Professor Jeffrey Sachs, distinguished faculty, dear students, ladies and gentlemen. It is a pleasure to greet the Oath Institute at Columbia University, the Global Masters of Development Practice, the Sustainable Development Solutions Network and all others taking part in this gathering. One year ago, world leaders agreed on a plan for the future of our world, the 2030 Agenda for Sustainable Development. It aims to secure the well-being of all people and the renewal of our planet. It's a remarkable framework, comprehensive, interconnected and universal, applying to everyone and everywhere. World leaders also reached the historic Paris Agreement on Climate Change. Now we must bring these packs to life and promote positive change across the world. More than 50 governments are moving ahead, making the SDGs an integral part of development planning. But many others have a role to play in bringing about the transformation we seek, parliamentarians, businesses, investors, scientists, civil society, faith groups, the media, the creative artists, and of course, universities across the world. Implementing the SDGs calls for different ways of thinking. That is one of the strengths of the academic community. We will count on your strong engagement in fulfilling our core promise to leave no one behind. Thank you.


It's a very small group, yes. Are we on video already? OK, thank you. Actually, it doesn't matter. Go for it. Yeah. This introduction is the first slide. So you want to say something about yourself? Yeah, well, my name is Bernd Helmner. I'm the technical lead at Creative in the database team. I'm doing Postgres since 2002, starting doing my studies. My favorite projects in Postgres actually are my migration and high availability and performance tuning. Yes. Just being here, the mics are just getting bigger. But it's just the introduction in Europe. So I might need to introduce myself for the video. I think everyone here in the room knows me already. Just very, very briefly, all those dates given is when I started to actively develop software for those projects. So I'm kind of an old-time when it comes to open source. We didn't even have the name open source when I started. But anyway, let's keep the introduction short. Today, I'm more or less busy not doing open source software development, but running a company. Obviously, we both work for that company. And again, I'm not going to read you that slide. It's enough for marketing, right? So when it comes down to power systems, when we just briefly touched the topic already, it's a huge area that we as a community don't have that much contact with. And on the other hand side, all those users don't have much contact with the community here, as we can see from the empty room. Here are some quotes I took from Computer Weekly about power systems in general. And again, you can read them yourself. There are huge advantages, really huge advantages that you can get by switching to power technology. And we will see some of them during this presentation. One is pretty obvious when talking about open power. Let me use a train as an example here. We all know that trains are, well, in general, safer than cars, despite recent events, like slightly north from here. But looking at this train ride, I'm not so sure that that is safer than using a car. Similarly, in the IT, we see security problems coming up from unexpected sources. Like a couple of weeks ago, when Apple found malware on their service in the firmware of their service, which is something you cannot really check, right? It's embedded in your hardware. With open power, it's different. You can check the source code. With those systems, literally everything is open source. The firmware is on, I think, GitHub. And of course, you can use Linux then, well, you should use Linux. So I don't think there's anything else you can do. For our systems and our tests, we stayed with the completely open versions and with little end-in distributions. I guess you all have heard about Debian. The picture is pretty old. But I wanted to just give you a short introduction to what is Debian about. It's about different, obviously, stable is the release of the distribution. But we have the unstable branch where all the development and testing in the distribution goes on, which migrates automatically to testing, which then becomes the next stable. I'm not going to talk about experimental and all those details because we don't need it here. The two important things for Debian in particular is we have backpots. We just had a discussion, like 10 minutes ago, about running the most current Postgres on fairly old CentOS. I'm not even sure how old that one was. But it had version 9.2 in it as a distribution provided Postgres. And it's not that easy to upgrade then. Where Debian offers you backpots in general in the area of the distribution where maintainers just upload the newer version for the old stable release. Yes, Debian doesn't release that often. But you get the newest versions of the more important pieces of software to run on it. And at the same time, since the last release, well, the one that's out at the end of life now, Debian offers long-term support. Or as the other one we used for our test, Ubuntu, which is based on Debian, does as well. The other thing that you should know is different when using the Debian or Ubuntu packages, which are jointly developed, is we do multi-version, multi-cluster. Meaning it's not that you install a package and you have one version of Postgres on your server and that's it. You can run directly out of the package without any manual adjustments. You can run a 96 and a 95 and a 92 at the same time by just installing those packages. All the infrastructure needed is readily available, which has the big, really big advantage that you can do a migration without really doing it in place, essentially. So you can run the old version and then migrate the new version and test the new version all on the same server if you like to. Obviously, a distribution offers you usually at least only one version of a database pack or any package. For Debian or Ubuntu, there's a community-driven project called apppostgresql.org. App is the Debian and Ubuntu package manager. And this is run inside, as you can see, from the top level domain inside the Postgres project. And the idea is to give you packages for all Postgres versions, for all Debian and Ubuntu versions. So whatever you want to have, just use it. It could be a developer version. It could be the latest stable. It could be an older one. For all of them, packages are available just at, well, essentially the click of a mouse or the command line alternative. So far, available only for AMD64, i386, and LittleIndianPower. And also, I have to read that up here. It's stable for Debian, old stable, long-term stable, and unstable. And for Ubuntu, it's long-term stable, one and two, stable, and development. And for all of these, we have the five supported Postgres versions available, plus the current one, one currently in development. Just do the math. You get three to four Debian and three to four Ubuntu releases, six Postgres releases, all the server packages, all extensions, all modules, with three architectures, meaning out of roughly 150 different source packages, we built 16,000 binary packages. And that almost constantly, every change that is done is reflected on those systems. That, as a background of what we used for all the tests, originally, I was planning to talk to you about those tests, too, but then I could get them to join me for the trip. And since he did the evaluation, I think it's better for him to tell you more about those tests. Oh, I think that was on the slide of your orange. OK, as Michael already had lined out, in the Postgres community, it's not only the Postgres database, it's the complete ecosphere. And with the PGR project, you get basically all the helper tools like backup, high availability from one repository. And with the introduction of PPC64, Little Indian, I have the possibility to get Postgres or with all its tools around into the power world. I skipped that because that's not interesting for this audience now. Why was IBM, or why had they decided to do the Little Indian job? Well, the big problem is that big Indian Linux on power doesn't have the adoption at all in the community. You still need a commercial Linux to run on it. You can do a Big Indian too, but, well, the attraction on open source developers wasn't that broad. With Little Indian introduction, they suddenly have much more distributions available on the platform. That's Debian, Obuntu, CentOS7, Fedora, OpenSUSE, all the Little Indian PPC64 packages. And for them, it's easier to do the QS for quality assurance for their ports. Another options are projects which aren't available on Big Indian at all. For example, prominent example, Docker. Docker doesn't run on Big Indian on PPC64. With Little Indian, you get it for free now. I think Michael already mentioned it. Two, IBM decided to open source their freeware one day in the past and to get other manufacturers the possibility to license the power hardware. We get access to a fairly new open power machine provided by the Chairman Thomas Green, AG. It's a single 8-core machine with a complete open freeware. It's called the OPAL environment. This one can be downloaded by GitHub. You can compile it on, for example, your x86 machine. It takes around three hours. And then you can do all your modifications in there and upload the firmware on the server and you can run it. For example, if you want to do some debugging or something like that or code evaluation, it's possible to just cross compile it and to debug it there. The machine provided by Thomas Green has 512 gigabytes of RAM, has a mega-rate SAS controller from Avajo, and was running with Davy and Chessie with a PG app. It's bare metal. It's not virtualized. The open power freeware can be downloaded. I have already mentioned it on GitHub slash open-minus-power. It's adapted by other companies, too. For example, Talos. They provide workstation lineboards with power CPUs. You just need to license the power hardware, and then you can do everything you want, customizing and so on. The OPAL firmware can be virtualized with KVM. You can either do power KVM. It's a specialized IBM KVM distribution, or you can do it on your own. We have also