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castrian-amore · 10 months ago

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Bitter had the Heart

Dead Tired(Tim Drake x Danny Fenton), Tim Drake-centric, unfinished, the author is plotting, temporary character death, please check out ao3 for full tags list

3/46 Chapters | Chapter Length: 3584 words

Chapter 3: We are Not Translating Fanfiction

Tim didn’t understand why he had even picked this class for this particular credit. He technically didn’t need it. Then again it seemed more interesting than the other classes and Tim had been hoping for a challenge for once. The teacher was big on working as team and while, yeah Tim could do it. He preferred to work alone on his topics and thankfully there was an odd amount of people in his class so when he requested to do the group assignments he allowed it.

Until today.

One Daniel “Danny” Nightingale, was a late transfer into the class for unknown reason. It was also the mysterious kid in the alley. He looked a little better in person but the vote was that he was definitely sick, whether just right now or long term had yet to be determined. He leaned heavily on a cane at the moment walking with a heavy limp.

Tim could point out his handsome features though. The higher cheekbones. The stunning raven hair, his piercing blue eyes. The kid definitely wasn’t immune to the streets. The way he held himself on the verge of running. The sunken wary eyes. This kid was far too comfortable with living in fight or flight mode. If he even knew anything else it would be surprising.

The teacher pointed to Tim giving him the spot right next to him advising sitting next to the person he would be partnered with. It wasn’t required by any means but it certainly was an option, and he did.

“So, now that that’s out of the way, where was I? Oh yes the IPA. The International Phonetic Alphabet.” Professor Kaivan began his speech as Danny pulled out a piece of notebook paper and pencil sitting next to Tim.

“Uh, hi, I’m Danny,”The kid held out his hand and Tim shook it. A cold chill going up his spine from how cold he was, damn.

“Tim Drake-Wayne,”he introduced with ease, expecting the man to back away or at least move seats because of his name. The Wayne name caught most people off guard but Danny seemed unfazed by it all. In fact he didn’t even flinch or stutter or reel at who he was talking to even.

“Nice to meet you Tim,”Danny gave him a bright smile. “Apologies for having you stuck with partnering for me after I’m already a late transfer.”

“No issue. Can I ask why you had to transfer?”Tim raised an eyebrow at the man. Their words quiet as the professor droned on.

“I was in Latin, and I can fluently speak and read latin. The professor kept getting things wrong and I kept correcting them. They kept insisting because they’re the ‘professor’ but I kept insisting I was right, which I was. She didn’t like that so she kicked me out. She got so annoyed she refused to teach me. Thus leaving me with about to loose my credit I really needed this semester so I asked if I could late transfer into another language based class.”

“And here you are?”

“Here I am. Only teacher that was willing to give me a chance.”

Tim snorts a little. Tim had only almost been kicked out of a class one, and that was one of his law classes. Tim kept correcting the professor over and over and over again, and it kept pissing off the professor so bad. Tim had a sneaking suspicion he was going to like this guy. He just hoped the guy was as intelligent as he seemed.

Being fluent in a dead language was no easy task. None of the bats were fluent in a lot of dead languages but they all knew several spoken languages and a little of a few dead ones. Tim more than others. Books were always his specialty. He preferred to spend the house researching alone in his room or the bat cave. It was part of the reason the other claimed he had a coffee addiction. He did not by the way. He didn’t know what Dick was even talking about.

“Professor Kaivan is pretty relaxed about that kind of stuff. He assigns minimal homework and prefers to do the group projects over everything else.”

“Yeah his rate-my-professor score is pretty high.”

“Sounds about right,”Tim agrees, turning back to the topic at hand for the moment.

“Now, learning the International Phonetic Alphabet is not for the faint of heart. Having someone to listen and assist when learning this is vital. One of the many reasons everyone in this room has a partner. Learning it is vital for the rest of your success in this class. Breaking down specific sounds a language makes and making it easy for everyone to read any language in this format.”

Professor Kaivan was an interesting man. Until four and a half years ago he had some of the worst rate your professor scores, but it was rumored that after the death of his partner he sobered up and wanted to help people. Since then, he has been a great teacher. Using his partner method to teach people, becoming a caring professor, giving students days in class to study and work on whatever work needed to be done. He wasn’t a super hard professor to have.

His hair was graying as the man was into his late 40s going on 50s. Sideburns and his beard graying though. He dressed pretty chill too, half the time coming into class wearing a casual cardigan and a beanie. He was an accomplished guy with a full on doctorate in linguistics. Masters in Psychology and bachelors in the study of Italian. Most of his focus seemed to be on the intricacies of the Italian language but Tim was fluent in Italian and didn’t care to take any of his italian classes. Not that the man had many.

“I know the 107 letters can be difficult and if you don’t know what to listen for they can sound similar to each other, but that’s why this whole unit is just on breaking down the IPA, and making sure all of us can read, and understand it. Okay?”

Mummers of okays and yesses echoed through the lecture hall. Tim opened his phone, scrolling to Dick’s phone number and clicking on it.

Timmy Boi: Guess who just walked into my Linguistics class as a late transfer?

Dickie Bird: Who?

Timmie Boi: Alley kid

Dickie Bird: No fucking way. Is he that rude in person?

Timmie Boi: No not yet at least. We’re partnered up for the semester though, so plenty of time for me to find out heh. Dude’s got a cane.

Dickie Bird: So not our so-called mystery vigilante Jason wants us to meet?

Timmie Boi: Unlikely, He also looks sick as a mother fucker Dick. Like it’s bad.

Dickie Bird: Damn, so still no leads until Friday?

Timmie Boi: Unfortunately not. Cams still distorted as fuck with those symbols?

Dickie Bird: Just like all the others. Only copies we have are hand drawn references. No one can get a clear pic.

Timmie Boi: Anyluck on the Distortion dude? Anything on him?

Dickie Bird: Uhh, he showed up 3 years ago? Works for Jason mostly. Started as a runner, then became body guard and personal protection for a lot of the shipments going in and out of Jason’s domain. That was only after bribing over 15 inmates too.

Timmie Boi: How the fuck did Jason keep someone, a meta namely, from us for so long?

Dickie Bird: Who knows. One guy said something about protecting a child. The child is Jason’s guard dog. Brutal when he needs to be. Maybe he’s scarier than he looks? People kept quiet over fear?

Timmie Boi: You’re the people person, but even then if people are scared we would have heard something else. I just think we have something else in the picture here that we’re missing it all.

Dickie Bird: Well, any cameras he passed by that night went to static. I had Barb check it out for us.

Timmie Boi: So his gift can mess with cameras? Only mildly concerning.

Dickie Boi: Wait, why are we having this conversation right now Tim? You’re in class?!?!?! I’m leaving you alone. Pay attention, and don’t fall asleep, and DRINK WATER FOR ONE IN YOUR CAFFEINE ADDICTED LIFE.

Timmie Boi: YOU CAN’T STOP ME DICK. I’M GETTING COFFEE RIGHT AFTER THIS.

Speaking of coffee, he could probably get mystery-dude’s phone number for their homework and stuff. Maybe he could even get coffee with him and help him with his classes. And maybe find out more about that night in the alley.

“What are you doing after class?”Tim spoke up to look over at the man. Danny wasn’t even paying attention to the lecture. He was… drawing? Way better than anything Tim could draw that was for sure. Maybe he would get along with Damian? Tim liked the easier stuff, taking pictures. He could draw but he didn’t like it nearly as much as being able to get behind a camera and take some beautiful photos. Man, he should get back into that again. Dick was always pressing him to get back into a hobby outside of crime solving. He liked to stick with what he was good at though.

