resources for studying for particular undergrad level classes?

A few “classic” online references:

Paul’s online math notes (https://tutorial.math.lamar.edu/): algebra, calc 1-3, diff eqs though I’ve mostly only used the calc ones. A common favorite

Khan Academy: haven’t actually used any of their math stuff for years but I remember their videos were good

3blue1brown: he has a series on calc, diff eqs, and linear alg. I haven’t actually watched many of these either but his videos are generally good and I know people who like the series in particular

If you mean higher level math, I tend to just use a search engine and end up referencing a mix of wikipedia, wolfram mathworld, random pdfs from various universities, and math stack exchange. And of course textbook pdfs

If you give me more details, I’ll see if I can think of anything else!

[newtafterdark]

Taste of Metal - Chapter 5:  Reality Check

AO3 Link: https://archiveofourown.org/works/26157634/chapters/64305886

Summary: What if the overwhelming VR experience Gordon went through, had a deeper purpose than just being a simple simulation & a freelance debug job for him?

But most importantly- what if Gordon Freeman listens to Metal & used to be in a band? aka. the "Metalhead Gordon AU"

PS: This is the E-Bass mentioned in this chapter.  !t’s a real beauty, honestly!

- - -

It took Gordon a while to return to the others. For one, he always kind of zoned out for a bit when having a bath… and additionally, the reality of what had happened to him in the past few hours (or days? He wasn’t entirely sure and that unnerved him to no end-) had slowly started to sink in as well.

Zoning in and out of what was his reality now screwed heavily with his perception of the passage of time… and if getting his leg stuck while trying to slip into his comfort PJs and almost falling on his face added a few extra minutes… then that was between him and his checkered bathroom mat.

He rubbed the fabric of his dark floral-print pants between his thumb and pointer finger. It was a comfort thing. Always had been. Just something to help him stay in the moment with the help of adding the sense of touch when everything else was a tad clouded.

His still very much wounded arm was pressed lightly against his chest, the smooth fabric of the worn Nine-Inch-Nails shirt adding another layer of comfort to his current self-care choices.

Gordon hoped the Science Team would not question his comfort outfit… too much. It was just what he needed right now, as silly as the combo of rose-patterned pants & band merch might be.

His long hair was a mess as well. Yes, he had managed to get it clean and untangled most of the messy strands… but man, it was apparent that he needed to fix his undercut sometime. Right now though, he’d just have to deal with the state of his messy (and now also very fluffy post-hand-dryer) mane. Being able to run his fingers through it again and fluffing it up a bit further in the process... was a very nice thing though.

Gordon didn’t really look at anyone when he exited the bathroom and made his way to the couch- only to settle down on the floor, his back leaning against the front of the couch. He leaned his head back, staring at the ceiling.

“Do you- Do you feel a bit better now, G-Gordon?”, he heard Tommy ask from a few feet away. Gordon managed a soft smile and a nod in affirmation.

“I… yeah, I do. I am exhausted to all hell and back but… yeah. I think I’m actually here... if that makes sense. Don't feel as removed anymore. So… uh… thanks. Everyone.”

He lifted his head carefully, giving himself the time to catch a glimpse of each Science Team member in the room. G-Man must still be around as well, as the man’s ominous briefcase was still leaning against a nearby wall.

The silence that followed was not one of comfort, Gordon could tell. There was an aura of unease and worry in the air. Even from Benrey, who had been seemingly calm previously.

“Guys, I… I still have a lot of questions, not gonna lie. But… first I do want to thank whoever sweetvoice’d my stump. I… I don’t know how to react to my arm actually being gone and frankly….. I am actually freaking out slowly but surely… but still… thanks. Hurts less and all that.”

Gordon jumped a bit as a high pitched noise escaped Benrey, followed by a hiccup and the guard trying to sink further into the bean chair he was sitting in.

“Dude, you don’t have to swallow your Sweet Voice around here. I am way past freaking out about it, believe me.”, Gordon assured him, followed by a short laugh- “It’s actually nice. And helpful. I can fully admit that now, honestly.”

Benrey let out an orb of pink Sweet Voice at that.

“Glad it- that it helps, man. Wasn’t sure if it would... now that we’re all here in... uh, in person.”

Gordon lifted his injured arm carefully, looking the wound over.

“I still have no idea how it works… but yeah, it does help a lot. Again, thanks.”

“Welcome.”

