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mysteriousquantumphysics · 3 years

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Nonseparability: Replacing causal inference with grounding inference.

Usually the conclusion of Bell's Theorem is reduced to a binary decision one has to make: Either one has to give up realism or locality. I've mentioned before that realism is a very broad notion and that misconceptions can easily arise from ambiguity of terms. The story is similar with locality - before one can talk about giving it up, one has to define first what locality actually is. Most commonly, locality denotes the absence of superluminal causation (i.e. cause and effect relations between spacelike separated events). In order to keep up realism (where I consider ontological models of this entry to satisfy the required notion of realism) proponents of many interpretations/theories of quantum mechanics accept nonlocality in the sense of superluminal causation, and therefore accept clashes with the theory of relativity to a certain extent. Usually they claim that nonlocality is an unavoidable and inherent characteristic of nature (see [1]). Examples for theories going along this path of nonlocality are for instance Bohmian Mechanics, GRW collapse theories and Spekkens' ψ-epistemic approach. However, it is important to be aware that the formulation of locality requires a prerequisite called separability. Without separability, i.e. the idea of distinct events taking place in distinct areas of spacetime, any notion of superluminal causation loses its meaning. (Note that separability is often explicitly assumed, even in nonlocality proofs such as in p.9 [2]). Thus, why don't simply conclude from Bell's Theorem the violation of separability? This would entail maintaining a sense of realism (here ψ-completeness) and avoiding nonlocality in the sense of superluminal causation, thus avoiding the clashes with relativity realistic theories have to deal with usually. In the following we will illuminate what (non)separability exactly is and by which principle causation can be replaced then.

What is (non)separability?

The issue of (non)separability was already discussed in the Bell-literature of the 1980s. Howard [3] defines separability of states as:

"Contents of any two regions of space-time separated by a nonvanishing spatiotemporal interval constitute separable physical systems, in the sense that (1) each possesses its own, distinct physical state, and (2) the joint state of the two systems is wholly determined by these separate states." (p.226 [3])

Therefore nonseparability means that either one or both of the aforementioned conditions are violated. This is directly connected to a concept of holism, which states, roughly speaking, that the whole is more than the sum of its parts. (At this point I should mention that Howard's principle as well as the claim that separability is assumed in Bell's Theorem is object of critisism, see [4])

Causal inference v.s. grounding inference

Well, so far so good, but in the case of nonseparability and therefore denying the crucial prerequisite of (non)local causation, which principle formalises what is going on then? At first we should get a idea of the concept of grounding:

"Grounding is thus a metaphysical relation characterizing the connection from the more to the less fundamental entities. [...] [O]ne can think of causation as driving the world through time from the earlier to the later, so one can think of grounding as driving the world through levels from the deeper to the shallower." (p.5, [5])

We see that grounding and causation are principles which show structural similarity, though being fundamentally different. Causal inference is the concept to which fundamental relevance is commonly attributed, since it is crucial for the formulation of Bell's concept of local causality (which I won't discuss any further right now because this entry is already getting too long) To see the structural similarity of causal and grounding inference, we shall have a look on how these principles can be formalized:

"Causal inference: If distinct events e1 and e2 are statistically correlated, then either (i) e1 causes e2, or (ii) e2 causes e1, or (iii) e1 and e2 are joint effects of some common cause d." (p.3, [5])

And similarily:

"Grounding inference: If non-identical entities a and b are modally connected, then either (i) a grounds b, or (ii) b grounds a, or (iii) a and b are joint results of some common ground c." (p. 7, [5])

Grounding inference in Quantum Mechanics

Now consider the Bell setup: There are two (spacelike separated) systems; the measurement outcomes on each side regarded separately seem to be completely random, whereas taken together the quantum correlations between them unravel. This might already suggest that the 'whole is more than the sum of its parts'. The events in each spacetime region are therefore modally connected and their joint system - as described by the entangled singlet state - can be regarded to be more fundamental than each system on its own. Consequently the whole composite system is a common ground which is described by its entangled quantum state. There is no need of any superluminal causation or adding structure (hidden variables, i.e. a ψ-supplemented view) to the theory. Thus, the view of nonseparability and grounding inference makes most sense in a ψ-complete view. Ismael and Schaffer [5] argue that ``the quantum states of systems are all that is needed for the formalism'' and therefore one should ``treat the quantum state description as complete if possible, since nothing else seems needed empirically''. Nonseparability makes hidden variables superfluous, but relies on keeping up the ontic character of the wave function as well as metaphysical and semantic realism.

All in all, the idea of giving up separability might give us the chance to maintain rather conservative notions of realism and simultaneously avoiding the usual problems with relativity - although of course imagining a world in which entities are not separable though spatiotemporal distance is far from being intuitive. Any hope of establishing a consistent view of quantum mechanics which does not clash with our classical understanding of the world seems to be a hopeless intention.

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[1] Travis Norsen - Bell Locality and the Nonlocal Character of Nature, arXiv:quant-ph/0601205

[2] Robert Spekkens, Nicholas Harrigan - Einstein, incompleteness, and the epistemic view of quantum states, arXiv:0706.2661

[3] Don Howard - Holism, Separability, and the Metaphysical Implication of the Bell Experiment”. In: ed. by J.T. Cushing and E. McMullin. University of Notre Dame Press,1989, pp. 224–253.

[4] Joe Henson - Non-separability does not relieve the problem of Bell's theorem, arXiv:1302.7188

[5] Jennan Ismael, Jonathan Schaffer - Quantum holism: nonseparability as common ground, http://www.jonathanschaffer.org/quantumholism.pdf

#mysteriousquantumphysics #physics #metaphysics #philosophy #philosophy of science #causation #Bells theorem #Quantum mechanics #quantum physics #studyblr #physicsblr #education

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rora-s · 3 years

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The Derivative Chapter 8: Sports

Chapter 1 <- Chapter 7

“Do I even need to ask?” David snapped. Uncle Charlie just smiled smugly turning his hand around. The entire table groaned in annoyance.

“It’s not what it looks like, promise” Don spoke up.

“You brother hustling us?” one of Don’s friends Mike muttered.