“Oh? Uh nothing really, just contemplating existence. Why what’s up?”Danny gave a soft shy smile. Oh no. His smile was cute. Also wait, contemplating existence?

“Well, I figured if we’re gonna be stuck together all semester we could get coffee and talk about the project and get to know each other a little better.” Tim could watch a wave of anxiety slip over the man.

“Well, I don’t know maybe,”a small shrug then a quiet moment of contemplation. “Actually, sure that’d be nice!”

“Great!”

“Wait, we already have a project?”Danny’s eyes widened looking from his doodle of something? Tim couldn’t make it out but it was pretty? Looked like a pool of swirling water sketched in a gray scale. Who knows. This guy must have been so distracted he didn’t hear the teacher’s words about their project. Rewriting a speech in a non-english language into the phonetic alphabet.

Tim couldn't help but laugh a little at him.

This caught a small look from the teacher and Tim stifled his laughter a little even as Danny began to fight his own laughter as the two looked at each other. That was so dumb. Why was he even laughing at that?

“I’ll explain after class.”

“Sounds good to me, I’m just sitting here… doodlin’.”

“I see that..” Tim gave him a smile as Danny chuckled himself turning back to his drawing. The man stretching his arms upwards turned to actually pay attention to the teacher. A small frown coming across his face noticing the thin spindly scars edging up the side of his neck across the back of his neck. What the fuck was that? He shook his head.

Tim stayed mostly alert the rest of the hour long class. Kaivan had started going through the various letters of the IPA and their origins and why they were chosen. It was interesting to say the least. He had learned a lot and the class was definitely different than what he was used too. Danny on the other hand.

Fuck Tim hoped the dopey smiles and spaced out stared was how he payed attention or their partnership was going to be a lot more strenuous than he originally thought. He swore he saw him falling asleep a couple times there before jerking himself awake. Not that Tim could blame him. He averaged only about 3 hours a night if he was lucky. Then again, Tim didn’t exactly play the whole “catch up on sleep” game.

It did take a gentle nudge from Tim to get the man away and on their way to the coffee shop. He was slow as he walked with the cane but Tim didn’t say anything about it. Everyone had their little quirks and issues. Lord knows Tim had his.

The cold autumn air in Gotham was settling around them.

“What’s your major?” It was Danny who spoke up with a quiet smile.

“Oh, business. I plan to take over my father’s company,”Tim replied.

“Wow, impressive.” Danny looked up at the sky with a small chuckle as Tim raised an eyebrow at him.

“Thanks, what’s yours?”

“Engineering, I was going to do Astronomy but we’ll the Gotham Skies aren’t exactly the clearest.” Danny chuckled softly as Tim gave a nod.

“The smog helps no one. Glad you found a major you like though.” There was a silence settling between them but it didn’t lessen the mood in fact it almost felt welcomed in a quiet way.

“Same to you!” Danny looked up at the crows stopping the duo in their tracks. There were almost 10 crows just watching them. Tim, had never seen that. All them staring at Danny. “Boo.” The man whispered and with a small chuckled, all 10 flew off the branches and into the air leaving Tim to watch and then follow. Missing how the birds simply landed up ahead.

Tim was sort of lost in thought about the revelations they could possibly have about the whole Distortion situation.

“Heyo, Timmy,”Danny’s voice dragged him from his thoughts and his slow pace holding the door open. “Don’t hurry up and you’ll be soaked.” He hadn’t even noticed a slow drizzle starting to fall from the sky. He held his hand out before running to meet the man.

Tim joined the man into the warm coffee shop. The scent of pumpkin spice filling their noses as they moved to get in line.

“Didn’t get too wet did you?”Danny asked concern surprising Tim.

“Ah, no, don’t worry about me though. I might be more concerned for when we leave here though.”

“I’m not too worried.” The man gave a nonchalant shrug. “Can’t kill me worse than I already have been.” Was that a death joke?

“Oh?”Tim gave a smirk. He wasn’t normally one for puns, those were Dick’s thing but also… Dick wasn’t here. “Did it have you rolling in your grave?” Dick could never find out about this but then Danny’s shit eating grin only widened across his face.

“Oh, for sure it was to die for after all.”

“I can’t I’m sorry,”Tim laughed with a smile. “What’re you getting? I’ll pay since I invited you out.”

“Oh, I might scare you with my order.”

“I promise you won’t. Mine is insane myself.”

“One of those extra large pumpkin spice lattes with 10 shots of espresso.”

“Extra large americano with 8 shots of espresso,”Tim quipped. “I see you’re a man just as insane as I am.”

“Oh, for sure. I’ve never met someone with an order just as bad as mine,”he admitted as he stared up at the menu. “How are the sandwiches here? Are they pretty dead-licious?”

“Oh god..”

“Or I don’t know, pretty frightful?”

“Please Danny.”

“I bet they’re boo-mbastic.”

“Who ever uses that word anymore.”

Okay Halloween was coming up admittedly. Yes there were halloween and fall decorations coming but, but god dammit Danny. It was like having another Dick around.

“You decided to fuel this.”

“I did not decide to fuel anything!”Tim complained just as they got to the counter ordering their coffees. It was a barista Tim was familiar with. A kind girl named Sarah who seemed to be all too familiar with the two of them.

“Oh! Can I also get the mac and cheese please!”Danny offered another charming smile putting some money in the tip jar. “I can pay you back Tim.”

“No worries.” Tim gave a shrug.

“Alrighty and here you are Tim.” Sarah handed him his card back with the receipt as he himself put some money in the jar.

“Damn, she knows your name?”

“I know you too Danny, Mr. 10 shots of espresso at midnight last week. You also fucking work here.”

“Love you guysssss, and I don’t know what you’re talking about.” Danny practically purred out with an innocent smile.

“You two together, scare me,”the barista motioned between the two of them. “But honestly, we were waiting for you two to meet.”

“I’m innocent,”Tim vouched.”Also wait, what?”

“I watched you order an extra large cup with only espresso shots in it for Finals last semester.” Sarrah refused to answer the apparent group that had been waiting for Tim and Danny to meet each other.

“I was busy!”

“You weren’t sleeping!”

“Anyways I’m going to go over there,”Danny pointed to an empty table by the window.

“Yeah, Tim. How about you go over there. With your little Date,”She emphasized the word as Danny was already over sitting down unpacking his backpack onto the table.

“He’s not my date! We literally just met!”

“Yet. Next in line please!”

“Sarah-- no-- I swear to--”Tim could have sworn he saw an exchanging of cash behind the counters. Were they betting on something. What the fuck were they betting on?!? He hissed and moved to join Danny in the opposite seat.

“So did you even catch what the group project is? How much have you studied of the Linguistics 101 class anyways?” Tim pulled out his laptop setting it in front of him. He logged in giving a small smile of the silly chaotic and group picture they had gotten last year at Christmas. Bruce stood on the far right and Jason on the far left Dick’s arm wrapped around his shoulder. Damian was trying to stab Tim again who was moving to dodge it. Steph chaotically cheering the gremlin on. Cass quietly wondering if she should intervene in the middle. Duke full on panicked at what was going on as it was his first Christmas with the family. Barb covering her mouth in laughter in front of Bruce. He wanted to make sure she was included. It was his favorite photo of him and his siblings.

Fuck. Danny had been talking to him.

“Earth to Timmy.” A wave of a hand in front of his face.

“Please just Tim,”he laughs. “Sorry, yes?”

“I was asking about the IPA. Are you familiar with it? I have no idea on anything about it.”

