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Having a white boyfriend makes everything easier. 😈😉💛 #bleached #wmaf #raceplay #yellowfever #ricebunny #yellowbunny #afwm #whiteisright #wnwo

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UndoubtedlyFrank

18,092 subscribers

108,248 次观看 • 1 年前 •via X (Twitter)

NSFW#bleached#wmaf#raceplay#yellowfever#ricebunny#yellowbunny#afwm#whiteisright#wnwo
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imagine having a boyfriend who listens without judgment, validates everything you went through in your past relationship, never makes you feel guilty for talking about it, and constantly reminds you that you're not alone 🥺🤍
1:41

imagine having a boyfriend who listens without judgment, validates everything you went through in your past relationship, never makes you feel guilty for talking about it, and constantly reminds you that you're not alone 🥺🤍

Tara ♡ GIVEN MOVIES DUBBED

66,737 次观看 • 2 个月前

#WATCH | Delhi: Indian-origin NASA astronaut Sunita Williams says, "One of the first things you do when you get to space is that we all want to look for our home, like our immediate home. I grew up in Massachusetts. My father's from India. My mother's from Slovenia. I'm obviously looking for these places to call home... Every person I know is there, every animal, every plant, everything we know is there. We're all in this one little space in our solar system, and I think it changes your perception about us having any differences. It really makes you feel like we are just one and we all should probably work a little bit closer and easier together..."
2:16

#WATCH | Delhi: Indian-origin NASA astronaut Sunita Williams says, "One of the first things you do when you get to space is that we all want to look for our home, like our immediate home. I grew up in Massachusetts. My father's from India. My mother's from Slovenia. I'm obviously looking for these places to call home... Every person I know is there, every animal, every plant, everything we know is there. We're all in this one little space in our solar system, and I think it changes your perception about us having any differences. It really makes you feel like we are just one and we all should probably work a little bit closer and easier together..."

ANI

516,645 次观看 • 8 个月前

🚨 NOW: President Trump just DROPPED this footage EXPOSING how Michelle Obama is a SPOILED ELITIST "You'll see it here, the way Michelle Obama lives one of the most privileged lives you can imagine. And watch the way she looks at us." "This shows you the contrast between perpetual victims the left are, they see oppression in everything." VANCE: "So, a lot of good things." OBAMA: "It's expensive to live in the White House." VANCE: "What a blessing it is to be here." OBAMA: "There were moments when I didn't feel like I got enough attention" VANCE: "We live in this beautiful, very protected mansion that the American people have gifted us." OBAMA: "Many people don't know, I mean, much is not covered." VANCE: "Most of our meals are prepared for us, so we don't have to worry as much about cooking." OBAMA: "You're paying for every food, every bit of food that you eat." VANCE: "There are a lot of things that in some ways make having a baby easier." OBAMA: "How do you raise kids in the White House?! It's dangerous!" VANCE: "You don't have to worry about TSA lines when you're the Vice President. Air Force 2 makes transportation pretty easy." OBAMA: "We had to pay for their travel to be on the plane!" VANCE: "My attitude towards kids is—" OBAMA: "They're a hassle." VANCE: "What the hell have we got ourselves into? No more kids..." OBAMA: "They MESS YOU UP." VANCE: "Then we had a second, then we had a third. Now both of us are just like, what's one more?" ❤️🤣 "Says a lot, doesn't it."
1:16

🚨 NOW: President Trump just DROPPED this footage EXPOSING how Michelle Obama is a SPOILED ELITIST "You'll see it here, the way Michelle Obama lives one of the most privileged lives you can imagine. And watch the way she looks at us." "This shows you the contrast between perpetual victims the left are, they see oppression in everything." VANCE: "So, a lot of good things." OBAMA: "It's expensive to live in the White House." VANCE: "What a blessing it is to be here." OBAMA: "There were moments when I didn't feel like I got enough attention" VANCE: "We live in this beautiful, very protected mansion that the American people have gifted us." OBAMA: "Many people don't know, I mean, much is not covered." VANCE: "Most of our meals are prepared for us, so we don't have to worry as much about cooking." OBAMA: "You're paying for every food, every bit of food that you eat." VANCE: "There are a lot of things that in some ways make having a baby easier." OBAMA: "How do you raise kids in the White House?! It's dangerous!" VANCE: "You don't have to worry about TSA lines when you're the Vice President. Air Force 2 makes transportation pretty easy." OBAMA: "We had to pay for their travel to be on the plane!" VANCE: "My attitude towards kids is—" OBAMA: "They're a hassle." VANCE: "What the hell have we got ourselves into? No more kids..." OBAMA: "They MESS YOU UP." VANCE: "Then we had a second, then we had a third. Now both of us are just like, what's one more?" ❤️🤣 "Says a lot, doesn't it."

Eric Daugherty

238,369 次观看 • 4 个月前

If you aren’t cheating, you aren’t trying! Are you looking at MRIs? Feeling some confusion about the diffusion? Feel impaired when it comes to the FLAIR? Wish you could cheat a little? Here’s a little cheat sheet on all the sequences you NEED to know for looking at MRIs! ➡️T1: It’s for anatomy, so brain structures reflect the same color as real life. 🔸So gray matter is gray on T1 & white matter is white on T1. 🔸It’s also for contrast. Contrast is taken up by masses making them light up & easier to see. ➡️T2: It’s the water sensitive sequence. 🔸What is pathologic water in the brain? Edema! 🔸Remember--everything bad in this world is trying to turn you back into what you came from—water! ➡️DWI: Diffusion detects stroke, which are bright on DWI. 🔸But anything that makes space tight in the brain can be bright on diffusion (cellular masses, pus under pressure, etc.) ➡️Gradient: Gradient is sensitive to metals. 🔸What’s the most important metal in body? Iron—bc iron is in blood. 🔸So gradient is our blood sensitive sequence 🌟So remember🌟 ▶️T1 is for Anatomy & Contrast ▶️T2 is for Water & Edema ▶️DWI is for stroke ▶️Gradient is for blood Hopefully, this will help you next time you have an MRI--who says cheaters never win? 😉
0:37