…

Another moment of awkward silence was beginning to start when Bubby suddenly stood up-

“Can we stop with the sulking? Seriously?! We’re OUT! FINALLY! We should be going outside and having the time of our lives-”

“Uh-”, Gordon suddenly looked very alarmed-

“-steal a car! Go on a real goddamn road trip-”

“Bubby-”

“What?!”, the tall man almost hissed out, immediately regretting raising his voice as Gordon curled up a bit into himself at the noise- “M-My apologies. But you get my point, don’t you?!”

Gordon nodded at that, despite shaking a bit.

“I absolutely do! Hearing that you guys were legit locked up for god-knows how long… I would want nothing more than wanting to go outside and explore this world if I’d be in your shoes! It’s just... how aware are you guys of what has been going on on the surface for the past 10 years? Do you… do you guys even know what year it actually is?”

Tommy perked up at that-

“It’s 2020! Not all of us had a good grasp on time, but my dad and I do!”

“Me as well, Gordon!”, Dr Coomer added with a smile- “As much as we as a group had our jokes about Wikipedia, it was basically our only window to the world outside for a very long time. So thanks to it we do know about a lot of things… in theory.”

Gordon let out a short sigh of relief.

“O-Okay, that’s actually good to know- I mean, it sucks that that was all you guys had! But… at least we don’t have to start on nothing.”

“We’ll be perfectly fine dealing with the outside world, thank you very much!”, Bubby threw in, arms crossed.

Dr Coomer reached over and put a hand on Bubby's shoulder-

“Bubby, dear, I can still see us getting overwhelmed with it though. It might not be all new for me, but it is for you! And for Benrey as well. Do trust me that we all need to take this slow.”

Gordon slowly sat up, actually deciding to move up onto the couch, pulling one of his legs under him while stretching the other out.

“Guys… if you want, you all can stay here as long as you want.”, he said, earning himself a collection of surprised looks from everyone- “I know my place is small but… you saved my ass. I want to at least try to even that out by letting you stay for as long as you need.”

He ran his intact hand through his hair again, a few strands falling over his right eye.

“And I know G-Man said not to worry about what Black Mesa might do with you all on the loose now… but honestly, I will sleep better knowing you all are closeby and not in imminent danger. Call me selfish, but I’ve grown to like you guys. And I do care for your chaotic asses.”

Gordon went on, grateful for the patient silence the team graced him with at the moment-

“I need to be upfront about this and not bottle this shit up, so let me be absolutely clear: The shit that happened in the simulation? I do not hold that against any of you. Knowing the context of that whole thing… yeah, it was horrid, not gonna lie- but we all ran on fumes… b-but it was also kinda… cool?”, he added with a nervous chuckle.

“Like, how you all tweaked the code in small ways? It added up to such a chaotic mess that was hella stressful… but really fun to experience too? Like- Benrey!”

“Huh whu-?!”, the guard in question sat up in the beanbag, eyes wide.

“Your no-clipping for bits? Your entire goddamn boss fight?! It was terrifying and So. Fucking. COOL!”, Gordon explained, wildly motioning around with his intact hand and then looking at the others in the room one after the other- “Look, I didn’t really know what you guys’ deal was, along with this being a professional job, so I didn’t really get to talk about all the stuff I get excited about but MAN!!”

The entire gang turned at the sudden sound of a low chuckle coming from the doorframe to the kitchen. G-Man was leaning against it, a soft smile on his lips.

“I… am glad that it wasn’t as traumatizing for you as it could have been, Mister Freeman. I take it, you are quite comfortable with the themes you saw in the simulation, yes?”

He motioned at the walls of Gordon’s living room, causing the man in question to blush and curl up a bit into himself. The Science Team exchanged a few confused glances before taking the opportunity to actually take in Gordon’s apartment properly.

“Look guys, I-”, Gordon started in a slightly defensive tone, before suddenly getting stopped by Benrey’s hand on his chest. Gordon snapped his head up, staring at the guard- whose whole attention was focused entirely on taking in the apartment's aesthetic.

The furniture around them was a wild collection of thrifted items. Wear and tear showed on the dark wooden table and on the clunky shelves on the walls.

Several big moving boxes sat in the corners, stacked on top of each other. It looked as if they hadn’t been moved in months, as if Gordon had not bothered opening them after moving into the place whenever ago.