“I’ve only played once before” Charlie informed as they collected the cards to deal another round of poker. “I actually have a one in eight chance of hitting a set when I’m holding a pocket pair. I’m about 50/50 to draw a flush with suited cards in my hand, two off the draw. I also count my outs I- I multiply by two. I add one. That’s roughly my percentage of hitting.” he explained.

“Card math” I muttered over my father’s shoulder as I walked past the table. Leaning over to snag some chips out of the snack bowl.

“Mr. Eppes you need to take my seat, your son is killing us” David declared as Alan brought out more chips.

“No, not me” Gramps objected “the only other time Charlie played, I learned my lesson about gambling with a mathematician”

“Hey could I-”

“No” Don cut me off “Ms. I-can’t-help-but-card-count”

“Not my fault I was born with perfect visual memory” I muttered as my father got up and headed to the kitchen.

“Hey weren’t we playing with bottle caps?” Charlie pointed out to his father.

“Yeah or else you’d have walked away with the pink slip to my car” Alan informed.

“You know, there is some element of chance here” Charlie explained “you know I- I may just be getting lucky.”

“Or you're just unlucky,” David joked to Mike.

“That’s funny Sinclair keep that up. It comes back to me when baseball starts” Mike countered taking a swig of his beer as dad returned and handed me a Mountain Dew as he sat down with his glass of water.

“Baseball?” Charlie questioned “”the FBI have a team?”

“Yeah, we got a whole league.” David explained “there’s, uh, LAPD, Sheriffs’ department”

“D.A.’s got the killer squad” Mike commented “Now that Kraft’s in San Diego, you guys don’t have a power hitter.”

“What about Don?” Charlie suggested.

“It’s not my thing” Don objected

“Oh, you play?” Mike inquired.

“Don went to college on a baseball scholarship,” Charlie informed. “What are you talking about? You played pro second base.”

“Single A about a million years ago” Don muttered.

“That’s great. It means you’re this year’s ringer.” Mike grumbled.

“Nope. I’m sorry.” Don objected quickly “not interest buddy”

“Come on, you gotta do it” David asked hopefully as Don’s phone rang.

“Excuse me” he murmured to us answering it. “Eppes… we’ll be right there” he declared, getting to his feet.

I sighed and shuffled back toward the kitchen where Alan was. “Looks like I’m spending the night,” I informed.

He looked up at me confused “really? Why?”

Just then Don popped into the doorway pulling on a jacket “hey dad I just got called in can she stay here tonight?”

I gave my grandfather a look who sighed “yes of course”

“Thanks,” Don murmured heading out.

______________

3rd POV.

“I’ve never seen him before,” Mr. Bayle declared, handing Don back the photo of Salazar.

“Are you sure?” the agent asked.

“Yeah” the man confirmed.

“I mean, maybe he did some work for you guys around here.” Don persisted.

“Yeah, he could have. I wouldn’t know” Bayle explained “Lisa was in charge of all that.”

“I’m just trying to figure out if there’s any possibility that this man knew your wife.” Don insisted as they stepped from the other man’s kitchen into his living room.

“Why?” Bayle inquired with a shrug as he stopped to face Don.

“You’re not going to want to hear this” Don prefaced reluctantly “but there are some questions about Cliff Howard’s conviction”

“The bastard said he did it,” Bayle scoffed.

“I know,” Don nodded.

“I haven’t seen you in a year” Bayle continued “I haven’t seen you since you interrogated me for 48 hours.”

“Sir..” Don tried to speak up but the other man continued.

“I had to call the funeral home handcuffed to a table.”

“I was pursuing your wife’s murder wherever it took me” Don attempted to explain his actions. “So help me..” he paused shaking his head and biting his lip and Bayle took the moment to speak again.

“Now you want to tear these wounds open again.”

“I don’t want to do that,” Don objected adamantly.

Both men paused to breathe and Don’s eyes wandered over to the mantel where he spotted a picture he recognized he shuffled over to point at it “that’s your, uh, your daughter. What’s her name? Paula?” he asked, trying to remember.

“Yes” Jonas answered, his voice still tense with emotion.

“Right. May I?” Don gestured to the photo.

“Go ahead,” Bayle allowed. Don took the photo from the mantel and looked at the young girl. “She’s a sophomore now.”

“Yeah, so is my daughter,” Don admitted.

“You have a daughter?” Jonas asked, surprised.

Don nodded “her names Abby.” he chuckled slightly with a bittersweet spike in his gut “yeah she came to live with me not too long ago after her mother died, car crash”

“I’m sorry” Bayle murmured, shifting on his feet.

Don replaced the photo and turned to face the other man. “Jonas, don’t you want to know the truth about your wife’s death?”

“Cliff Howard is the truth,” Bayle insisted.

______________

Abby POV.

“Okay tell me I’m crazy” Larry declared, setting his pencil down and rubbing his face with his hands. “I think I’ve just found a way to express Calabi-Yau manifolds in a way that goes beyond the existence of a nonvanishing harmonic spinor.”

“You're crazy,” I muttered, taking another bite of my food.

“Ch- Charles” Larry whined when he received no response from his fellow mathematician.

“Has he been out there all night?” Uncle C questioned turning away from the window he had been gazing out of. Watching my father play basketball.

“Well, on the bright side it seems like Don’s taken up an interest in sports again.” Alan commented.

Charlie sighed taking the seat next to me “it’s like the evidence proves him right and wrong at the same time”

“Oh, yeah, the old paradox of Schroedinger’s cat.” Larry murmured.

“Is that that persian that keeps hiding out in our garage?” Alan inquired.

“No, that's the Myers down the street’s cat” I muttered, taking a sip of my drink.

“It’s an intellectual exercise,” Charlie explained.

“I knew that,” Alan lied.

“Okay this is vastly simplified” Larry prompted “there’s a cat in a box. 50/50 chance it’s been poisoned, but now here’s the paradox: until such time as we can open the box and observe the cat, for that time, that cat is both alive and dead.”

“Larry I-I fail to see the analogy, though.” Charlie objected “I mean, in reality Don can’t be both right and wrong at the same time.”

“Well, of course not.” Alan chimed in “I mean, if a man is both right and wrong, then something’s gotta be wrong.”

“Positive and a negative equal a negative?” I scoffed.

“No. the truth of Schroedinger’s cat is that the question itself is meaningless until we look inside the box.” Larry informed.

“So you could ask a whole different question” I voiced.