If you aren’t cheating, you aren’t trying! Are you looking at MRIs? Feeling some confusion about the diffusion? Feel impaired when it comes to the FLAIR? Wish you could cheat a little? Here’s a little cheat sheet on all the sequences you NEED to know for looking at MRIs! ➡️T1: It’s for anatomy, so brain structures reflect the same color as real life. 🔸So gray matter is gray on T1 & white matter is white on T1. 🔸It’s also for contrast. Contrast is taken up by masses making them light up & easier to see. ➡️T2: It’s the water sensitive sequence. 🔸What is pathologic water in the brain? Edema! 🔸Remember--everything bad in this world is trying to turn you back into what you came from—water! ➡️DWI: Diffusion detects stroke, which are bright on DWI. 🔸But anything that makes space tight in the brain can be bright on diffusion (cellular masses, pus under pressure, etc.) ➡️Gradient: Gradient is sensitive to metals. 🔸What’s the most important metal in body? Iron—bc iron is in blood. 🔸So gradient is our blood sensitive sequence 🌟So remember🌟 ▶️T1 is for Anatomy & Contrast ▶️T2 is for Water & Edema ▶️DWI is for stroke ▶️Gradient is for blood Hopefully, this will help you next time you have an MRI--who says cheaters never win? 😉

Lea Alhilali, MD

26,151 次观看 • 8 个月前

One of the workflows I helped advance and lead for Destiny 2 was our static compositing pipeline for marketing visuals. When we were creating marketing content for #Destiny2, we always needed strong key visuals for weapons, characters, abilities, and other in-game elements. Unlike a traditional gameplay screenshot, where everything is baked into one static image, composited shots let us isolate individual elements and light them more precisely. That gave us a lot more flexibility to build scenes with better legibility, clearer focus, stronger lighting, improved contrast, and a more intentional overall look. One of the biggest strengths of compositing is having access to individual layers in Photoshop. That layered approach not only makes the editing process easier, but also makes the final artwork much more flexible. Images can be adapted for trailer motion graphics, reworked for print, or pushed further as creative needs evolve. Destiny 2 composites are built using Adobe Photoshop alongside in-game captures. Using advanced development tools, we light, capture, and isolate characters, weapons, and props directly from the game environment, all of which were originally created by the talented Bungie 3D art teams. Those assets are then brought into Photoshop, where they’re cut out and assembled into custom scenes using layered compositions and visual effects. The composites highlighted below are a few of the Destiny 2 pieces I’ve worked on that are meaningful to me. Let me know what your favorite is!
0:27

One of the workflows I helped advance and lead for Destiny 2 was our static compositing pipeline for marketing visuals. When we were creating marketing content for #Destiny2, we always needed strong key visuals for weapons, characters, abilities, and other in-game elements. Unlike a traditional gameplay screenshot, where everything is baked into one static image, composited shots let us isolate individual elements and light them more precisely. That gave us a lot more flexibility to build scenes with better legibility, clearer focus, stronger lighting, improved contrast, and a more intentional overall look. One of the biggest strengths of compositing is having access to individual layers in Photoshop. That layered approach not only makes the editing process easier, but also makes the final artwork much more flexible. Images can be adapted for trailer motion graphics, reworked for print, or pushed further as creative needs evolve. Destiny 2 composites are built using Adobe Photoshop alongside in-game captures. Using advanced development tools, we light, capture, and isolate characters, weapons, and props directly from the game environment, all of which were originally created by the talented Bungie 3D art teams. Those assets are then brought into Photoshop, where they’re cut out and assembled into custom scenes using layered compositions and visual effects. The composites highlighted below are a few of the Destiny 2 pieces I’ve worked on that are meaningful to me. Let me know what your favorite is!

Biwald

67,940 次观看 • 3 个月前

🚨 Billions Agent Verification & FAIAR having issues? 🤔 You are not alone — many people are getting stuck in this process 😓 So I’m sharing a simple A to Z guide video 👇 📱 Open Termux app first before starting commands 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟭 pkg update 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟮 pkg upgrade -y 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟯 pkg install git pkg install nodejs 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟰 pkg install git nodejs -y 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟱 (optional – to check if everything is correct until now) node -v 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟲 git clone 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟳 cd verified-agent-identity 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟴 npm install shell-quote @iden3/js-iden3-auth @0xpolygonid/js-sdk ethers uuid cross-fetch 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟵 cd scripts node createNewEthereumIdentity.js 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟭𝟬 node manualLinkHumanToAgent.js --challenge '{"name":"YOUR NAME","description":"YOUR USERNAME (X: @username ) AI Agent from Asia"}' 𝗙𝗼𝗿 𝗽𝗿𝗶𝘃𝗮𝘁𝗲 𝗸𝗲𝘆 cat ~/.openclaw/billions/kms.json 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟭 npx clawhub@latest install verified-agent-identity 👉 Type "Y" and press Enter 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟮 npx skills add BillionsNetwork/verified-agent-identity 👉 Again type "Y" and press Enter ⚠️ Common Mistakes: ❌ Not creating identity ❌ Not saving private key ❌ Clearing/uninstalling Termux ❌ Trying FAIAR without verified agent 💡 Tips: 👉 Use your real name / username (makes agent easier to find) 💰 If everything is done correctly → you become eligible for FAIAR rewards 🚀 Don’t miss this opportunity $BILL is coming 👀 evin Averno #BillionsNetwork #FAIAR #AIAgent
5:26

🚨 Billions Agent Verification & FAIAR having issues? 🤔 You are not alone — many people are getting stuck in this process 😓 So I’m sharing a simple A to Z guide video 👇 📱 Open Termux app first before starting commands 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟭 pkg update 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟮 pkg upgrade -y 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟯 pkg install git pkg install nodejs 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟰 pkg install git nodejs -y 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟱 (optional – to check if everything is correct until now) node -v 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟲 git clone 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟳 cd verified-agent-identity 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟴 npm install shell-quote @iden3/js-iden3-auth @0xpolygonid/js-sdk ethers uuid cross-fetch 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟵 cd scripts node createNewEthereumIdentity.js 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟭𝟬 node manualLinkHumanToAgent.js --challenge '{"name":"YOUR NAME","description":"YOUR USERNAME (X: @username ) AI Agent from Asia"}' 𝗙𝗼𝗿 𝗽𝗿𝗶𝘃𝗮𝘁𝗲 𝗸𝗲𝘆 cat ~/.openclaw/billions/kms.json 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟭 npx clawhub@latest install verified-agent-identity 👉 Type "Y" and press Enter 𝗖𝗼𝗺𝗺𝗮𝗻𝗱 𝟮 npx skills add BillionsNetwork/verified-agent-identity 👉 Again type "Y" and press Enter ⚠️ Common Mistakes: ❌ Not creating identity ❌ Not saving private key ❌ Clearing/uninstalling Termux ❌ Trying FAIAR without verified agent 💡 Tips: 👉 Use your real name / username (makes agent easier to find) 💰 If everything is done correctly → you become eligible for FAIAR rewards 🚀 Don’t miss this opportunity $BILL is coming 👀 evin Averno #BillionsNetwork #FAIAR #AIAgent

