Hello, and welcome to this presentation of the STM32 General Purpose I.O. interface. It covers the general purpose input and output interface and how it allows connectivity to the environment around the microcontroller. General Purpose I.O. pins of STM32 microcontrollers provide an interface with the external environment. This configurable interface is used by the MCU and also all other embedded peripherals to interface with both digital and analog signals. Application benefits include a wide range of supported I.O. supply voltages as well as the ability to externally wake up the MCU from low power modes. This table shows the differences with the STM32F0 microcontroller. When STM32G0 microcontrollers are in reset state, most of the I.O. ports are configured in analog mode to minimize energy consumption. The Cortex M0 Plus Core has direct access to the GPIO registers through the single cycle I.O. port bus. This provides a low-latency direct path to change the state of outputs or to read the state of inputs. The pull-up or pull-down resistors independently configured for any I.O. pin may remain active while entering a low power mode. It is configured in the PWR module. General Purpose I.O.s provide bidirectional operation, input and output with an independent configuration for each I.O. pin. They are shared across up to five ports named GPIOA to GPIOD and GPIOF. Each of them hosts up to 16 I.O. pins. I.O. ports support atomic bit set and reset operations through BSRR and BRR registers. I.O. ports are directly connected to the single cycle I.O. port bus. This allows fast I.O. pin operations, e.g., toggling of the pin every two clock cycles. No conflict with the DMA can occur because this Cortex M0 Plus port is private to the CPU. Most of the I.O. pins are 5V tolerant when supplied from VDD I.O. X above 1.6V. General Purpose I.O. pins can be configured into several operating modes. An I.O. pin can be configured in an input mode with floating input, input mode with an internal pull-up or pull-down resistor, or as an analog input. An I.O. pin could be also configured in an output mode with a push-pull output, or an open-drain output with an internal pull-up or pull-down resistor. For each I.O. pin, the slew rate speed can be selected from four ranges to ensure the best compromise between maximum speed and emissions from the I.O. switching and to adjust the application's EMI performance. I.O. pins are also used by other integrated peripherals to interface with the external environment. Alternate function registers are used to select the configuration for the peripherals in this case. The configuration of the I.O. ports can be locked to increase application robustness. Since the configuration is locked by applying the correct write sequence to the lock register, the I.O. pin's configuration cannot be modified until the next reset. Several integrated peripherals, such as the USART, Timers, SPI, and others, share the same I.O. pins in order to interface with the external environment. Peripherals are configured through an alternate function multiplexer, which ensures that only one peripheral is connected to the I.O. pin at a single time. Of course, this selection can be changed during runtime of the application through the GPIO XAFRL and AFRH registers. The configuration of any I.O. pin is achieved through three registers GPIO X MODE R or MODE register GPIO X O type R or output type register and GPIO X PU PDR or pull-up pull-down register. Register GPIO X MODE R selects the functionality of the I.O. pin, digital input, digital output, digital alternate function, or analog. Register GPIO O type R is relevant when the pin is in output. It selects open drain versus push-pull operation. Register GPIO X PU PDR is relevant when the pin is not configured in analog mode. It enables, disables, pull-up, and pull-down resistors. The two pins PA9 and PA10 can remap the two GPIOs PA11 and PA12 respectively in order to give access to their functions when the pins are not natively available on the package. With the remapping, alternate functions related to pins PA9 and PA10 are available. Note that this remapping also applies when the package supports pins PA9 and PA10 as independent pins. During and after reset, the alternate functions are not active. Only debug pins can be used in alternate function mode. Pin PA14 is shared with boot zero functionality. Caution is required as the debugging device can manipulate the boot zero pin value, which selects the boot mode. When the external oscillator is switched off, pins related to this oscillator can be used as standard I.O. pins. This is the default state after a device reset. When the external clock source is used instead of a crystal oscillator, only the related OSCI in-pin is used for the clock, and the OSC out-pin can be used as a standard I.O. pin. A new multi-supply scheme of I.O. pins brings new I.O. pin structures. Previously used naming FT for 5 volt tolerant and TT for 3 volt tolerant has been extended by abbreviation suffixes to highlight alternate supply source for each FT and TT I.O. pin. Previously used name FTF for FM plus capable pins has been transformed to FT underscore F. Suffix underscore A marks pins supplied by analog supply. Suffix underscore C is used for pins supporting USB type C power delivery. The absolute maximum rating for each I.O. pin is defined by the lowest voltage of the supplies listed for each I.O. pin. I.O. pins remain active in all modes except standby and shutdown, where the only available configuration is input with internal pull-up, pull-down resistor, or floating input. When exiting shutdown mode, the I.O. configuration is lost. When the MCU is under reset, I.O. pins are forced into an analog input mode. VBAT domain GPIOs, PC13, PC14, and PC15 are supplied through the power switch. Since the switch only sinks a limited amount of current of 3 milliamps, the use of GPIOs PC13 to PC15 in output mode is limited. The speed should not exceed 2 MHz with a maximum load of 30 picofarad. These GPIOs must not be used as current sources, for example, to drive an LED.


