Good evening ladies and gentlemen, I am starting this week With headphones on just to make sure that the audio is working. So let's just see here Good to good to be back in the studio with all of you. Welcome So exciting. Okay. I'm just gonna jump into the chat here and see And if everyone could give me an update as to how The audio is sounding. Let's see Alright Welcome everybody. Okay, it's working perhaps. Oh my goodness, I spent a little extra time this evening troubleshooting the audio and Okay, great. It looks like we are working and anyway, so I spent maybe 20 30 minutes extra just Listen, just trying to make sure it doesn't have an echo that you can hear me and that it is synced up In fact, let me know in the chat if my lips are synced up with the audio Why that was not working last week is beyond me. So that would be amazing Okay, good. Good. Good. Good. It looks like it's working. Well, awesome Yes, indeed a lot of butter my bread in the chat. You better believe it butter my bread indeed Robert and Welcome everyone. It is 7 p.m. We're Starting on time that means we're getting a little better, right? Just a little better at doing this so it's good to see everybody and Let's see as usual Let me know where you're from and where you're watching and maybe you're traveling around the world And you're not in your hometown and if that's the case, let us know in the chat. That'd be amazing Good to see everyone streaming in here. Oh So synced that is awesome Kenneth. Welcome Kenneth. Thank you all Chad's here Robert Angie Scott tropical runner shout out to everybody. Oh my goodness It's good to see everyone and let me just let me just get mine going here actually Just to see what it looks like live. Okay. Looks like it's working So actually, let me just adjust this light a little bit here in one second. I'm You know me. I love I love good lighting. So I'm just gonna adjust this real quick here There we go, that's a little better. There we go. There we go. So Let's see. We've got Indiana in the house Brazil flat, Florida Thailand Montreal Fort Bragg, North Carolina South Carolina Lafayette, Indiana. That's what I'm talking about. Oh, that's what I'm talking about Kansas City, Missouri Orange County, California upstate New York near Canada. Whoo. That's chilly up there Lola run that is chilly up there. Oh my goodness Los Angeles, California. Awesome Good to see everyone streaming in Jimmy from Louisville. Just ran a 444 mile That's what I'm taught that must have been an indoor mile because we're not in the outdoor track season yet So that's fast for indoors. Good work, Jimmy. It's fast for outdoors, too But that's that's good to see Minnesota Sacramento, California the UK Ohio Portland, Maine whoo man cold up there as well Singapore all man the other side of the world. What time is it in Singapore right now? If you don't mind letting us know a mod that'd be awesome. And ooh, Jason's in the house. What's up Jason Austin, Texas Yes, oh man, I must say blue collar runner. I am ready for summer. I don't I just love summer. It's just so much more enjoyable for running. So good to see everyone and Bernard six currently in Tokyo. Are you racing Bernard? Did you know the Tokyo marathon is that you must know the Tokyo marathon is I believe on Sunday You must be racing. That's awesome. If you could say go Eagles that would make my day Go Eagles. Is that year? Is that your hometown mascot? That's awesome. Jojo. All right So good to see everyone and as I always like to ask how was your run today? I actually doubled up I did two runs today Both six miles and I just squeezed in the last one before coming into the studio this afternoon So maybe you saw it on Strava Doubling up, you know, the mileage is getting higher. So as Many of you know the marathon is in 12 weeks. And so I'm doing a double peak. So I this is the biggest Week of volume for me before I dip back down and then I'm gonna dip back down make sure I'm not Holding that high volume for too long and then I'm gonna rise back up again So I'm going for about 85 miles this week. So whenever I go over 80 miles. I usually Whenever I go over 80 miles. I usually start doubling. So all right. So yeah, how was your run today? What'd you guys do? Oh That's sorry to hear that Robert your knees are busted. I biked with them and iced Andy's in the house from South Australia Awesome Andy. Welcome Andy. You're the man. Oh man. Andy has his own YouTube channel. Good to see you here Andy That's awesome Just came home from a 20 mile trail run. That's from run vertical productions. Holy smokes 20 mile trail run That's awesome. Good work. That's that's my type of run. That's my type of run Let's see here. All right, so merit copa Arizona's in the house awesome Great to see everyone. Okay, let me just pull up a few as your thoughts are coming in on your run today I'm gonna update you on a few things and of course as always Spread this link around If you have a running club or a high school cross-country team, maybe they're just hanging out And they're not doing their homework and they want to tune into the live stream and ask questions feel free to share This link out anywhere, you know, the more the merrier in my book. So spread it around I would appreciate it tweet it out send it send it to Facebook. That'd be amazing Okay, Liam ran eight miles Carl ran an hour in the beacons. There you go Carl. I took out wait Where is it? Here we go Liam in my second run? I took out the no Carl in the second run I took out the beacons love love the beacons Kieran five miles steezy run Let's see Jesse four miles for me today. Good work. Jesse Scott six miles with eight by two minutes hard in the middle Super cold but good speed where it that's awesome. Scott Blue collar runner just ran a half marathon trail race Saturday muddy muddy muddy burnt up the legs Oh, man. I'll tell you what mud is mud is rough mud is rough Actually blue collar runner. Did you take what shoes did you race in let us know in the car in the chat? I'd be curious because I think I have a guess then maybe the new Solomon's right But let us know in the chat. That'd be awesome Okay, so in addition tonight. I want to talk about running culture nutrition and then of course always an open Q&A and We have some questions from last week in this new balance box. I'll be pulling from that as well I'm excited to talk about running culture and I really want to hear your thoughts as well in the chat as far as your Outlook and Perception on running culture in the United States, but also outside the United States And I have a huge list of topics we can hit on with that So we will bring that up in a minute. And of course, there's always the super chat if you want to ask any questions and get it highlighted So let me just pull up here real quick. Make sure I don't miss any super chats There we go Okay, good to see everyone. All right. Here we are so All right, we're looking good. We're looking good here. Let me just pull this back up and If you are not a part of the D'Amore global running group on Strava Listen, it's getting exciting. In fact, we're almost to a thousand runners there If you don't use Strava, that's okay. No, I'm not saying like I Think keeping running simplistic and and simple is a beautiful thing But at the same time I do enjoy I do enjoy Connecting with all of you and learning about your training and where you like to run and like the different Trains you're running on and looking at your photos from literally around the world So anyway, the D'Amore global running is doing very well and it's I anyway Don't be if you are part of the group Don't forget to go give people kudos because I don't know like supporting each other and encouraging each other is One of the best parts of Strava in my humble opinion. So Patrick is in the house from Alamo Justin from Charlotte Justin. Oh, man. Actually, I'm gonna give an update about some things Justin in a second and Let's see here Let's see here. Let me just make sure I'm not missing any chats Chat had an off day today six years six ish miles tomorrow. Awesome. So in addition a couple more updates I Have been reduced to a webcam. That's right I bought if you say if you watch today's vlog, you already know this, but I bought a webcam So if you are in high school, listen up my brother Joseph who many of you have already seen on the vlog. He's fast He's very fast and he was very very successful in high school. He qualified for Footlocker. So I Want to interview him live for all of you to ask questions live But they as you know the Canon camera has not been working So I bought a webcam the quality will not be as high But I think we figured it out yesterday. We did a test So the plan mark your calendars this Sunday. What day is that? Oh boy? Help me out I think it's March 3rd this Sunday. I'm gonna interview my brother live at 8 30 PM mountain time So it's a little later, but it works better for his schedule. So 8 30 p.m. On Sunday. All right I hope it's gonna work. We tested it yesterday and it was working. So 8 30 p.m. Mountain time I plan to interview my brother about his high school training about how he qualified for Footlocker the whole Recruiting experience getting recruited into college to run in college. So if you're a high school runner I think you're really I think you'll really enjoy hearing his thoughts and if you're not a high school runner That's okay, too. Like you'll learn a lot from him because he's done a lot of other very impressive Endurance activities. I'll just put it in that category since high school. So all right Let me just dive here in the chat. Make sure