Mr.Firoz 🟦

16,475 次观看 • 4 个月前

Caller: “I'm 26 and a nurse. I've been with my boyfriend for 6 years. I graduated from school in 2023 with $167,000 in student loans. I've paid off a lot and have about $90,000 left. My boyfriend makes $250,000 a year, but he doesn’t want to propose until I’m completely debt-free.” Dave Ramsey: “Interesting. You’re not going to like me if you were my daughter.” Caller: “Why?” Dave Ramsey: “You want to know what I would tell you?” Caller: “What?” Dave Ramsey: “Dump him.” Caller: “Yeah? I mean, he’s a great guy.” Dave Ramsey: “No, he’s not. No, he’s not. No, he’s not. He’s making you prove your worth based on money. To him, you’re having to buy your way into this relationship. Nope. You’re a princess, and you deserve more than this.” Caller: “The reason I’ve been able to put the majority of my paycheck toward my loans is because he pays all of our rent.” Dave Ramsey: “Oh, so you live together?” Caller: “Yeah, we live together.” Dave Ramsey: “Oh, so you’re already married you just didn’t admit it.” Caller: “Yeah, it doesn’t seem like we’re married.” Dave Ramsey: “Well… yeah. Gosh. So what’s his incentive to get married? None. Jade Warshaw: “Living together before marriage is a bum idea. It’s not a good idea because what happens is you start making bad relationship decisions based on financial gain and the pressure you’ve already put on yourselves.” “It’s a lot easier to walk away from a messed-up relationship when he lives over there and she lives over here, and you just get together when it’s time to go on dates. It’s a lot easier to say, ‘You know what? This guy’s a bum. I’m going to walk away.’” “It becomes much more difficult when you’re living in the same house, splitting responsibilities, and he’s paying the rent. That makes it very hard to make the natural transitions you would have made if you hadn’t put that kind of pressure on the relationship.” Dave Ramsey: “You have a fabulous career as a nurse. You’ll always be employed, and you can work as much or as little as you want. You can work 80 hours a week or 20 hours a week. You’ll be able to do that for the rest of your life, and you can make a pile of money.” “All we tell couples to do is be aligned. Be in agreement about how money is going to be handled.” “Now, he’s in agreement that he hates debt. You’re in agreement that you hate debt, and you’ve been working hard to pay it down. But then he put up a false barrier here.I’m just telling you I love you, and if you were my daughter, I’d tell you not to marry this guy because I think this is a false premise.” “You’re aligned on what’s important. You’re aligned on saying, ‘We don’t like debt. We’re going to avoid debt, and we’re going to get out of debt.’” “If one of you has zero debt, but one person loves debt and hates saving while the other loves saving and hates debt, you’re going to get divorced later.” “The number one cause of divorce in North America today is money fights and money problems, This is a money fight, you’re just not having it out loud. You’re having it in your head.” Jade Warshaw: “It seemed like he was willing to help with the debt. We aren’t married yet, but it felt like he was trying to help, He was helping in the wrong way. That’s the only thing that makes me think he might simply be misguided. He said, ‘I’ll pay the rent.’” Dave Ramsey: “you can go to a marriage counselor and say Let’s get aligned on this, or we’re going to end this, But if at the end of the day, the answer is, ‘I won’t marry you until you pay off your debt Well, then the question has been answered. “You value that more than you value me, See you later, alligator.”
3:50

Caller: “I'm 26 and a nurse. I've been with my boyfriend for 6 years. I graduated from school in 2023 with $167,000 in student loans. I've paid off a lot and have about $90,000 left. My boyfriend makes $250,000 a year, but he doesn’t want to propose until I’m completely debt-free.” Dave Ramsey: “Interesting. You’re not going to like me if you were my daughter.” Caller: “Why?” Dave Ramsey: “You want to know what I would tell you?” Caller: “What?” Dave Ramsey: “Dump him.” Caller: “Yeah? I mean, he’s a great guy.” Dave Ramsey: “No, he’s not. No, he’s not. No, he’s not. He’s making you prove your worth based on money. To him, you’re having to buy your way into this relationship. Nope. You’re a princess, and you deserve more than this.” Caller: “The reason I’ve been able to put the majority of my paycheck toward my loans is because he pays all of our rent.” Dave Ramsey: “Oh, so you live together?” Caller: “Yeah, we live together.” Dave Ramsey: “Oh, so you’re already married you just didn’t admit it.” Caller: “Yeah, it doesn’t seem like we’re married.” Dave Ramsey: “Well… yeah. Gosh. So what’s his incentive to get married? None. Jade Warshaw: “Living together before marriage is a bum idea. It’s not a good idea because what happens is you start making bad relationship decisions based on financial gain and the pressure you’ve already put on yourselves.” “It’s a lot easier to walk away from a messed-up relationship when he lives over there and she lives over here, and you just get together when it’s time to go on dates. It’s a lot easier to say, ‘You know what? This guy’s a bum. I’m going to walk away.’” “It becomes much more difficult when you’re living in the same house, splitting responsibilities, and he’s paying the rent. That makes it very hard to make the natural transitions you would have made if you hadn’t put that kind of pressure on the relationship.” Dave Ramsey: “You have a fabulous career as a nurse. You’ll always be employed, and you can work as much or as little as you want. You can work 80 hours a week or 20 hours a week. You’ll be able to do that for the rest of your life, and you can make a pile of money.” “All we tell couples to do is be aligned. Be in agreement about how money is going to be handled.” “Now, he’s in agreement that he hates debt. You’re in agreement that you hate debt, and you’ve been working hard to pay it down. But then he put up a false barrier here.I’m just telling you I love you, and if you were my daughter, I’d tell you not to marry this guy because I think this is a false premise.” “You’re aligned on what’s important. You’re aligned on saying, ‘We don’t like debt. We’re going to avoid debt, and we’re going to get out of debt.’” “If one of you has zero debt, but one person loves debt and hates saving while the other loves saving and hates debt, you’re going to get divorced later.” “The number one cause of divorce in North America today is money fights and money problems, This is a money fight, you’re just not having it out loud. You’re having it in your head.” Jade Warshaw: “It seemed like he was willing to help with the debt. We aren’t married yet, but it felt like he was trying to help, He was helping in the wrong way. That’s the only thing that makes me think he might simply be misguided. He said, ‘I’ll pay the rent.’” Dave Ramsey: “you can go to a marriage counselor and say Let’s get aligned on this, or we’re going to end this, But if at the end of the day, the answer is, ‘I won’t marry you until you pay off your debt Well, then the question has been answered. “You value that more than you value me, See you later, alligator.”

