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Hello, so basically i had already done an answer similar to the same question, but the great Quora decided to collapse it after it hit 50K+ and oh boy that hurt because i spent hours doing it.Okay let’s just get started:1. BTS didn’t pave the way:Armies: Wow! Our BTS oppas paved the way internationally! They’re the best! They’re kings! They’re the legends of Kpo--Hold on, wait a minute, legends of K-pop? BTS? I am a huge fan of BTS, like huge, but did you guys forget 2NE1, BigBang, Super Junior, SNSD, TVXQ, BoA, RAIN, Lee Hyori and Wonder Girls? If these groups didn’t pave the way through Asia, BTS would’ve never been this big. These are the legends of K-pop But i guess the newbies forget/ don’t know the real legends of K-pop. But still, BTS did play a huge role in the western market. And if you don’t agree:2. PSY is the solo legend of K-pop:Who paved the way internationally? Yup, PSY did. PSY is known in America, Africa, Europe, Asia, Australia. Who doesn’t know Psy? Even my Grandparents do. Also, he is one of the best dancers of K-pop. This man is 42, isn’t that fit, but his dancing skills are out of the world. Do you want to know another reason to why Psy is the solo legend of K-pop? Psy isn’t just Gangnam style, he has been in the industry since 2001. Do you know how hard it was for him at the beginning? The managers of YG argued about his “ugly” looks right in front of him. They didn’t want to except him after seeing his face, but they didn’t have a choice because they had already signed a contract. He had to cover/ hide his face at the beginning of his career because he didn’t fit the beauty standards despite being a respected artist in South Korea. He was a well known artist there but fans never knew how he looked like. But look where he is now. This legend made us stan K-pop before we even knew it was K-pop, ugh the power he holds.3. Lee SooMan was the best CEO in the industry:First of all a little message to the newbies, Don’t send hate to Lee SooMan when your fave gets mistreated. He isn’t the CEO anymore and left like 10 years ago (February 2010) after his wife found out+died because of cancer. Imagine how hurt he must’ve been that he left the Empire he made with his sweat and tears for like 2 decades. So just leave him alone. Yes SM entertainment does have a very hard training and overworks his idols but don’t every companies? *cough JYP* *cough give twice a- cough- break*. Lee SooMan is amazing, and only created bops and legends, and we must be thankful for that. He reminds me of my father, and any other Asian fathers, very strict from the outside but loves his kids genuinely. And that’s Lee SooMan, don’t you see how proud he gets when his artist get their 1st wins, he even visits his artist’s concerts to support them and brags about them like a Mom lol. -Haters: But he hit TVXQ! -First, that was just from an article, it was never proved and the artists didn’t say it themselves, second, JYP and other companies hit their idols. Jay Park himself said it, that the trainees at JYP would constantly get hit. That’s just an Asian thing for discipline. At least he’s not as creepy as JYP who always sexualizes females in his MVs and doesn’t gamble with it’s artist’s money like YG. Also, SM himself is an Orbit, and helped produce Loona’s “So What!” If y’all orbits aren’t thankful for this amazing man then idk what to say.4. SM ent. is the best company:It isn’t the #1 company for nothing. Yes, the trainees are overworked and the training is extremely hard but that’s simply because it’s SM ent. The trainees need to work hard because it’s an honor for them to be accepted there. Another reason is because it doesn’t force a certain image on it’s idols, like YG forces the baddie image and JYP the cute one. In SM groups they have multiple personalities, some members are quiet, while others are talkative, introverts and extroverts, baddies and cuties, colds and warms. Idols can honestly be themselves. They also diss Lee SooMan 24/ 7 and never get into problem, and that’s another sign showing how humble SM is and they don’t fear him at all. I’m not surprised tho, SM himself goes to Halloween parties disguised lol. Plus there are no dating bans, instead they are encouraged to date. The idols in SM are more free. Even other idols recommend SM and not their own companies when fans want to join. Here is a photo of SM with his favorite kids.Here’s a photo of SM with older generation idols. I remember