“I know like half of it? I’ll have to learn the other half,”he admits. “But yes, the project.”

“Fuck, yeah okay what’s this project?”

“It involves reading.”

“No! WHY!”

“In another language.. That neither of us speak.”

“Oh god.”

“Yeah, so we’re supposed to write down a 1,000 minimum word speech, or chapter from a book or whatever and put it into the International Phonetic Alphabet.”

“I don’t know about you but I speak a lot, like A lot of languages.”

“Yeah.. I feel the same way.”

“What do you speak?” Danny playfully pushed Tim’s computer screen down from booting up the program the professor had given them to use to type out the phonetic alphabet. It was still apparently a nightmare program, but he had decided to type it so he wouldn't be deciphering shitty handwriting.

“Mandarin, Chinese, Italian, German, French, russian, Japanese, tagalog, spanish, I think that’s all of them?”

“You speak Tagalog too!” Danny’s words switched with ease to the language.

“No fuckin’ way,” Tim had to laugh at that one. “What else do you speak?”

“Same things are you but, Esperanto, Swahili, Cantonese, javanese, Sardo(technically a dialect but you know same difference), Ukrainian, I think that’s all?”

“I thought I was the Polyglot. Oh! I also speak ASL and BSL.”

“I know bits and pieces of ASL, definitely no BSL though,”he laughs softly. “But wait what other languages does that leave?”

“Well, a lot but I mean. We could always pick an easy one we both know.”

“Italian?”

“Yeah, please. I do not want translate someone in a non-latin based alphabet. It registers funny in my brain.”

“I gotta ask though Danny… Esperanto?”

“Okay, leave me alone! I had a friend who spoke it and taught me it so we could shit about others.”

“That’s fuckin’ hilarious though,”he smirked. “But what should we translate?”

Danny looked like he was about to burst out laughing. “What if we just fucking translated the Divine Comedy.”

“Danny Nightingale, are you telling me we should rewrite one of the most famous works of Italian writing, ever. That is also notoriously translated, a lot? And is--- you know.”

“Ma Divine Commedia,”Danny laughed. Tim could not with him right now. “E la fanfiction Tim.”

“YEAH I KNOW, that’s why I can’t believe you’re suggesting it.”

“COMMEDIA.” Danny proclaimed with a snort. Fuck that was cute. Thank god his name was called to grab their stuff. He could ignore the small twinge in his chest as he brought them their coffee and the food for Danny.

“Let’s get this over with I guess.”

“YES!” Danny threw his first into the air in excitement. “This is the start a beautiful friendship Tim, I promise.”

“Are we about to be nightmares to our poor professor?”

“What? Nooooo.”

“Oh yes we fucking are,”Tim rolled his eyes and smiled as he sipped his drink pulling up the original document. They were so fucked, but at least it would be funny. If Danny was his new partner for his class maybe Friday would come sooner than he thought.

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lakemojave · 6 months ago

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what drink are you having?

I have some drake's brewing co denogginizer double IPA. I usually do red wine on my drunk streams, but today i opted for this beer that is 9.75% ABV

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cyarskaren52 · 1 year ago

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YEAR IN REVIEW

The 100 Best Songs of 2023

Lana, Drake, Miley, Tyler, and many more

BY ROLLING STONE

DECEMBER 1, 2023

KYLIE MINOGUE RACED back to the center of the dance floor with a viral smash. A surprise Shakira track broke the internet. Sexyy Redd owned every summer DJ set. And NewJeans rode a drum-and-bass beat to pop heaven. It was a massive year for música Mexicana and Afropop, for noisy guitar bands, left-field hip-hop, and fearless country storytelling. Taylor Swift had a pretty good year too.

100

Foo Fighters, ‘Under You’

ERIKA GOLDRING/GETTY IMAGES

But Here We Are, the 11th album from Foo Fighters, explores grief in unflinching detail — it was recorded in the wake of Foos drummer Taylor Hawkins’ March 2022 passing and the death of leader Dave Grohl’s mother a few months later. “Under You” has the sunny power-pop-adjacent feel of earlier Foo Fighters tracks like “Learn to Fly,” but its lyrics depict Grohl being nearly suffocated by the pain of losing someone. “Someday I’ll come out from under you,” he declares, well aware that despite the catchy melodies he’s laying down, grief still hangs over him. —M.J.

Jung Kook feat. Latto, ‘Seven’

YOUTUBE

BTS member Jung Kook’s soulful vocals are backed by an insistent garage beat on this swirling confection that’s squarely focused on getting down every day of the week. He drives home his lust with some well-placed falsetto runs, while his foil, the “Big Energy” MC Latto, delivers a winking verse that manages to turn the dance-floor-filling DJ staple “Cha Cha Slide” into a teasing come-on. —M.J.

Hemlocke Springs, ‘Enknee1’

YOUTUBE

Don’t let Hemlocke Springs’ beloved TikTok bridge “girlfriend” give you the wrong impression — this new indie artist is no one-hit wonder. “Enknee1” is both a hyper-pop sensation and a sharp coming-of-age analysis — and who better to reflect on that subject than a Dartmouth Ph.D. hopeful turned viral star? “But I have learnt people aren’t puzzles (No),” she sings before sliding into the sweeping synth chorus emblematic of her awkward, authentic charm. “But thеy puzzle me, be thе things they don’t want to be.” She turns that confusion into something relentlessly catchy. More, please. —C.J.

Geese, ‘Mysterious Love’

YOUTUBE

These Brooklyn kids are just passing the age when they can order an IPA in the bars they play, but they’ve clearly spent plenty of their prodigious youth immersed in the vicissitudes of their parents’ (OK, grandparents’) record collections. They really know how to fuck up the oldies. “Mysterious Love” sounds like post-punk guerrillas laying siege to a classic-rock radio station, piling up prog power, avant-rock chaos, boogie wonderment, and psychedelic sprawl. It’s proof that their 2021 hype-magnet debut Projector was no fluke. —J.D.

Addison Rae feat. Charli XCX, ‘2 Die 4’

OSCAR DEL AGUILA/VARIETY/GETTY IMAGES

Addison Rae’s pop career felt conspicuously short after she dropped her debut single, “Obsessed,” in 2021. But after several songs leaked online — and exploded on TikTok after— it was abundantly clear that was only the beginning. The star of the leaks was “2 Die 4,” a slinky hit with the type of ear-worm hook that burrows in your brain forever. For the official release, Rae linked up with Charli XCX, who adds a little sexy soul to match Rae’s budding pop princess prowess. —B.S.

Aespa, ‘Spicy’

YOUTUBE

The K-pop group Aespa tried something new this year with “Spicy,” the lead single from their third EP, My World — The Third Mini Album. Previous releases had an experimental sound and leaned heavily into AR and virtual reality with a unique concept featuring an imagined world, villains, and avatar members. “Spicy” showcased a new side of Karina, Giselle, Winter, and Ningning. With strong vocals, grimy synths, rolling bass, and huge drum buildups, the song brought the girls closer into the real world of universal pop thrills, reminiscent of early 2000s pop a la Britney Spears. As they tell us in the lyrics, it’s a “10 out of 10, honestly.” —K.K.

Samia, ‘Charm You’

YOUTUBE

On “Charm You,” Samia makes a cathartic breakthrough over a sunny, simple instrumental. “I just saw my whole life flash before your eyes/and I don’t want to charm anyone this time,” she sings. A declaration that vulnerable might deserve either pity or fanfare, but Samia sounds surprisingly relaxed as her vocals float over buoyant guitar strums. The effervescent track is a standout on Samia’s second album, Honey, which showcases what she does best: pointedly chronicle the nuances of desire, devastation, and the delight of learning how to dance through it all. —L.L.