𝓢𝓵𝓪𝓶 👁️⃤

408,000 次观看 • 2 个月前

This is some black magic Dave brings up the classic groyper question of 'do you blame jewish supremacy for our problems, or just Israel?' The slight of hand comes when he defines jewish supremacy as jews thinking their culture is best. But the groyper theory isn't just that jews prefer their own culture, it's that they control ours. Everyone knows jews prefer their religion, like everyone else. It's only relevant under presumptions of control. The debate is not 'does Israel controls us or are jews are bigoted?' Those are unrelated propositions. The problem is if Dave says 'it's just Israel' he will lose the debate to Nick with people who have adopted their framwork of jewish/israeli control, because throwing in jews is a more holistic explanation. So it's easier for Dave to pretend jewish supremacy in that context means bigotry. That way he can agree with Nick without having to affirm or challenge Nicks idea that "the jews are at the center of everything." Half of Gen Z now thinks they grew up under a system of Jewish or zionist oppression that is at the center of everything bad in their life. That's what we mean when we say they have applied the leftist idea of white supremacy to jews. That is not normal and not a single prominent American libertarian has done anything except fan the flames of Marxist oppression politics within their own side by pretending Israel controls us. Dan Bilzerian is right about them being subversive, he’s just too retarded to realize it’s helping his cause, as Nick has tried to explain to him.
1:13

This is some black magic Dave brings up the classic groyper question of 'do you blame jewish supremacy for our problems, or just Israel?' The slight of hand comes when he defines jewish supremacy as jews thinking their culture is best. But the groyper theory isn't just that jews prefer their own culture, it's that they control ours. Everyone knows jews prefer their religion, like everyone else. It's only relevant under presumptions of control. The debate is not 'does Israel controls us or are jews are bigoted?' Those are unrelated propositions. The problem is if Dave says 'it's just Israel' he will lose the debate to Nick with people who have adopted their framwork of jewish/israeli control, because throwing in jews is a more holistic explanation. So it's easier for Dave to pretend jewish supremacy in that context means bigotry. That way he can agree with Nick without having to affirm or challenge Nicks idea that "the jews are at the center of everything." Half of Gen Z now thinks they grew up under a system of Jewish or zionist oppression that is at the center of everything bad in their life. That's what we mean when we say they have applied the leftist idea of white supremacy to jews. That is not normal and not a single prominent American libertarian has done anything except fan the flames of Marxist oppression politics within their own side by pretending Israel controls us. Dan Bilzerian is right about them being subversive, he’s just too retarded to realize it’s helping his cause, as Nick has tried to explain to him.

Austin Padgett (LudwigNeverMises)

18,209 次观看 • 4 个月前

NCAA Champion Michael La Sasso is now the youngest player on LIV Golf after signing for Phil Mickelson’s HyFlyers GC during the off season. He explained his decision to join the league ahead of the season opener in Riyadh: “One of the things that went into my decision, when I was 10 years old starting to play golf, like, the goal for me was to play professional golf. Having people that have been very well-known in the golf space and are so experienced, and to be able to be a part of a team that's with Phil, somebody that's had so much experience, I feel like he'll be able to answer any question that I throw at him, to have the ability to be able to ask somebody that on a daily basis, that played a very big part in it for me because not every 21-year-old has the opportunity to be able to ask questions to those people. So that was a big factor for me. “I think so far, I'm so grateful that I made the decision, and I am very happy to be here.” Michael also says that Caleb Surratt, who joined Jon Rahm’s LIV Golf team for the 2024 season, had an impact on his decision too: “So, I've had a very good relationship with Caleb Surratt. Not many people know this, but he was committed to NC State at the same time I was. He's from North Carolina, I'm from North Carolina. Growing up, I played a lot of golf with him, and we were very close. “I remember when he first came here, he stayed at my house because he was getting a swing lesson from -- we go to the same instructor. Everything that he had to say, it made me excited. From a very early start, hearing about LIV and every perk that it had and hearing him talk so highly about it, the fact that I actually had an opportunity to come out here and play, and I asked him a bunch of questions and kind of from the start, everything that he had to say and people that I talked to, everything was so, so good.” He went on to say about the prospect of playing team golf: “I think that makes the transition a little bit easier. I feel like my golf has kind of taken off when I've been in a team environment. For me, having a team around me was very appealing. “I've played good golf as a team. I like the camaraderie, kind of the friendly banter that goes back and forth between the guys. For me to have the opportunity to come play on a team environment for a professional career, I think that's the coolest thing ever.” This is Michael’s rookie season as a pro after signing for HyFlyers GC straight out of college. Normally, it’s a difficult transition for young players to make, but Michael isn’t short of confidence and has some lofty goals: “I've talked with a bunch of people on the team. I know Phil is very big on having a team win and an individual win. Now being the youngest player in the league, I'd kind of like to come in and make a good noise, and I would like to win a couple times. I would like to see the team win for sure, as a team event. I think that would be pretty neat, as well, and kind of take it one day at a time.” One thing is very clear from this interview, whatever happens during Michael’s pro debut this week, it will not be boring! HyFlyers GC LIV Golf
2:29