The couch, beanbag chair and the two additional armchairs had several patches messily stitched onto them. A dresser to the side had been painted with various spray paints… and had a ton of smaller tags written on it with dripping pens at some point.

All his was the base… but what left the team staring with wide eyes were the small decorations of the place. The walls were absolutely plastered with band posters. And not the kind they would have expected from Gordon-

Countless of them had hard-to-read fonts on them, flames, lightning… and the number of bones and skeletons were honestly a bit overwhelming. Especially Benrey, who was now letting out a constant stream of excited-sounding Sweet Voice.

The skeleton theme actually continued with the other decorations around the room as well. Several different skull-themed items sat on the shelves, really putting the room together. And not cheap-looking stuff either! Some of them had a metal finish, others were carved out of wood and a rather big amethyst skull divided Gordon’s decently-sized DVD and Video Game collection.

There was what could only be described as faux-taxidermy all over the place as well. Small bottles labelled with things like “void eyes” and “dragon blood” instantly drew Darnold’s attention.

Dr Coomer ended up walking up to the wall-mounted dragon head with a colour-changing skull in its mouth and just gave it an approving nod.

Bubby, however, was still scanning the band posters until- “GORDON?!”

“Y-Yeah? Wha-”

“YOU PLAY ELECTRIC BASS??? AND YOU DIDN’T TELL ME?”

Gordon grinned and got up, walking over to where Bubby was standing.

“Oh yeah! That’s my old Fender! Haven’t touched that babe in a good while… probably needs a bit of re-tuning, now that I think about it...”

Bubby shot him a look-

“I repeat: you play e-bass???”

Gordon let out a warm laugh.

“Yeah! Sometimes guitar too, electric and acoustic. Just haven’t really had a reason to in a while.”

A pained expression suddenly appeared on Gordon’s face. “Not like I will again anytime soon, you know?”, he added, lifting his stump.

Bubby waved him off.

“Oh please. Harold told you he has a plan to get that “fixed”. Trust him on that. He doesn’t break his promises. And his work is extremely high-quality and responsive. You will be able to play again with no issue.”

Before Gordon could reply to that, he suddenly felt a hand on his healthy arm, only to find Dr Coomer right beside him.

“Indeed, Gordon! You will have a proper prosthetic arm in no time! Well… I hate to admit that the entire process will probably take at least a full week.”

“Oh! T-That’s still extremely fast! I… I don’t even know how to thank you for that, Dr Coomer. Do you need any specific tools? I think my computer building tools should be around here somewhere-”, Gordon rambled on, only to be stopped by Coomer’s laugh.

“Oh Gordon, don’t worry! I’ll be able to find everything I need with ease! Most of it I already have! I plan on stripping your VR Suit for parts, you see!”, the older scientist explained to him- “You go sit down and let yourself relax and heal. Which is something that needs to happen before I can even think about fitting the prosthetic properly to your arm anyway! I am sure Benrey’s Heal Beam will be of much-needed assistance with that in the following days!”

A loud “HELL YEEEEAH” was heard from the other side of the room.

Gordon chuckled.

“Alright then- uh…. Do you guys want some snacks and get comfy? I think I still have-”

“Mister Freeman… I took it upon me... to get that covered. I hope you don’t mind too much.”

G-Man walked into the living room with a big baking dish and wearing Gordon’s flame-print oven mitts.

“G, my good man, you will never hear me complaining about such perfectly baked Mac’n’Cheese- oh shit, is that sliced ham in there too?”, Gordon stared at the perfectly brown cheese layer on top- “… yeah, you are allowed and encouraged to cook whatever and whenever you feel like it while you’re in my four walls, holy shit.”

“Ah… thank you for the high praise Mister Freeman, but-”

Gordon shot G-Man an unimpressed look, which startled the taller man a bit-

“Alright, Rule Numero Uno of Hotel Gordon: You will be complimented here and you will take it. That goes for everyone here. Yeah, sometimes we will get salty over things, as we have before… but guys, here comes a fun IRL fact about me: I am aggressively supportive.”

“G-Gordon, I am not sure that is needed-”, Tommy stammered out, only for him to slightly freeze as Gordon turned towards him with an intense stare-

“Oh? Wanna test me? Think I won’t say that I still deeply appreciate how you selflessly dragged my sorry ass along when I was too weak to walk on my own? That you had my back in ways that I will be in debt for until the end of my life? You sure??? Absolutely sure?”, Gordon said, grinning and pointing a finger at Tommy… who was now hiding his face behind his hands, letting out a soft “buuuuuuh” sound, followed by a flustered laugh.