Ellie Goulding and Calvin Harris, ‘Miracle’

YOUTUBE

Nearly a decade had to pass for Ellie Goulding and Calvin Harris — the duo responsible for “I Need Your Love” and “Outside” in 2013 and 2014, respectively — to reunite for another electro-pop smash. “When you have that connection with someone, you miss it,” Goulding told Rolling Stone earlier this year. “It’s hard to just put that aside.” The result of their unique chemistry was “Miracle,” a psychedelic EDM hit in which Goulding asks, “Are you too cynical to believe in a miracle?” in her effervescent voice, backed by ethereal piano, Nineties synths, and a pumping bass. It was a gift to see these two back together. —T.M.

J Hus feat. Drake, ‘Who Told You’

BURAK CINGI/REDFERNS

Beautiful and Brutal Yard, the J Hus album from this summer, had the feeling of being just ahead of its time. Hus, a reliable provider of diaspora-spanning hits, connected with Drake on the pitch-perfect “Who Told You.” Of all of Drake’s globe-trotting ambitions, his forays into Afrobeats and sounds from West Africa bear the most fruit. Here we’re greeted by “One Dance” Drake, laying on the accent just a tad more subtly. Along with J Hus’ infectious hook, the song is an ideal anthem, one that I suspect finds a permanent spot in the pantheon of summer hits. —J.I.

Tove Lo, ‘Borderline’

YOUTUBE

Tove Lo co-wrote “Borderline” with fellow pop titan Dua Lipa, and it’s brimming with the kind of unforgettable melodies that are a hallmark of both artists’ best work. Built on a foundation of burbling bass and a Prince-like drum pattern, the song puts Tove Lo’s edgy lyrics about insecurity and codependence front and center. “I like to push you to the edge as long as you say you’re mine,” she sings, ramping up the intensity for an almost-shouted chorus that promises to make this relationship work, whatever the personal toll. Deeply unsettling in all the right ways. —J.F.

Tierra Whack, ‘Chanel Pit’

RAHUL BHATT*

The bars might look silly on paper (“What is that shit I smell?/I am that shit you smell”), but that’s half the point — the way Ms. Whack sends that nonsense caroming off the music-box beat, bouncing new flows like rubber balls, is what makes this absurdist gem shine. And, as always, her brilliance doesn’t come into full focus until you see the video, where she raps the entire thing while going through a car wash, minus the car. Plenty of artists made music that addressed the world’s pain and suffering in 2023. Let’s hear it for someone who knows how to keep it fun. —S.V.L.

Soccer Mommy, ‘Here’

DANIEL TOPETE

Sophie Allison, the indie-rock singer-songwriter who records as Soccer Mommy, delivered a great covers EP this year with Karaoke Night. Along with songs by Taylor Swift, R.E.M., Slowdive, and Sheryl Crow, she delivered a for-the-ages version of Pavement’s classic powerless-ballad “Here,” tapping into the heartbreak that only exists on the edges of Stephen Malkmus’ imperious performance on the 1992 original. It takes guts to throw yourself into a sacred indie-rock text like this, but she lovingly makes it her own to give us one of the all-time great Nineties covers. —J.D.

Myke Towers, ‘LALA’

YOUTUBE

There’s magic buried in the vocal chant from “LALA,” making the track so catchy that it stays planted in your brain long after it’s ended. The song has been blasting out of cars pretty much from the moment a snippet first came out in June — and that infectious sample sent it flying around TikTok with force. In a flash, it rose up the charts, making it onto the Billboard Hot 100. It also became testament to Myke Towers’ star-powered versatility: The sharp-as-nails spitter can launch caustic raps like no one else, but he’s also down for upbeat bangers that turn into streaming goliaths. —J.L.

Dijon, ‘Coogie’

STEVE JENNINGS/GETTY IMAGES

Dijon has never been afraid to expose the cracks of his voice in his folk- and R&B-inflected songs, but “Coogie” reveals him pushing himself and his songwriting to wrenching effect. As he sings of being held down by some inherent “meanness” or a bad spirit, he sounds increasingly more raspy and self-destructive. Along with an equally haphazard electric guitar, everything sounds like it’s drowning underwater. As the song never reaches a climax or moment of release, Dijon keeps the listener tight within his gripping performance — making way for a raw and slippery vision of indie music. —M.H.K.

Taylor Swift, ‘You’re Losing Me’

KEVIN WINTER/GETTY IMAGES/TAS RIGHTS MANAGEMENT

For her Eras Tour stop at MetLife Stadium in May, Taylor Swift caused mastermind chaos by exclusively releasing this Midnights-era track on a CD sold only at that weekend’s shows. That hasn’t stopped fans from turning to bootleg YouTube uploads to hear one of Swift’s most devastating songs about a relationship on its last pulse. Over a sample of her heartbeat, she delivers a gut-wrenching bridge that only a Sagittarius could write: Swift proclaims, “I’m the best thing at this party,” then immediately confesses, “I wouldn’t marry me either.” No bait-and-switch has ever cut so deep. —M.G.

Hotline TNT, ‘I Thought You’d Change’

YOUTUBE

A proud son of Chippewa Falls, Wisconsin (well, probably not that proud), singer-guitarist Will Anderson has wound up in New York in his mid-30s fronting the fantastic shoegaze band Hotline TNT, unfurling his Midwestern sad-guy glory on the band’s new album, Cartwheel. On “I Thought You’d Change,” he takes a wicked case of relationship malaise, slathers it in gilded distortion and surging melodies, and what comes out is at once heartsick and heroic. The “you” in question probably won’t be changing anytime soon, but the noise in our boy’s head is there to pull him through. Always has, always will. —J.D.

CMAT, ‘Have Fun!’

YOUTUBE

Since debuting a few years ago, Dublin’s Ciara Mary-Alice Thompson has distinguished herself for songs long on clarity, wit, and killer melodies. This standout starts off vivid (and clear): “One hundred bright green birds atop a Tesco in Clapham/Me on you, it didn’t make sense, but it happened.” From there, Thompson laments a shitty relationship while riding bright, piano-led funk, flowing catchily as violins slash in and out and those damn birds start to haunt her. It adds up to something irresistible, and one of the year’s best breakup songs. —C.H.

The Rolling Stones feat. Lady Gaga and Stevie Wonder, ‘Sweet Sounds of Heaven’

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“Sweet Sounds of Heaven,” the Stones’ greatest latter-day gospel-rock rave-up, reaches an emotional peak two minutes and 38 seconds in, when Mick Jagger and Lady Gaga bellow, “I’m not going to hell in some dusty motel/And I’m not going down in the dirt … I’m finally quenching my thirst.” It’s a genuinely moving moment of catharsis, like they’ve survived some dark night of the soul, and it builds from there into soulful jam reminiscent of “You Can’t Always Get What You Want” or Sticky Fingers’ “I Got the Blues,” thanks to Stevie Wonder’s funky keyboards and a fiery horn line. Has any other band sounded this good 60 years in? —K.G.

The Hives, ‘Bogus Operandi’

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Twenty years ago, the Hives blasted out of Sweden with their matching suits, over-the-top bravado, and killer garage-punk tunes. After a long break, they came back this year with a new album, predictably titled The Death of Randy Fitzsimmons. “I go to work!,” Howlin’ Pelle Almqvist shouts on their blazing return single, and his fellow Hives answer his call with the same sugar-sharp energy that made them such a blast back in the day. Times may change, but some operandi remain as beautifully bogus as ever. —J.D.