did some performance comparison on our four socket E8 50 machine with eight cores, four CPUs, sorry, and 3.7 gigahertz. This is a little bit faster than the open power machine with 3.32 gigahertz. It has a little bit less RAM, 128 gigabytes. It was running Ubuntu LTS, but the main opposite is this was running virtualized on PowerVM. PowerVM is the commercial virtualization on the power architecture. And it's not really called guest, but it's called an LPAR logical partition. So that's the known of used by IBM. It's a little bit different than what we know from KVM, because KVM is a hypervisor which does everything. PowerVM does just the virtualization. For example, storage handling or virtualized storage handling is done by the. I think so, yes. It's basically borrowed from them, yes. The PowerVM basically is a very small hypervisor. It's always running on such an enterprise IBM servers. You can mix, for example, big engine, little engine. If you are forced to run AIX, for example, together with Linux big engine and little engine, you can do so. One advantage of the power technology is the so-called SMT, so simultaneous multi-threading. I mentioned it here, especially because I have some numbers about it, what it brings to you. It's basically the same Intel does with hyperthreading, but IBM has put big effort into it to get more parallelization out of one core. So for example, one Power8 core has dedicated resources for up to four SMT threads. They can access, for example, registers or memory or CPU caches without interlocking. The PowerCPU can do SMT1, 2, 4, and with Power8 SMT8. OK, let's some numbers. Let's dive in. I've used the PostgreSQL internal benchmark, PGBench. It's also used by the hackers to prove performance improvements or performance patches in the project. I have slightly tuned the PostgreSQL configuration, mainly the biggest or most important ones, like shared buffers, MUX, and main wall sizes, and so on. TPCB is basically the known use by PGBench, but it's just a transactional throughput test. It has nothing really to do with what an application does in reality, but I think to get some idea of what we can expect from the Power Platform, that's the right tool. Each test database was 15 gigabytes. It was a scale factor of 1,000 in PGBench. I mainly used prepared statements. I will tell you where the numbers are, where I use a different method. And every run of PGBench was previously done with PGPreWalm to get the caches of the operating system on the database warmed up. If you have any questions, just raise your hands. Because most of the numbers you see, for example, on the hackers list are usually done with 100 or 1,000. And it fits completely into the shared buffer pool. That's another. I've tried bigger ones. The problem was that because I wanted to use huge pages on the Power Machine, but Power VM didn't let me choose more than 16 gigabytes to reserve huge pages on the bigger one. I've talked with the IBM guys in E-Hingen in Germany, where the machine was located. But I didn't know either what's the reason for this limitation. But there is actually a limitation in Power VM. So to get all of the numbers in common, I decided to go with that number. And you want to be memory central just to scale the machine itself and not rely on storage or something like that. Yeah, yeah. Those numbers I present here are basically just to get an idea about the scalability of the CPU itself. It's basically CPU and in-memory performance. That's where power and inter-architecture are different, right? Storage is probably the same as attached to. So you don't have to benchmark the storage. You have much bigger caches on a Power 8 CPU. And for example, on common Intel CPUs. But the main difference is the memory speed. For example, open power can up to 230 gigabytes per second, if I recall it correctly. If you choose to correct memory, the bigger enterprise machines can even do more than 200 gigabytes per second. I think they can do 320 gigabytes per second. That depends on the hardware you purchase. You can go back a little bit. The reason why we have 512 gigabytes here in that machine is because the central memory system used on that tie-in board, it's a board actually purchased from tie-in, can do the full memory speed only if you have put all banks full. If you don't put all memory banks full, you have lesser memory speed. That's the reason why we have used your 512 gigaliter in here. OK, let's start with some numbers. That's a comparison graph. The E850 machine, the logical partition with Ubuntu LTS compared to open power. Again, it's bare metal. We can see that the open power machine is slightly faster even than the E850. This is one socket only. So the L-PAR was restricted to run on one socket with eight cores. So it's comparable to the open power machine. And we see it's slightly faster, the open power machine. That's not surprising because it's nearly the same CPU. The open power machine is even slightly a little bit slower. But it's bare metal and nothing is virtualized on that machine. The E850 L-PAR is also using VOS, so storage virtualization, which might give here some influence. Not sure about that. We have to try it without a storage virtualization here but what was not possible on that machine. So we can do up to 450,000 with 100 connections and 360,000 with the E850 machine with eight cores. To give roughly an estimation where we are here compared to an Intel CPU, I've had some graphs from a customer project from November with an Intel machine. It's using two E2650 10-core CPUs on that machine. And I've decided to put that number in there. The problem with that benchmark was that I only have three different client connections tested with that. But I think that's still enough to see that the... I have to look around the corner. The E850 platform is performing a little bit better, starting with 32 connections than the Intel platform. And interestingly, with 32 clients, if you test that against 28 cores on the E850 machine, it's even faster. I have to say that PGBench is running on the same machine with Unix domain sockets. The reason for that is that to be comparable with the open power, I need to use that because I don't have a second machine for the open power machine to test against it. But the Intel machine is always a little bit slower. Just to get an idea of it, you have 20 physical cores against eight cores and against 28 cores. Any questions? We're also running on the same cores. Yes, it's always. That might explain the swarm, that we have 64 logical CPUs, and it's just decreasing a little bit before we reach that. The problem is that you have many 64 threads and 64 Postgres pagans. What do you mean with sucking out? Well, if you have eight cores dedicated to Postgres, there would be equally close connection between PGBench and the same cores. How many cores does PGBench need? It was always 1 to 1. If you have 100 database connection, I have used 100 PGBench threads.  And if you run on full speed. Well, the interesting part is, just give me a few minutes because I have another slide, which might be interesting for you then. OK, that's some detail. OK, I have to get back to the red line. Well, you can see basically that Postgres is scaling very well, about 28 scores. The intermission isn't scaling linearly, but much slower than the power architecture here, for example, just to get an idea. Here are some details against the eight core and 28 core. Why 28 cores or CPUs on that LPA? The problem is that, and that was told by the IBM guys from A&N, that the hypervisor and the Vios on the IBM machines use itself CPU cores. So it's a bad idea to use an LPA which spread up across all cores. You have to reserve some for the hypervisor and for the Vios server. That's why we have reserved four cores for them and 28 cores for the Ubuntu LPA. And that's why we have 224 logical CPUs here. So we can do up to 600,000 transactions per second with 28 CPUs. That seems fairly good, I think. I've also did some comparison between Power 8 SMT modes and Postgres code because I was interested how big the influence of SMT is to postgres code performance. I've decided to go just with SMT-1 at the start. SMT-1 means basically SMT-off. So you have only eight CPUs available. And the virtualization guest peaks out at 150,000. SMT-2, it doesn't double. But it effectively gets about 230,000. And with SMT-4, you get above 300,000. SMT-8 doesn't give you that much more as you might expect. The reason is that the Power 8 CPU has dedicated resources for up to four execution threads. And with eight execution threads, they are just divided. That's the reason why SMT-8 gives just a slight improvement. I think Power 9 will go back to SMT-4, basically. I'm not sure about, because Power 9 will come with different architecture designs, I think. There might be some Power 9 CPUs with SMT-8, but I think they'll go back to the Power 7 architecture which just provided SMT-4. That's actually my information what I have. I also did some comparison with older post-crest releases available in PG app, basically 9.3, 9.4, 9.5, and 9.6. The numbers for 9.6 and 9.5 are basically identical, because you have some noise from PG benches and so on. But the curves are nearly identical, so I don't think there's much difference. The biggest difference, of course, is against 9.3. That might depend on the scalability patches which went in since then. But it's remarkable that you get nearly 100,000 transactions more than with 9.6 than with 9.3 or 80,000. 