“For a whole different result” Larry finished. Uncle Charlie immediately straightened and turned to look at the window again. Before getting up and heading outside after his brother. “Well and off he goes again to help solve the unjust of the world”

“You can always tell when he gets an idea he spaces out then runs” I muttered.

Larry hummed in agreement “you know you are quite insightful young enigma quite like your uncle I’m surprised you’ve yet to push ahead of your peers in academia like he so did”

“Oh here we go” Alan muttered.

“Well I’ve tried they won’t put me in advanced classes because I wasn’t in school consistently as a kid.” I explained.

“Well that’s absurd a brilliant mind shouldn’t be held back by the amount of desks they haven’t sat at or lectures they’ve witnessed” Larry voiced in annoyance.

“Preaching to the choir,” I told him.

“Yes but do me a favor and don’t get on the soap box of yours again” Gramps asked me.

I nodded in agreement and picked at the last bits of food on my plate. “You know what?” Larry spoke up causing me and Alan to look at him but his eyes were trained on me “you should attend CalSci once you’ve escaped high school. We have no such requirements if you show the aptitude”

“I don’t know I’m still looking at quite a bit of time being forced to look at this stuff in school let alone do I want to keep having to do school work beyond it.” I pointed out.

“No no no” Larry objected waving his hands “it’s not like that at CalSci you can learn what you want and gain knowledge and work to gather more knowledge of the universe itself with a very hands on approach”

I sighed finishing off my dinner and gathered my dishes. “I’ll think about it”

“Very well” Larry accepted the answer as I stood up.

“You done?” Alan asked.

“Yeah” I murmured, taking my dishes into the kitchen. I glanced out the window and spotted my Uncle joining my father in his basketball playing. I loved basketball. The one sport I was decent at. As I watched my mind different back to just shortly before I went to live with my father here.

~_~_~_~_~_~_~_~_~

3rd POV.

“Yo Calvin” Abby looked up from where she was sitting with her back to a wall in the courtyard book in hand. A girl named Naomi was looking at her from the basketball court with the ball tucked under her arm. Other girls around her were glancing in Abby’s direction and muttering to each other. “We need a even number get over here”

Abby hesitated. Veronica was standing on the court eyeing her with the same hate in her eyes. However after one of her accomplices came over and whispered in her ear she nodded her agreement with the situation.

Abby sighed and closed her book getting up and heading to the court. “‘ight y’all line up me and V will choose the teams,” Naomi declared.

Abby stood in line with the seven other girls they had goated into playing with them. Veronica stuck to choosing her pals and Naomi was smart enough not to choose them but Veronica only had three friends and Abby ended up being the last one on the line as Naomi chose the girl next to her.

“Calvin and V on the same team” one of the girls on Naomi’s team voiced “this’ll be interesting.”

Abby scoffed and took her position on the court. “Hey bookworm don’t get in the way” Veronica snapped.

“Then stay out of mine” Abby shrugged. Veronica shot her a glare as the other girls jeered.

“Hey let’s play” Naomi called everyone’s attention.

The game started out easy. Naomi had the ball and was heading down the court. Abby intercepted her snagging the ball easily and heading down the court when she was slammed in the side hitting the ground. Veronica had the ball now and shot it into the hoop.

“Hey!” Abby yelled getting back to her feet “thought we were on the same team”

“Thought I said stay out of my way” Veronica retaliated coming up to get Abby’s face.

“Hey knock it off” Naomi pushed between the girls “either play or leave and sort your shit out the way you normally do and land in the infirmary”

“You telling me what to do, china?” Veronica snarled at Naomi.

Naomi shifted back a bit “I’m actually Korean not that it matters but what I’m trying to do is play some basketball. Now you two can go duke it out if you want at least it’ll keep the teams even”

Veronica scoffed “whatever” she stalked back onto the court.

Abby sighed and followed the game started up again and Abby barely touched the ball as it was passed from player to player. Until it got to a point where they had five minutes left of courtyard time and Naomi’s team was up by one.

“We need to score. You beat Naomi at ball, that's a serious brag even with dead weights like Harp and Richards on her team” Veronica’s lacky Fiona stated.

“Yeah well we aren’t going to if Veronica tries to score again” Abby muttered to the rest of the huddle.

“You saying I can’t shoot Calvin?” Veronica turned to her angry.

“No I’m saying our entire strategy has been geared to give you glory this entire time and they’ve figured that out” Abby explained “that’s why they’ve blocked our last five attempts.”

“What? You want us to pass it to you?” Veronica asked “that ain’t how that works Calvin”

“I don’t care who you pass it to” Abby shrugged “you just gotta pass it”

Veronica thought about it a moment “Alright Fi you take it” she declared. “Let’s go”

“Okay” Fiona muttered, sounding unsure.

The game started and Naomi’s team got the ball dribbling down the court. Veronica intercepted as Abby and Fiona headed down opposite sides of the court. Veronica looked to pass it and saw Naomi guarding Fiona who was looking less than confident. Then she saw Calvin raise her hand. She was completely open. No one expected Veronica to pass the ball to the one girl she beat up every other day.

Veronica passed the ball. Abby caught it easy and dribbled it a step before shooting it circled the hoop before dropping in to the cheers of the team.

“Alright ladies time to get inside” one of the matron’s called from the door the girls shuffled to the door Naomi scooping the ball.

“Nice shot Calvin” Naomi told her, shoving her shoulder as she passed.

Abby grabbed her book and headed inside. She was heading down the hall at a casual pace before she was pinned to the wall. Veronica had her collar. “That was a one time thing you got that?”

Abby blinked at the other girl “really? You're so insecure about your status you have to make that point?” she asked with every ounce of sass she could muster.

Veronica growled and threw her to the floor Abby got on her feet and shoved Veronica’s middle. The bigger girl pushed her away and soon they were grabbing at each other pulling hair and scratching. Soon someone was there to pull them apart.

“Why do any of us expect different of those two?” Abby heard Naomi mutter to Fiona as Abby and Veronica were led to the infirmary.

~_~_~_~_~_~_~_~_~_~_

Abby POV.

“Bye Uncle Charlie” I called from the shade as the mathematician peeled off the fence of the batting cages and headed back to his car.