BoA even said that Lee Soo Man is like her father. And older generation idols said that SM was very caring of them and that they would like him back as the CEO. (I’ll insert links or videos if I find some, I don’t remember where exactly I got these informations as it used to be a while ago.)6. Black Pink isn’t the best girl group and Blinks are the most toxic fandom:Blinks will literally kill me for this. But guess what? I used to be a Blink myself. I never really stanned them but liked their music. But as soon as i saw how toxic the fandom is, i immediately left and i don’t regret it. Armies have become mature these 2 years and aren’t as childish as before, I can even say they have become one of the most respectful fandoms. But Blinks? Oh boy, just because me and my mom (who is a plastic surgeon) said that Lisa had rhinoplasty, they went crazy. They literally threatened my mom saying they will track her down, find her email/ job details and ruin her job. The hate i got was shocking. I know not all Blinks are like that, but we can only see the childish ones. That’s how you guys protect your idols? By threatening people and sending hate? Grow up. Okay back to Black Pink, some of their songs are really nice, but they rarely have comebacks and are just a modern version of 2NE1. The only reason why i was a Blink was because of the amazing personalities these 4 girls have! Even if i’m not a Blink anymore, i love all 4 members for who they are and not for what they do. Don’t kill me for this, and calm down.7. Fandoms should stop exaggerating stuff and ruining other the celebrities career.Here are 2 examples: 1. Do you remember when comedian/ host Shin Dong Yup teased Heechul after the dating news with him and Momo? And Onces went crazy saying he made her cry? That was just unbelievably stupid. Momo is an amazing and strong woman with a strong mentality, why would she cry? This is what happened: Heechul, Dong Yup and a female artist (idk her) were hosting an award ceremony, and Shin Dong Yup said: “Heechul, i bet you’re happy to see you’re special people here”. Heechul and Momo got embarrassed but he immediately continued saying: ”Super Junior! I was talking about Super Junior!”. Onces went crazy and spammed him with hate. But did they bother to know who Shin Dong Yup really is? I grew up watching him and he’s like a hero. An extremely open minded, bright and funny person. He’s an amazing adviser and teaches everyone to except people the way they are since he himself has a deaf brother. He protected/ defended idols who were getting hate/ were depressed his own way. Sulli was very very very happy to meet him before her suicide, she had nothing but good words about him.2nd example: Do you remember when Blinks hated on Momoland and Nancy to have “glared” over Lisa and Black Pink out of “jealousy” since they won? What on earth was that? Nancy was exhausted after the performance and dozed out. Momoland were rising at that time and were finally getting the fame they deserve, but after this incident they were hated on, and are always accused of stealing music. This unintentional incident, ruined their careers. They started to rip apart and a couple members left the group because of the hate. Luckily, the hate has calmed down now. Show Momoland your love and support, they’re amazing!8. Super Junior and Exo are the best boy groups, Alongside NCT:Do i even need to explain? Nope. I love them with all my heart.9. Leeteuk is the best K-pop Leader:This man is amazing and it’s sad to see he still gets hate during these past 15 years for something he didn’t even do. It’s not his fault if his Father killed his Grandparents and then committed suicide to make ends meet. He never wanted this to happen. It’s sad that people judge others not for who they are but where they come from. Do you know what’s amazing in Leeteuk? The way he takes care of Super Junior. The members are so close and no one has left the group during these 15 years, except for kangin, who left because of personal reasons, and sungmin, inactive, because he got married. The way he leads his group is amazing. And do you know what is even more wonderful about him? His strong mentality. Imagine coming home from military and discovering that your grandparents were strangled by your Father and your Dad hanged himself after that. And his father’s letter? “Do you truly believe you achieved success all by yourself?” Not only that, but he inherited all his father’s debts. I would be heartbroken and