9.3 has another implication here. It couldn't use huge pages. It's not there yet, or it wasn't there yet. The other, the 9.4, 9.5, and 9.6 instances all used huge pages. I did some, I don't have a slide for it, but I did some comparison. Oh, I have a slide for it, because the next one, and that might answer the question. This performance test, because I thought that when running the benchmarks, the scalability benchmarks, I thought that the machine wasn't really setarized. So even if you run PG bench on the same platform or the same host, it didn't really setarize the whole machine, especially if you get into a configuration with 28 cores or just sitting down. And well, it does did something. But the CPU seturation wasn't over 60%. But Postgres couldn't do more, actually. And that's actually what that figure says. With one instance, with four sockets, so 28 cores, we are saturating nearly 450,000 transactions. If I start a second instance with this Postgres 9.6 installation, so complete another port, another instance, and run PG bench at the same time against that machine, it gets the same with both numbers concurrently. If I start a third instance, I get some lower numbers, nearly 350,000. And then the system suddenly starts to saturate. And with four instances, you see some fluctuation in the numbers. And that's an indication that the system is nearly saturated. And it was really, we had 100% CPU time used. And with four instances, the machine did two million to contact switches per second. So I think in Alexander, I couldn't do that because I didn't have the machine available yet. Then yeah, that's a pity. I really would like to do that. Yeah, yes? That was really an interesting picture, I think. The problem with that machine, well, it went into production because the machine was tested at the customer side. And they wanted to complete their project. But yeah, that would be interesting to see that. This was done with 15 gigabyte share buffer pool each without huge pages. Because it's always the same like the number of connections. So minus C100, minus J100. I did linearly. I think my colleague, Julian Scholder, he did some interesting tests with different notions. He, for example, using 128 database connection and just 16 PG bench threads that give slightly different numbers. I think the problem is all the outcome of his findings was that you always have to use a power of two in PG bench because otherwise you have really strange results then. But PG bench is a beast. I also did some ride scaling. The ride scaling was only done with one socket L power with eight cores with PG bench. You can do up to 32,000 ride transactions per second on that instance. But you have to tune it a little bit. So the blue curve was actually max wire size 20 gigabytes. And the red curve is with max wire size. So the size of the transaction log 120 gigabytes. So checkpoints, player role here. My colleague, Julian, also repeated the tests with aggressive wall writer settings, but it didn't give anything more. The system was still not saturated here. Just sitting around and doing all the stuff, but the CPU time was plenty still available. My other colleague, Christoph Berg, who is one of the maintainer of the PG app project, then asked me, well, what about power special optimization for post-credits called binaries? You can do some power eight optimization with GCC. EBM itself provides the advanced tool chain, the customized GCC build environment with a special or newer version of GCC on Ubuntu. PG apps normally builds with the standard distribution compiler in Ubuntu. It's GCC 5.4 with IBM advanced tool chain. You have GCC 6.3. And what they also ship is a specialized or an optimized crypto library. For example, you have a special optimized open SSI library in there and so on. And the compiler per default enables O3 optimization level instead of O2, what PostgreSQL usually does. And it's the MCPU and M-tune options for power eight, which activates some power eight tweaks, like Altywake options and so on. So he asked me to compare that. Maybe it's worth for PG app to get also some optimization in their build environment. The outcome was actually for that benchmark run. That's PG bench without SSL or other things. It's just plain transaction throughput. It doesn't matter. If you use a plain GCC or an IBM tool chain, advanced tool chain, you don't get any difference. That might depend, of course, on the workload. If you're using SSL connection, for example, you might get benefit from it. It's for transaction throughput tests. Well, you are saturating the data. The database drops out at nearly 150,000 transactions per second if you use SSL, for example. SSL has a huge impact on the CPU. So it might be worth to do that with an SSL benchmark. So what about AIX? We have plenty of people, well, I know plenty of people which are still using AIX on the Power Platform. I've did some comparison with AIX71. It's basically the same environment, the same storage, on the E850 machine than the Linux tests. The problem with AIX and even the experts at IBM had a hard time to figure out to get high transaction rates out from Postgres on that platform. It's really difficult to tune. So here's a small excerpt what we have tried. First, I'd all use GCC. If you are wanting to use a Postgres on the AIX, XLZ doesn't like Postgres at the moment. I think there are patches around. From Konstantin Krznyk, he reported that on hackers that there are some lab logs with the XLSE compiler and provided some patches. I haven't tried it, unfortunately. You have to make sure to build in object mode 64. So you get 64-bit XCov binaries. The XCov binaries allow you to tune some tweaks into your binary after compilation that's done with the AliEdit command. I was advised to use the fork policy core. I'm really not an AIX expert, but I believe that guy. And that's especially important for PgBench. You have to export matter options with AIX. Because otherwise, when you use PgBench threads, AIX always uses one dedicated heap for the threads. So every thread which is modifying, the heap has to wait for each other. The default setting is 32, for example. So you are safe. But if you make it too large, you have a problem that the maintenance of all thread heaps is costly. So you have to get some tweaks to find the right balance. That's what we have done with recommendation from our AIX kernel guy in the USA. And the schedule command to force some special scheduling policy in the AIX kernel. For the bottom line is it's much easier for little NNM Postgres. But if you still want to use AIX, it's better to use packages like Michael Perzl from Germany has a special AIX repository available where all the Postgres stuff is put into RPMs. And you can easily install it with YAM, for example, in AIX. So long story short outcome. That's a comparison between the E850 core Alpar instance AIX versus Linux. Again, same benchmark, scale factor 1,000. Postgres configuration was completely the same, except that AIX didn't use huge pages there. Yeah, I think that shows everything. And that's even a tweaked binary. So it drops out nearly 200,000 transactions compared to 350,000 transactions per second. But again, the system is not centralized, even under AIX. So I have no idea what it is actually. A kernel guy had a look on some traces on AIX. And he suspected that he has something to do with inter-process communication. I think there was also a threat on hackers telling that the M-map implementation on the AIX is suboptimal. Because every time you do an M-map on an M-map region, which is our share buffer pool, basically, you have to put a log on it. I have done some tweaks to relax that a little bit. That's the legend says all about it. It's the red alias option. It was set to 200 in the AIX kernel. But it didn't give that much benefit. It's a slightly plus compared to the other results. But the problem is it lies all between 10%. And everything between 10% is, for me, like, peachy bench noise a little bit. So we have to take that carefully. So bottom line, actually, from my findings is, yes? Well, I have to talk with that guy for that. This is just interesting information here, right? Again, it doesn't know about those benchmark. And they do know that we are presenting them here. They know that, of course. One of those guys told me that the set of one guy in the zone on the AIX is low on the project itself. Yeah, that's actually my outcome, too, so my opinion. With PVD64, Little Indian, you get basically everything from the open source world. And you are open with that architecture. I think what I am, power is, I think, more prominent in Germany than actually in other countries. I know many companies, for example, are dedicated to SAP HANA, for example. And they run on Big Indian, but they also want to use other open source project for their IT infrastructure. And with that, China was, I've heard an IBM guy told me that China was one of the first countries which purchased a power license. And the other thing, maybe it should, before we finish, I guess we are running out of time, right? We have five minutes. The way I understand it is, if I put kind of the same money on the table for an open power system and for an Intel system, I get more performance out of the open power system, right? If you look into where's the number, you get with, I don't have the open power machine here because I didn't have the possibility to do that test again with the open power machine. The open power machine was traveling through Germany to different customer sites. So I have only small time slots to do my benchmark there. There are not that many machines available right now. Where is the? That was too fast. So it's with just eight physical cores, it's much faster. You get nearly 400,000 transactions per second. But this is comparing to? Yeah, I'm just interested in the blue line. And with Intel, you get with 32, nearly 150,000, 64, 200,000. So it's lower, yes, in that comparison. With that interzip, you get more. Yes? It just needs more work in the machine, right? It depends. If you're using PowerVM, for example, on a big enterprise machine, it's getting more difficult. But I think these smaller open power machines you get from IBM are fairly easy to use. I have talked with some guys from Thomas Kren, which are implementing that machine. And he says it's not that big of a problem. So essentially, those open power machines run on Linux, right? Yeah. Because we're using it so that the people a few years ago, it didn't think, like? On what machine? Well, it wasn't some power machine. We have customers still using the old Power7 machines. And I didn't hear anything about that. It's really hard to get it running. Maybe his contact was one of the first to try Linux on open power. Maybe that might be possible, yes. I have compiled it on my federal workstation at work. It took three hours, and it worked. So the Power9 CPU, for example, gets a hardware compression, which Postgres might benefit to with the LZ4. Because of the expectation of all the questions? Yeah, thank you very much.


One thing I never expected to worry about, but now do a little, is you being lonely.  I regret it and I'm the worst for it. You can do better.