NCAA Champion Michael La Sasso is now the youngest player on LIV Golf after signing for Phil Mickelson’s HyFlyers GC during the off season. He explained his decision to join the league ahead of the season opener in Riyadh: “One of the things that went into my decision, when I was 10 years old starting to play golf, like, the goal for me was to play professional golf. Having people that have been very well-known in the golf space and are so experienced, and to be able to be a part of a team that's with Phil, somebody that's had so much experience, I feel like he'll be able to answer any question that I throw at him, to have the ability to be able to ask somebody that on a daily basis, that played a very big part in it for me because not every 21-year-old has the opportunity to be able to ask questions to those people. So that was a big factor for me. “I think so far, I'm so grateful that I made the decision, and I am very happy to be here.” Michael also says that Caleb Surratt, who joined Jon Rahm’s LIV Golf team for the 2024 season, had an impact on his decision too: “So, I've had a very good relationship with Caleb Surratt. Not many people know this, but he was committed to NC State at the same time I was. He's from North Carolina, I'm from North Carolina. Growing up, I played a lot of golf with him, and we were very close. “I remember when he first came here, he stayed at my house because he was getting a swing lesson from -- we go to the same instructor. Everything that he had to say, it made me excited. From a very early start, hearing about LIV and every perk that it had and hearing him talk so highly about it, the fact that I actually had an opportunity to come out here and play, and I asked him a bunch of questions and kind of from the start, everything that he had to say and people that I talked to, everything was so, so good.” He went on to say about the prospect of playing team golf: “I think that makes the transition a little bit easier. I feel like my golf has kind of taken off when I've been in a team environment. For me, having a team around me was very appealing. “I've played good golf as a team. I like the camaraderie, kind of the friendly banter that goes back and forth between the guys. For me to have the opportunity to come play on a team environment for a professional career, I think that's the coolest thing ever.” This is Michael’s rookie season as a pro after signing for HyFlyers GC straight out of college. Normally, it’s a difficult transition for young players to make, but Michael isn’t short of confidence and has some lofty goals: “I've talked with a bunch of people on the team. I know Phil is very big on having a team win and an individual win. Now being the youngest player in the league, I'd kind of like to come in and make a good noise, and I would like to win a couple times. I would like to see the team win for sure, as a team event. I think that would be pretty neat, as well, and kind of take it one day at a time.” One thing is very clear from this interview, whatever happens during Michael’s pro debut this week, it will not be boring! HyFlyers GC LIV Golf

Flushing It

208,019 次观看 • 7 个月前

HAVE YOU EVER SEEN THE BEST CRYPTO AI? IF NOT, YOU’RE MISSING OUT! I tried the new CoinMarketCap AI today, and it feels like a real game-changer for crypto research. It’s like having a personal research assistant. HOW I USED IT FOR EXPERIENCE Before I even asked my first question, the AI let me customize how I wanted it to respond. You can choose both: Tone Style:>> >Default (neutral and clean) >Journalist (news-style reporting) >Storytelling >CT vibe >Concise (short and straight to the point) Crypto Experience Level:>> >Newcomer (zero prior knowledge) >Regular (knows the basics) >Degen Lite >Full Degen (CT warrior in the trenches) I set mine to Journalist tone + Full Degen for experience. The Question I Tested “What tokens are gaining momentum this week?” It answered in under 30 seconds and gave me a clear list with details like: •why those tokens are moving •what trends are behind them •risks •market sentiment •and key points to watch It even suggested extra follow-up questions, so I didn’t have to type anything else, just tapped and continued. WHAT STOOD OUT •It’s fast •The layout is clean and easy to understand •It doesn’t hype coins , it gives real reasoning •it makes research easier because everything is in one place My though after using it (and showing it in my video), I can say this feels like a strong tool for anyone who creates crypto content, trades, or just wants to stay updated without spending hours searching. So far, I’m impressed and I’m definitely going to explore more features. Which coin or feature do you want me to test next?? Gm Roh Rush Mazza Haha 💙💙
0:55

HAVE YOU EVER SEEN THE BEST CRYPTO AI? IF NOT, YOU’RE MISSING OUT! I tried the new CoinMarketCap AI today, and it feels like a real game-changer for crypto research. It’s like having a personal research assistant. HOW I USED IT FOR EXPERIENCE Before I even asked my first question, the AI let me customize how I wanted it to respond. You can choose both: Tone Style:>> >Default (neutral and clean) >Journalist (news-style reporting) >Storytelling >CT vibe >Concise (short and straight to the point) Crypto Experience Level:>> >Newcomer (zero prior knowledge) >Regular (knows the basics) >Degen Lite >Full Degen (CT warrior in the trenches) I set mine to Journalist tone + Full Degen for experience. The Question I Tested “What tokens are gaining momentum this week?” It answered in under 30 seconds and gave me a clear list with details like: •why those tokens are moving •what trends are behind them •risks •market sentiment •and key points to watch It even suggested extra follow-up questions, so I didn’t have to type anything else, just tapped and continued. WHAT STOOD OUT •It’s fast •The layout is clean and easy to understand •It doesn’t hype coins , it gives real reasoning •it makes research easier because everything is in one place My though after using it (and showing it in my video), I can say this feels like a strong tool for anyone who creates crypto content, trades, or just wants to stay updated without spending hours searching. So far, I’m impressed and I’m definitely going to explore more features. Which coin or feature do you want me to test next?? Gm Roh Rush Mazza Haha 💙💙

MK🤴☂️

30,025 次观看 • 9 个月前

Desire thrives on friction, and a culture that made everything permissible also made much of it less appealing. There are several paradoxes here. Young people have more access and more opportunity than previous generations, yet they also report higher levels of anxiety and depression. There is a similar paradox in dating and relationships. Hookups are supposedly less stigmatized. Dating apps were meant to remove friction, expand people’s options, and make it easier to meet. Young people also have more sexual autonomy than earlier generations. Yet they are forming fewer relationships and having less sex. There has been a great deal written about the so-called sex recession. How do you explain the fact that greater access, autonomy, and openness have coincided with less intimacy? There may also be a mirror image between certain messages aimed at women and those found in the red-pill manosphere. In both cases, the opposite sex is portrayed as deceptive and calculating. Men are told that women may present themselves as kind and sincere but are actually Machiavellian and constantly evaluating their options. They are therefore warned never to appear needy or vulnerable. Women often receive a parallel message about men. If both men and women are being taught, from different corners of the culture, to distrust the opposite sex and conceal any sign of vulnerability, it is not surprising that they might become more guarded and less willing to interact. This may apply beyond sex and relationships. Many stigmas around once-taboo behaviors have declined, yet participation in some of those behaviors has declined as well. Alcohol and marijuana use, for example, have fallen among young people. It makes me wonder whether friction, prohibition, or stigma can sometimes make an activity more appealing. Once something becomes completely available and socially acceptable, perhaps it loses some of its allure.
1:11