The Last Dinner Party, ‘Nothing Matters’

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The U.K.’s latest buzzy export is a baroque-rock dream. On “Nothing Matters,” the group is part ABBA, part Nineties Brit-pop throwback, and entirely bewitching. Lead singer Abigail Morris resigns herself to a surface-level romance of “a sailor and a nightingale dancing in convertibles.” The juicy chorus is increasingly raucous as the song wears on, exploding into irresistible, singalong-worthy “da-da-da”s. The song was a success on alt-rock radio this fall, and the band’s been getting themselves on the road ahead of their debut album, Prelude to Ecstasy, meaning that “Nothing Matters” is just the appetizer. —B.S.

Feeble Little Horse, ‘Freak’

With a name like Feeble Little Horse, the chances for dinky annoyingness are staggeringly high. But this Pittsburgh twee-noise band don’t just not suck, they transcend. “Freak,” from their album Girl With Fish, goes by in the space of a hardcore blurt, at just 1:47, with singer-bassist Lydia Slocum’s voice barely rising above a shy mumble as she sings, “I know you want me, freak/Sports star honeybee, on my team.” Yet she exudes tepid swagger, and the guitars go off like a mushroom cloud inside a snow globe, creating a lush little biosphere of shy, torrid gorgeousness. —J.D.

Tems, ‘Me & U’

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Tems builds this sweet jam on supple Afrobeats with the simplest of words, and if its title conjures Prince, so does its conflation of the spiritual and the carnal, which comes across despite Tems’ professed intention to write about her relationship with Jesus. Between this, her co-writes with Rihanna, and her breakthrough cameos with Future, Wizkid, and Drake, this Nigerian queen clearly remains choosy about the company she keeps. —W.H.

Eladio Carrión feat. Bad Bunny, ‘Coco Chanel’

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With the help of Bad Bunny, “Coco Chanel” — and its dembow influences and sexy lyrics — served as the anchor for Eladio Carrión’s great LP 3MEN2 KBRN. In its bars, Carrión and Benito reference everything from Ferragamo and Sega video games to Julieta Venegas and Avengers’ Thanos. When it dropped, the track also fed speculation that Benito was dating Kendall Jenner with the line, “The Puerto Rican sun is warmer than the one in Phoenix,” which was taken by many as a clever reference to Jenner’s ex, Devin Booker of NBA’s Phoenix Suns. —T.M.

XG, ‘Left Right’

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On “Left Right,” XG masterfully creates the kind of late-Nineties and early-2000s-channeling hit that would otherwise only emerge from the use of an obvious sample. The record is nostalgic in presentation, but futuristic in delivery. The seven-piece Japanese girl group — based in South Korea — are evident students of the K-Pop titans. Each member’s strengths are highlighted as they demonstrate a vocal expertise that brings to mind their other prime influences: the R&B girl groups of the TRL era. —L.P.

Drake feat. Sexyy Red and SZA, ‘Rich Baby Daddy’

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Drake’s “Rich Baby Daddy” sounds like an outtake from a So So Def Bass All Stars comp. It gets plenty of fuel from a Jessica Domingo vocal loop sample and kicks off with a command by Sexyy Red to “Bend that ass over! Let that coochie breathe!” In short, it’s a song where Drake lets women’s voices take center stage, even as he chimes in to add, “I’ve got some love inside of me/Please drag it out of me.” A guest vocal from 2023 MVP SZA only adds to the appeal of “Rich Baby Daddy” as a sweet and summery confection. —M.R.

Fifty Fifty, ‘Cupid’

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The breakthrough single from K-pop group Fifty Fifty is a delectable chunk of happy-sad bubblegum, its plush harmonies and sing-song lead vocals making its gently frustrated lyrics (“So skeptical of love … but still, I want it more, more, more”) feel like they were transposed straight from a fluffy pink diary with a stubborn lock and entries written in loopy, heart-adorned script. Sadly, Fifty Fifty’s tenure was as fleeting as the romance “Cupid” longs for; three of its four members were cut from the group by its agency Attrakt in October, a few months after the track peaked in the Hot 100’s Top 20. —M.J.

Summer Walker feat. J. Cole, ‘To Summer, From Cole (Audio Hug)’

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Summer Walker reportedly cried when she heard the “audio hug” J. Cole recorded for her 30-minute EP Clear 2: Soft Life. Indeed, “To Summer, From Cole” is a showcase for the North Carolina rapper, a soothing neo-soul track he co-produced with Kelvin “WU10” Wooten. “I just heard you had you another little baby, congratulations/I hope you got through it with no complications,” he raps in a mellow, gentlemanly tone. “On days you feelin’ like you on your own/I wrote this for you to put on.” Walker opens and closes the song with a simple melody and the words: “Call me when you need some love.” —M.R.

Chris Stapleton, ‘White Horse’

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“White Horse” is a powerhouse rock anthem that presses into uncharted territory for Chris Stapleton. “If you want a cowboy on a white horse/Ridin’ off into the sunset/If that’s the kind of love you wanna wait for/Hold on tight, girl, I ain’t there yet,” he belts over a stadium-worthy guitar riff. Co-produced with his wife, Morgane Stapleton, and Dave Cobb, and co-written alongside Semisonic frontman Dan Wilson, “White Horse” served as a rocking reminder that Stapleton is one of the greatest voices we’ve got. —J. Lonsdale

Armand Hammer, billy woods, ELUCID, and EL-P, ‘The Gods Must Be Crazy’

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“Your money’s no good here,” warns ELUCID on this standout cut from Armand Hammer’s We Buy Diabetic Test Strips. It’s a roundelay between two Brooklyn rappers who offer riffs on a Eurocentric world in disorder as they portend a post-apocalypse society where money and celebrity are meaningless. “White women with pepper spray in they purse/Interpolating Beyoncé/Illegal formations,” raps billy woods with brutally dry wit. Meanwhile, El-P of Run the Jewels accompanies the duo with a loopy, arrhythmic beat that mimics a globe slowly spinning off its axis. —M.R.

Gina Birch, ‘I Play My Bass Loud’

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Bassist Gina Birch is a DIY music legend whose work in the iconic London post-punk band the Raincoats helped lay the foundation for Nirvana, riot grrrl, and more. She released her solo debut this year, at 68 years old, and its title track was one of 2023’s most inspiring artistic declarations. The song recalled the Raincoats’ otherworldly feminist statement ”No One’s Little Girl,” with Birch’s joyful bass leading the way as she sang with wit and wisdom about grabbing your instrument and creating music that transforms your life, every time you poke out a note. —J.D.

Del Water Gap, ‘All We Ever Do Is Talk’

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Del Water Gap is a master of lovelorn melancholy on “All We Ever Do Is Talk,” a mournful ode to the honeymoon phase. The singer and songwriter finds himself riding a ceaseless emotional carousel in the wake of the realization that he can at once be full of love, but also fully devoid of those early feelings that once sent electricity through his veins. Over a moody Eighties-tinged track, he sprints through a maze of synths in search of understanding, asking over and over: “Will we ever get that feeling again?” —L.P.

Code Orange feat. Billy Corgan, ‘Take Shape’

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If your favorite part of high school was screaming along to Incubus on the drive home, don’t sleep on Code Orange. But even if they nail that 2000s period sound, that doesn’t mean they sound like something off an old CD that’s been skittering around on the floor of your car. “Take Shape” — featuring haunting vocals from Billy Corgan — exemplifies everything that makes Code Orange tick: absolutely punishing guitars, Jami Morgan’s harsh yet melodic vocals, and brain-flexing lyrics about breaking free from societal expectations. Just try not to run any red lights while listening to this track. —B.E.