Gordon looked at all of the Science Team with an affectionate glint in his eyes. It felt so good to actually be himself around this chaotic bundle of people he learned to care for so deeply.

[goonlalagoon]

The Great Haus Bake-Off || Check, Please!

I have no memory of what caused me to start writing this, but been re-reading some Check Please fic and finally got motivated to go back and finish it...

(also on Ao3 here)

No-one was quite certain, later, who started it.

 It had been a post-practice brunch, they all agreed, sometime in that period when everyone on the Internet - or at least, about thirty percent of the parts of the Internet that Bitty frequented and re-tweeted things from - was obsessed with Great British Bake Off, and someone had eventually said “It’s baking, it isn’t like it’s exciting”, and it seemed like almost everyone in the room made a sound of thoughtless agreement.

Then came the terrible ‘clang’ of an oven door being closed.

 Instantly, the room fell silent. The look Eric Bittle turned on them all would freeze enough water for an ice rink, and for a long moment everyone at the Haus kitchen table was both trying to remember whether they had said the terrible thing, and wondering with deep seated horror whether if no-one owned up Bitty would actually withhold all baked goods.

 Chowder actually gulped when he began to smirk.

 “Oh, really? Y’all better be ready to put your money where your mouths are.”

It’s really only supposed to be a small thing. Bitty plans to just get the boys to try and make something - maybe a pie, or maybe he’d give them something fancier, patisserie of some kind - which they would all inevitably fail at but would probably make fools of themselves in some deeply entertaining fashion while baking. But Lardo listens to him patter on about it for fifteen minutes, swallows her pie, and grins.

“Say, Bits? You reckon we could turn this into a Samwell Men’s Hockey publicity thing?”

 They even manage to get a sort-of sponsorship out of it by dint of Lardo sidling up to the manager of the cute little store Bitty goes to for baking apparatus - he’ll compromise on many things for the sake of budgeting, but when he needs another pie dish or his scales go on the blink, Eric Bittle is not afraid to invest - and cheerfully explaining the entire story. The manager is delighted and insists on being a judge in exchange for giving them a deal on some of the key equipment, because Bitty loves his teammates to pieces but wouldn’t dream of letting them near his mama’s set of cake tins for love nor money.

When the delivery arrives he discovers that the manger has even managed to get them cake stands patterned with skating boots and little snowflakes.

One of Lardo’s arty friends agrees to film it in exchange for permission to submit it as part of his film and media portfolio, and Bitty indulges himself in a full rerun of every episode of Bake Off aired so far to gather ideas.

Lardo joins him for most of it, already planning the spiel she’s going to stick up on the SMH website to cover the event and organising a few people for taste testing (with a guarantee of a Bittle produced rendition of the days challenge in case all other offerings are truly inedible as they both half suspect they will be)

 Meanwhile, the rest of the boys begin to panic. Baking is not a skill that was widely associated with the SMH Haus before the arrival of Bitty, and their main interaction with baked goods is still firmly on the consumer end of things.

Ransom is seen carrying a stack of cookbooks up to his chin across campus from the library, and spends his evenings memorising recipes with the fervour he usually saves for last minute test revision. No-one quite dares use the Haus kitchen to practice, because what if they damage Bitty’s baking stuff he will either cry or kill them or both, and take over miscellaneous dorm kitchens to try and memorise the basic sponge recipe. A bemused Farmer lets Chowder use her kitchen, and promptly tracks down Bitty to ask what on earth is going on, because “he accidentally used salt instead of sugar and I know for a fact he’s done that several times before, why is he trying to bake again now??”

(She joins in with the GBBO re-watch and makes some excellent suggestions for possible challenges.)

Shitty attempts to make macarons, because he suspects that Bitty is going to make them all suffer. He pokes his failed attempt and concludes that Bitty may be prepared to make them all suffer, but he also loves baking too much to inflict this level of horror on himself, surely?

He largely stops trying to prepare himself and instead starts waxing lyrical about baking in the context of gender roles, mostly the hypocrisy that being able to bake a cake is still considered an essential life skill for a girl, but no one has ever thought it unreasonable that he has never baked a cake before in his life, and winds up on Wikipedia at three fifteen A.M. having gone down a Google rabbit hole that has somehow led to him reading the page about the societal structure of meerkats.