Desire thrives on friction, and a culture that made everything permissible also made much of it less appealing. There are several paradoxes here. Young people have more access and more opportunity than previous generations, yet they also report higher levels of anxiety and depression. There is a similar paradox in dating and relationships. Hookups are supposedly less stigmatized. Dating apps were meant to remove friction, expand people’s options, and make it easier to meet. Young people also have more sexual autonomy than earlier generations. Yet they are forming fewer relationships and having less sex. There has been a great deal written about the so-called sex recession. How do you explain the fact that greater access, autonomy, and openness have coincided with less intimacy? There may also be a mirror image between certain messages aimed at women and those found in the red-pill manosphere. In both cases, the opposite sex is portrayed as deceptive and calculating. Men are told that women may present themselves as kind and sincere but are actually Machiavellian and constantly evaluating their options. They are therefore warned never to appear needy or vulnerable. Women often receive a parallel message about men. If both men and women are being taught, from different corners of the culture, to distrust the opposite sex and conceal any sign of vulnerability, it is not surprising that they might become more guarded and less willing to interact. This may apply beyond sex and relationships. Many stigmas around once-taboo behaviors have declined, yet participation in some of those behaviors has declined as well. Alcohol and marijuana use, for example, have fallen among young people. It makes me wonder whether friction, prohibition, or stigma can sometimes make an activity more appealing. Once something becomes completely available and socially acceptable, perhaps it loses some of its allure.

Rob Henderson

11,575 次观看 • 1 个月前

100/100 for India But not an achievement - as today the 100/100 warmest cities of the world are in India And apart from summers, phenomenon like formation of Urban Heat Islands is making the life of city residents literally hell And our govt’s poor urban planning is adding to the woes Concrete, asphalt, and buildings absorb sunlight during the day and release that heat slowly at night (unlike soil, grass, or trees which cool faster). No trees or vegetation means less shade and less evaporative cooling (plants “sweat” to cool down). Air conditioners, cars, factories, and people are pumping out extra waste heat. Tall buildings are trapping heat and blocking wind that could cool things down. Dark surfaces (roads, roofs) absorb more sunlight than lighter natural surfaces. And it is having Real-world effect in India: In April heatwaves, a city like Delhi or Mumbai can be 4–8°C (7–14°F) hotter than nearby villages at night. This makes the already extreme weather feel far worse, higher heat stress, more deaths, higher electricity demand for cooling, and worse air pollution Do have a look at these Quick numbers: • Rural area: 38°C day / 22°C night • City center: 42°C day / 28–30°C night This is why big Indian cities often top the “hottest places on Earth” lists during heatwaves, the natural heat + urban heat island effect combine Simple fix ideas (though hard to scale fast): - More trees - white/painted roofs (IAS Supriya Sahi has already proved it on a large scale in Chennai) - Green spaces, and, easier said than done - Better urban planning 🙏
1:12

100/100 for India But not an achievement - as today the 100/100 warmest cities of the world are in India And apart from summers, phenomenon like formation of Urban Heat Islands is making the life of city residents literally hell And our govt’s poor urban planning is adding to the woes Concrete, asphalt, and buildings absorb sunlight during the day and release that heat slowly at night (unlike soil, grass, or trees which cool faster). No trees or vegetation means less shade and less evaporative cooling (plants “sweat” to cool down). Air conditioners, cars, factories, and people are pumping out extra waste heat. Tall buildings are trapping heat and blocking wind that could cool things down. Dark surfaces (roads, roofs) absorb more sunlight than lighter natural surfaces. And it is having Real-world effect in India: In April heatwaves, a city like Delhi or Mumbai can be 4–8°C (7–14°F) hotter than nearby villages at night. This makes the already extreme weather feel far worse, higher heat stress, more deaths, higher electricity demand for cooling, and worse air pollution Do have a look at these Quick numbers: • Rural area: 38°C day / 22°C night • City center: 42°C day / 28–30°C night This is why big Indian cities often top the “hottest places on Earth” lists during heatwaves, the natural heat + urban heat island effect combine Simple fix ideas (though hard to scale fast): - More trees - white/painted roofs (IAS Supriya Sahi has already proved it on a large scale in Chennai) - Green spaces, and, easier said than done - Better urban planning 🙏

Shekhar Dutt

194,296 次观看 • 5 个月前

As some of you know I have data that is not in the public domain - Burnham knows a lot and hasn't done anything but made empty promises and the IOPC woman on my case is former GMP employee hence the coverup and corruption. Neither can be trusted with everything besides I wasnt allowed to be part of any official process only GMP were. Why the IOPC would think its a good idea to further retraumatise a rape victim by assigning them a former GMP employee is beyond me. No doubt deliberate along side their paid outside 'professionals' who have written 'reports' for them. However, saddened by what I've recently learnt. 'Allegedly' 3 of the 5 officers who attended my home were promoted. 🐷1 from a temporary PS to a PS 🐷1 from a PC to CiD 🐷1 from a PC to firearms 🐷1 still a big specs wearing PC known 🤥 and pally with a certain response pair (tutors/affairs/new recruits) 👮🏼‍♂️1 raised a complaint about my treatment and as a result was bullied and later 'sacked' - I remember this PC as was a 'good egg'. On a side note, 4 officers were named as the abusers to me by a recent whistleblower - 1 of which I named to Burnham. I have all 4 names. 2 of which were promoted above and an Inspector too who was conveniently not on my redacted custody records. Random to anyone reading but will/may make more sense to GMP and the IOPC ... 'disabled toilets' before 'male changing rooms' and before entering the 'criminal justice unit' various floors at Pendleton (Independent Office for Police Conduct (IOPC) Greater Manchester Police ???) I'm assuming the PC's report re my treatment that led to bullying and 'sacking' is in your white wash report IOPC? No worries if not 😉🤫 Hypothetically: wtf do I do with the data I have not released yet and the recent nuggets of info above? Having certain names confirmed by third parties is the bit erm 😓 For the complaints bodies... nothing is kept at home but me 🙂
0:28