“Bye Abbs” Charlie replied with a wave. I glanced over at my father as another crack of baseball on bat sounded. He was really starting to get into a rhythm, a proud smile on his face. I smiled lightly and returned to my reading. However there was only a moment of peace before Don appeared grabbing his water bottle and taking a swig.

“You want to take a few whacks?” He asked, gesturing to the batting cage.

I shot another look over at the ball spitter. “Uh no thanks I’ve never really..” I trailed off gesturing at the cage with an implied statement and apathetic wave.

Don looked at the cage then back at me with a small amount of shock evident in his face. “You’ve never played baseball before?” He asked in disbelief.

“Maybe once in gym class” I shrugged answering honestly. “I don’t know if you’ve noticed Donald but I’m kinda on the nerd side of things”

Don scoffed. “Come on” he grabbed my book and much to my relief remembered to put the bookmark in its place before closing it. “No daughter of mine is going to go through life without playing baseball”

I scoffed as I was pulled to my feet and given a helmet. I would normally put up a bit more of a fight but I knew that this sport meant a lot to him. So I kept my remarks to myself and went along with it. We headed out to the cage. He showed me what position to take. How to hold the bat properly and watch the ball.

Even with his coaching it took a while before I actually hit the ball. When I did it was quite auspicious to us both. Despite it not going anywhere near where we wanted it to go. There was a lot of laughing and joking and we both left happy reliving the events in story with some subtle elaborations. Don excited to take me back some time.

Chapter 9 ->

#Don Eppes #Charlie Eppes #Alan Eppes #Larry Fleinhardt #amita ramanujan #Terry Lake #David Sinclair #Numb3rs #numb3rs season 1 #don has a daughter #Episode Related #episode per chapter #also on quotev #Also posted on AO3

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utagoe · 4 years

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IDOLiSH7: Labyrinth Lyrics

Kanji, romaji and English translation for Labyrinth by Isumi Haruka

(kanji source)

本気で投げた言葉も夜風に紛れてしまったrays of light 時計の針は10時を示して儚さ知らせるまるでチャイム(ここから出して) 鏡に写っている(ここから出してよ) あの日の自分があまりに無力で

それでも(ここから出して) 消えない掠れた声(ここから出してよ) 嘆きのようなメロディを奏でてるよ

断ち切るしかないんだろう注いだ冬は心のLabyrinth 後戻りなんて出来ないからやりきるしかないんだろう黒い気持ちと手を繋いだって構わない抱きしめたっていい

疑うことを知らない瞳に戻れたらなんといいか時計の針は日付を変えてく虚しさ絡まる地味なジョーク(ここにいるんだ) 見つけてほしいと思う(ここにいるんだよ) 怒りも痛みも全て受け止めて

今なら(ここにいるんだ) もう一度願えるかな(ここにいるんだよ) 信じるもの見つめて歌えることを

極めるしかないんだろうかけ違えてたボタンも何もかも元通りなんて出来ないけど証明して見せるんだ強い気持ちで立ち続けることだけが自分でいられると

断ち切るしかないんだろう注いだ冬は心のLabyrinth 後戻りなんて出来ないからやりきるしかないんだろう黒い気持ちと手を繋いだって構わないほら

極めるしかないんだろうかけ違えてたボタンも何もかも元通りなんて出来ないけど証明して見せるんだ強い気持ちで立ち続けることだけが未来へ繋がると

Romaji

honki de nageta kotoba mo yokaze ni magirete shimatta rays of light tokei no hari wa juuji wo shimeshite hakanasa shiraseru maru de chaimu (koko kara dashite) kagami ni utsutteiru (koko kara dashiteyo) ano hi no jibun ga amari ni muryoku de

sore demo (koko kara dashite) kienai kasureta koe (koko kara dashiteyo) nageki no you na merodi wo kanadeteruyo

tachikiru shika nain darou sosoida fuyu wa kokoro no Labyrinth atomodori nante dekinai kara yarikiru shika nain darou kuroi kimochi to te wo tsunaidatte kamawanai dakishimetatte ii

utagau koto wo shiranai hitomi ni modoretara nan to iika tokei no hari wa hizuke wo kaeteku munashisa karamaru jimi na jooku (koko ni irun da) mitsukete hoshii to omou (koko ni irun dayo) ikari mo itami mo subete uketomete

ima nara (koko ni irun da) mou ichido negaeru kana (koko ni irun dayo) shinjiru mono mitsumete utaeru koto wo

kiwameru shika nain darou kakechigaeteta botan mo nanimokamo motodoori nante dekinai kedo shoumei shite miserun da tsuyoi kimochi de tachi tsuzukeru koto dake ga jibun de irareru to

tachikiru shika nain darou sosoida fuyu wa kokoro no Labyrinth atomodori nante dekinai kara yarikiru shika nain darou kuroi kimochi to te wo tsunaidatte kamawanai hora

kiwameru shika nain darou kakechigaeteta botan mo nanimokamo motodoori nante dekinai kedo shoumei shite miserun da tsuyoi kimochi de tachi tsuzukeru koto dake ga mirai e tsunagaru to

English

The words I've seriously thrown, too, were diverted In the night wind, rays of light The hands of the clock show 10 o'clock They inform me of transience like a chime (Take me from here) Myself from that day (Take me from here) Who's reflected in the mirror, is way too powerless

Nevertheless (Take me from here) My nonvanishing cracking voice (Take me from here) Is playing a melody that sounds like lamentation

I have no choice but to break it off, do I? The falling winter is my heart's labyrinth I can't backtrack, so I have no choice but to go the full distance, do I? Even if I hold hands with these dark feelings, I don't mind I can even hold them close

How great would it be if I could Go back to when my eyes didn't know distrust The hands of the clock change the date A plain joke entwined with emptiness (I'm right here) I think I want you to find me (I'm right here) Accept all of my anger and pain

Now (I'm right here) Could I wish once again? (I'm right here) For looking at what I believe in And being able to sing

I have no choice but to go to the end, do I? I can't undo everything that I Did wrong from the start But I'll prove it to you That I'll keep standing with these strong feelings And that I can be myself

I have no choice but to go to the end, do I? I can't undo everything that I Did wrong from the start But I'll prove it to you That I'll keep standing with these strong feelings This will be connected to my future

#request #idolish7 #idolish 7 #i7 #ainana #zool #isumi haruka #haruka isumi #hirose yuya #hirose yuuya

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anniversary-magazine · 5 years

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Rooms, Tbilisi : Objects as Figures – as Guests of a Space

Being the Tbilisi-based Interior and Product Design studio with the two founders behind it – Keti Toloraia and Nata Janberidze, whose aesthetic focus was determined by their Soviet childhood, in a synthesis of European and Asian cultures inhabiting the country, Rooms is perceived an on-growing practice at both local and international Design stages.