Ladies and gentlemen, welcome to the club. It's bell time. My name is Drew Kazoo, joined at this time by Mark Green and Joe Business, and we have the VCW Can Am championship ready to be defended. This is going to be a doozy, fellas. After what we just witnessed, nothing's going to shock me. No, not at all. Well, you say that, and then the homeless guy comes out with the bell. I stand corrected. VCW champion Sidewalk Sam with his trademark Will Wrestle for Food sign. Interesting piece of trivia, Drew. Sidewalk Sam is the second homeless person to hold that VCW heavyweight championship. Who was the first? Homeless Harry. Wow. Years ago. A history of homelessness for the VCW title. And I'll tell you, don't let the home. It is the preferred championship of the homeless. I'm ready for a whole bunch of homeless puns now. Here we go. I know there's homeless puns, guys. Absolutely. See, don't let the exterior fool you. Sidewalk Sam is a tremendous competitor. Unbelievable skill in that ring. But here we see the freshman, Jeff James. I'll tell you what, I was the lead announcer for years for VCW prior to their move to Canada. I haven't kept up quite as much as I'd like to with the product, but I know the history of that is better than anybody. The freshman, Jeff James, hoping to leave Fenway Park with that VCW Canadian title. I would just put that on your head. God knows what's in that hat. This probably lies. Animal parts. God knows. He's brave. Could even be some spare change in there. I'm pretty sure he has scabies now. Or at least herpes. He is a freshman. I heard he got some A's, some B's, and some C's. But enough about his hepatitis test. Wow. Wow. No comment, folks, not on that one. Sidewalk Sam is in a zone. He is being accompanied by the legend, Bull Montana. Bull Montana has been in a match with Shawn Michaels. Come on. 100%. It's on YouTube. You can look it up. Now that is interesting. Bull Montana and his partner took on the Midnight Rockers back in the AWA. Wow. Sidewalk Sam might not have an address, but this place that he's in right now might as well be his home. Mark Green, a virtual encyclopedia of professional wrestling here. Right now he's inside a house or inside a home. He can't be his place. He's homeless. He doesn't own, like, no. Well, I can't. Homeless puns, house puns, fish puns. You do it all. Well, Sidewalk Sam's going to have to, you know, he's the champion here. But the freshman, Jeff James, is going to have to think outside the box. Is it cardboard? Sorry. Mark, you take care of the puns. Yeah, yeah, yeah. I'm done. All right. Literally. Yeah? Yeah. Well, I'll tell you. Go ahead. I thought somebody had had a little accident out here. I just thought it was kazoo. That's possible. No, it really is. Anyway, all jokes aside, one of my favorite things about professional wrestling is the chemistry, the mixing of styles. And we really got a styles clash here, to say the least. Oh, my God. Yeah, you got a young guy up in Cumber. Looks like a talented young athlete. Oh, hang it on. Yeah, but Jeff James is just getting manhandled by Sidewalk Sam. Freshman Jeff James trying to get the Bell Time Club faithful behind him here. He's hoping that that VCW K&M championship finds a home tonight, because the other guy's homeless. Yeah, I'm not inviting you over. Well, Sam can't invite us anywhere, because he doesn't have it over to invite us to. I couldn't make out what Sam said. If he loses, would that add to the plight of the homeless? Well, I don't know. He should be an inspiration to homeless everywhere. Go to wrestling school, panhandle, get all that change together, and go over to the Bell Time Club. On the way in, I saw him with a coffee cup looking for his payday. Crazy. Ooh, brutal knee, right in the corner to the side of the face of the freshman, Jeff James. That's not how you want to be introduced. He can go in the ring, no doubt about it, but quick two count there. Almost had a new champion. Yeah, look at all the energy Jeff James had to exert, just to get out of that pinning predicament. Oh, watch out, here, roll up. We've seen a few of those work here today. Only got two, though. Can you use a schoolboy and a guy who's never been to it? Looks like he just did. Oh, double-handed shop. The freshman's got his work cut out for him today. Tremendous competitor, but. Now, welcome to the club, kid. Hey, stop stealing Drew's lines, OK? Slides under. Two. So for the freshman, will this count the summer school? Yes, so let's see. I'm just wondering if next year we're going to call him the sophomore.  Right. Then he becomes homeless. Everything come in full circle here at the Bell Time Club. Bull Montana, I'll tell you what, nobody has guided more people to championships than the legend of Bull Montana. Well, you can be sure that, uh. He's also guided people to a lot of Chinese food. And Jeff James wants to leave this with high honors. No, sidewalk, Sam. One, two, no. He's wearing them down, though, big time. I know it's legal in Massachusetts, but we can't talk about that stuff on there. Sidewalk, Sam, now he's got that chin lock applied, wearing down the freshman, Jeff James. Did you just say Boston can't afford a dollar? Well, as Sam said, we'll wrestle for foods. I'm wondering, is he going to get paid, or are they going to give him a meal? I feel like sidewalk, Sam, and Bull Montana are just communicating with each other in grunts. Do you pay with sidewalk, Sam, and vouchers? Oh, wow. Big heart and reverse elbow. And there you go, he's starting to cook. Two. I'm sure he'd like to cook. The freshman's still in this one. Sam should definitely renegotiate his contract. He's a champion, he should be able to get a house. I'll tell you, what a notch in the belt it would be for young freshman Jeff James to walk out of here with the DCW Can-Am championship. Poor Jeff James looking at us for help. Nothing we can do about it now. Yeah, he's in a rough way. For sure. Trying to crawl up now.  That's about it. After that, I'm no good. Such a humanitarian, Drew. It's me. She already got him in the corner with that food stamp. That's his prized possession. I thought that was the aim of his finisher. Hard into the corner.  And look at Jeff James. He's just exhausting. No, nobody home. Out of the way. Nobody home. You're good. And you know what's funny? I didn't even mean that one. One, two, no. So close to call. That might have been the best unintentional one of the day. Congratulations. That might have been. That's why they pay me the big bucks. Wait, you're getting paid for this? Referee Rob Tuttle right on top of that. Yeah, Jeff James in a bad way right now. Yeah, absolutely. Oxygen's getting cut off. Also, we got to take the heat into consideration. Would you say the lights are on, but nobody's home? I can't even. Here we go. He's trying to muster up a little bit of strength. Here we go. Belt time club faithful now getting behind the freshman. Jeff James. Let's see if it pays off. Oh, some separation. Oh, big instaguri by Jeff James. And now he's going to roll him over into the cover. One, two. No, not going to take out the champion. Almost a spoiler of a victory there. He's fired up now. You almost feel like Jeff James would be doing a favor. It's one less thing he has to carry around while he pushes a shopping cart. Maybe that extra 15 pounds has got to be a real. Oh, wow. To the face and all joking around the side. Sam is now in prime position. Could be in that title. That's the cover. Oh, I thought he had him so, so close. Lot of heart in this kid, man. Oh, here we go. How could he call anybody? There's no fault. Hey, can he do anything but trash talk? Nice. Well done. There you go. Sidewalk, Sam now up top. Second rope. What are we going to see here? I'm glad this has been a competitive match. I was worried it would be a dumpster fire. Pun after pun after pun. It's raining puns here. Jeff James. Wow. Wow. Showing the power there. And look at how he short arms that close line to add a little extra impact. It's almost like a half STO. Rolling neck breaker. This could be it. Into the cover, hooks the leg. Two, almost, wow. I thought we were going to see the title change hands right there. OK, not bad. Thank you. Not bad. Not your best. Crowd here chanting, Jeff, Jeff, Jeff. They want to see the freshman walk out here with that VCW title, but. Spine on the pine. That's doubtful at this point. One, two, and no. Again. I thought that was it for sure. The freshman, Jeff James, refusing to quit, refusing to give up in this contest. Did he just say, give me a dollar? It feels like we're in the home stretch of this match. Here we go. The freshman, one, two. Sidewalk, Sam, able to kick out. I thought it was over right there. I thought we had a new VCW KMM champion. Both competitors are very spent right now. I mean, winning a title is always especially real. To say you won a title at Fentway Park. Has to be really cool. Part of it. Oh, my goodness. Maybe not something Jeff James will have to worry about. Into the cover one. Again, unbelievable.  What a showing by both, Matt, really. Yeah, I'm very impressed. This kid's got a lot of heart. Definitely proven something here to the Bell Time Club. Faithful, promising future for this young man. Jeff James' company right now. This match may go on forever. Because Sidewalk, Sam can't take it home. Fun about that. Oh, wow. Right in the bush. Look at him giving it back. All it did was anger the freshman who's now on the top rope here. Huge cross body. He's coming in. One, two. What a match we are seeing here today, folks. Unbelievable. I would have thought we had a new champion right there. Tell you, the freshman, Jeff James, is really showing us something here. Might have a new champ. Oh, here we go. Wait a minute. Hold on. Wait, wait, wait. Two, three. Got him. Handful of tights. I don't know if you could see it from that vantage point, but it looked like Sidewalk, Sam had a handful of tights.  He's going home with the Winner's share of the food stamps. Oh, man. Is that his flatware? I'll tell you, man, what a heartbreaker of a loss for the freshman, Jeff James. I can't lie. I really thought he was going to be leaving here with that title. But Sidewalk, Sam, with a handful of tights and walking away with that championship belt. I'm in on Jeff James' face right now. Yeah, not his day. But what an unbelievable showing from him. And we're going to see nothing but good things from this young man in the future. Well, my name's Drew Kazoo for Joe Business and Mark Green. Thank you to everybody watching at home on YouTube, and we will see you next time. Headin' home.