I'm not missing anything Cape Gerardo, Missouri. That's what I'm talking about Uh, okay. So let's see here Um All right, let me just make sure. Okay. We're doing good here. So One other update is that the t-shirts are Um, actually they're a test print has happened and tomorrow I believe is the 28th of February. So tomorrow Uh, t-shirt should be arriving to my p.o. Box And I'm gonna go see if I like the the look the feel and I think you're really going to enjoy the updated design and But I want to get my hands on an actual T-shirt just to see how the material feels before we start Pumping them out to all of you guys. So stay tuned on the t-shirts But hopefully tomorrow a t-shirt will arrive at the p.o. Box And of course, I will keep you updated on all of that. So all right, Daniel is in the house from Greeley, Colorado Kurt is here from Layton, Utah today was seven by eight minutes on three minutes recovery Oh, man any recommendations for books about running from morgan I'll just answer that right now because I feel like it running with the buffaloes, of course It's I it's my go-to answer because that book helped inspired me to train and Train alone and walk on to the University of Colorado cross-country team. So it's called running with the buffaloes It's a very easy read. It's awesome. It's like very enjoyable very easy You could read it in a couple days easily So a good question from morgan Let's see and robert you make a good point about the leaderboard on strava is broken for you Guess what? It's not working for me either right now. So who knows? I think the strava is still working out some bugs when it comes to the clubs and Anyway, it's last week. Can anybody a guess in the chat? I think I already told everyone on facebook Guess in the chat how many miles we ran together in the in the demore global running club Guess how many like guess in the chat. I won't tell you yet.  I'm going to take a quick drink here. Oh, man Joel is in the house from main swap kneel from singapore amazing Jesse asks how much do you expect the t-shirts to cost? Jesse it's a great question After doing more research it appears that most t-shirts are sold around $20 Which in my mind like I think that's actually what you would usually pay at a race Um, I would love to see a t-shirt for sale for like 12 to 15 But I just don't know if that's practical in today's market with how much printing costs have gone up Um with the explosion of different t-shirt printing opportunities And jesse just so you know the goal is also to print like long sleeve t-shirts or long sleeves and then Even possibly like hoodies and maybe someday like hats. I don't know. We'll see so jesse. Good question. Thank you for Thank you for that. All right. A lot of good a lot of good guesses coming in and guess what? We are almost at a hundred people watching already. That's amazing. Okay 23,000 miles together we ran last week last week the group together ran 23,000 miles That is amazing. So kudos to everybody butter my brand. You better believe it. That is impressive. So, okay Let's dive in to running Culture running culture. What a topic. Oh my goodness Actually, let me pull up my notes here Um, and I know you just so you know as far as the chat goes again There's super chat available if you want to get a comment highlighted and I don't think I've seen any yet, which is fine Um, but I'm not going to monitor but you can you can tag each other in the chat and actually have a conversation with everybody else here because I can only read so many of the comments and also Always always put a question mark at the end of a question because it's way too hard to Sort through the chat if you have a specific question if it doesn't have a question mark So just putting that out there. That's I wanted to remember to mention that. Um, okay So here we go running culture. I have a list here. Let's do this. Um, oh, yeah, and by the way We will be opening. Can you guys even see this here? Yeah, you can see this We're going to be opening a pair of shoes here Toward the end of the live stream. So stay for that Basically, um, I'm pretty excited about this. So stay tuned for that. We got a box back there that arrived Very recently. All right. I'm gonna I'm gonna read off now And you've got to have to just listen to me for a second and then we'll dive into it a chatter here Running culture I think that running culture in the united states is getting better. I think it's Getting stronger. Um I think it was really strong and okay I'm I'm in the united states. So I can't speak to other countries and I'll talk I'll mention a couple others here in a minute Uh, but you know when running really exploded on the scene in the united states in the 70s I would say they those people were really really blazing a trail For all of us to follow and it's really Inspiring to go back and watch some old documentaries on the new york city marathon the boston marathon Eventually later the the chicago marathon and just to see how these people Literally like people thought they were crazy Absolutely insane. First of all, they're running shorts. Like I like short shorts You'll see it this summer like I prefer short shorts when I'm out running It was just like how I was like running in college like everyone just wore short shorts That's just how you did it. Well, if you think my shorts are short Go back and watch documentaries from the runners in the 70s We're talking really short short a little too short if you ask me But these guys were blazing a trail for us to follow in the 2000s and now almost 2020 And um, it was so new and that was what was beautiful about it Like I know there had been running earlier before the 70s and it was around in the 60s But I just really looked to the 70s as this moment Where kind of a watershed moment for running in the united states But of course we have a lot of viewers on this channel who are from Who are from the uk and I am beginning to realize the immensity Or the the magnitude of running culture in the uk It's amazing and I don't know I don't know exactly if it's like Maybe it's a little bit connected to roger banister and the breaking the four minute mile I don't quite know Why like the part okay, so like the park runs Um, it's just blowing my mind the uk has these park runs every saturday Across the entire country where you can go run a 5k for free and try and set a pr Like that's amazing. That's like bringing people together and forming a running culture Uh and then you look at um And then you look at true love is in the house. Oh, that's awesome And then you look at japan and japan is I've heard japan Might have the strongest Running culture in the entire world Uh now obviously you have ethiopia and kenya, but they are more like elite runners You know what I mean like they're just crushing it at the elite level It's not quite I don't see it as much as a Let's like everyone in the towns or the villages or the cities is running It's more like let's go Be an elite runner and see if we can go win races abroad and make some good money. Um, but anyway Yes, carl park runs are brilliant. So Running culture. I think it's growing in the united states. Um personally I think um So you have obviously you have the marathon world you have track and field You have high school cross country, which is very strong but you know because of footlocker and Nike cross nationals, but then you also have ultra running which maybe some of you are not familiar with But I tell you what oh, I just want to mention this like ultra running is now a viable option for people to Become professional runners just so you know There are professional ultra runners and what is an ultra runner in case you don't know It's anyone that's racing 50 k's 50 milers 100 milers And I'm telling you the culture of ultra running is is really strong right now if you're not familiar with that Now I'm beginning to dabble a little bit more in Marathon culture in 2019 since I'm getting ready for my first I'm getting ready for my first Marathon in in may and I also just want to mention one other thing Um, and I want to jump into the chat here and I want to hear your thoughts So get them ready as far as how you feel like running culture is Right now in the united states and do you feel like welcomed into the running world? um So running shops. I think we listen. I I think this yeah, this box is from Is this no this one is not from running warehouse, but listen. I order stuff from running warehouse. I'm sure you do as well However, I really think that local running shoe stores and shops Need to be supported because that is where we can go as runners hang out Ask questions and guess what there is a running shoe shop in north denver Unfortunately, I don't go there very much because it's it's on the other side of town But it's called berklee park Running company.  