“By always seeking something new and unfamiliar, we are rarely fully aware of what is around us at any given moment. That’s why we decided to capture the simple forms of our daily life and freeze them in time - to “monumentalize” them. This collection is all about celebrating the Life on Earth.”

– Rooms

The curiosity and the awareness of permanence of the things that were created centuries ago, with a concentration on mixing simple organic and geometric forms, yet juxtaposed with composite materials, makes their archetypal collection Life On Earth an assembly of one-of-a-kind sculptural objects.

Keti and Nata have known each other since their interior design faculty days at the Tbilisi Academy of Arts. Having started working together straight after the graduation in 2003, in another four years, they decided to found their own design studio. By holding onto “think globally but act locally,” in a short time this approach helped ROOMS gain recognition far beyond the borders of their homeland in the Caucasus.

Wild Minimalism is the collection where a mix of archaic and modern, wild and minimal intersect. The nod from the Soviet era’s architectural forms, traditional folklore and local ethnic furniture have led them to get back to their roots and express the feeling of being grounded using simple natural materials, which transformed into a series of gently handcrafted yet primitively shaped wooden pieces out of timber that is more than 100-year-old.

Everything that they design has a blend of modern and archaic, and ever with a notable twist. Bravely playing with past and present, their throne-like pieces in addition to contrasting brass against dark stained wood acquire both heavenly and human-made portrayal of inner and outer space.

Rooms' collaborations include local artisans, among which is the Georgian stone company Kamara; as well as being exposed at the collectible design galleries like Mint Gallery (London), Spazio Rossana Orlandi (Milan) and The Future Perfect (New York); but are also not limited to the companies with shared ideology of respecting traditional crafts.

“A rug – in itself is a magical object, but for us it is also a symbol of cultural heritage and a chance to explore both – history and magic.”

– Rooms

In the matter of their 10th Anniversary celebrated during Milan Design Week 2018, they showcased pieces from the collaboration with cc-tapis, the Italian company that produces contemporary hand-knotted rugs created by expert Tibetan artisans in Nepal. It turned into a capsule collection of rugs, entitled The Night of a Hunter, with reinterpreted authentic Georgian motifs, as another ageless craft deeply rooted in Georgian culture.

Nata and Keti do not only bring their souls into every piece they create but leave a nonvanishing impression of multi-faceted depth of both the intricate and refined – and all in a humble clear approach as the solid foundation at large.

“Simplicity and the clear paths of life bring us to the solid state of mind.”

– Rooms

#Tbilisi #Georgia #Product Design #Design #Designer #Keti Toloraia #Nata Janberidze #Rooms #Studio #Featured

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arxt1 · 2 years

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What is the fate of Hawking evaporation in gravity theories with higher curvature terms?. (arXiv:2205.13006v1 [gr-qc])

During the final stages of black hole evaporation, ultraviolet deviations from General Relativity eventually become dramatic, potentially affecting the end-state. We explore this problem by performing nonlinear simulations of wave packets in Einstein-dilaton-Gauss-Bonnet gravity, the only gravity theory with quadratic curvature terms which can be studied at fully nonperturbative level. Black holes in this theory have a minimum mass but also a nonvanishing temperature. This poses a puzzle concerning the final fate of Hawking evaporation in the presence of high-curvature nonperturbative effects. By simulating the mass loss due to evaporation at the classical level using an auxiliary phantom field, we study the nonlinear evolution of black holes past the minimum mass. We observe a runaway shrink of the apparent horizon (a nonperturbative effect forbidden in General Relativity) which eventually unveils a high-curvature elliptic region. While this might hint to the formation of a naked singularity (and hence to a violation of the weak cosmic censorship) or of a pathological spacetime region, a different numerical formulation of the initial-value problem in this theory might be required to rule out other possibilities, including the transition from the critical black hole to a stable horizonless remnant. Our study is relevant in the context of the information-loss paradox, dark-matter remnants, and for constraints on microscopic primordial black holes.

from astro-ph.HE updates on arXiv.org https://ift.tt/XD6SizN

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a-little-bit-oddish · 2 years

Note

google "there is no nonvanishing continuous tangent vector field on even-dimensional n-spheres"

I feel so blessed. Thank you. I am enlightened.

#ask

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karishmamulani · 3 years

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Nonlinear Optical Crystals Market Evolving Opportunities, Covid-19 Impact, Strategies And Forecast

The global Nonlinear Optical (NLO) Crystals Market size is expected to reach USD 7,766.4 million by 2026 according to a new study by Polaris Market Research The key players in the market include Covesion, HC Photonics, AdvR, Red Optronics, Inrad Optics, Eskma Optics, among others.

Nonlinear optics is the part of science that manages the collaboration of light with issue under conditions to such an extent that the direct superposition guideline is disregarded. Instances of nonlinear optical associations incorporate consonant age, whole and distinction recurrence age, the force reliance of the complex refractive record, light-by-light dissipating, and invigorated light dispersing. These procedures lead to applications including all-optical switching, optical power limiting, picture control, and picture preparing.

Insulating gems structure a significant class of second-request nonlinear optical materials. It is settled that solitary precious stones that come up short on a focal point of reversal evenness can have a nonvanishing second-request vulnerability. This prerequisite restrains the selection of precious stones to those of certain balance classes. An extra prerequisite on materials properties is set by the way that second-request nonlinear optical procedures can happen with great effectiveness just if a standard stage coordinating condition is fulfilled.

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Albeit all materials should show this conduct, the proficiency of this procedure is commonly little and can’t be controlled remotely. Presently, accomplices of the Graphene Flagship venture in Cambridge (UK), Milan, and Genova (Italy) have shown just because that graphene demonstrates a decent optical reaction, yet in addition how to control the quality of this impact utilizing an electric field.