exhausted, but he, even though that literally scarred his life, he continued, and despite the hate he gets and his depression, he continues and never gives up, for the sake of Super Junior, because of his love for Super Junior. ❤︎10. Loona is the best girl group, alongside Red Velvet:These two groups are amazing. No words can explain how much i love them and how amazing they are.11. K-Quorans are the best and most mature K-pop fans:I literally love you mature K-Quorans so much. Like so much. So so much. You guys attack my heart with your kindness, love and sense of humor.12. There’s no Big 4:Seriously though, wtf is a Big 4?There is, was, and will only be Big 3. What some fans don’t get is that the Big # aren’t the companies with the most popular artists, but it’s the companies who helped form K-pop, who helped shape and make K-pop. And the companies who did that are SME: the one who basically started K-pop by debuting H.O.T, YGE: after Seo Taiji and boys, Yang Hyun suk made YGE and debuted his own groups, and JYPE: who followed their path. These 3 are the ones who created, started, and shaped K-pop and that’s why they’re called the Big 3. Not because they have famous groups. The ones who usually use the term Big 4 are newer K-pop fans so kids, there is no Big 4.Yup, that was it, thanks for reading!❤︎(all photos from google/ Quora)Edit: Don’t blame Mr. Lee for Tao, Kris and Luhan. Exo debuted in 2011, a year after SM left :(

Officially they are not, but…When I started to learn some basic Turkish (I am a native Polish) i found a lot similarities which shouldn’t exist, because those languages are not officially related.I do not care about words which have been borrowed from one language to another, but I really care about words and language constructs which seem to be old and more less native to both languages and still seem similar.I love etymologies, so I do not learn languages by heart (in dictionary way), I learn etymologies and try to learn how language works instead. Obviously I can be wrong, and those words are just coincidents and their similarity is just apparent. But even then, they can be used as mnemonics.Some examples of similarities (there are MUCH MORE!):Word roots in brackets (usually just main consonants without prefixes, infixes and sufixes)Colors:Black: pl:Czarny ↔ tr:Kara (ČR↔KR)Red: pl:Czerwony ↔ tr:Kırmızı (ČR↔KR)White: Biały VS Beyaz (BŁ-BY) Ł-R-J/Y are half consonants and are usually interchangable between languages. Another example: Milić/Miłować/Maić ↔ Maya (Polish and Sanskrit “Love”/”Illusion”)Purple/Navy blue: tr:Mor ↔ Seablue: pl:Morski (Sea: Morze)Yellow: tr:Sarı ↔ Gray: pl:Szary (Compare Slavonic Płowy/Plavy in polish means Yellow/Gray in Czech: Blue/Gray)Green: tr:Yeşil ↔ pl: Zielony. (Šil ↔ Ziel)Food:Eat: pl:Je ↔ tr:Ye (pronounciation is the same). Examples: pl: Jem, Jesz, Je, Jemy, Jecie, Jedzenie, tr:Yemek, Yerim, Yemiyorum, Yedim, Yedin, Yemek. Especially past forms look extremely similar: Jadłem ↔Yedim, Jadł ↔ YediShashlyk: Szaszłyk ↔Şişlik. It is officially borrowing from Turkish to Polish, but… Polish has the same root meaning almost the same. We have Szycha and Szyszka. That root means something above something else. Compare Persian: Shah whence Polish Szachy (The chess game). Shah means King (somebody above others). Szycha means important person (somebody above others). Szyszka is a tree cone (growing above others) and Szaszłyk is a kind of food where new part of food is put above others. Szyszka and szaszłyk look more less the same.Watermelon: pl:Arbuz ↔ tr:Karpuz (officially borrowing from Turkish)Cherry: pl:Czereśnia ↔ tr:Kiraz (CZRŚ ↔ KRZ). Name probably comes from red/black colour (see above)Sour Cherry: pl:Wiśnia ↔ tr:Vişne (WŚ ↔ WŠ). Comes probably from Wisieć (to hang on the tree).Watermelon officially: pl:Kawon ↔ Melon: tr:Kavun (also officially Turkish through Ruthenian/Ukrainian Kavun).Zucchini: pl:Kabaczek ↔ tr:Kabak (officially borrowing from Turkish)Others (may be coincidents):Water: pl:Woda ↔ Wet: tr:vıcık (in polish transcription: Wydżyk) (WD↔WĎ)Child: pl:Dzieciak ↔ tr: Çocuk (in polish transcription: Czodżuk) (ĎČ ↔ ČĎ)King: pl:Król ↔ tr:Kral (direct borrowing from Slavonic Kral/Król coming from Kraj (Country)).Queen: pl:Królowa ↔ tr:KraliçeEye: pl:Oko Read (use eye): tr:OkuWho: pl:Kto, Kogo, Komu, Kim ↔ tr: Kim, Kimin, Kime, KimiRock/Fortress: pl:Skała ↔tr:Kale (KŁ→KL) Compare: ar:Qala, hi: Qila.He: pl:On ↔ tr: O/On (On is used as a root for other cases like Onun, Ona, Onu and even