Previously on Go Forth, Jesse set his goal to hunt for investment, launched picky drizzle, and began rehab to get back into competition. I'm nearing 40. I'm getting tired and beat up. But Tia started working on his TEDx presentation. He hopes we'll jumpstart his public speaking career and pitch sweet protection for sponsorship at OR. It's not guaranteed, but I have a really good feeling about it. And Lizzie kicked off her goal to double her revenue, started training, and pitched her mentorship program to the North Face. It was great to meet you guys. Great to meet you. Great to meet you. We'll be in touch. There was no solid answers. They only have so much funding to provide, and so they can't say yes, because they don't know what else they're going to see over the next couple of days. It's kind of just like a wait and see. That seemed to be great. Woo! So we are at the booth of Camp USA. We're going to meet with the marketing manager Jesse Mattner. I'm evolving more towards the route of ski-alternism. I need to work with a legit brand that has light, solid gear to be able to climb mountains. How are you, man? Good, man. How are you? Tia, how are you? Tia, how are you? Tia is salty. Salty? Ah! I need to work with a company that helps me save weight, be safe, but also efficient. So that's the whole philosophy now. We can do that. I'll be sick, man. It's an obvious fit, I think. So our contract is basically like all the gear you need. We really don't care. Your job is to use the gear. Give us feedback. Make it visible. Like, that's it. If you're pitching for a sponsorship, especially like Mattias, the best you can do is to align your goals and to make it known that you do believe in their product and your value system is aligned with the company. Wallpire that email over and... Good, man. Game on. Thank you. Step to work with you. Thank you so much. All right, cheers. Man, that was so amazing. We totally aligned. Same number of vision. Same view about the product. Same philosophy. That's it. I just made it on-camp USA team. So successful. Super exciting. And most importantly, I'm going to have the right gear to do the stuff I want to do. So this is really cool. That ending the show on a high note. Back here, I have my pain cave. The thing that's been bothering me, that's the big X factor for my race at the Quadrathlon is the cycling more than anything else. The running is starting to feel okay. My foot's kind of starting to feel okay, but the cycling on my knee has really been bothering me. So I'm going to do a little bit of a tester here. You know, hopefully it feels good, but make some assessments on how everything feels. Sometimes, even if it's nice outside, I'll do this because it's more efficient use of time too. The main thing that's sweet is that I can just do work on this too. If I have like a one to three hour just aerobic ride, I will ride inside because during that one to three hours I might be able to do 30 minutes to two hours of work. Also checking this out. A few weeks away, 40th birthday party. We launched Rizzle last Friday and we were just backed up with orders. You know, my goal was to sell about 1,000 jars in the first month or so. We sold 740 in the first eight hours and now we're up over 2,000 units and are pretty sold to our subscription service, which is awesome. Just non-stop. Lots of stuff going on. Busy. I view work-life balance as things are never actually balanced in the moment. You balance them over macro cycles. If I was just working on picky bars all day and I didn't have some type of athletic goal or some type of exercise outside of that, I think I wouldn't be very happy. Well, as you get more successful, the best thing you can do is prioritize your time and only pick the projects or the goals that will resonate the most. You got to make time for yourself, you got to make time for your family, and that's the bottom line. What is worth your time? I mean, at some point, the only currency you have is your own time. I still want to compete, but I don't want to compete at the sacrifice anymore of my body or of my family or of my business. I really want to do this race. It'd be an awesome challenge, something I've never done, but it's not a world championships. I'm not making a big paycheck from it anymore. I'm not putting food on the table. At what point am I just the value proposition, the cost versus value. It does not make sense anymore. I think I'm going to wrap it up here pretty soon. My knee, unfortunately, honestly isn't feeling that great. It's kind of a bummer. I kind of feel it on both sides. It just feels like it's radiating through the joint significantly below my kneecap. Quick of it is that I've got a knee that looks really aged. Like I've got a 60-year-old knee. That ride that I just did, which is the real indicator of what I'm capable of at this point, just didn't feel that great. I will have to see how it feels over the next couple days, but maybe it'll feel all right, but right now it's not looking that awesome. Everybody says age is just a mentality or whatever.  I've dealt with a lot of ups and downs with my body, and my body definitely feels different. This is the Black Diamond booth, and they're super important to Schema's Mountains because, one, they give us all the gear for all of our clinics, and they're coming to cosponsor the biggest event we're hosting, which is opening weekend at the last weekend of March. They're going to bring some of their athletes, and now I'm just going to go check in and see what they're doing, so I can find my contact just and go from there. Our opening weekend is going to be incredibly different than it has been in the past. We changed venues. We went from hosting it at a hostel to a really nice, trendy hotel. We are going to have Black Diamond here with athletes. We rented out the Tower Theater, which is the biggest theater in Bend, Oregon, to bring the film pretty strong. The first all-women's climbing film, we also increased the price by, I think, 15 to 20%. You're trying to convince 32 people that what you've created is worth spending nearly $600 to come to. On top of that, I'm trying to, like, stay strong and train for this climate I want to do in Zion, and it's just so much to do. It feels, like, quite overwhelming. I think the first sign of someone that will be successful is that they continue to challenge themselves no matter how far they get. Stay the course. Put in the work. Little by little. Baby steps. So I practiced my presentation in the closet because this is what it sounds like outside. Oh! And this is what it sounds like inside. So pretty much when you are speaking at the TEDx events, I see it as almost a job interview that showcases your work and your personality to the whole world. Moonshaw, small steps to giant leaps. Hopping your dues eventually leads to escaping an avalanche by base jumping of a 600-foot cliff with a pair of skis. Like anything in life, when the challenge is scary, that means that you have to take it on. It absolutely is terrifying to try something new. In any nature. If you're outside your comfort zone, you're fully laid bare. In an example, like Matias, who has done some of the most brave stunts and he wants to do a TEDx talk, and that is frightening to him. And so a lot of people think, well, you guys are crazy. Why would that scare you? It's a totally different skill set. It's a totally different frame of mind. Five minutes work for your rehearsal. None of the speakers have been able to do their whole presentation. It's going to be more like blah, blah, blah, blah, blah, blah, blah. Would you like to just focus on the right then for what's currently playing? Okay. And the light is going to be about like that tomorrow when we're presenting? Okay. Because otherwise, I don't know if people might hear what I'm saying or not. A little bigger than I expected for sure. I think I didn't expect the third row up there. I think I expected something a little more intimate. It's intimidating. I like it. All great things in life are intimidating. The more I'm going to spend time here, the more I'm going to psych myself out. It's almost like walking on the edge of a cliff too much. Kind of to check it out and then know the variables what you have to look for and then just walk away. That's probably one of the worst rehearsal I've ever done and obviously it's the night before the event. What's happening right now is that stress is getting to me. That's when you got to dig deep in terms of finding confidence elsewhere. And I think that Matthias knows time has come. Step up. So I don't want to get hung up on just delivering the perfect words but he actually kills the vibe and the flow of this thing. I got to get amped a little bit. After weeks of training, Lizzie is finally ready for her big climb in Zion. Yeah, I've really tried to keep the nerves down but just everything is happening now and it definitely feel really nervous. It's time to go. Zion, here we come. My van is a home to me and it's been the most consistent thing in my life over the last like four or five years and so I love getting to go back to life on the road. Soon after getting on the road, Lizzie received a call back from the North Face with an answer about her pitch for funding. I'm grateful to have had the call just in time a little bummed because we aren't going to get funding for the mentorship program from them. I still feel really passionately about it. I'm gonna have to pay for the beginning of the program for sure like the training for them. I did that last year as well and it doesn't really feel like a loss. It just feels like a new challenge to be honest. As an entrepreneur, you have to have perseverance and determination because you're gonna get a lot of rejection and you're going to endure a lot of failure but if you're willing to keep going something's gonna work. Back in Bend, Jesse has been trying to recover from his knee injury for the Mt. Taylor quad so he's out for a long distance training ride to see how his knee would hold up for the bike portion of the race. It wasn't everything I'd hoped for. Most of my body feels alright but my knee is still really bugging me. Every few minutes it's just like a really sharp pain. I just don't know if it's a good idea to do that Mt. Taylor race. You know, I spent the last 10 years sacrificing my body for racing and I think as I enter this next phase that's probably not something I need to be doing anymore. It's not the Ironman World Championships anymore. Well, Jesse's had an amazing career as a pro athlete but that kind of career doesn't last very long and you can't keep it going forever so as soon as you recognize that you had that success and that you may be able to parlay that into something else, the better. With his knee causing him continued trouble, Jesse has made the tough decision that he won't be competing in the Mt. Taylor quad. The auditorium is supposed to be close to full today which is close to 2,000 people. It's pretty exciting. 