It's in a little teeny tiny house But it's like they are trying to build Running culture in denver. So I just want to put that out there to you. Um And propose to you that listen. I think we need to Yes over a hundred watch and that's right eddie. I think we need to continue to Um build running culture and frankly it's happening right here on this channel. Okay Let me know your thoughts about it. I'm going to dive into the chat here. Make sure I didn't miss any super chats or anything Uh, let's just see here Liam said pre-started the distance running craze in america in the 70s Liam I don't know if he if he started it, but I tell you what he was really darn close Um, Liam if you look at Um, I mean, yeah, it's hard to deny that steve pre-fontaine did not start it But he I mean he he's he's the man like he's he's the king of Standing up for what he believed in as far as the sport was concerned And taking care of professional runners. Um, so no Liam great point pre was he was the man He's the man like he he didn't uh, he didn't hold back Um, I would also throw out fred labo go on to youtube not now Google and you I don't know if you can watch it for free. I think you can on youtube I'm not positive on that, but it's fred labo Started the new york city marathon and it's a documentary. It's about an hour long It's not incredibly well well done as far as the quality of the filming But you will learn so much about running culture in america in the 70s. Um, so I would really encourage you to go Um to go watch that Uh, that documentary. All right, let's just see here MCMs, let me just say hey seth will you be doing anything 10k related to celebrate 10 000 subscribers? You are brilliant. I was not even thinking that like do you do you mean running a 10k like racing a 10k or Doing a 10k time trial.  I think we are I think we just passed like 9500 subscribers. So we're less than 500 subscribers to go Thank you for being here. Thank you for subscribing and since you brought it up. I'm just going to jump on it If you could help get this channel to 10 000 in the next week That would be incredible because guess what? We've got a lot of running shoes piling up here that I want to give away And I'm waiting for that 10 000 subscriber mark. So that would be amazing. Thank you for bringing that up MCM Um, okay diving back in here. I think I saw frank shorter's name come up So frank shorter bill rogers alberto salazar Yeah, those guys were kind of the king right they were the kings of of the roads And they really blaze the trail. Um, let's see here Let's zack says youtube channels like yours ginger runners and sage are doing great things for running culture and community by reaching new people and creating a sense of belonging That is from zack. Thank you zack. I appreciate that Um, I really appreciate that and we're trying right we're trying to help you You know by giving you insights into Running shoes and training advice But I think frankly most importantly Building that running culture and community and family, right? That's what I like. That's how I like to look at it Let's see here anything else on running culture specifically Um, jason said the people I meet on the trails are super friendly. I love meeting runners. That's awesome jason And let's see here um Great idea mcm 10k time trial. Oh Man, I don't know if I'm ready for it. I actually I feel really ready. I just don't know if Man rahul you're putting me on the spot. You're putting me on the spot. Thank you for that cut that chat Uh, let's see here Okay, joe. I'll get to favorite spikes here in a little bit. Uh, we'll come back to that in a little bit Frankly, I'm a it's a little beyond me because I haven't raced short distances But I'll I'll see what I can do Okay So any other thoughts on running culture? I'm gonna take a quick drink here Larry I'll get to your question here in a second one second here Larry asked and this connects to running culture really well The new york city marathon drawing was today. Did anyone get selected? Anyone get selected? Let us know in the comments. Let us know in the chat I did not I did not larry. I know I just read the email like an hour ago kind of broke my heart But um, we'll see if we can get in another way But larry good question and I think that The boston marathon the new york city marathon to a certain extent the chicago marathon it all has um It all has helped really solidify and build that running culture But obviously like the entry fee for the new york city marathon the first year I think it was like 55 cents or maybe it was a dollar bottom line is It's turned into a business and i'm okay with that like everyone's got to pay their bills Um, but at the end of the day We're still getting on the starting line In running shoes and we're letting it loose and we're seeing how much how fast we can run and how many goals we can achieve so Anyway, I know like the marathon world has evolved a lot and by the way the tokyo marathon is on sunday It's going to be fascinating to watch and even though bekele had to had to drop out Um, but it's going to be fascinating to watch and of course to see what shoes they are racing in. All right It's going to be amazing to watch that um Let's see here eddie said the more global running virtual 10k. I like it eddie I think that's a great idea And uh, let's do it. So I think I have to figure out how to do that I have never done a virtual run before in my life. I've never set one up before but we will make that happen and I tell you what Let's like let's come up with a challenge. What is today today's wednesday? What if we said like by Sunday I don't know like could we get to 10 000 by sunday because we're less than 500 to go I think that'd be amazing. Hmm. Could we do it youtube family? Let me know in the chat I don't know. Could we get there by sunday? That'd be amazing. All right diving back in here um perth australia is in the house thorax, that's amazing Uh, all he asked any 1600 meters spike recommendations. I am just oh my goodness It's like so outside my wheelhouse right now Um because I just don't race at that distance right now But I will send me an email ollie and I'll try and help you out. Okay Um cowboy function leaving for tokyo tomorrow morning to watch Wow, that's amazing. That'll be so fun. You got to send us updates. That's amazing. Uh, okay I think the tokyo marathon is saturday night here in north america trevor I think you are correct because they are ahead in time um, okay, great. All right, just seeing here and All right, so if there's no other thoughts on running culture and I hope I got all my thoughts out clearly um, I want to move on to nutrition next but I just want to reiterate that We are the running culture. You know what I mean like how we Um, how we approach our living how we allow the running to guide the choices that we make how How you know our our swag on the starting line like our grit our our just um Our ability to support each other and like how we support each other and go out and cheer for each other Even if we're not racing like cowboy function go into tokyo. So Um, okay, let's see here. Let me just make sure here Victory threes dylan says that's awesome And rec runner says 10k sub reflection video and what it means to you like your new year film. Oh interesting Yeah, we could we could try and figure that out. I don't know if I quite have time to edit that but we could see um Ross asked thoughts on japanese running culture. Why are they so good ross? It's a good question and I would say ross I've heard that well first of all they train in groups Um, and it's big group. It's kind of like the kenyans. They train together And it's from a very young age. I've also heard that as well Like it's it's just part of their culture from an earth like we love soccer We love football. We love t-ball as kids They love running and um, I think their elite athletes are very It's very regimented very disciplined very to the book like to the t um Maybe it's also You know to a certain extent Like they're eating habits to it. I mean that's a little bit of a stretch I we'll talk about that in a minute, but maybe they're just a little bit on the healthier side Um genetics anyway, I don't know. It's a good question ross, but I do know that their road running is off the charts Here's another just one quick point China is exploding right now with with running china like they have Uh, they've increased the number of races in their country by like 300 percent in the last um It's like the last three years like they are adding marathons ultra marathons So china watch out like I would predict not this olympics in 2020 but 2024 I bet china has some really great runners represented at the olympics just i'm i'm calling it now All right, let's see here. Who else is here? um Kurt good good point about running otaku Talking about japanese running culture. I don't know that I didn't watch that video. I didn't have time. Good point Uh, let's see. Okay. Well, let's dive in. I'll just answer a few questions real quick favorite running spot for distance in denver um, jero, it depends on dirt or Uh, concrete, you know, so if you're looking for dirt like the highline canal is great um, if you're looking for hills Mount falcon deer creek green mountain um Yeah, so anyway jero also You know the cherry creek path if you're looking for like seven to eight miles. Good question. Uh, let's see here. Okay All right, let's move on democratic republic of chuck your opinion on honey stinger waffles I ate I ate one the other day before 10k ran fine, but didn't feel too well the whole way through Yeah, I think the waffles are designed a little bit more for Longer races and we're going to dive into nutrition now just so everybody knows um Basically, yeah, I think the waffles are maybe a little more tuned into like the 50k distance I do think for the 10k it probably your your stomach probably couldn't process it quickly enough Um, so anyway, that's a thought on the I do love the taste And I eat them all the time when I'm running up in the mountains. Good question, uh from from chuck there. Okay nutrition I am not a nutrition expert. I am not a dietitian. I um I eat what true love cooks me because it's delicious and I don't I don't complain like eating eating for me I do wish like I I envy a little bit like I've traveled to italy. I've traveled to france I'd say my my the two best meals of my life were in one was in france. One was in italy like I really Admire their attention to eating and how it's really communal And it literally takes like two to three hours almost every night Like they just sit around and they eat good food and they talk and I envy that Um, but in america, it's like we just it doesn't seem like we have time here from for some reason But who knows maybe I'm over exaggerating. Um, so I'll also say that I do think eating well Is smart like I don't think going to mcdonald's every day is smart.  