Looks into imagine the production of new graphene optical switches, which could likewise bridle new optical frequencies to transmit information alongside optical cables, expanding the measure of information that can be transmitted. At present, most business gadgets utilizing nonlinear optics are just utilized in spectroscopy. Graphene could make ready towards the creation of new gadgets for ultra-expansive transmission capacity applications.

Nevertheless, these are obviously delegate arrangements, intended to purchase time to recuperate high speculation costs inline innovation (principally burrowing), before at last taking off Fiber-to-the-Building or even Fiber-to-the-Home (FTTB/FTTH). This pattern for fixed-line administration is probably going to persevere for quite a while. Moore’s law will win for at any rate another five to seven years with regards to storage (it is less sure for processor speeds). And keeping in mind that development in screens may slow fairly, higher screen definition will proceed, to 8K and past, until we arrive at the farthest point of the human eye’s capacity. Normally, portable broadband improvement has pursued the patterns in fixed broadband, but with a postponement of a couple of years.

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The application of Nonlinear Optical Crystals includes high cost owing to the high price of raw materials. It not only increases the cost of end-product but also discourages manufacturing companies to adopt the same. Despite Asia Pacific having cheapest workforce across the globe, the cost of end product ascends drastically. This in turn acts as a major restraint for the Nonlinear Optical Crystals Market.

Various nonlinear optical crystals techniques exist or are being produced for different zones going from maritime sensing of biological systems, gas air pockets, and submerged items to restorative sensing of the human body. The methodology is to utilize essential frequency occurrence waves to produce second-arrange nonlinear whole or contrast frequency handle that convey data about an article to be detected. Here we demonstrate that when all is said in done nonlinear sensing of an article, many confused and conceivably surprising systems can prompt total or distinction frequency fields.

China’s telecom segment proceeded with relentless development a year ago, with vigorous portable system benefits and improving web infrastructure. The segment’s income rose 3 percent year on year to 1.3 trillion yuan (in excess of 190 billion U.S. dollars) in 2018, as indicated by a report of the Ministry of Industry and Information Technology. Given vivacious improvement of interpersonal interaction applications, the extent of telephone call charges in the all-out telecom income dropped further to 13.7 percent a year ago from 17.9 percent in 2017. As a result, it is expected to have a positive impact on the market growth.

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#Nonlinear Optical Crystals Market #Nonlinear Optical Crystals Market size

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thousandmaths · 7 years

Text

Nonvanishing of Littlewood-Richardson Polynomials is in P

This talk was given by Alex Yong at this year’s CA+ conference. He cited Robichaux as a collaborator, as well as high school student Anshul Adve.

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Factorial Schur Functions

As with all the best combinatorics, we start with a game.

Given a partition (possibly with some zero parts), draw its Young diagram but replace the boxes with black dots and the “positions without boxes” with white dots. Don’t have any extra rows, but extra columns are okay. For instance, the partition $(2,2,0)$ corresponds to this picture

We then make moves according to the following rule, anytime we see a black dot in a TL corner of a square that’s otherwise white, we can move it to the BR corner:

We make this move wherever possible until there are no more available. The set of all diagrams that can be obtained this way, starting with the partition $\lambda$ will be called, uncreatively, $\text{Black}(\lambda)$. To keep with our example, here is $\text{Black}((2,2,0))$:

Now it is time for some algebra: we are going to describe a polynomial in two sets of variables $X=x_1,\dots, x_r$, where $r$ is the number of rows; and $Y=y_1, y_2, y_3,\dots$ representing the columns. First, we define the weight of a diagram $\text{wt}(D)$ to be the product of every $x_i-y_j$, for all $i$ and $j$ such that there is a black dot in row $i$ and column $j$.

Finally, define the factorial Schur function $s_\lambda(X,Y)$ to be the sum of $\text{wt}(D)$ over all diagrams $D\in\text{Black}(\lambda)$. As a formula:

$$ s_\lambda(X,Y) = \sum_{D\in\text{Black}(\lambda)} ~~ \prod_{(i,j)\text{ is black}} x_i-y_j. $$

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Littlewood-Richardson Polynomials

The reason that factorial Schur functions are called that is because if you plug $y_i=0$ for every $y$, the resulting polynomial is really, honestly, the Schur polynomial. Schur functions form a basis for the symmetric algebra, and so we might hope that the symmetric Schur functions are the basis for something. This hope turns out to be validated: it is a $\Bbb Z[Y]$-module basis of $\Lambda_n\otimes \Bbb Z[Y]$ (The last symbol there is polynomial algebra in the $y$-variables, and the symbol in the middle is a tensor product)

Because of that, this means that $s_\lambda(X,Y)s_\mu(X,Y)$ must be some linear combination, and so we can ask for the structure coefficients $C_{\lambda,\mu}^\nu(Y)$. We write the $Y$ there because in general these things can be an element in $\Bbb Z[Y]$; in other words, can be a polynomial in the $y$-variables.

Since they specialize to the Littlewood-Richardson coefficients when $y_i=0$, we call these $C_{\lambda,\mu}^\nu$ the Littlewood-Richardson Polynomials

[ Because of the geometric interpretation of ordinary Littlewood-Richardson coefficients, we know that they are nonnegative integers; you may ask whether the LR-polynomials are also positive (in that all the coefficients are negative). The answer is no, but they are positive as polynomials in $z_i:=y_{i+1}-y_i$. ]

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Polynomial Time

In 2005, one day after the other, two papers were posted to the arXiv, both claiming to have proven the following theorem:

Theorem (DeLoera–McAllister 2006, Mulmuley–Narayanan–Sohoni 2012*). There is an algorithm for determining whether or not the Littlewood-Richardson coefficient $c_{\lambda,\mu}^\nu=0$ in polynomial time.

If you’re not super familiar with “polynomial time”, feel free to substitute the word “quickly” anywhere you see it; this isn’t necessarily true but it’s a respectable approximation.

This naturally raises the question of whether the Littlewood-Richardson polynomials can also be determined to be zero or not in polynomial time. As the title of the talk suggests— and as Adve, Robichaux, and Yong proved— the answer is yes. The rest of this section is devoted to a proof sketch.

There is a celebrated proof due to Knutson–Tao which proves the so-called saturation conjecture, that $c_{\lambda,\mu}^\nu=0$ if and only if $c_{N\lambda,N\mu}^{N\nu}=0$ for all $N$. At this point, Yong talked a little bit about the history of that conjecture:

In the 19th century, people were asking this question about Hermetian matrices.