50% of me is really chill and 50% is really, really anxious but while anxiety is uncomfortable it's really important I think to put things to click in in the moment so I'm just like a baser I'm just trying not to overthink it I'm trying to feel it all. Speaker hurls himself down mountains and off cliffs on purpose. So please join me in welcoming the daring Matthias Draub. Moonshot from small steps to giant leaps. How pain you do eventually leads to escaping an avalanche with a parachute and a pair of skis. I know it's a ridiculous way to make a living but I can assure you it's been a rational and intentional journey every step of the way. I didn't commit to my goals until a traumatic event. The suicide of my sister. 18 years old at the time legally an adult I took the responsibility to give the news to my sisters and on the way back from her funeral I had a realization she didn't have something to live for past her suffering nothing existed beyond her misery no existential quest recovering from any reconstruction at the time in addition to using my sister I pictured myself base jumping while rehabbing every day I mean these goals may seem completely trivial but they represented goals past my suffering goals that involved emotional mental and physical commitment so my new vision combined alpinism Steve skiing and maloneering in true alpine style I wanted to earn the descent by climbing to the top of the mountain with all my gear first the ultimate goal being to climb and ski base jump from the summit of Mont Blanc the rooftop of Europe the crown jewel my first application to my vision was a complete total dramatic failure I slimmed back in the cliff four times and I managed to turn around but then I passed out in the parachute I flew 4,000 feet unconscious and I crashed landed in a forest fell another 50 feet on two dirt I was rescued by helicopter spent three days in a coma suffered a double fracture on my left femur and a brain hemorrhage and to top it all off that happened three weeks before the birth of my son five years later after the accident on the way back from the skate park it told me papa when you'll be old I'll teach you how to skateboard and when you'll die I'll bury you with your skis and your skateboard because my heart knows your heart the fear is the greatest emotion in my opinion because it's the only emotion that will help you tap into your full potential after eight years of preparation and applying these principles I could finally combine alpinism big mount skiing and base jumping all at once and on June 24th, 2019 I climbed to the summit of Mont Blanc with 45 pounds of gear and ski base jump from the summit closing the trilogy Iger, Matterhorn Mont Blanc and also setting a world record in the process first ski base from the summit of Mont Blanc let's have the courage to honor our passions be there for the people we love and always always stick our landing thank you very much for your attention tear it up, thank you appreciate it thanks guys, appreciate it do you want some soup? some soup good enough? is that what you were hoping for? absolutely, sweet thanks man when I walked off stage I knew it was I knew I had nailed it it felt like an A plus I think the main lesson that I learned through this whole process is to not doubt your skills actually and what you've learned and your competence you have a unique set of skills and that you have to trust having the confidence and the adrenaline of doing something you've never done and then getting it done there's nothing like it ultimately when you know you're capable of such things that maybe you doubted in your past that's what it takes and that's probably the most rewarding thank you so much I appreciate it thanks for listening to the talk I appreciate it coming up on Go 4th Jesse has to answer some tough questions from potential investors so you gave away 13,000? we didn't give away anything Matias sets out on a training mission for his upcoming ski based projects in France in between all this you have to find the time to train not just go to the gym but actually go and spend a few hours eating in the mountains and climbing while Lizzie takes on the toughest climb of her life and they all get some news that changes everything it's been the biggest event I've ever tried planning it's like everything I've worked for it's a lot of memories in this place this is pretty much the worst case scenario


Welcome back to our lecture series Math 1220, Calculus II for students at Southern Utah University. As usual, I'm your professor today, Dr. Andrew Misseldine. In this video, we're starting lecture 20 in our series. And before we get started with that, I just want to remind the viewers here that throughout any of the videos in this lecture series, if you have any questions whatsoever, don't hesitate to post your questions in the comments here, and I'll be glad to answer them for you. So in lecture 20 here, we're going to start our discussion about arc length. How can we find the length of a curve in the plane here? And so let's start off with that plane. We'll have our x-axis and our y-axis, which we'll label there. And consider two points. The first point we'll call point one, whose coordinates are x1, y1. And the second point, we'll call it the second point, whose coordinates are going to be x2 and y2. So let's consider the distance between these two points. So we connect the dots that we have this line segment. What's the distance between these two points? Well, we can compute this using the classic distance formula, sometimes referred to as the Euclidean distance formula. So the distance is going to be computed by first taking the difference of the x-coordinates. So take x2 minus x1, and we're going to square that. Now notice here, it doesn't matter who is x1 and who is x2. If you switch up the order, it doesn't make much of a difference. Because x2 minus x1, when you square, it will be the same thing as x1 minus x2. So in this situation, we have the literal same difference going on here. Continuing on, we have to also take the difference of the y-coordinates, y2 minus y1. Likewise, we'll square it, so don't worry about who comes first. And this will all sit inside of the square root. Again, this is a classic distance formula that many of us have seen before. Now just as a quick reminder, where does this distance formula come from? Well, given any two points in the plane, there is a natural right triangle associated to these points, which you can see right here. Now this third point, which now we're going to color in red here, its coordinates are going to be the following. You're going to notice that the y-coordinate of this point is going to match up with the first point, but its x-coordinates going to match up with the second point. And so if we start measuring the horizontal distance from the blue point on the left to the red point, it's going to be the difference of their x-coordinates, because it's just a horizontal line. This gives us x2 minus x1. If we want to measure the distance along the vertical line, this would be the difference of the y-coordinates, which is y2 minus y1, like so. And so if we call the hypotenuse of this triangle d, as it's the distance between the first point and the second point, applying the Pythagorean equation, we take the adjacent side, x2 minus x1. We're going to square that. We're going to take the opposite side, y2 minus y1. We're going to square that as well. And then that should equal the hypotenuse squared, which is, in this case, d squared. So the typical Pythagorean equation gives us this distance form. We're going to play around with that for a little bit longer. Now when you look at these values, x2 minus x1, we've seen something like this before. This right here is a difference of the x-coordinates as a change of the x-coordinates. And in the past, we typically called this delta x. And so in this form, we have a delta x squared. Similarly, if you take the difference of the y-coordinates right here, y2 minus y1, this change of y, we typically refer to as delta y. And so in this Pythagorean equation, we get this delta y squared. So the left-hand side here looks like delta x squared plus delta y squared. So what we're going to do is we're going to make a slight modification to this problem here. We're going to define the distance from x1, y1 to the origin. We're going to call that s1 for distance there. And then if you take the line segment that connects the origin to the second point, x2, y2, we're going to call that s2. And so be aware that the distance, there's a little bit of geometric argument here, but the distance from x1, y1 to x2, y2, that is d, is actually going to be the difference of s1 and s2 right here. So the d value could be replaced with s2 minus s1. We get this squared. And then the reason we introduce this new variable here is that if we have this variable si, then s2 minus s1 would be the difference of s's. And so we get this delta s squared. And so this equation right here is going to be very much what we build upon to derive our arc length formula. Notice here this is telling us that the change of this distance s squared is equal to the sum of squares of the change of x and change of y. Solving for delta s here, we get that delta s equals the square root of delta x squared plus delta y