So he burned it off like that but I would say that My um I think like I'm not who I'm not a vegan. I'm not opposed to eating. Um, uh, wheat or eating carbs or Um, you know, I eat, uh, thank you for the super chat. Uh, uh, I'll get to that in a minute. So I anyway, I just I guess I like to keep things simple and I just don't have a lot of time to research A ton of nutrition things In college as many of you know, I had a lot of injuries So I read this book the paleo diet for athletes And I tell you what I learned a ton about eating and how to fuel As an athlete now, I don't like the fact that they have the word diet on there I wish they would have said the the paleo way of eating because I think diet has a very not a good, uh, Perception from the world when you hear that word as far as diets But I did learn a lot and I would actually recommend this book. Um, but I don't eat like a paleo diet now And guess what I the reason I switched to eating like this is was to try to Stay healthy and it didn't work. I still had injuries after switching to eating How they suggested in this book Um, but I gave it a shot and I'm glad I did Uh, I'll also just make one last or two more points My grandfather he lived to 92 and he never Darkened the doorstep of a whole foods or a natural grocers or any organic grocery store So I think I think it's good to eat healthy. Of course. I think it's smart to fuel well But I also think you Don't always need to overthink it Especially as distance runners When and this is just my opinion But we are burning like if you're running pretty high volume We are burning a ton of Um, we are burning a ton of calories and we're like we need fuel to burn So I think if you know anyway, that's just my thought like I'm all about putting fuel in the body and enough of it To really make sure I can burn the engines when I need to and one last point on supplements And I'd love to hear your thoughts on supplements in the chat. I take a vitamin d I take a multivitamin I take a vitamin b for energy. Uh, I take a fish oil Um, I take a turmeric which helps with inflammation. I take a green tea Green tea, it's just like green tea that you drink, but it's green tea It's like an antioxidant basically And then I used to take a probiotic just to help like stay healthy so I don't get sick Anyway, just putting all that out there. I know I just talked for a long time But I'd love I'm going to dive into the chat now and I'm going to read your thoughts on nutrition Um, I don't want to say diet just like nutrition and overall eating for all of you Let me just take a swig speaking of uh nutrition here Okay Let me jump in to the chat because guess what two super chats came in. Thank you so much Oh my goodness from a lake keaton builder who is um will no Oh my gosh, I'm drawing a blank Dave or will I'm so sorry Um gonna hit 10 000 by saturday in more ways than one that would be amazing Let's hit 10 000 subscribers by saturday. Let's do it. I'm game. I'll do my part. All right. Let's do this I think we can do it. All right. Let's jump in and kurt said Okay, sorry late here was listening in the car Uh culture in my opinion is the most important thing to generate success in distance running work hard and together Kurt you are man. Kurt you're correct. So Kurt I believe you are from I can't remember where you are from If it's the east coast or if you're in the I don't think you're in the uk But or maybe it's ohio bottom line kurt.  They've got a great instagram. Excuse me a great instagram feed called tin man elite And they're just crushing it like they're running fast marathons One of the guys that's part of the group. He just won the two mile indoor usa championships I do believe I forget his name if anybody knows let me know in the chat But anyway kurt great point. Thanks for listening and uh, I love it. I love it Okay, let's see here Let me look here 106 watching that's right Oh, you need to eat a lot of protein or a lot of carbs or both for recovering from running I eat both. I tell you what I love eggs. I love bacon After like a 20 mile run like just getting that fat back in me The body and just so you know, I've heard That in the first 30 minutes after a long run that is the best time to eat Like your body is craving food and it needs to rebuild those muscles And so the first 30 minutes after a long run is the best time to eat. So good point. Rahul, okay Let's see here. Uh potassium is very important Brent. I know Brent. I need to eat more bananas, right? I agree with that. Okay, let's see here Um Hi, is it okay to run slow and steady for ultra marathon? We're going to be running 50k here in rihada tomorrow Congrats. Where is that at re re re hod? I'm not sure boy. It almost sounds like it's in india Yes Slow is good and that's that's brilliant. That's the best way to run a 50k slow and steady Especially the first 15 miles And even 20 miles get to the 20 mile mark and then see how you feel And see if you can start to explore going a little faster or just hold it Brilliant idea. I love it Um Let's see here Drew hunter. Yes, liam. You nailed it. You nailed it drew hunter. Uh, good job Drew hunter. Yes, okay Um Angie said you have to be careful on supplements because if you have normal amounts of vitamins mineral it can cause damage That's and I have heard that as well. Angie. That's a good point Um, it's a good point and I've also heard you got to watch the source of the supplement So good point. Uh, let's see Do says the most difficult thing for those of us that do not cook is to find healthy very easy to prepare Or micro microwavable lots of junk in the frozen food section, but doesn't fuel very well It's a good point man. It's tough and and it can cost a little more money To buy nice, you know, and if you're on a budget So it's oh man, I hear you. Um, we love shopping at trader joes Shout out to trader joes. We think their prices are pretty fair And they usually they have great, uh, they have good food They also have treats like they have good treats and they have good food like, uh, candies and Good chips and salsas, but they also have delicious food. So shout out to trader joes Tin man is a great guy Have had conversations with him has given me some of the best advice I ever got for marathon training Interesting curt, um, Saudi Arabia, mr. Seth. Thanks. Oh neat. You're racing a 50k in Saudi Arabia That's amazing. Wow. Oh my goodness. Wow. Okay. Jacob says I take magnesium supplement daily Otherwise I get leg cramps during the night.  I have my second marathon coming up my taper run I went home and had cold shivers and shut down right at mile 13 Could this be dehydration or lack of electrolytes? I would say lack of electrolytes. Um Yeah, I would say I don't know if that's ever really happened to me ricky Maybe somebody else that's happened to them. But I would say lack of electrolytes. That's a good, um That would be my guess, but again, I just don't experience there. Okay all right All right, so any other thoughts on nutrition and listen again, not a dietitian I um, I'm a simple like I just I eat I eat what my body Like I literally think like, okay, what Not not what I'm craving But what do I think my body needs to get ready to sleep to get ready to run again in six hours To get ready for a big mountain run the next day or in two days and on that note I like to eat carbohydrates two days before a race not the night before a race like A spaghetti dinner two nights before so that it has time to to process into your body Anyway, good, uh luke. Okay luke, uh luke. Sorry about that. Um Okay, this is awesome. All right luke said do try organic chicken tenders in frozen food aisle Organic girl farms has low carb chicken meatballs and tenders and I eat it on salads easy peasy daily Boom shaka laka. That sounds delicious right about now. Good work. Uh, thank you luke for helping out do all right Let's see jason said there's more potassium in an avocado than a banana. I believe I think I may have heard that and what is avocado? Is it um What what is the fat that avocado? It's the good fat The omega threes. No, I don't even know. Anyway, I know avocados are good for you. So that's good.  Okay. Joel said I'm a broke college runner So it's hard to eat healthy every day.  