In 1962 Horn conjectured a bunch of inequalities which resolved the question.

In 1994 Klyachko solved the problem, but didn’t use Horn’s inequalities.

Soon after, it was realized that the saturation conjecture was sufficient to prove Horn’s inequalities.

In 1998, Knutson and Tao published their proof.

The argument they made in this paper was refined by a 2013 theorem of a different ARY team: Anderson, Richmond, and Yong. They showed that the analogous statement is true for the Littlewood–Richardson polynomials: $C_{\lambda,\mu}^\nu(Y)=0$ if and only if $C_{N\lambda,N\mu}^{N\nu}(Y)=0$ for all $N$.

The major innovation made by the new ARY team (Adve, Robichaux, and Yong) constructed a family of polytopes $P_{\lambda,\mu}^\nu$ with the following properties:

scaling the polytope by a factor of $N$ is the same as scaling the partitions by a factor of N, i.e. $P_{N\lambda,N\mu}^{N\nu} = NP_{\lambda,\mu}^\nu$,

and the crucial bit: $P_{\lambda,\mu}^\nu$ has an integer lattice point if and only if $C_{\lambda,\mu}^{\nu}(Y)\neq 0$

In particular, this implies that the “polynomial saturation conjecture” can be used to reduce the question of $C_{\lambda,\mu}^{\nu}(Y)\neq 0$ to figuring out whether $P_{\lambda,\mu}^\nu$ is the empty polytope. And this, finally, is a problem which is known to be solvable in polynomial time, which concludes the proof.

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[ * The dates listed above are the publication dates of the papers that the two teams wrote. “So that tells you something about publishing in mathematics”, Yong says. Perhaps, but... I’m not sure what. I’m assuming that what he was getting at is this: The names in the latter team are nothing to scoff at, by a long shot; I mean, I have heard all five of these names before in other contexts. But the prestige associated to the names in the former team might have made that paper subject to less scrutiny than the latter. Or perhaps he just meant that the capricious turns of fate can turn what “should be” a short procedure into a long one. ]

#math #maths #mathematics #mathema #algebra #combinatorics #algebraic combinatorics #geometry #symmetric functions #complexity #caplus #caplus2017

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deafeningmusicfury · 4 years

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Nonlinear Optical (NLO) Crystals Market - with Focus on Competitive Landscape and Growth Factors 2026

The global Nonlinear Optical (NLO) Crystals Market size is expected to reach USD 7,766.4 million by 2026 according to a new study by Polaris Market Research. The report “Nonlinear Optical (NLO) Crystals Market Share, Size, Trends, Industry Analysis Report By Type (KTP, PPLN, BBO, LBO, CLBO, DKDP, ADP, KDP, and Others); By Application (Laser Technology, Medical, Underwater Photography, Optical Communication, Optical Ranging, Quantum Information Sciences, Atomic Sciences, Remote Sensing, Others); By Regions, Segment Forecast, 2020 – 2026” gives a detailed insight into current market dynamics and provides analysis on future market growth.

Request for a sample copy of this research report @ https://www.polarismarketresearch.com/industry-analysis/nonlinear-optical-crystals-market/request-for-sample

Complete Summary with TOC Available @ https://www.polarismarketresearch.com/industry-analysis/nonlinear-optical-crystals-market

The key players in the market include Covesion, HC Photonics, AdvR, Red Optronics, Inrad Optics, Eskma Optics, among others.

Polaris Market research has segmented the Nonlinear Optical Crystals Market report on the basis of type, application, and region

Nonlinear Optical Crystals Type Outlook (Revenue, USD Million, 2015 – 2026)

KTP

PPLN

BBO

LBO

CLBO

DKDP

ADP

KDP

Others

Nonlinear Optical Crystals Application Outlook (Revenue, USD Million, 2015 – 2026)

Laser Technology

Medical

Underwater Photography

Optical Communication

Optical Ranging

Quantum Information Sciences

Atomic Sciences

Remote Sensing

Others

Nonlinear Optical Crystals Regional Outlook (Revenue, USD Million, 2015 – 2026)

U.S.

Canada

France

Germany

Italy

India

Japan

China

Korea

Mexico

Brazil

Purchase This Report @: https://www.polarismarketresearch.com/checkouts/6141

About Polaris Market Research

Polaris Market Research

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Email: [email protected]

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#Nonlinear Optical (NLO) Crystals Market #Nonlinear Optical (NLO) Crystals Market s #Nonlinear Optical (NLO) Crystals Market size

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blogyamini · 4 years

Text

Nonlinear Optical (NLO) Crystals Market Analysts Expect Robust Growth in 2026

New York, NY 22 June 2020: The global Nonlinear Optical (NLO) Crystals Market size is expected to reach USD 7,766.4 million by 2026 according to a new study by Polaris Market Research. The report “Nonlinear Optical (NLO) Crystals Market Share, Size, Trends, Industry Analysis Report By Type (KTP, PPLN, BBO, LBO, CLBO, DKDP, ADP, KDP, and Others); By Application (Laser Technology, Medical, Underwater Photography, Optical Communication, Optical Ranging, Quantum Information Sciences, Atomic Sciences, Remote Sensing, Others); By Regions, Segment Forecast, 2020 – 2026” gives a detailed insight into current market dynamics and provides analysis on future market growth.

Request for a sample of this research report @https://www.polarismarketresearch.com/industry-analysis/nonlinear-optical-crystals-market/request-for-sample

Get Exclusive Discount on This Report @ https://www.polarismarketresearch.com/industry-analysis/nonlinear-optical-crystals-market/request-for-discount-pricing

The key players in the market include Covesion, HC Photonics, AdvR, Red Optronics, Inrad Optics, Eskma Optics, among others.

Polaris Market research has segmented the Nonlinear Optical Crystals Market report on the basis of type, application, and region

Nonlinear Optical Crystals Type Outlook (Revenue, USD Million, 2015 – 2026)

KTP

PPLN

BBO

LBO

CLBO

DKDP

ADP

KDP

Others

Nonlinear Optical Crystals Application Outlook (Revenue, USD Million, 2015 – 2026)

Laser Technology

Medical

Underwater Photography

Optical Communication

Optical Ranging

Quantum Information Sciences

Atomic Sciences

Remote Sensing

Others

Nonlinear Optical Crystals Regional Outlook (Revenue, USD Million, 2015 – 2026)

North America

Europe

Asia Pacific

Latin America

Middle East & Africa

U.S.