squared. Again, this equation should not be interpreted as anything different than just the Pythagorean equation with the introduction of these delta symbols right here. So we can use the distance formula to calculate the length of any straight line who has a finite length. Can we use the distance formula to calculate the length of a curvy line or what we would call an arc? Hence why we call this the arc length problem. And the answer to this question, of course, is going to be yes, we're going to use calculus here. And so let us consider the following problem, right? We are going to have again our x-axis and y-axis. Here's our x-axis and y-axis. And consider we have some continuous, yet curvy function f like so. So we have these two points in the domain. So we're going to have a starting point A. We're going to have some ending point B. And so what we're interested in is we have this point A comma f of A. We have some other point over here, B comma f of B. Can we measure the distance from A to B along the curve f? What is going to be that distance right there? Now, the way that we're going to handle this problem is going to be identical to how we solve so many other calculus problems using this technique of accumulation. That is to say we're going to take our interval A to B and we're going to subdivide it into smaller pieces. So taking this domain, we subdivide it into smaller pieces. Each of those pieces we want to be equal distance, right? So we want each of these sediments right here to be a delta x thickness. So we have an x one, we have an x two. You get the idea, we're going to have some xi in the middle, xi minus one, continue on all the way down to B. B of course is xn. We're going to have n subdivisions, B is the last one, and then xA as usual, sorry, xA is just x0 as usual. Now we're not going to be drawing rectangles under the curve per se, but what we want to do is we're going to use the subdivision along the x axis to subdivide the curve. So there's an A point on the curve. Let's get a point for x1. So we get x1 f of x1. We're going to get a point for x2. We're going to get a point for xi minus one for xi. For all of these points along the curve, we're going to get these points. So we get this like point p0, p1, p2. This would be pi minus one. This is pi, you know, keep on going, right? All the way down to pn, something like this. Now for the sake of illustration, I think I'm going to move things just a little bit. We're going to put, because again, it looks a little bit cleaner on the picture. I'm going to move pi to be right here, and this one's going to be pi minus one. So this is my pi minus one. Like I said, just slightly modifying the picture. This is going to be our xi, and we'll just clean this up right here. All right? No harm, no foul there. All right. Now the reason why I kind of moved this again is I wanted a little bit more space so we could clarify what's going on here. What I want to do is if you take two arbitrary points along the way, pi and pi minus one, we can estimate the distance between these two points just by using the usual distance formula, right? That is, what if we calculate, what if we calculate the linear distance between pi and pi minus one? Not the distance along the curve, but if we take the linear distance, that is, if we play connect the dots, we connect P zero to P one, P one to P two, P two to P three, and keep on going, right? If we draw straight line segments, and maybe my hand is too wiggly here, so let's actually do some straight line segments. So we do a straight line, a straight line, a straight line, straight line, straight lines. You get the idea here. Straight line, straight line, like so. We could approximate the curve using these straight lines. And we can kind of see, like in this illustration right here, if the points are close enough together, the approximation of using a straight line is actually not that bad. And the closer together we get, the better the approximations get. You might be able to see where we're going from here. So associate any two points, pi and pi minus one, we get this right triangle, like we saw before. And so we're gonna take this picture right here, and we're gonna zoom it, zoom in, right? So if we expand this picture a little bit, we're gonna get something that looks like the following. We have this right triangle, like so, with the points, right here. Here is our pi minus one. We have this point right here, pi. The function is doing something a little bit different than the line, right? It might be doing something like this. But the idea is for a small enough interval, the hypotenuse of this triangle will be approximately the same thing as the blue curve. So we see that with respect to pi minus one, the adjacent side is gonna have a length of delta x. The opposite side will have a length of delta y. And then the hypotenuse will have a length of delta s. So this triangle relationship we saw earlier, delta s squared equals delta x squared plus delta y squared. This is what we get from these little triangles right here. And in which case delta s is the type, this delta s is the arc length that we're trying to compute. Now again, the length between pi and pi minus one is only, delta x is gonna be approximation of s here. But as we take smaller and smaller delta x's, delta s will be smaller, smaller, smaller as well. And so we will see here, we're gonna see here that if we take the sum as i goes from one to n, we're gonna get the sum of these delta s's, delta si, we should put a subscript here because the delta s does depend on which interval we're at here. If we call s little s the true arc length of the curve, this will be approximately the same thing as this sum where i goes from one to n of the delta si. Now our goal is to be able to calculate an integral from this. And so we have a sum, this isn't quite a Riemann sum yet, but we're getting closer here. Using the substitution from the Pythagorean equation, this sum could be broken up as the sum from i equals one to n and then we take the square root of delta x squared plus delta y squared. Now again, we should probably put a subscript here on the delta y because delta y, the height will depend on where we are. Like with this trinora here, it's a much bigger delta y than like this one right there. It's just de-de-de-de. Delta x is gonna be uniform throughout this whole calculation, but the s and the y's do kind of depend on the location. So let's see, we will continue to make the assumption that delta x is constant for each subinterval, like we said before, but y and s, the delta y, the delta s are not necessarily, they'll depend on where we are in this segment. That's okay. It won't make much of a difference because as we take the limit of this thing, these things will, will, these differences will kind of go away. You know, to get the true arc length, which we're again, we're calling s right here, we need to take the limit, right? Because this is just an approximation. To get the true arc length, whoops, s, we need to take the limit as the number of subdivisions goes to infinity of this sum, try that again, of this sum i equals one to n delta si, which this will equal the limit as n goes to infinity of this sum i equals one to n, the square root of delta x squared plus the square root, oh, sorry, the square root of delta x squared plus the square delta y i squared, like so. That's what I meant to say. Now taking the limit of these deltas here, so the sum of the deltas, these can be written as integrals right here. So for the first one, the limit as n goes to infinity of the sum of delta si, this thing would be the same thing as the integral of ds. It has some specified bounds here. You know, there should be stuff going on there, but I'm not gonna worry about what those are right here. And likewise, the second one is to take the limit because basically we're using the fact here that as n goes to infinity, delta x is gonna approach dx, delta y will approach dy, and then in this case, delta s is gonna approach this ds. So s is equal to this integral of ds, but then we get, whoops, then we're gonna get the limit as n goes to infinity of the sum of the square root. This will look like the integral of the square root of dx squared plus dy squared, like so. And so this one on the right is starting to get, this one right here, is starting to get a little bit closer to integrals we're used to. It does have a dx and it does have a dy in it, but it has multiple, it has both of them. How does one deal with such a situation like this? Well, let's summarize what we've done so far because after all, our variable y, our variable y here, it was given as a function of f. So y equals f of x right here. And so we're gonna actually use this to our advantage. You might remember from Calculus I that if we take the expression dy over dx, this is equal to the derivative of a function. And this notation is used for a reason, right?  Limits of different quotients. And we're gonna use that to our advantage here. Taking back s equals integral of ds, which equals the integral of the square root of dx squared plus dy squared. What we're gonna do is looking at this expression dx squared plus dy squared, we're gonna factor out a dx squared, right? So we factor out this dx squared. Well, if you factor the dx squared away from the dx squared, you're gonna leave behind a one.  And so rewriting this one more time, you get the integral of the square root of one plus. Remember, well, if you take away the squares, you're gonna get dy over dx quantity squared. And if you take the square root of the dx squared, well, by usual arithmetic rules, this would simplify just to be this puppy right here. That we can calculate the arc length of our function by the arc length s is gonna equal the integral of the square root of one plus f prime f of x squared dx. That is, we can calculate the arc length by taking the square root of one plus the derivative of our function squared dx. And this gives us a nice formula for arc length for which we'll compute an example of this in the next video. So take a look for that one in the link you can see right now.