So it's a valid. Uh, it's a valid concern. Okay We're gonna move on and hera hera rem napal. I will get to your question in one second. Um Open q&a Let's do this and we can always if you have more questions or thoughts about running culture or nutrition Bring it up, but we'll jump into the open q&a Uh right now you can ask me anything about life about running about Uh cinematography and filming about youtube Anything open q&a. All right. So let's get in here Herrera napal asked how can I cure a ligament problem? Um, what ligament? Um, like where is the ligament? Is it on your foot? Uh, so I don't know. Uh, gosh My guess would be You know, maybe gentle gentle massage Stretching a little bit of ice and heat ice and heat alternating, but anyway, again, I'm not a doctor Just always put that out there. But um, let us know where your ligaments at. Okay jumping back in here All right. Do you utilize fueling methods during your long run? Ross yes, and Ross. Um, so I I wear a vest actually Here we go. I'm glad I always have this here. This is uh, the vest. I'm using more so right now it's a raid light vest and um Actually, it's in the car right now, but I actually tried a new bar today And I'm not going to remember the name of it, of course But I usually have like two bars a honey stinger waffle So if I'm running like 25 miles, which I do every now and then as you know on Strava Um, I'll have two bars a honey stinger waffle. Um, I so I'm exploring Uh, you can you the letter you can Okay as a possible marathon Um hydration Drink, you know, I need to figure out what I'm going to drink during the marathon because a marathon is a lot different than an ultra marathon In an ultra marathon You are stopping at aid stations along the way and you're literally stuffing your face with like gummies and sometimes cookies And if it's a hundred mile race like I did in September, you're eating like potato soup It's just a totally different ball game. But in a marathon, it's so fast. Um, I'm really starting to explore the option of You can the letter you can as my fueling option for long run. So good question From oh, I don't even remember who that was from, but thank you. All right moving on here um Let's see here How long does it take you to edit each day? That's from brian brian. That's a great question I would say it's about two hours. It's about two hours. Sometimes it's faster. Sometimes it's slower But about two hours. Good question brian, uh, like tonight, I'll go in and start the editing. Yep You better believe it. Uh, let's see when you began running. What pace did you plateau? Well I mean I ran 16 27 for a 5k in high school So I would say that I plateaued at about the 5 20 ish pace Approximately But now as a 33 year old I can hold five. Excuse me. I can hold 5 20 pace for a half marathon Easily um at altitude so I'm really excited to go to sea level and see what I can do at the cleveland marathon But good question. Um, yeah, I probably plateaued at about 5 20 ish Okay, have you heard anything about beacon v2 launch day? Can't find anything online Mike, I think I've heard July 1st That's what I I don't remember where I read that but I believe it was July 1st. Good question I wish it was now. I wish it was in like, let's do this new balance. Come on now Um, so anyway, good question from Mike. Um, how long does it take you? Okay, I've already answered that How do you bust through plateaus from zeke? Oh I see, um depends on the distance zeke and I'm guessing you're in high school is my question is my is my guess um strength I would say strength a little bit more volume not too much Strength and not necessarily from a gym. So how do you get strength? If you can find some hilly running, you will get stronger focusing on your form Making sure you're not losing it in the form and um, so anyway, good question. Uh, gosh We could I need a little more specifics on what uh, distance you're trying to get ready for zeke. Good question Yes 114 watching. Thank you all for being here by the way I like goo for marathon fueling from robert I have tried the morton drinks and they have been great to this point but quite expensive That's from curt. Interesting. All right, curt. That's good to hear. Um Rise up nutrition by lindsay. You can is great for a slower release of energy It's actually a starch based drink instead of sugar So good for longer races or people sensitive to too much sugar Boom, that's what I'm talking about. That's the kind of information I need. Thank you lindsay and that's exactly it I'm starting to research this you can and I'm intrigued. So thank you Um, the fact that your handle is called rise up nutrition by lindsay Means that it means you probably know quite a bit about nutrition. So thank you for that. I appreciate that What shoe are you most excited to buy in 2019 that is from jesse? Oh jesse. Oh jesse. Yeah, I got to pull that question out um It's hard not to say Um, well frankly the beacon two is exciting, but it's hard not to get excited about the next turbo. I must I'll be frank Um, so the turbo two Um, oh man Okay, I'm interested in the new balance Summit king of the mountain as a trail as a trail shoe. I'm interested in it I'm interested in the solemn s lab since seven since I I have the sense six I don't know where it's at right now. Uh, but anyway, there's a few for you to chew on jesse But yeah, oh good. That's a hard one. Oh my goodness and I you just reminded me I got to open this box up here in a minute. So if you're still here, thank you for being here We're going to open up a brand new pair of shoes. Um Let's see. Um, okay. I've been using that tailwind Brent. Let us know Brent, I'm interested in tailwind. Let us know what you think about Maybe give a few more thoughts in the chat. That'd be amazing. I'm really I haven't tried it yet, but um Okay, let's see here just diving back in. Uh, let me make sure I didn't miss any How Let's see here. What do you What do you think about the epic react slash audience odyssey react? That's from jordan You know, I never got excited about the react shoes. I actually don't own them. Um They just seem not quite they seem more like a Cross trainer slash I know they're a running shoe, but I just I wore them once in a shoe in a shoe store And I just couldn't get excited about them. So I am not the right person to uh to ask jordan I apologize about that, but um, sorry if somebody's an uh epic react fan or an odyssey react But it's just not my wheelhouse and so many shoes so little time. Okay moving here Um, all right. Good night, angie. That's awesome turbos. Yes tailwind is legit Uh, let's see and if again if I don't see a question. I apologize. There's a lot coming in. Oh my goodness Okay Way out question. How many years will it take till 3d custom printed running shoes for a perfect fit? Well, it's happening. I think it's happening right now for the elites, right? Correct me if i'm wrong Do I would say five years Maybe eight at the most. I would say five years. I think it's going to be a pretty penny But I would say it's not that far off actually I I think it's going to be the economic question that probably it's not going to be worth it to most of the consumers and Yeah, I just don't think it's going to be worth it to most of the consumers, but good question Okay, from ricky the least I could do thanks for sharing knowledge. That's amazing. Thank you for the two dollars super chat Ricky, that's amazing. Okay all right, um Liam asked do you think the beacons can be used as an everyday trainer? I liam I do I prefer the beacon for an easy day shoe But uh, yes, it could be used definitely for A daily trainer. I wouldn't take it like some people I liam just so you know, I've heard some people race marathons in this shoe I wouldn't do that And I wouldn't really take it past 10 miles But if you're like hanging around the five to eight mile range like great shoe great shoe I I love the shoe as you know, uh, let's see here and sorry if i'm missing some in fact I'm gonna dive into Um, and we're gonna open Give me three minutes. We're gonna open this box in like three minutes. Hold on Um, I'm gonna dive in I want to make sure because people are of course as you know sending me questions via email and instagram And uh, so that's they end up in this box and every week I reach into here Uh, I'm I reach into here. So let's see here. All right. Just diving in. All right. Let's see So this one asks, um Okay, that one Okay, this is asking about the vermeros and basically never bought nike running shoes Do I like the vermeros right now? I do not like the vermeros because they're making my left foot hurt So I'm a little scared to run in the vermero 14s right now. Oh my goodness. What are you gonna do? What are you gonna do youtube? Um Okay, and I'll get swap neil. I will get to your question in just a minute. Um Okay, here we go. Let's see here Hey, Seth. I've got a question. Normally I run my usual easy days between seven and 745 pace And my friend wanted someone to run with the other day. So I ran with him But we ran at about 10 minute pace I know you preach keep your easy days easy But I am am I getting any aerobic benefit from running that slow and having such a low heartbeat? Thanks, Matthew Matthew the easy way to answer that is yes Anytime if you go outside and you're walking you are raising your heart rate, okay? So yes, you're getting a teeny Tiny Stimulus to your aerobic system. It might be small But the more important question is on easy days and this is why you see me I almost said strava. You see me on strava Um run so easy on easy days because yes, I'm getting a teeny tiny aerobic stimulus But all that matters on easy days is that you're getting your legs rested and ready For the next hard day whether it's a long run whether it's a workout That is more important to let your muscles recover because guess what when you go to the gym and your pump and iron You're literally breaking down your muscles therefore You have to and then the next day you rest and that is how muscles get bigger Is you break them down and then they rebuild and then you break them down and they rebuild so easy days In my humble opinion. Well need to be easy So and and you're still getting a teeny tiny Aerobic stimulus. It might be small, but even even if you're just going outside walking you're also getting a stimulus. Good question. Um, okay Let's see here a hundred hundred and four 114 of us in here. Can