Onlar)Me: pl:Mi/Mnie tr: Ben. Similarity is not seen clearly, but M and B are often changable between languages as M is a nasal version of B. M is used to form personal forms related to “Me” in Polish. And “B” is used for the same purpose in Turkish. “M” is also used in Turkish for the same purpose as a verb ending ex. GeliyoruM, GidiyoruM. That M in the end means “Me” in Turkish.You: pl:Ci/Cię/Ty/Ś/SZ tr: Sen. Similarity is not seen clearly, but T/Ć/Ś/SZ is etymologically one letter (made on teeth). Ś/SZ is an ending used to make “you” verbs in Polish in all tenses ex: Jesteś, Robisz, robiłeś, zrobisz. T/CI/Ś/SZ is used to form personal forms realted to “You” in Polish and “S” is used for the same purpose in Turkish.Się/Kendi. If you know the Satem/Kentum rule (Google it). Kentum version of Się (does not exist but I’ll try to form it) in a language without nasal vowels (like Turkish) would sound something like Ken. Ś/Si → K. Ę→En. Się in Turkish s Kendi. What a coincidence :).Garden: tr:Bahçe ↔Swamp: pl:Bagno. Compare Turkmen: Bag (Garden). Meaning: Wet Land.Grandfather: pl:Dziad/Dziadek ↔ tr:DedeRoot DN. In old Slavonic that root is responsible for water (Now root WD/WDR is used more (Woda)) and flat land usually close to water. Root is preserved in big rivers names like: Dunaj (Danube), Dniepr, Dniestr, Don, Dźwina. It is the same root as Hungarian: Tenger (Sea/Lake) and Kazakh/Mongolian Tenge (Sky/Heaven - also big and blue). Compare also Kazakh currency Tenge. And the Mongolian god: Tenge whence Asian religion: Tengri. In the meaning of land there is pl:Dno (bottom of the sea) and pl:Dania (Denmark - the flat country on the Sea). In Turkish the same root is seen in Deniz (Sea) and in Dünya (Earth), which sounds the same in Arabic (Dunya) and ar:Adna (Low). It may be also related to he:Eden (Garden, Paradise, Heaven). And the number One as lowest number (pl:Jeden, ua:Odyn, ru:Adin).Possesions. Turkish possesions use the same rules and endings as polish verb endings. It looks like turkish grammar of possesions was the same grammar as polish verb conjugation. Example: EviM, EviN, Evi ↔ JesteM, JesteŚ, Jest. M↔M, N↔Ś, No ending↔No ending. Interchange between N and Ś is not seen clearly, but N and Ś are interchangable as both are the same tooth consonant. N is a nasal version of Ś.Big. tr: Büyük (Big, the root also means to Grow). Polish needs some explanations. The old polish root for big is Bol. L↔Y are interchangable as both are half consonants. Root Bol is now seen in polish: Bolesław (Big fame - Name), Bardzo (Very) and Russian Bolszoj (Big). B changed to W (The same letter. W is just pronounced a bit longer than B) and we have now: Wielki (Big), Wiele (A lot), Wierch (Peak), Wierzch (Top) and so on.tr:Tepe ↔ pl:Topić. In Turkish it is a hill or mountain. In polish topić means to Melt which is related to go up. Other words related are: Ciepło (heat), Ciapa (something melted), Cipa (Vagina) and Topór (through persian, weapon with huge top). English also has related words like Top, Tap (ending of a pipe) and Tampon. German Zapf is also interesting cognate.Lehistan. Like (almost) all countries which did not get christianity before Poland and do not use Romance and Germanic influence (like Scandinavia, India, China, Malaya and so on). Turkey uses old name for Poland which is related to previous name of Poland - Lechia (Lech is a mythical founder of Poland). In modern Turkish name of Lehistan (Country of Leh) is used for Poland up to 1918. Poland after 1918 is called Polonya, but Poles are still called Leh and Lehler and Polish language is Lehçe. Other languages using same root are: Lithuanian: Lenkas/Lenkija, Ukrainian: Lah/Lahy, Hungarian: Lengyel/Lengyelorszag, Persian:Lech/Lechistan, Arabic: Lah/Lahestan.There are also common words which are borrowings in both languages so they look similar even if they are not Polish and not Turkish ex. Cinema: pl:Kino, tr:Sine (Satem Kentum?). Park: pl:Park, tr:Park. Tea: tr:Çay, Kettle: pl:Czajnik, Movie: pl:Film, tr:Film, Tourist: pl:Turysta, tr:Turist, Photographer: pl:Fotograf, tr:Fotoğraf, Cousin: pl:Kuzyn, tr:Kuzen.There are muuuuch more similarities. As I said. Some of them may be just miraculous coincidences, but some of them I believe are real similarities inherited from very old pre turkic/slavonic/altaic/indoeuropean language.I hope I helped a bit in founding interesting similarities. Sorry for mistakes (Turkish words are written from memory, so there may be some misspellings).Best regards!