 In the end, Bitty decides on three challenges, as a nod to the format and a fun way to get some variety; cookie decoration (he’ll provide the prepped dough, bake ‘em once everyone’s used whatever cookie cutters they want, and then they do the decoration), mini-cake construction (everyone gets a batch of miniature sponges, their choice of how to glue the two layers together and add finishing touches), and one actual baking round - the showstopper pie.

Lardo makes a schedule, because the Haus kitchen won’t take all seven of the team who got themselves into this mess trying to work in it all at once, so that they rotate between stages and go in batches to Murder Shop ‘n Stop to buy their pie filling ingredients.

 It’s a disaster, and Bitty watches the chaos unfold with entirely unconcealed glee, keeping up a cheerful voice over - and if his chirps happen to distract the boys and lead to much panicked responses and second guessing, well, that’ s just the nature of baking in a high-pressure environment, isn’t it?

The first round of judging involves a lot of guesswork. Admittedly, Chowder’s blue and white creations are a lot easier to figure out if you’ve seen the inside of the boy’s room and could reliably guess what he was going to attempt, so there are a lot of puzzled looks exchanged amongst the judges until someone makes the link with the Sharks hoodie he’s wearing.

It turns out that Dex can do a pretty neat galaxy icing pattern if he puts his mind to it, even if he got the consistency wrong; Bitty may actually have to try it himself, sometime.

(”Jack, did you…did you actually do maple leaf cut outs with a maple glaze? That’s…”

“Gotta stay on brand, eh? And I was told I wasn’t allowed to do plain circles and decorate them as hockey pucks.”

Most of the minature sponge cakes are gradually sliding more and more lopsided as the various attempts at butter-cream or other fillings prove unable to hold. Holster has somehow managed to cut his at almost a perfect diagonal instead of in half; Nursey simply gave up and presents his as an ‘open sandwich’ rather than trying to glue the layers back together.

 (“Shits, what did you even put in the middle of - is this marmite? Did you - did you seriously - why?”

“Listen, love it or hate it, and I happen to love it. Sweet and savoury, a classic combination -”

“Marmite victoria sponge is not a classic combination, Shitty.”

“I was told to be creative, thank you very much, unlike those of us who went with jam and butter-cream.”

“I like jam and butter-cream. Anyway, I did use apple jam, that’s not typical. And I put maple syrup in the -”

“Bro, I am also from Canada, and even I will say that is incredibly Canadian of you.”)

Bitty almost weeps when he sees the final range of pies produced. He was braced for them to be terrible; he just wasn’t quite prepared enough. For a moment, he wonders if this whole stunt was really worth it.

 Fillings are burnt while pastry is undercooked to the point of being raw - or the filling is horribly flavoured and the pastry overcooked until it’s about the consistency of wood chips.

Ransom has managed a surprisingly pretty lattice over three-quarters of his pie, but ran out of pastry for the last section. Chowder forgot to leave air-holes in the lid of his (and put salt instead of sugar in the filling).

Nursey isn’t sure what ingredient he forgot, but it was clearly one of the essential ones.

But there is one pie that actually looks…if not something that Bitty would have baked himself, at least something he wouldn’t be instantly offended to be connected to. The lid is a near perfect golden brown, with precisely spaced snips to let the steam waft gently out. The pastry is precisely crimped around the edge of the pie dish, with the excess trimmed away to leave a clean margin. The filling is sweet but not sickly.

 The decorative pastry maple leaves add a certain artistry, the main judge declares with the pleased smile of someone who knows they were created with a cookie cutter bought from his own shop.

The video of Jack being presented with an ice-skate patterned cake tin and a matching apron as he’s declared the ‘Samwell Hockey Haus Bake-Off Champion gets re-tweeted by Bob Zimmerman within five minutes of being posted, to a flurry of Twitter activity.

Lardo and Bitty were definitely not expecting their slightly-spite-motivated publicity stunt to go quite this public.

 (It was a really good pie, though.)