we all hit the like button for sef? Please? Yes, that's awesome mcm. I appreciate it and Just spread this around and what's really cool about live streaming is that as soon as I hit Stop live stream It automatically publishes the entire chat live on the channel For a replay so like everyone in europe right now. Hopefully is sleeping So when they wake up they can watch uh the replay and therefore Once I hit stop you can then share the link out, you know, if you know what I mean If you know what I mean, okay, should we open the shoes? Let me just see here I know I missed a little bit here. Okay swap neil. Uh, I'm sorry. I'm not saying your name correctly ultra boost 2019 this was my bummer bummer shoe of the year I of 2018 I just don't like the upper And I don't I think the midsole is a little mushy I don't love the boost midsole and I know there's people watching right now who love Odidas and ultra boost and I'm not trying to rain on your parade I'm just telling like everyone reacts to shoes differently I think this shoe is a little bit more in the category of a cross trainer um And I think it did and it's and it's a heavy it's in my opinion It's a little bit of a heavy shoe, but guess what this shoe Very comfortable. I think you could use it for easy days. Definitely And that's how I used it in 2018. Um And I just as far as like training and running fast and getting it just I I struggled in this shoe in 2018 so, um I think it has a little ways to go adidas before it's perfected and I bet they I bet it will improve In the future. So good question. I hope that helps. Okay. I'm going to take a drink of water And uh, let's do this. All right, let's open up these shoes. Can you guess what is in the box here? All right All right, here we go. Can you make a guess? What is in the box? Oh, man Oh, man Let's see here Let's see here. Okay. Sorry. I was just touching the uh Sorry, I was just touching the microphone Hold on By the way, I grew up up in the mountains and this is a elk elk antler Or maybe it's a deer. No, I think it's a deer antler and my buddy made me this knife And so, uh, we used to go out hunting and I would just go help carry the meat out And uh, so I never was I never got my hunting license, but anyway, if you're wondering why does Seth have a huge Gargantuous knife. That's why my buddy made this for me. All right, here we go All right alive Alive unboxing All right, what's it going to be? What's your guess is I'm reading here solomons Oh drum roll Ultra hello from raymond Uh, otty zero. Oh my goodness. Uh, yeah, you guys are you guys are kind of getting it. How do you guys know? How do you guys know so well? Boom, boom the three stripes the three stripes. There it is Oh adidas and I actually made a vlog. I think in 2018 a little bit about the history of adidas It's really fascinating. Uh, a company, uh based in germany started in germany and southern germany Oh, man. So here we go. What's inside? Dun dun dun dun Dun dun dun dun No, it's not a sketchers or an asics Oh, man the anticipation I can't can you handle it? Yes, oh do you all know what this is hold on The audios for the audios for oh my goodness Wow, so I Okay, I held one in a running shoe store But I definitely didn't appreciate it at the moment ready Oh, yeah. Oh, yeah, we got the sniffs. It's a little sniff sniff. Oh, yeah, there we go. Okay Well, as you know, I'm getting ready for a Marathon in May many of you know that and so therefore I am exploring all the marathon Running shoe options. I am going to make two videos tomorrow on the channel And the second video will publish at 3 p.m. And of course it will be all about The audi zero audios for okay, so I'm going to talk about this shoe It will not be my first impression shoe first impression because I can't go running in it tonight But I just want to talk to you about this shoe the history of the shoe the history of world records and marathon Marathon world records in the shoe. So come back for that Oh, that's nice to see that's nice to see You know, what's you know, what's going to be happening in the next couple weeks You know, what's going to be happening in the next couple weeks? Oh, man. So All right, uh ladies and gentlemen as always I always want to Respect your time and we've been going for an hour. Thank you for being here Any other questions that come in from this point forward in the chat? Um, I will answer. All right So I will answer all of them get get them coming in the chat and then we will wrap up here in a minute. Um All right dev said I respect that you have been exploring all different shoes Even though it's unquestionable that the four percent is king hands down right now. That's from dev All right A lot of the tin man elite guys train in that shoe because they're sponsored by adidas Liam good good point. I actually didn't realize they were sponsored by adidas. Um Okay, kurt said one of my favorite shoes of all time is the original Audio back in 07. I think they were like neon orange. I think I went through four or five pairs. Nice Thanks for the chat great show man. Thank you new fan from ricky awesome. Thank you for being here. Um Okay Kurt did I talk about the adidas for his pumas? Issues kurt. That's a great point. I think I mentioned it briefly. But yeah, that's an interest It was the two brothers, right? Correct me if I'm wrong. There was a split there between the two brothers At adidas. Okay Rhonda asked june is coming my first marathon. What kind of shoes do you recommend? Our hook is good. I run in nike epic fly knit But I don't think they would be good for going long distance like that ronda Rhonda, let's see. I would say that Definitely a shoe that has me. Yeah a little more Cushion than the uh than the epic uh fly knit. Um I would look at hoca, but hoca you got to be careful with hoca because It is a narrower fit in hoca shoes And uh, some people don't like the meta rocker feel in hoca But as you know, like hoca is known like that's what they're known for is a lot of good cushion Gosh, there's so many options out there Maybe the explore like the adidas Boston as a shoe that has a little more support than the audios Let's see what else What is new balance going for um, or sorry, is it the new did I say that right? Anyway, ronda There's a few ideas. Let me think what else? Um Hmm Yeah, I mean Gosh, I would start there. I would start with the with the boston look that one up And that could be an option for you and as far as the hoca lineup I believe it's the tracer that is known for going that distance. Um, so good question from ronda Let's see here Vapor fly five percent in 2019. You are correct Um Let's see here. I would go for anything that has some decent cushion but lighter weight. Yeah, that's good Okay, zack ask i'm racing a series this summer comprised of eight races between 5k and half marathon I'm running a lot of 20 minute tempo runs as I progress should I focus on pushing them faster or longer So zack, I would focus on pushing them longer You might be able to go a little faster, but again as we talked about what was it two days ago, uh, basically Approaching that lactate threshold, but you don't want to push through it in a in a threshold run or a tempo run But I think it would be brilliant to increase the distance, especially if the races are getting longer and longer Um, I'm a big fan Of longer tempo runs. It's just how I love to train. So good question from zack um James asked what is your favorite current soccany shoe? So james Oh james. I james. I'm sorry. I just don't have a ton of experience in soccany I have the soccany fast twitch eight, which I think is going to be a great 5k Road racing shoe. All right, maybe 10k um And then I'm interested in the soccany um Freedom iso no is yeah freedom iso And I think it's the five is out right now. I haven't tried it yet I tried it on us in a store once, but I just didn't pull the trigger on it. So Anyway, the soccany freedom iso um, and then for a trail shoe, uh, of course, I never say it correctly the peregrine or the peregrine Everyone seems to love that shoe. So good question there um Yes, there you go Uh, so let's see uh Yeah, that's good kurt. That's a good point the zoom fly flying it could be an option a little way more well More affordable than the um more affordable than the 4% So yeah, it and it has a carbon fiber plate in it. So maybe that could help All right, let's see what else here Let's see Yes, and the turbo. Oh my goodness. Absolutely. Totally spaced on the turbo um Andrew asked, what are the best racing flats? Well Andrew I am Excited to try this guy hasn't happened yet. It's the rebok float ride run fast pro Definitely a lightweight shoe. I think this is going to be a great 5k shoe Maybe 10k we'll see Very lightweight. We're talking three ounces lightweight um, so I don't know if it's the best yet. I haven't raced in it yet. I actually haven't even run in it yet I'm I'm waiting until the snow melts in denver. So uh, good question and okay Let's see here. You can get peg turbo for 120 on bikes website right now. Wow. That's awesome Okay, and let me make sure i'm not missing any um Let's see Adidas boston rebok float ride adidas audios. Yeah, there's the name I tell you what it's like a memory game trying to remember these These names of these shoes. What about a 5k trail shoe from law? Oh man 5k Depends on how rough the trails are, but if it's a 5k, I'm guessing the trail is pretty buffed out Unless it's like a short trail race. Um I'm going to be racing a lot in the solemn s lab since seven s g in 2019 But it has quite a bit of lug action. So if you're in a muddy