Tyla, ‘Water’

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This year, 21 year-old year South African siren Tyla flooded the airwaves with her global smash, “Water.” This summer, after it’s just-challenging-enough choreography became a mainstay on TikToks and Instagram, the song itself rose to the top hip-hop and R&B radio. The fluid Amapiano-meets-Afrobeats production cascades beneath a saturated, choir-style vocal top-line that goads a lover to “make me sweat, make me hotter, make me lose her breath, make me water.” The track and its dance are fun, sexy, inspiring, and even a little humbling–since emulating Tyla’s control of her hips is no small thing.–M.C.

Jisoo, ‘Flower’

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Jisoo was the last member of Blackpink to release solo music, creating a feverish anticipation among fans. It was the worth the wait. “Flower” cemented the singer as a certified solo star. A sophisticated track with a staccato, Latin-tinged melody and Caribbean-inspired percussion, “Flower” feels instantly familiar yet unlike anything else on the radio. There’s a confidence to her voice that isn’t always as apparent when it’s blended with three other singers. But on this solo track, it’s clear that Jisoo is firmly in control. —T.C.

Thundercat and Tame Impala, ‘No More Lies’

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On this psychedelic-soul gem, Los Angeles is to blame for a relationship that doesn’t quite work. “I’m sorry, girl, didn’t mean to drag you in my dreams,” Thundercat sings, as he and Tame Impala’s Kevin Parker create a beautifully hazy track. The two musicians let the groove move them toward a sense of understanding that always seems to be alluringly out of their reach. “It just felt like we were definitely long lost bandmates from another era,” Thundercat told Rolling Stone about working with Parker. —L.P.

Becky G and DannyLux, ‘Cries in Spanish’

EMMA MCINTYRE/GETTY IMAGES/ COACHELLA

As música Mexicana finds recognition on a global scale, strains of those same folk roots — the lovely melodic turns, those quirky accents in the strings — are beginning to penetrate mainstream pop. A ballad of quiet despair, this track from Becky G’s superlative third album — a tribute to her Mexican roots — reaches a majestic kind of transcendence when young prodigy DannyLux enters the stage riding a lilting sad sierreño pattern. The spiraling organ notes at the end add sophistication, but “Cries in Spanish” is all about the vocal luster of its two stars. —E.L.

Fall Out Boy, ‘Love From the Other Side’

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Fall Out Boy’s eighth studio album, So Much (for) Stardust, was the first time they’d worked with producer Neal Avron in nearly 15 years. The record’s lead single “Love From the Other Side,” was proof of how well their reunion was going to work. Everyone was firing on all cylinders: Avron built a soundscape of theatrical urgency around Pete Wentz’s unmistakable songwriting, while Patrick Stump braced for the impact of sacrificing himself to the beast of infatuation. Without falling back on regurgitative nostalgia, they created the most Fall Out Boy-sounding Fall Out Boy song in recent memory.—L.P.

Yahritza y Su Esencia and Grupo Frontera, ‘Frágil’

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Yahritza y Su Esencia’s “Soy El Único” was the first song to put the Mexican American trio on people’s radars. But “Frágil,” with Grupo Frontera, was the song where they really took off. On the norteño-cumbia track, Yahritza and Frontera’s Payo Solis sing about giving their entire, fragile heart away to a love interest. Yahritza’s high notes complement Solis’ masculine vocals as they sing about an ex-lover “whose soul doesn’t feel pain when it lies.” It was the first track from Yahritza to hit Number One on an airplay chart, and it marked out a pivotal point in Frontera’s ever-growing career. —T.M.

That Mexican OT With Paul Wall and DRODi, ‘Johnny Dang’

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One of the feel-good stories of rap in 2023 is the emergence of Virgil “That Mexican OT” Gazca. The Bay City, Texas, artist grinded on the mixtape circuit for years before breaking through with Lonestar Luchador and its centerpiece, “Johnny Dang.” Produced by TobiAli, it’s a legitimate banger where OT bounces all over the track even as he teases, “I’m just rhymin’ words, I don’t even know how to rap.” Guest spots from Freeport’s DRODi and Houston all-star Paul Wall add excitement to a hit that promises to “slide down your block, light it up with flames.” —M.R.

Jenny Lewis, ‘Psychos’

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Jenny Lewis proclaims herself a “rock & roll disciple” on “Psychos,” and proves her devotion with a series of truths on the Joy’All soft rocker, custom made for Seventies AM radio. Her Tao includes acknowledging that “life goes in cycles [like] a merry-go-round,” that when you sing about turning down the treble and dropping the bass, your music better sound gloriously tinny, and that, most transparently, “I’m not a psycho/I’m just trying to get laid.” Lewis knows, of course, that it’s that fun and funny candor that won rock & roll all its disciples in the first place. Respect to the guru, namaste. —K.G.

Mitski, ‘My Love Mine All Mine’

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When you listen to any love song from the 1940s, you get the distinct sense that everyone’s singing to ghosts — lovers are always lost, lonely, or waiting. Mitski captures that swoony mood of exquisite loss in this goth-country epic, which sees the protagonist asking the moon to remember her to her loved one even after her death. Sweeping and gorgeous, this is as close to a ballad as you’re going to get with Mitski, who — even in her lighter moments — seems always tethered to the fact that even the greatest love stories end.—B.E.

Earthgang and Spillage Village, ‘Die Today’

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They make it sound so effortless — like they’re just coming up with these super-catchy hooks and funny-AF lyrics on a summer Sunday, in between hammock swings. But the greats have a way of making the hard jobs look easy. And this track cements Earthgang’s status as one of the greats: loose and free, like your favorite pajama bottoms; witty and a little maudlin, like an episode of Six Feet Under. “Tell me baby if I die today,” the Atlanta duo sing, “Would you come and kiss my cold face?” Sounding like that? For sure. —N.S.

V, ‘Rainy Days’

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Each BTS solo project has its own distinct musical personality. V is the member of the group with the deepest love of R&B, soul, and jazz, a fan of legends like Chet Baker and Frank Sinatra who’s also a former saxophone player. He unfurled his old-school credentials on “Rainy Days,” crooning over a forlorn piano and laidback beat as he explored the refined depths of his deliciously cloudy baritone. The result was an undisputedly umbrella-worthy, new-look, quiet-storm pleasure. —J.D.

Yng Lvcas feat. Peso Pluma, ‘La Bebé’

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“Ella Baila Sola,” Peso Pluma’s corrido with Eslabón Armado, was a Top 10 hit, but it wasn’t his only major hit of the year. “La Bebé (Remix),” a Pluma-featuring track by the largely unknown Mexican reggaetonero Yng Lvcas, seemed to dominate Latin nightclubs overnight — and it played a huge role in Pluma’s 2023 takeover. Lvcas and Pluma sing to a muse who just wants to dance to a good reggaetón beat. “La Bebé” delivers exactly that. Mexico isn’t your typical reggaetón exporter, but with “La Bebé,” Lvcas told Rolling Stone he hopes it “propels Mexicans to look at their own people for the genre.” —T.M.

Tyler, the Creator feat. Vince Staples, ‘Stuntman’

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One of the highlights of Tyler, the Creator’s Call Me If You Get Lost deluxe is “Stuntman,” a track that exemplifies his creative genius. Vince Staples opens things up with a characteristically sharp verse over a minimalist mesh of claps, clangs, and colossal 808s, then Tyler arrives with a swagger that he carries throughout. The song’s de facto breakbeat is interspersed by a hook with a crescendo of synths that is indeed a perfect soundtrack for a multitalented artist to let us know, “I’ll show you how to stunt.” —A.G.