As some of you know I have data that is not in the public domain - Burnham knows a lot and hasn't done anything but made empty promises and the IOPC woman on my case is former GMP employee hence the coverup and corruption. Neither can be trusted with everything besides I wasnt allowed to be part of any official process only GMP were. Why the IOPC would think its a good idea to further retraumatise a rape victim by assigning them a former GMP employee is beyond me. No doubt deliberate along side their paid outside 'professionals' who have written 'reports' for them. However, saddened by what I've recently learnt. 'Allegedly' 3 of the 5 officers who attended my home were promoted. 🐷1 from a temporary PS to a PS 🐷1 from a PC to CiD 🐷1 from a PC to firearms 🐷1 still a big specs wearing PC known 🤥 and pally with a certain response pair (tutors/affairs/new recruits) 👮🏼‍♂️1 raised a complaint about my treatment and as a result was bullied and later 'sacked' - I remember this PC as was a 'good egg'. On a side note, 4 officers were named as the abusers to me by a recent whistleblower - 1 of which I named to Burnham. I have all 4 names. 2 of which were promoted above and an Inspector too who was conveniently not on my redacted custody records. Random to anyone reading but will/may make more sense to GMP and the IOPC ... 'disabled toilets' before 'male changing rooms' and before entering the 'criminal justice unit' various floors at Pendleton (Independent Office for Police Conduct (IOPC) Greater Manchester Police ???) I'm assuming the PC's report re my treatment that led to bullying and 'sacking' is in your white wash report IOPC? No worries if not 😉🤫 Hypothetically: wtf do I do with the data I have not released yet and the recent nuggets of info above? Having certain names confirmed by third parties is the bit erm 😓 For the complaints bodies... nothing is kept at home but me 🙂

(was) Seeking Justice (now) Raising Awareness

58,342 次观看 • 1 个月前

This post has 411k Likes. It’s clear Americans have had enough “I'm so sick and f*cking tired of hearing about privilege. Privilege isn't being white — Privilege is living in government housing and calling people oppressors while they pay your f*cking bills - Privilege is being able to protest every little thing that offends you without worrying about calling in sick to work because you don't have a f*cking job - Real privilege is wearing $200 sneakers when you haven't worked a day in your life - Privilege is walking around with $300 Beats headphones while you're living on f*cking food stamps - While you're on public assistance, and it's paid for by people who wake up and grind every day - Privilege is having the latest smartphone with unlimited data and having zero idea where the bill goes because somebody else is always picking up the tab - Privilege is being able to cheat, lie, fail over and over again in life and still get bailed out while people who play by the rules get punished. That's privilege This isn't about race. This isn't about class. This is about accountability. We've got a culture that rewards victimhood and demonizes work ethic and responsibility. Meanwhile, the people holding everything together for the rest of society, they get taxed into the f*cking ground, their businesses get choked by regulation, and they get personally vilified for speaking up and saying that this is bullsh*t. You want to talk about privilege? Then start with the people who've never paid the price, but who also scream the loudest. Because they've never had to build anything, they've never had to defend anything, they've never had to carry any real weight. And the reason they get away with it? It's because we don't live in a society of strong men anymore. No. That's been dismantled on purpose over the last 50 years because a society of strong men would never put up with any of this bullshit. And that's exactly why they came after us first” “I'm done pretending that any of this bullsh*t makes sense”
1:36

This post has 411k Likes. It’s clear Americans have had enough “I'm so sick and f*cking tired of hearing about privilege. Privilege isn't being white — Privilege is living in government housing and calling people oppressors while they pay your f*cking bills - Privilege is being able to protest every little thing that offends you without worrying about calling in sick to work because you don't have a f*cking job - Real privilege is wearing $200 sneakers when you haven't worked a day in your life - Privilege is walking around with $300 Beats headphones while you're living on f*cking food stamps - While you're on public assistance, and it's paid for by people who wake up and grind every day - Privilege is having the latest smartphone with unlimited data and having zero idea where the bill goes because somebody else is always picking up the tab - Privilege is being able to cheat, lie, fail over and over again in life and still get bailed out while people who play by the rules get punished. That's privilege This isn't about race. This isn't about class. This is about accountability. We've got a culture that rewards victimhood and demonizes work ethic and responsibility. Meanwhile, the people holding everything together for the rest of society, they get taxed into the f*cking ground, their businesses get choked by regulation, and they get personally vilified for speaking up and saying that this is bullsh*t. You want to talk about privilege? Then start with the people who've never paid the price, but who also scream the loudest. Because they've never had to build anything, they've never had to defend anything, they've never had to carry any real weight. And the reason they get away with it? It's because we don't live in a society of strong men anymore. No. That's been dismantled on purpose over the last 50 years because a society of strong men would never put up with any of this bullshit. And that's exactly why they came after us first” “I'm done pretending that any of this bullsh*t makes sense”

Wall Street Apes

2,601,526 次观看 • 1 年前

“Community” has become the most overused word on the internet. But a community isn’t a group chat. It’s people — sitting across from each other, sharing a meal. 🚀 That’s why today we’re launching something big: DNNR (pronounced dinner) A white-labeled dinner club engine that lets any creator, community, or brand bring launch their own dinner club — in one city or around the world 🥂 What makes it special You customize your club page and short personality quiz — then all you have to do is announce it. Your audience takes the quiz, pays to book a seat, and our matching engine does the rest: Tables of six, smartly matched, in restaurants revealed the morning of. After dinner, everyone meets up for cocktails with the other tables. It’s part dinner party, part mystery, part social magic. The algorithm is yours — customized to your community — and the night unfolds like a beautiful game of clue. Compared to meetups, something wild happens: Because people pay, everyone shows up. Because it’s dinner (not networking), everyone shows up *on time*. And because they already share something in common, every table feels like it was meant to be. 🧠 Why it works There’s something ancient about breaking bread together. We’ve been gathering around the table for thousands of years — it’s the oldest technology for human connection. DNNR makes it effortless. We’ve taken everything we’ve learned from years of building meetup communities and made it plug-and-play: the restaurant reservations, the group matching, the reminders — all handled. 💸 For creators, communities, and brands We’ve been quietly testing this with a handful of communities — and it’s thriving. Dinners are selling out. People are having incredible experiences. And for creators, it’s become a meaningful new income stream. When your audience is local, you don’t need millions of followers to make it work — just a few hundred people in one place and a reason to meet. You’re not pushing ads, not hawking merch. You’re creating belonging — and getting paid for it. It supports local restaurants, strengthens communities, and makes your brand tangible. 🌍 The movement begins Today we’re officially launching DNNR to the world. Five communities are already hosting monthly dinner clubs, and dozens more are lined up to announce. If you have an audience — even a small, local one — we’d love to help you build your own club. If you don’t, you can still be part of the movement through our affiliate program — earn 5% of first-year revenue from any dinner clubs you refer. We believe this is a step toward curing loneliness — not with another social event app, but with something truly social. Because belonging isn’t built online. It’s built at the table. DNNR — Send your audience to dinner and build belonging that pays 👉 Visit dnnr dot io to join our affiliate program or book a demo.
1:23