condition, it'll be great But I think it's a great Like 5k to half marathon shoe for the trails. Uh, that's I love I love the fit of solemn for my foot Uh, gosh, what else man? um And yeah, gosh, you might just want to look at a road shoe if it's a buffed out trail You know, you might just want to look at a road shoe. Yeah. So anyway, good question. Hopefully that helps a little bit um Any suggestions for good trainers to do sprint workouts in i'm looking for some new shoes now the track season is starting up The turbos, I know that's like an easy answer, but You can use the turbos for For for fast workouts faster workouts not like all out but like good solid workouts And you could go run eight miles in them 10 miles in them like they're just a very Diverse shoe like you can do a lot of different things in them In fact, you could even race in them if you wanted. Um Okay, Liam says I use the zoom flies for tempos and track workouts and they do really well Nice. Okay, the rec runner. Are you going to have a demore global running shakeout run the day before the cleveland marathon? I would drive from illinois for that Wow, that is awesome Rec runner, guess what we just bought plane tickets. That's right. True love is coming So it'll be michael true love and I in cleveland So we will fly out on friday and the race is on sunday Gosh rec runner. Here's the deal Maybe we could do a shakeout the day before perhaps But maybe even more so it would be fun to have like a post race Party like party like let's go out to a restaurant. Let's meet and greet and hang out and have fun and share stories about the race and Um, so anyway, we could maybe we could do both but at the very least I would love to meet everybody After the race that'd be amazing. Okay Um All right, I think all right. I think we're gonna wrap it up. Let me just answer a few more Gooders sunglasses from ollie. I use them ollie, but um, I use them because they're affordable But the quality I definitely don't think the quality is quite there. I that's the ones i'm using right now I prefer I love my smith sunglasses. I'm just saving up a little bit more money to replace the ones I lost So, all right mark is here. Hello, everyone. Um, all right. I think Uh, I think we're gonna wrap it up chris the longest run on a treadmill. I haven't run on a treadmill in 15 years chris. I just don't do it. I don't own one and I do not enjoy it Um, but I see the benefit of doing treadmill work when it's crazy out But in denver, we just don't get crazy crazy weather here. I know that's strange to hear Um So sorry, I don't have an answer for you there. It's probably like five miles. Um Eddie's coming to cleveland. Awesome. All right So cool, um Awesome raj. Thank you all for being here. That is that again Tomorrow, we're going to be talking about Plyometrics on the vlog We're going to be talking about the audios for on the vlog and we're just going to have a great time On youtube. Thanks for being here. Thank you for watching. Wow. That was a good one That was a good one so good to open shoes with you and just to share stories And to talk about running culture. Whoo. Seek beauty work hard And love each other See you tomorrow Now I just gotta I just gotta figure out how to shut this thing down. It's always an adventure trying to shut this thing down


Welcome back to our lecture series math 3130, Modern Geometries for Students at Southern Utah University. As usual, I'll be your professor today, Dr. Andrew Misseldine. So I want to point out that if you've been following along with this lecture series. In lecture eight, we talked about the idea of affine geometry. So we saw last time that the Euclidean parallel posture was in fact a very, very powerful axiom and that the inclusion of it, even into the most broad axiomatic system such as incidence geometry, because that's what an affine geometry is. It's just the four incidence geometry axioms equipped with the Euclidean parallel postulate. So just those five axioms, affine geometry is enough to lead to some very powerful results. We listed some combinatorial results about how all lines have the same number of points. And there's just a lot of uniformity that happens, a lot of symmetry that happens with affine geometry. This is a fact, this fact, this observation about affine geometry, the Euclidean parallel postulate, is the reason why geometers have been fascinated with Euclid's fifth postulate for centuries. Because in the book, The Elements, when Euclid began the work of axiomatic geometry, he had his four postulates, which admittedly, in Euclid's work, his axiomization was incomplete, but given he's probably the first, at least from historical records, the first mathematician to really axiomize geometry. I'd say he did pretty good for thousands of years ago. But yeah, in the modern sense, we see there are a lot of unstated assumptions that Euclid used in his proofs. And so because of that, it made studying Euclid's work very problematic. It was cutting edge when it was first developed, but nowadays we're much better about many of these things. And so for many centuries, geometers believed that Euclid's fifth postulate, which is equivalent to what we call the Euclidean parallel postulate, about uniqueness of parallel lines. The Euclidean parallel postulate that we have been using is actually due, not to Euclid himself, but actually due to play fare. But anyways, Euclid's fifth postulate, which is logically equivalent to the play fare version of the Euclidean parallel postulate we're using, it was believed to be a theorem of the other axioms of Euclidean geometry. And it's such a powerful result that we want Euclidean's parallel postulate, but they couldn't prove it because it turns out it's actually not equivalent. This is actually one of the, one could argue, one of the starts of modern geometries, the discovery of non-Euclidean geometries. There are other geometries besides the geometry studied by Euclid in the book, The Elements. In particular, we're only going to focus on Plainer, that is two-dimensional geometries. And so our discussion in this video will be two-dimensional non-Euclidean geometries. But this lecture, number nine, will focus on a couple of non-Euclidean geometries. That is geometries where the Euclidean parallel postulate fails. In particular, our main focus is going to be on two geometries. We call elliptic geometry and hyperbolic geometry, which we're going to study in the future. And they get their names from the elliptic and hyperbolic parallel postulates that we've studied before. So in this first video, we're going to give an example of a elliptic geometry, which is commonly known as spherical geometry. This is honestly, assuming you're watching this video from Earth, this is the geometry of our world. Earth is a sphere and the geometry of Earth is therefore spherical geometry. So what is spherical geometry? Well, spherical geometry is the geometry of a sphere for which to borrow topology terms, we're going to refer to the sphere as S2. Just so you're aware from topology, S1 is a circle. That is, it's a one-dimensional circle, one-dimensional sphere, I should say. The sphere, as we usually think about it, is a two-dimensional sphere. And topology, they do consider higher-dimensional spheres, like three-spheres, four-spheres, five-spheres. These spheres can always be described using distance. For example, the two-sphere, which is what we're talking about right now, we're only focusing on two-dimensional geometry in this lecture series. The two-sphere is the set of all points of unit distance from the origin in R3. So if you take the intersection of the x, y, z axis, the two-sphere is all of those points which are one unit away, but in any direction that's forming the sphere. Just like the unit circle in the plane is all those points which are one unit away from the origin and makes a circle. You can do the same thing that in four-dimensional space R4, so this will be four-dimensional Euclidean space, we could take the set of all points which are one unit away using the Euclidean distance formula, one unit of distance away from the origin that would make the three-sphere. We can do this. So as long as we can talk about higher-dimensional Euclidean space, then we can talk about higher-dimensional spheres as well. But like I said, this video will focus just on the two-dimensional geometry right there. So how do we make sense of this as a geometry, right? A geometry, like I said, it needs to have points and these have lines and these have incidents. Well, the lines are just gonna, excuse me, the points are just gonna be the elements of the set. So S2 is a subset of a geometry. So the elements of S2 are elements of R3, so we can actually think of those as points. But as we restrict from the larger set to the smaller set, the notion of lines doesn't necessarily have to stay the same anymore. And in fact, when we think of lines on the sphere, we really are talking about great circles. Well, that's a great circle, right? A great circle is actually just a diameter, excuse me, it's a circle that goes around the surface of the sphere, but the diameter of this circle is identical to the diameter of the whole sphere. So if you think of a planet Earth, for example, one such great circle would be the equator, right? Those are, that's a great circle using the usual topographic meanings of the equator. You can also take any line of longitude as they go from the North Pole to the South Pole. That also would be a great circle. I guess technically I have to put two lines of, excuse me, two lines of longitude together