Twice, ‘Moonlight Sunrise’

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Twice played their first stateside stadium show last summer (which made them the first K-pop girl group to headline a stadium in the U.S.). It was a peak moment in their eight-year run. “Moonlight Sunrise,” the group’s second English-language single, was inspired by the moonlight at that Banc of California Stadium performance. “Baby, you can hit up my line when you need it/Said that you tried?/Baby, you succeeded,” they rap with elevated English skills. Twice underscored their maturity by showing an artistic range beyond their signature bubblegum pop, with a Miami bass-infused R&B track. —K.K.

Tainy feat. J Balvin, Young Miko, Jowell and Randy, ‘Colmillo’

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This masterful deluxe-edition bonus highlight from Puerto Rican superproducer Tainy’s stunningly brilliant Data is three or four bangers in one, the sound of an artist chasing his wildest musical impulses in whatever wild-style direction they take him. “Colmillo” opens as a house-music hallucination, then mutates into a club-swallowing reggaeton anthem that invites us to commune with the perreo gods, as if Tainy and his teeming crew of guests (veteran stars J Balvin, plus Jowell and Randy, as well as newcomer Young Miko) are holding our hand as we ascend to a velvet-rope party on the astral-plane. —J.D.

Shamir, ‘Oversized Sweater’

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Comfort is the theme of Shamir’s dreamy single, off his 2023 album, Homo Anxietatem (Latin for “anxious man”). “Oversized Sweater” delivers gorgeously on that warmth and familiarity, with Shamir making a perfect pastiche of Nineties indie pop and soft rock, reminiscent of Liz Phair, the Goo Goo Dolls, and Lisa Loeb. Inspired by a sweater he knitted in the months following a stint at a psych ward, the song is an uplifting tribute to the ways we look to soothe ourselves after a love has gone sour. “So I cuddle in the space/Of my oversized sweater/And sing until I believe in love again,” he sings on the chorus. The song fits as snugly as his favorite item of clothing. —B.S.

Feid, ‘Nx Tx Sientas Solx’

PATRICIA J. GARCINUNO/REDFERNS

Decades of Latin pop songs have drilled into our heads the questionable message that romantic love is the answer to everything, but Feid begs to disagree. The most intimate track on Mor, No Le Temas a La Oscuridad — the Colombian star’s sixth studio album — this dark expressionist miniature proposes replacing those post-heartbreak tears with an evening of dancing and self-acceptance. Anchored on deep bass accents and a nimble loop whose restless shuffle mirrors the protagonist’s emotional turmoil, “Nx Tx Sientas Solx” underscores the vulnerable, healing side of neo-reggaetón. —E.L.

Troye Sivan, ‘Rush’

Troye Sivan

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A sweaty, lusty ode to physical connection, Troye Sivan’s “Rush” combines a pumping house beat and a horny-guy-gang chant to staggering effect, with the Australian pop enigma playing winking ringmaster at its center. The unrelenting three minutes of “Rush” feel like a snapshot of those summer parties that seemingly never end, stretching from the not-late-enough sunset to the too-early sunrise and beyond, bodies pressed up against each other even after everyone has collapsed from giddy, gleeful exhaustion. —M.J.

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#Best songs #year in review #2023

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brews-and-pubs · 1 year ago

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Degrees Plato, Oakland CA

26 June 2023

After a lazy day, Frank and I headed to Degrees Plato for a couple of pints. Degrees Plato is a measurement used in the brewing of beer, so it's appropriate this little spot has used this as their name. They don't brew themselves, but they do focus on craft beers with a decent tap list as well as large beer coolers with all sorts of things available.

In addition to their indoor space, there's an enclosed outdoor space with what is most likely a stage for live shows.

My first pint was Sister Frida, a 6.2% Hazy IPA by Laughing Monk Brewing in San Francisco. Such a tasty pint and a great color!

The second was Mini Separation Anxiety, a 4% Session IPA by Berryessa Brewing in Winters CA. Not only was the flavor great, but this didn't taste "thin" as so many beers with low alcohol content like this one do.

This concludes the Oakland stay on this trip. Other beers that I had while here include:

Paulaner Oktoberfest

Hacker-Pschorr Munich Dunkel

21st Amendment Hazy IPA

21st Amendment Blood Orange IPA

Drake's Brewing Denogginizer Double IPA

(plus one or more two I don't recall the names of)