[seventhsunflower]

this stack overflow stuff is really going wayward.  i was caught completely off guard about the whole website being turned upside down.

so after some digging...based on this post, it sounds like there was a retroactive (and possibly illegal) content license change (also referenced here ) that a bunch of the mods disagreed with, vehemently. 

moreso, it’s turning out SO has been making big changes recently, and some of those have not been well received. 3 months ago they changed the homepage in a way that pushed visitors too aggressively towards making an account. one week ago one of the founders was replaced as CEO, which was seen as a sign that SO might be putting more emphasis on the business side of the website and less on the community.  as anyone can gather, this is all late-stage captailism rearing it’s ugly head in the wake of a leadership change initiated to seek more effective ways of monetizing the platform.

which gives context of the influx of of recent resignations regarding the new Code of Conduct (CoC) and the new licensing.

the new CoC (which AFAIK is not out yet, but soon will) has some interesting clauses in it, and mods that raised objections towards them were demodded/fired.

the licensing issue, on the other hand, is that SO has forcibly relicensed all content in the website (fucking what?). the change by itself is not major, but 

a. this is not how licensing work, and 

b. it's uncharacteristically aggressive.

all of these points indicate a very strong change in the internal culture of the site, and many mods are protesting in return, because, again, what the fuck?

a big thing about stack overflow is that its an open source knowledgebase like wikipedia.  people use code from others to help fix software problems.  going on with the licensing: if person a writes a program using code they obtained for free from stack overflow, and the license previously said that anyone could freely use the code to write whatever program they want and then sell that program to make profit for themselves. its been postulated if stack exchange can now say "oh, anyone who had previously gotten code for free off our website that is in a program you are selling, you now have to start paying us, otherwise you can't sell your program anymore and we'll sue you if you try to keep selling it"?

luckily, CC BY-SA 3.0 and CC BY-SA 4.0 are irrevocable licenses. if the author/publisher later revokes the content, it does not revoke your license.

one of the mods (monica cellio) was also apparently fired because she was asking questions (probably like this) about the licensing changes. it was this incident that kicked off the other resignations.  mods resigned over a mod getting demodded for asking questions about another pending change... because, really, stack overflow?  really?

ancient internet history does relay that wikipedia also had a license change from GFDL to CC... the difference is that WP was still open-sourced. there was a discussion about changing licenses, and folks were free to fork into another site using the old license if they wanted.   that change was legal, was made by referendum, and with good justifications — and was towards a license that the community felt was more appropriate for wikipedia.GFDL certainly has its flaws, CC-BY-SA was felt to cover for those flaws in a way that worked well for the platform. 

and SO, one of the most resourceful places on the internet (it’s reddit and wikipedia molded into one for programmers -- which, hello, most of our existence is being shifted towards software), hasn’t taken this route at all.  in fact:

staff make several statements explaining things to the press (e.g. the Register) instead of on Stack Exchange

staff make ill-judged "we're sorry you feel that way" canned responses

multiple volunteer moderators resign for a variety of subtly different reasons

a well-respected volunteer moderator was terminated in a disrespectful manner

(non-public) New draft changes to the Code of Conduct are both objected to and questioned for clarity

the remaining co-founder of the site is replaced as CEO

a legally-dubious retroactive change to all content licensing is suddenly announced, with no justification or response to concerns

staff admit that they don't consider browser fingerprinting or animation in their adverts to be a problem, contradicting previous assurances

and it’s all just *ugh*

[thingsillneverdomyphdon]

The Equivalence Principle

The Equivalence Principle is a thing that’s so fundamental to your everyday life that you never even realize it’s a thing, or that it’s weird that it’s true. Here it is:

Inertial mass and gravitational mass are the same.  

This means that if you want to push a heavy curling stone across the ice*, you can figure out the amount of energy you’ll need by how much the stone weighs**. Now, what just happened when you read that sentence is one of two things. Either you thought:

“I have no idea what you’re saying right now,” or

“Yes, doy. And?”

In either case, I’d say that’s due to the fact that you already completely intuitively know this, so much so that you don’t think it’s weird. But it is weird.

*In this example you are, like, totally Canadian.

**Almost. Ice still has a little bit of friction.

When I tried to explain this to Laurie we ended up talking about Randy Johnson floating in space holding a baseball that was made with lead inside instead of cork, and him being all, “What the fuck?” when he tried to throw a fastball. Then we got hung up with how it would be hard to throw a fastball in space because there’s no gravity and you can’t push off with your legs. The point being, I haven’t yet figured out a way to give someone an intuitive sense of this thing which is so fundamental to your everyday experience that you don’t know that it’s weird. It’s like saying, “isn’t it weird that a thing weighs exactly the amount that it weighs?” Except right now there are physicists at the University of Washington trying to measure whether it’s actually true or it just really, really seems true. It is apparently critical to a lot of unification theories that it almost, but not quite, be true.