I’m not writing a proof because I’ve got classes, and Hallie Black did most of the work already. She figured out that[math]\displaystyle \mathcal{I}=\int_{0}^{1}\ln(x)\ln(1+x)\ln(1-x)\mathrm dx = \frac{5}{2}\zeta(2)+4\ln(2)-6-\ln^{2}(2)-\frac{5}{8}\zeta(3)+2\mathcal{J}\tag*{}[/math]whereby[math]\displaystyle \mathcal{J}=\int_{0}^{1}\frac{\ln(x)\ln(1-x)}{1+x}\mathrm dx\tag*{}[/math]I just wanted to note that there certainly is a solution for [math]\mathcal{J}[/math] in terms of Apery’s constant. Hopefully, Hallie can give us a full proof after my 2-cents xD. A benign substitution yields[math]\displaystyle \int_{0}^{1}\frac{\ln(x)\ln(1-x)}{1+x}\mathrm dx=\int_{0}^{1}\frac{\ln(x)\ln(1-x)}{2-x}\mathrm dx\tag*{}[/math]Now we’re going to move into summation territory…[math]\displaystyle =\sum_{k\geq 1}\frac{1}{2^{k}}\int_{0}^{1}x^{k-1}\ln(x)\ln(1-x)\mathrm dx\tag*{}[/math][math]\displaystyle =\sum_{k\geq 1}\frac{1}{2^{k}}\frac{\partial}{\partial k}\int_{0}^{1}x^{k-1}\ln(1-x)\mathrm dx\tag*{}[/math]This integral is concisely represented by Harmonic numbers [math]\mathcal{H}_{k}[/math](gasp)[math]\displaystyle = \sum_{k\geq 1}\frac{1}{2^{k}}\frac{\partial}{\partial k}\Bigg(-\frac{\mathcal{H}_{k}}{k}\Bigg)\tag*{}[/math]All that’s left is to take the derivative[math]\displaystyle = \sum_{k\geq 1}\frac{1}{2^{k}}\Bigg[\frac{\mathcal{H}_{k}}{k^{2}}+\frac{\mathcal{H}_{k}^{(2)}}{k}-\frac{\zeta(2)}{k}\Bigg]\tag*{}[/math]…And welcome to the world of Euler sums. It takes a lot of machinery to work with these that I don’t want to go through right now…a good load of them have been solved on StackExchange already; a couple I’ve tackled on Quora as well. Suffice to say,[math]\displaystyle \sum_{k\geq 1}\frac{\mathcal{H}_{k}}{k^{2}2^{k}}=\zeta(3)-\frac{\zeta(2)}{2}\ln(2)\tag*{}[/math][math]\displaystyle \sum_{k\geq 1}\frac{\mathcal{H}_{k}^{(2)}}{k 2^{k}}=\frac{5}{8}\zeta(3)\tag*{}[/math][math]\displaystyle \sum_{k\geq 1}\frac{1}{k 2^{k}}=\ln(2)\tag*{}[/math]In other words, there certainly is a closed-form solution to this integral if someone wants to waste a couple hours crunching through these Euler sums (requires some knowledge of Polylogs) and also provide a derivation for Hallie’s partial solution.Cheers!*Edit*In an effort to not leave everyone hanging with these sums…here’s the workFirst Euler Sum solved hereMore complicated version of Second Euler Sum solved hereThird sum is trivial.(Also, another way to solve [math]\mathcal{J}[/math] would be with derivatives of Euler’s Beta function…but it’s longer lol)