Canada

France

Germany

Italy

India

Japan

China

Korea

Mexico

Brazil

About Polaris Market Research

Polaris Market Research is a global market research and consulting company. The company specializes in providing exceptional market intelligence and in-depth business research services for our clientele spread across different enterprises. We at Polaris are obliged to serve our diverse customer base present across the industries of healthcare, technology, semi-conductors and chemicals among various other industries present around the world. We strive to provide our customers with updated information on innovative technologies, high growth markets, emerging business environments and latest business-centric applications, thereby helping them always to make informed decisions and leverage new opportunities. Adept with a highly competent, experienced and extremely qualified team of experts comprising SMEs, analysts and consultants, we at Polaris endeavor to deliver value-added business solutions to our customers.

Polaris Market Research Phone: 1–646–568–9980 Email: [email protected] Web: www.polarismarketresearch.com

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mathematicalrosebudthorn · 6 years

Text

28 may 2018

Rose:

for every metric g’ on a riemann surface there is a function u st g = e^u *g is a metric that is constant curvature (Berger’s theorem)

Thorn:

classification of irreducible representations of Clifford algebras

averaging over Clifford group = gen. by ONB of R^n, -1 to get inner product such that Clifford multiplication by unit vectors is orthogonal

Bud:

Wu formula, Steenrod algebra

map without fixed points S^n -> S^n is homotopic to antipodal map

antipodal map is homotopic to Id iff n odd (via nonvanishing vector field)

Lefschetz fixed point theorem

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utagoe · 4 years

Text

Hatano Wataru: realize Lyrics

Kanji, romaji and English translation for realize by Hatano Wataru

(kanji source)

いつでも探してる　足りないピース　日々違う形　色ノイズだらけの現代[いま]　僕は耳をすます my heart

わざと斜に構えて　必要ない違和感　演出して隠し続けるのは苦しいね　胸叩��　痛いや

touch　流れてく世界　逆らうために　衝き上げた

消えない　鼓動　愛　ストーリー　歌えば響かせて my life 嘘のない my life 掴んだ今が　語るさかけがえない my life 譲れない my life

変わらないでいるために　変わり続けていくんだ僕で在るから

わかんなきゃすぐ“hey”　答えて“OK”　なかなかの打率じゃない？でもねテクノロジー　君じゃ測れないよ I am

焦らなくてもいい　白いページ　四苦八苦　埋めていくヨレた文字も味さ　笑える日が来るから　いつか

light　僕は見せたい　綺麗だけが答えじゃない

予想外　急展開　時計は戻らない転んでも my life 揺らぐなよ my life もがいた過去の青さが彩るよ my life 抱きしめて my life

変わらないでいるために　変わり続けていくんだ守りたいから

醒めない夢は　果てない僕の現実(リアル) 息は止めないで　この先に待つ未来

鼓動　愛　ストーリー　歌えば響かせて my life 嘘のない my life 掴んだ今が　語るさかけがえない my life 譲れない my life

変わらないでいるために　変わり続けていくんだ僕で在るから

Romaji

itsudemo sagashiteru tarinai piisu hibi chigau katachi iro noizu darake no ima boku wa mimi wo sumasu my heart

waza to sha ni kamaete hitsuyou nai iwakan enshutsu shite kakushi tsuzukeru no wa kurushii ne mune tataku itai ya

touch nagareteku sekai sakarau tame ni tsukiageta

kienai kodou ai sutoorii utaeba hibikasete my life uso no nai my life tsukanda ima ga kataru sa kakegaenai my life yuzurenai my life

kawaranaide iru tame ni kawari tsuzukete yukunda boku de aru kara

wakannakya sugu "hey" kotaete "OK" nakanaka no daritsu janai? demo ne tekunorojii kimi ja hakarenaiyo I am

aseranakutemo ii shiroi peeji shikuhakku umeteyuku yoreta moji mo aji sa waraeru hi ga kuru kara itsuka

light boku wa misetai kirei dake ga kotae janai

yosougai kyuutenkai tokei wa modoranai korondemo my life yuragunayo my life mogaita kako no aosa ga irodoruyo my life dakishimete my life

kawaranaide iru tame ni kawari tsuzukete yukunda mamoritai kara

samenai yume wa hatenai boku no riaru iki wa tomenaide kono saki ni matsu mirai

kodou ai sutoorii utaeba hibikasete my life uso no nai my life tsukanda ima ga kataru sa kakegaenai my life yuzurenai my life

kawaranaide iru tame ni kawari tsuzukete yukunda boku de aru kara

English

I'm always looking for the missing pieces - Shapes and colours different from daily life My heart listens carefully to the present full of noise

I stand ready on purpose and direct an unnecessary discomfort It's difficult to keep on hiding, right? It beats in your chest and hurts

Touch - I pushed up so I could go against this flowing world

If I sing these nonvanishing beats, love, and stories Let it resound, my life No lies in my life I'll recite this present time I've grabbed No replacement for my life I won't hand over my life

I continue to change so that I can remain unchanging Because I am me

When I don't know something I just go "hey", just answer "OK" - That's quite a good batting average, right? But hey, you can't really measure technology - I am

You don't need to hurry, I'll bury your distress in these white pages Twisted letters also have their taste, because one day we'll be able to laugh

Light - I want to show you that beauty by itself isn't the answer

In an unexpected rapid development, the clock won't turn back Even if I fall over, it's my life Don't sway, my life The greenness of my struggling past Colours my life Hold tight my life

I continue to change so that I can remain unchanging Because I want to protect you

This dream I don't wake up from is my endless reality Don't stop breathing, your future awaits you after this

If I sing these nonvanishing beats, love, and stories Let it resound, my life No lies in my life I'll recite this present time I've grabbed No replacement for my life I won't hand over my life

I continue to change so that I can remain unchanging Because I am me

#i dont know who wrote this but i feel like they were high #request #hatano wataru #wataru hatano #realize #futuristic #seiyuu #lyrics #translation

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