to form a great circle, but a great circle is just the maximum circle you can go around here. And so if you take any two points on your, if you take any two points on your sphere surface, because again, when we're talking about the sphere here, we're just talking about the points on the sphere, not in the sphere or anything like that. There is a, excuse me, take any two points on your sphere, there will be a great circle that contains it. And so that's what we're gonna consider a line in this situation. After all, line is an undefined term. We can give it different interpretations. So line doesn't have to mean line, at least not in the Euclidean sense, right? So you're like, how can circles be lines? Well, lines are just Euclidean lines the way you usually think about it. But in spherical geometry, a line is actually a Euclidean circle, but it's a spherical line. This is that paradigm shift that's necessary, what many jobs are struggled for such a long time. And an incidence means what you usually expect it to mean that as a line is a set of points, we say that a point is incidental line, if that point belongs to the set of points which determines the line in a set theoretic sense, all right? So we have incidents, we have lines, we have points. We can talk about this as a geometry. And so it's important to mention that this geometry won't be Euclidean because you don't have unique pair of lines. In fact, all lines are gonna intersect each other. Like if you take these two lines, for example, clearly by construction, they intersect each other. But just imagine as you try to think of any, if you take the equator, for example, because after all, depending on your orientation of the sphere, the equator is an arbitrary line right there. If you take any other line, any other great circle, it's gonna have to intersect the equator somewhere. You can't avoid it. You can't try to do something like this, aha, right? I just have a smaller circle. That's not a great circle. The diameter of that circle is not the diameter of the sphere. So that would not be a great circle, thus it's not a line for this geometry. All lines will intersect the equator somewhere. So all lines intersect each other in this geometry. It's kind of curious that the Euclidean parallel postulate isn't satisfied. In fact, we actually get the elliptic parallel postulate. This is sort of like the poster child of elliptic geometry that all lines intersect on the surface of a sphere. So the spherical geometry, it satisfies the elliptic parallel postulate, like I said, since all great circles intersect each other. In fact, spherical geometry is probably the best understood and most studied version of elliptic geometry, at least historically speaking. And particularly this is because we live on planet Earth, which is a sphere. In fact, when you look at the word geometry itself, that we use in English here, this comes from the Greek word gematria. I apologize for my pronunciation here. But see Gamma is the Greek letter for G, Epsilon is for an E, Omega is for an O. So you get Geo right there, for which Geo is the Greek word for Earth. All right. Then the next word, Mu, is the Greek equivalent of M. Epsilon is an E, like I already said, that tau is a T, rho is an R, iota is like the I sound, and then you have an alpha at the end. So it's metria, right? So meter, metria here means like a distance, it means a measure. So gematria is the measurement of Earth. So geometry, the word itself, this study of mathematics with shapes and curvature, is comes from the Greek word for Earth measure. Some of those fundamental geometric principles came about because we were trying to study the geometry of Earth, because as the legend goes, ancient man believed the Earth to be flat, and it came from scientists and mathematicians and explorers and cartographers and what have you, that eventually we're all approved to the world that the Earth was in fact round, it had curvature, it was a sphere. And so that's why we get this word geometry. It comes from spherical geometry, because geometry, as the word translates from the Greek, is the measurement of Earth, the first spherical geometry we understood very well. Now, while spherical geometry is an example, it's sort of like the prototype for elliptical geometry, it's not without some problems. Let me mention that although it's a very natural elliptic geometry, that is it satisfies the elliptic parallel postulate, it turns out that spherical geometry is not an incidence geometry as we've defined it earlier. So spherical geometry is not a model of the incidence axioms plus the elliptic parallel postulate. And the issue comes down to line determination. So remember line determination says that given any pair of points, there exists a unique line that's on both of those. And most of the time, we're perfectly fine. Like if you take this point A and B right here, there is a unique line that contains both of them. It's the equator of the globe I have drawn right here. Or if you take the point C right here with A still, there's going to be a unique line that takes it. Between B and C, there's a unique line determined between A and B. For which the curious thing about incidence, curious thing about spherical geometry, this is part of the issue, is that there's actually sort of like two paths, two straight lines between A and B, between any two points. In this case, it's B and C right here. So like if we could walk straight from B to C, there's a short one and there's a long one, which clearly if you want to go from B to C, you're going to take the short one. So we kind of ignore that one. We look at the short one. And so we can talk about triangles. We can talk about distances. We can talk about angles. So you see, for example, on this diagram I'm coloring on, this is an example of a spherical triangle. All right. But there is one bigger important counter example. What if you're at the North Pole on your planet here and you want to go to the South Pole? What is the fastest way to go? And honestly, the answer is any path. You go any path. You go any direction, right? If you take, if as long as you go straight, you're going to reach the South Pole, right? There's no worries about that. It doesn't matter where you go. And so this diagram over here gives us a better example here. If we have a point P, there is a point on the opposite side of the sphere. These are referred, these two points are referred to as antipodes. The idea here is they're on opposite sides, on opposite poles of the Earth, the North Pole versus the South Pole. And so if you have an antipodal pair, P, and often it's called negative P, because as spherical geometry is a subset of our cube tier, this antipode is actually, it's additive inverse with respect to the vector addition that is present on the vector space R3 right here. So these antipodes are actually, they're additive inverses of each other with respect to the algebra. But geometrically, we call these antipodes. The problem with spherical geometry is that if you have an antipodal pair, there do exist, there does exist a great line, a great circle from one to the other, but there's actually infinitely many, there's multiple ones. And so there is, and a very important counter example to the line determination axiom that you do have that every pair of points has at least one line between it, but antipodes have more than one line connecting the two together. So that's a violation of line determination. But with regard to the incident axioms, that's the only violation. Point existence, yeah, we have at least three points, we have uncounted linear points. There is no great circle that contains all of the points, so we get non-collinearity. We get secancy, every great circle has at least two points. It has uncounted linear points, mind you. And this does also satisfy the elliptic parallel postulate. So what stops us from having an elliptic incidence geometry is that line determination isn't satisfied because of these antipodal pairs, but it is somewhat isolated that even though it's not, even though it's not an incidence geometry, it's really close to being an epi-activity careful. As we see in this diagram right here, two different circles intersect each other at two different places. That's not a phenomenon we saw in incidence geometry. Intersections of lines was unique. But in this situation, lines intersect at two different points. And so because of this problem, since it's not actually an incidence geometry, some people introduce alternative models for elliptic geometry. We'll explore those in subsequent videos here. But this spherical geometry is sometimes called two-point elliptic geometry. And the reason behind that basically comes down to lines can intersect each other at two different points because you have these two antipodes. That if you choose antipodes, lines will intersect at two different places, like so, of course. But that's of course only, you'll notice like with my other diagram over here, if I take any two lines, these two lines, this one and this one, they intersect at A, but they also intersect over here at negative A. So when lines intersect in spherical geometry, they always intersect at two points, but those two points are always antipodes. So because of that double intersection, this is sometimes, spherical geometry is sometimes referred to as two-point elliptic geometry. Now if you really want an incidence model of the elliptic parallel postulate, then we're going to proceed forward with that in the next video. We'll introduce projective geometry, aka one-point elliptic geometry.