“Community” has become the most overused word on the internet. But a community isn’t a group chat. It’s people — sitting across from each other, sharing a meal. 🚀 That’s why today we’re launching something big: DNNR (pronounced dinner) A white-labeled dinner club engine that lets any creator, community, or brand bring launch their own dinner club — in one city or around the world 🥂 What makes it special You customize your club page and short personality quiz — then all you have to do is announce it. Your audience takes the quiz, pays to book a seat, and our matching engine does the rest: Tables of six, smartly matched, in restaurants revealed the morning of. After dinner, everyone meets up for cocktails with the other tables. It’s part dinner party, part mystery, part social magic. The algorithm is yours — customized to your community — and the night unfolds like a beautiful game of clue. Compared to meetups, something wild happens: Because people pay, everyone shows up. Because it’s dinner (not networking), everyone shows up *on time*. And because they already share something in common, every table feels like it was meant to be. 🧠 Why it works There’s something ancient about breaking bread together. We’ve been gathering around the table for thousands of years — it’s the oldest technology for human connection. DNNR makes it effortless. We’ve taken everything we’ve learned from years of building meetup communities and made it plug-and-play: the restaurant reservations, the group matching, the reminders — all handled. 💸 For creators, communities, and brands We’ve been quietly testing this with a handful of communities — and it’s thriving. Dinners are selling out. People are having incredible experiences. And for creators, it’s become a meaningful new income stream. When your audience is local, you don’t need millions of followers to make it work — just a few hundred people in one place and a reason to meet. You’re not pushing ads, not hawking merch. You’re creating belonging — and getting paid for it. It supports local restaurants, strengthens communities, and makes your brand tangible. 🌍 The movement begins Today we’re officially launching DNNR to the world. Five communities are already hosting monthly dinner clubs, and dozens more are lined up to announce. If you have an audience — even a small, local one — we’d love to help you build your own club. If you don’t, you can still be part of the movement through our affiliate program — earn 5% of first-year revenue from any dinner clubs you refer. We believe this is a step toward curing loneliness — not with another social event app, but with something truly social. Because belonging isn’t built online. It’s built at the table. DNNR — Send your audience to dinner and build belonging that pays 👉 Visit dnnr dot io to join our affiliate program or book a demo.

Rae 🍽️

145,290 次观看 • 11 个月前

MIT filmed a mathematician proving the theorem behind every equation Maxwell ever wrote. Most engineers use it daily without understanding why any surface gives the same answer - and the ones who can explain it earn $350K at aerospace firms. Stokes' theorem is the reason Maxwell could write four equations instead of forty. Every result in electromagnetism, fluid mechanics, and differential geometry sits on top of it. Understanding it changes how you see every circulation and flux problem in physics. This is Denis Auroux. MIT, 18.02, Multivariable Calculus, Fall 2007. Lecture 31. It covers Stokes' theorem - the result that unifies line integrals, surface integrals, and curl into one statement. He opens with one confession. Then the statement. The work done by a vector field along any closed curve equals the flux of its curl through any surface bounded by that curve. Not a specific surface. Any surface you want. You pick whichever one makes the calculation easier. Then Green's theorem disappears. The result from the plane that converts line integrals to double integrals turns out to be Stokes' theorem in disguise. Same formula, restricted to a flat surface in the xy-plane. What looked like two separate theorems is one. Then orientation. Walk along the curve with the surface to your left and the normal vector points up. This rule is not chosen for elegance. It is the price of having a consistent coordinate system in three dimensions. Then the proof. Cut your surface into tiny flat tiles. Apply Green's theorem to each one. Sum everything up. All interior boundary edges cancel. Only the outer edge survives. The sum of tiny Green's theorems gives you Stokes' theorem for any surface. Watch the moment he computes the same line integral two ways. First directly - answer is pi. Then through a paraboloid instead of the obvious flat disk. Longer calculation, stranger setup, same answer. The theorem is not an abstraction. You can watch it work. A fluid dynamics engineer I know kept this lecture open during their first week modeling atmospheric circulation. Said it was the first time Stokes felt like a tool rather than a formula to verify on exams. Free on YouTube, MIT OpenCourseWare, 18.02. bookmark this and watch later - after this lecture every circulation, every flux, and every curl you encounter will feel like three views of the same object
47:56

MIT filmed a mathematician proving the theorem behind every equation Maxwell ever wrote. Most engineers use it daily without understanding why any surface gives the same answer - and the ones who can explain it earn $350K at aerospace firms. Stokes' theorem is the reason Maxwell could write four equations instead of forty. Every result in electromagnetism, fluid mechanics, and differential geometry sits on top of it. Understanding it changes how you see every circulation and flux problem in physics. This is Denis Auroux. MIT, 18.02, Multivariable Calculus, Fall 2007. Lecture 31. It covers Stokes' theorem - the result that unifies line integrals, surface integrals, and curl into one statement. He opens with one confession. Then the statement. The work done by a vector field along any closed curve equals the flux of its curl through any surface bounded by that curve. Not a specific surface. Any surface you want. You pick whichever one makes the calculation easier. Then Green's theorem disappears. The result from the plane that converts line integrals to double integrals turns out to be Stokes' theorem in disguise. Same formula, restricted to a flat surface in the xy-plane. What looked like two separate theorems is one. Then orientation. Walk along the curve with the surface to your left and the normal vector points up. This rule is not chosen for elegance. It is the price of having a consistent coordinate system in three dimensions. Then the proof. Cut your surface into tiny flat tiles. Apply Green's theorem to each one. Sum everything up. All interior boundary edges cancel. Only the outer edge survives. The sum of tiny Green's theorems gives you Stokes' theorem for any surface. Watch the moment he computes the same line integral two ways. First directly - answer is pi. Then through a paraboloid instead of the obvious flat disk. Longer calculation, stranger setup, same answer. The theorem is not an abstraction. You can watch it work. A fluid dynamics engineer I know kept this lecture open during their first week modeling atmospheric circulation. Said it was the first time Stokes felt like a tool rather than a formula to verify on exams. Free on YouTube, MIT OpenCourseWare, 18.02. bookmark this and watch later - after this lecture every circulation, every flux, and every curl you encounter will feel like three views of the same object

Zyphor

11,286 次观看 • 26 天前