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spito · 2 years ago

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2021 Nov 05 See all posts Halo and more: exploring incremental verification and SNARKs without pairings Special thanks to Justin Drake and Sean Bowe for wonderfully pedantic and thoughtful feedback and review, and to Pratyush Mishra for discussion that contributed to the original IPA exposition. Readers who have been following the ZK-SNARK space closely should by now be familiar with the high level of how ZK-SNARKs work. ZK-SNARKs are based on checking equations where the elements going into the equations are mathematical abstractions like polynomials (or in rank-1 constraint systems matrices and vectors) that can hold a lot of data. There are three major families of cryptographic technologies that allow us to represent these abstractions succinctly: Merkle trees (for FRI), regular elliptic curves (for inner product arguments (IPAs)), and elliptic curves with pairings and trusted setups (for KZG commitments). These three technologies lead to the three types of proofs: FRI leads to STARKs, KZG commitments lead to "regular" SNARKs, and IPA-based schemes lead to bulletproofs. These three technologies have very distinct tradeoffs: FRI Hashes only (quantum safe!) Large (10-200 kB) Medium (poly-logarithmic) Inner product arguments (IPAs) Basic elliptic curves Medium (1-3 kB) Very high (linear) KZG commitments Elliptic curves + pairings + trusted setup Short (~500 bytes) Low (constant) So far, the first and the third have seen the most attention. The reason for this has to do with that pesky right column in the second row of the table: elliptic curve-based inner product arguments have linear verification time. What this means that even though the size of a proof is small, the amount of time needed to verify the proof always takes longer than just running the computation yourself. This makes IPAs non-viable for scalability-related ZK-SNARK use cases: there's no point in using an IPA-based argument to prove the validity of an Ethereum block, because verifying the proof will take longer than just checking the block yourself. KZG and FRI-based proofs, on the other hand, really are much faster to verify than doing the computation yourself, so one of those two seems like the obvious choice. More recently, however, there has been a slew of research into techniques for merging multiple IPA proofs into one. Much of the initial work on this was done as part of designing the Halo protocol which is going into Zcash. These merging techniques are cheap, and a merged proof takes no longer to verify than a single one of the proofs that it's merging. This opens a way forward for IPAs to be useful: instead of verifying a size-\(n\) computation with a proof that takes still takes \(O(n)\) time to verify, break that computation up into smaller size-\(k\) steps, make \(\fracnk\) proofs for each step, and merge them together so the verifier's work goes down to a little more than \(O(k)\). These techniques also allow us to do incremental verification: if new things keep being introduced that need to be proven, you can just keep taking the existing proof, mixing it in with a proof of the new statement, and getting a proof of the new combined statement out. This is really useful for verifying the integrity of, say, an entire blockchain. So how do these techniques work, and what can they do? That's exactly what this post is about. Background: how do inner product arguments work? Inner product arguments are a proof scheme that can work over many mathematical structures, but usually we focus on IPAs over elliptic curve points. IPAs can be made over simple elliptic curves, theoretically even Bitcoin and Ethereum's secp256k1 (though some special properties are preferred to make FFTs more efficient); no need for insanely complicated pairing schemes that despite having written an explainer article and an implementation I can still barely understand myself. We'll start off with the commitment scheme, typically called Pedersen vector commitments. To be able to commit to degree \( 2\) signatures. From merging IPAs to merging IPA-based SNARKs: Halo Now, we get into the core mechanic of the Halo protocol being integrated in Zcash, which uses this proof combining technique to create a recursive proof system. The setup is simple: suppose you have a chain, where each block has an associated IPA-based SNARK (see here for how generic SNARKs from polynomial commitments work) proving its correctness. You want to create a new block, building on top of the previous tip of the chain. The new block should have its own IPA-based SNARK proving the correctness of the block. In fact, this proof should cover both the correctness of the new block and the correctness of the previous block's proof of the correctness of the entire chain before it. IPA-based proofs by themselves cannot do this, because a proof of a statement takes longer to verify than checking the statement itself, so a proof of a proof will take even longer to verify than both proofs separately. But proof merging can do it! Essentially, we use the usual "recursive SNARK" technique to verify the proofs, except the "proof of a proof" part is only proving the logarithmic part of the work. We add an extra chain of aggregate proofs, using a trick similar to the proof merging scheme above, to handle the linear part of the work. To verify the whole chain, the verifier need only verify one linear-time proof at the very tip of the chain. The precise details are somewhat different from the exact proof-combining trick in the previous section for efficiency reasons. Instead of using the proof-combining trick to combine multiple proofs, we use it on a single proof, just to re-randomize the point that the polynomial committed to by \(G^*_0\) needs to be evaluated at. We then use the same newly chosen evaluation point to evaluate the polynomials in the proof of the block's correctness, which allows us to prove the polynomial evaluations together in a single IPA. Expressed in math: Let \(P(z) = a\) be the previous statement that needs to be proven The prover generates \(G^*_0\) The prover proves the correctness of the new block plus the logarithmic work in the previous statements by generating a PLONK proof: \(Q_L * A + Q_R * B + Q_O * C + Q_M * A * B + Q_C = Z * H\) The prover chooses a random point \(t\), and proves the evaluation of a linear combination of \(\G^*_0,\ Q_L,\ A,\ Q_R,\ B,\ Q_O,\ C,\ Q_M,\ Q_C,\ Z,\ H\\) at \(t\). We can then check the above equation, replacing each polynomial with its now-verified evaluation at \(t\), to verify the PLONK proof. Incremental verification, more generally The size of each "step" does not need to be a full block verification; it could be something as small as a single step of a virtual machine. The smaller the steps the better: it ensures that the linear work that the verifier ultimately has to do at the end is less. The only lower bound is that each step has to be big enough to contain a SNARK verifying the \(log(n)\) portion of the work of a step. But regardless of the fine details, this mechanism allows us to make succinct and easy-to-verify SNARKs, including easy support for recursive proofs that allow you to extend proofs in real time as the computation extends and even have different provers to do different parts of the proving work, all without pairings or a trusted setup! The main downside is some extra technical complexity, compared with a "simple" polynomial-based proof using eg. KZG-based commitments. FRI Hashes only (quantum safe!) Large (10-200 kB) Medium (poly-logarithmic) Inner product arguments (IPAs) Basic elliptic curves Medium (1-3 kB) Very high (linear) KZG commitments Elliptic curves + pairings + trusted setup Short (~500 bytes) Low (constant) IPA + Halo-style aggregation Basic elliptic curves Medium (1-3 kB) Medium (constant but higher than KZG) Not just polynomials! Merging R1CS proofs A common alternative to building SNARKs out of polynomial games is building SNARKs out of matrix-vector multiplication games. Polynomials and vectors+matrices are both natural bases for SNARK protocols because they are mathematical abstractions that can store and compute over large amounts of data at the same time, and that admit commitment schemes that allow verifiers to check equations quickly. In R1CS (see a more detailed description here), an instance of the game consists of three matrices \(A\), \(B\), \(C\), and a solution is a vector \(Z\) such that \((A \cdot Z) \circ (B \cdot Z) = C \cdot Z\) (the problem is often in practice restricted further by requiring the prover to make part of \(Z\) public and requiring the last entry of \(Z\) to be 1). An R1CS instance with a single constraint (so \(A\), \(B\) and \(C\) have width 1), with a satisfying \(Z\) vector, though notice that here the \(Z\) appears on the left and has 1 in the top position instead of the bottom. Just like with polynomial-based SNARKs, this R1CS game can be turned into a proof scheme by creating commitments to \(A\), \(B\) and \(C\), requiring the prover to provide a commitment to (the private portion of) \(Z\), and using fancy proving tricks to prove the equation \((A \cdot Z) \circ (B \cdot Z) = C \cdot Z\), where \(\circ\) is item-by-item multiplication, without fully revealing any of these objects. And just like with IPAs, this R1CS game has a proof merging scheme! Ioanna Tzialla et al describe such a scheme in a recent paper (see page 8-9 for their description). They first modify the game by introducing an expanded equation: \[ (A \cdot Z) \circ (B \cdot Z) - u * (C \cdot Z) = E\] For a "base" instance, \(u = 1\) and \(E = 0\), so we get back the original R1CS equation. The extra slack variables are added to make aggregation possible; aggregated instances will have other values of \(u\) and \(E\). Now, suppose that you have two solutions to the same instance, though with different \(u\) and \(E\) variables: \[(A \cdot Z_1) \circ (B \cdot Z_1) - u_1 * (C \cdot Z_1) = E_1\] \[(A \cdot Z_2) \circ (B \cdot Z_2) - u_2 * (C \cdot Z_2) = E_2\] The trick involves taking a random linear combination \(Z_3 = Z_1 + r Z_2\), and making the equation work with this new value. First, let's evaluate the left side: \[ (A \cdot (Z_1 + rZ_2)) \circ (B \cdot (Z_1 + rZ_2)) - (u_1 + ru_2)*(C \cdot (Z_1 + rZ_2)) \] This expands into the following (grouping the \(1\), \(r\) and \(r^2\) terms together): \[(A \cdot Z_1) \circ (B \cdot Z_1) - u_1 * (C \cdot Z_1)\] \[r((A \cdot Z_1) \circ (B \cdot Z_2) + (A \cdot Z_2) \circ (B \cdot Z_1) - u_1 * (C \cdot Z_2) - u_2 * (C \cdot Z_1))\] \[r^2((A \cdot Z_2) \circ (B \cdot Z_2) - u_2 * (C \cdot Z_2))\] The first term is just \(E_1\); the third term is \(r^2 * E_2\). The middle term is very similar to the cross-term (the yellow + green areas) near the very start of this post. The prover simply provides the middle term (without the \(r\) factor), and just like in the IPA proof, the randomization forces the prover to be honest. Hence, it's possible to make merging schemes for R1CS-based protocols too. Interestingly enough, we don't even technically need to have a "succinct" protocol for proving the \[ (A \cdot Z) \circ (B \cdot Z) = u * (C \cdot Z) + E\] relation at the end; instead, the prover could just prove by opening all the commitments directly! This would still be "succinct" because the verifier would only need to verify one proof that actually represents an arbitrarily large number of statements. However, in practice having a succinct protocol for this last step is better because it keeps the proofs smaller, and Tzialla et al's paper provides such a protocol too (see page 10). Recap We don't know of a way to make a commitment to a size-\(n\) polynomial where evaluations of the polynomial can be verified in \(

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