My first step with this project, as it is with most things, is to develop an intuitive sense of the things we’re dealing with. So, for instance, I needed to understand why, in the Newtonian model, a person in orbit doesn’t feel the force of gravity pulling on him or herself (the answer to which turns out to be really interesting and non-obvious--you don’t feel it because the center of the Earth pulls on all your atoms more or less equally, so nothing compresses or expands in your body--i.e. there’s nothing to feel. Then, through a series of conversations with an actual Physicist, I learned this incredibly interesting thing: if you had a really, really accurate sense of balance in your ears and the mass in your body were unevenly distributed, you could “feel” being in orbit. This blows my mind).

And this is where I’ve run into this thing which right now is blowing my mind. At the top of the Wikipedia page about the Equivalence Principle is this quote from Einstein:

A little reflection will show that the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the acceleration imparted to a body by a gravitational field is independent of the nature of the body. For Newton's equation of motion in a gravitational field, written out in full, it is:

(Inertial mass) (Acceleration) = (Intensity of the gravitational field) (Gravitational mass).

It is only when there is numerical equality between the inertial and gravitational mass that the acceleration is independent of the nature of the body.

The first thing you notice, if you’re me, is the fact that the above equation doesn’t imply that conclusion at all. What he’s talking about is that in Newtonian Physics, there are two equations related to Force that are relevant when something is falling. There’s this:

\[F = \frac{GMm}{r^2}, \] 

and this:

\[F = ma. \]

Einstein is saying, since those both apply, the ‘F’ has to be the same. So the other two things on the opposite sides of the equal sign have to be equal, that is:

\[(1) \frac{GMm_g}{r^2} = m_ia\]

Now I’m writing \(m_g\) to mean “gravitational mass” and \(m_i\) to mean “inertial mass”. Galileo proved, by dropping stuff off the Leaning Tower of Pisa, that the \(a\) on the right-hand side is the same for everybody (big things and small things fall at the same rate), and it also happens that the other things in the other equation (the mass of the Earth \(M\), the distance to the center of the Earth \(r\), and the Universal Gravitational Constant \(G\)) are also the same for everybody. But, mathematically speaking, that doesn’t mean that therefore \(m_g\) and \(m_i\) are equal. It just means they’re proportional in some way (like, maybe \(m_i = 2m_g\)). 

But no, Einstein said he looks at the equation I have labeled (1), also knows the fact that everything falls at the same rate, and he knows that gravitational mass and inertial mass are the same. I don’t see how he can know that. Moreover, it is nowhere mentioned in the Wikipedia article that this is weird. I realize most of you have no idea what I’m talking about right now, but it’s as if I were literally the smartest person in history and wrote this equation:

\[ 9.8x  = 98cy\]

where c is any constant number I want it to be and claimed that since the value of 9.8 is completely independent of x, and I can make c = 1/10, that x must always equal y. It just isn’t a valid conclusion. 

If you follow me as a thinker of thoughts in the world, you know that I have a principle that applies in this situation which I have named, “The Undergraduate Misconstruction.” If I look at something that was said by a smart person and think it’s stupid, I am concluding that either a) this historically smart person said something stupid that has been misunderstood by everyone except me, or b) I am the stupid one. The odds of a) are incredibly low (in fact they are zero) and the odds of b) are incredibly high (in fact they are one). So I must conclude that Einstein has an extra intuitive sense about the equivalence of inertial mass and gravitational mass--something that was so obvious to him that he didn’t even bother to mention it. That is, when he says “look at this equation and observe this thing,” there must be something else he sees that I don’t see. 

I spent a year in math graduate school at The University of Wisconsin. There I encountered professors who were so brilliant that they thought everything--like, you know, Algebraic Topology--was intuitively clear and obvious. They also thought that everybody just understood what they understood. These guys were, as you might imagine, absolutely terrible teachers. My best guess is that this is the case here. So now I am on the hunt for an intuitive sense of something that, at least upon first investigation, seems rare and hidden. Asking the question on the Physics Stack Exchange got me nothing, so I’ve turned to the Astrophysicist that I’m currently corresponding with. Updates on that as I get them. In the meantime, I’ve started in on the General Relativity book, so I’ll probably start blogging about that next time.