Welcome to the Crimson Engine. My name is Rubidium. Today we are talking about transporting your camera and how a new type of bag is changing the game. So here's my C200 setup. It has changed quite a bit over the last couple of months. We've got V-mount battery, battery plate, Teradec Bolt 500 transmitter, top handle, 7-inch monitor, shape cage, wireless receiver, lens, matte box, all on a 15mm rail system. Now this is what I need to shoot my commercials and the narrative work that I do. This is kind of my go-to default configuration though I do use it in other ways. The problem is that this takes about 15, more like 20 minutes to build before I start shooting if I transport it around the way that I've been doing in a hard case. 15, 20 minutes doesn't sound like a lot but since I have to break the camera down to get it into the case, assemble the camera on set, break the camera down on set once I've finished and then build it back again to shoot here, it's an hour out of my day at least. But more than that, if I forget any one of these cables, if one of these, like if someone comes up to me and asks me something in the middle of one of those in that hour and this gets left behind, suddenly I get to set, I try building the camera and I can't shoot. I need to send someone back for this D-Tab limo cable or else we're not shooting anything and that's really, that's really started to bug me. What I want to do is transport this whole camera in a state to shoot from the studio to the set and from location to location while making sure that it doesn't get dropped or splashed or get wet or generally broken. So I discovered this. This is the Tenba CineLux 21 high-tup shoulder and it is a doctor's bag so it's just one large opening that fits the entire camera. Built, powered, functional, exactly as I want to shoot. I basically get to set, open the bag, put this on the tripod and I'm away. So I'm saving an hour a day doing that which on a film set is huge given it is not as secure as a rolling case, it is not as secure as taking all this giant camera apart and putting in individual components but you know for the addition of time it is and the addition of knowing that you haven't forgotten anything that you need it is a absolute game changer, lifesaver. So let's take a look at the bag. Tenba make these in different dimensions. They are incredibly well constructed. They are probably of all the bags I've ever owned in my entire life. Nothing is really being built like this. Everything is reinforced, everything has the highest quality as you'd expect carrying around you know $25,000 worth of film equipment. You can see the inside it has a little tie down so you can secure the camera to the bottom of the bag. It has front pockets where you can put your filters or store your cards. It has side pockets on either side. It has these nylon webbing attachments on the back and on the bottom that you can slip over another case so you can stack them on top of your lens case or something else and carry them.  This is their 21 high top. This is a special one that they designed for the C300 and C200 being such a tall camera. I love that I can get my C200 in it with the handle attached. I just have to fold the screen down. If you're not if you're not rocking this large a camera they almost also make a mini version. This is the CineLux shoulder 16. I use it for more run and gun setups when I'm not I don't have the 50 millimeter rails on or I'm powering the camera internally but it has a lot of the same features. Firm inserts padded front and back. It has the same slip over case. I took this to Vegas for NAB with my documentary configuration of the C200 in it and I slid it over the top of my carry-on and I had this under the chair in front of me and the carry-on above me when I flew and it was great. Had no problems at all. If you don't want to carry the camera they also make a roller style of these bags. This is the CineLux rolling 21. It's the same length as the high top but as you can see not as tall. This could be great if you're shooting with something like an Ava 1 or a Blackmagic Ursa Mini something that's not as tall as the Canon C200 and C300 models. I really think that for a soft bag they offer as much protection as you could possibly want and they're just a great solution for getting your camera to set ready to shoot and just saving you a ton of time and a huge piece of mind. Tempo was nice enough to send me a whole bunch of swag that we're going to do a giveaway with. Leave a description of your worst camera carrying experience in the comments and this time whoever gets the most upvotes is going to win a whole bunch of timber gear that you see here. If you travel a lot with your camera and you want to find a way to transport it safer quicker and more efficiently this could be what you're looking for. Thanks very much for watching. I will see you next time.


How guys, I'm going to give you my opinion on Minecraft the Dungeons, a game that I had been looking very much forward to. I remember talking about this game when I first started and I was really excited and I had huge expectations for Minecraft Dungeons. I thought it was gonna be super epic, big, a lot of bunch of things. I thought it was going to be like Diablo, even in its complexity. I was wrong. I was wrong. You know, I was wrong. My first 30 minutes with the game was actually good. I had a good first impression of this game. It was like, yes, this is exactly what I kinda want. This is what I was looking for. But then I started to get another sort of feeling further into the game. I was like, oh my god. It is not as complex as I thought it was going to be. But that doesn't mean that the game is bad. Just hear me out. So about the difficulty in this game. The beginning is very easy so it feels like it is definitely made for kids. But later into the game I kept dying and I was like, ah, take that back. It is not made for kids. It is sorta like kinda made for anyone because of the sick difficulty spikes that happens a bit into the game. The game can go smooth and nice for the longest time and suddenly there comes a super overpowered enemy that almost one hits you. Oh my god. The graphics are good. I wanna go over the graphics and it is that it is set in the Minecraft universe so everything is blocky and I like that it looks cozy. It is exactly what I was expecting in that regards. Some of the lighting is good. All the enemies from the original Minecraft is found here and Enderman, zombies, spiders. So it is good in that way. However, I was feeling a little bit disappointed after a couple of hours with this game and that was, like I said, my expectations were a bit higher. So I am trying to, you know, put down your expectations if you are looking into buying this game. Facts are fun. In this game I have found that I enjoy to have a pet with me, a dog, and I've also found a llama and I also like to have totems equipped. The healing totem and also the sprint boots. So that is my setup currently in this game. Performance. The entire game is feeling stuttering, not exactly lagging per se, but it is definitely struggling and stuttering on the Switch version anyway. Like I said on Twitter, I hope they are going to fix that because that is not acceptable. Just not acceptable. And I am not even a person that cares too much about frame rate. You know, I can play through very bad frame rates and still manage. I am just that sort of person, I guess. So after a little while I just got used to it. It's a shame to say that, but I just got used to it. So I hope that they will be fixing that sometime soon. The music and sound effects are satisfying. So satisfying. The music is exactly what you would expect. It is very Minecrafty, but sometimes there is just no music. But the little music that I have heard in this game is very Minecrafty and I enjoy Minecrafty music. Just really chill. Super chill music. I am sure you know what I mean. The game just feels small. It feels small and I am sure you are going to get that impression as well. There are not very many levels, incredibly few actually. And every level is also set up to be replayed a lot with different difficulties. So the price is correct, I want to say. I was surprised to see the price. I thought it was going to be like a $50 game or something, but it isn't. The price is good. The price was right. It's a very simple game in all meanings of the word simple. I think this is a good idea. I want to support this idea that Minecraft has the big and successful game that that is. Want to branch out to another genre. I want to support this all the way, actually. But I feel like they could have done better and it is just no way near Diablo. It is a fun game for fans. Really good. Absolutely. If you love Minecraft, absolutely get this game. It's kind of weird. You can't pause in this game. I was pausing, going to get something to drink and I am being hit. There is also, to my surprise, no real world interaction. You can't break blocks. I thought the world was going to be much more breaking blocks, more interactive that way. If a creeper is exploding, you would see blocks being exhumed. I also thought, I don't know why I thought this, but I thought I was going to be crafting in this game. There is not crafting in this game. You just find artifacts and gear and weapons and you can enchant your gear and weapons and that is very simplified. It's very simple. The map exploration is not very rewarding.  So after a while I just quit exploring, fully uncovering each map every time. You can, however, find a few of the secret levels that play. I want to say that this game is good for kids. It is good as a first ARPG experience in your life. If I had kids, I would buy this for them. You die a lot in this game. You do.   It's just that Minecraft dungeons, I like the idea, but I wish they had done more. I still recommend it though. I still recommend Minecraft dungeons. It is a nicely like weekend game to play in the weekend, sorta. It's a nice mindless game. You don't have to think so much when you're playing this. I love mindless games when I am tired. And I'm sure a bunch of people feel that way. I think it's probably more fun in multiplayer. I haven't played it in multiplayer yet, but it's probably more fun in multiplayer. The arrow shooting is very satisfying. But, like I said, the performance is not the best on the Switch right now. But I got used to the stuttering. And one time I got stuck on the environment. But I had to quit the level. So yeah, it's a nice game to just chill out with. But it isn't the best, but it's fine. It is just a mediocre game. I'm not gonna be too harsh on it. Because I wanna support this idea. This idea is really good. So I hope that Mojang will bring this Minecraft dungeons, I wanna say, series franchise, further maybe add more to the game and improve on it a little bit. And I would be very pleased. Now thank you for watching my video. You know it. I will see you later. Today I'm going to give you my opinions on Oh my God, what kind of opening is that?


That's a slip which has allowed Bradford in here and forward. They come with a chance for Donaldson It's a beautiful equalizer You know that People long from Donaldson. Oh, this is gorgeous football from the Bantams and they've got a second goal Pritchard sets up wood Hold up by Nova Just content to Occupy the clock always managed to thick it away for wood wood back across and they've got the third Clayton Donaldson gets it With 20 minutes left That's surely all but sealed three points It's Billy Clark with the chance to score his first since returning to the club Straight down the middle. It's one one