So, today we have released a brand new patch for Loads of the Fallen, version 1.1.282, today's date is the 2nd of November, today we go through the entire patch notes, it's pretty long, I won't lie, but let's go. How's it going guys, my name's DPJ and if you do enjoy the video, leave a like, it really helps out and if you like what you see and want to see more, be sure to subscribe. Okay, so today's date is live on all platforms. All platforms, greetings, lampbearers! First off, thanks to all of you who took part in our season of the Bleak event, it was incredible to witness you come together as a community to solve the riddle, claim your prize and then help fellow players do the same. Due to popular demand, we've decided to make the Halloween quest permanently available to ensure players or future players can also experience the event. However, please bid a fun farewell to the Halloween decorations as they return to the attic. Now onto today's update, featuring over 100 fixes, tweaks and enhancements, this includes improving the visual quality of HDR, adding extra save games, safeguards and addressing a number of rare crushes. We've also improved cooperative play, made PvP more diverse, buffed some bosses, refined AI behaviour and balanced a few spells and items. Please find further details below and once again a massive thank you to everybody for the continuous support. Okay, so we're going to go on to what's changed here, on to save game. An additional failsafe has been added to help reduce the threat issue some players have experienced with corrupted saves. If you ever experience this issue yourself and of course we hope you don't, please immediately send us your corrupted save to support at cigames.com so we can identify the potential origin of the issue. Your saves have truly helped reduce this issue already. Okay so onto stability. A very rare crush reported in Sentry where faction wars, AIs casting certain abilities would crash in certain GPUs under specific circumstances. A rare crush that could happen when Nanite was sending certain data to GPUs. A rare crush that could happen when AIs and players were targeting each other with specific abilities. Not reported in Sentry yet. A rare crush that could happen when activating a revenge and a selected AI was a specific one already dead. Not reported in Sentry yet. A very rare crush that could happen when the player is aiming in range mode under very specific circumstances. Again not reported in Sentry yet. Okay so we're going to move on to performance people. Fixed a FPS degradation issue that occurred when opening and closing the in-game menu more than 50 times in one session followed by a stamina consuming action just afterward. Conducted collision optimisation throughout lower carref to achieve an overall improvement in frame rate. Implemented a shadow optimisation pass in spurned progeny's area. Optimised several smoke VHX used globally. Enhanced target system performance when players or enemies target abilities toward each other. Conducted a cast shadow optimisation pass and a beautification up in and a beautification up a carref resulting in some additional frames while navigating the area without sacrificing visual quality. Optimised sky rest bridge by rearranging assets that cast shadows maintaining the same quality while gaining additional frame rate. Okay so on to new game plus. Now clients won't be able to restart current game and start new game plus in the whole world as intended. Co-op. In certain edge cases the client could enter a ignore move import state in the UI if interacting with the vestige at the same time as the host. It was reported that sometimes when creating a co-op session it could happen that you cannot create a second match after a disconnect on one of the two parties. We identified the potential issue and added a failsafe. Fixed an issue where the client would sometimes stop receiving sounds from the host with entrance back to air mode from the client's dead body. Under certain circumstances the client's gesture UI becomes partially unresponsive and remains on the screen after transitioning when the host rests at a vestige, walks to another vestige or dies. For a clearer user experience we've updated the session password introduction process to display the eight character limit and prohibit spaces. Please note that passwords for PVP sessions expire after a few minutes if you do not enter a PVP invasion area. This change is aimed at preventing the abuse of passwords for blocking PVP while still allowing friendly sparring. Fixed black material in umbral that could happen in co-op for clients when the host transitioned from axiom to umbral. Fixed an issue in which the co-op helper could enter the host world with reduced mana, ammo or HP if the level disparity between the two players was too high. Okay so unto PVP and boss weapons. We've observed that some players have heavily relied on specific boss weapons and spars for PVP which has led to a less diverse gameplay experience. To address this we've made quite a few adjustments to these items. Okay so this should be interesting. One, boss weapons will now have ten levels instead of five. Excuse me? And we've modified their upgrade curves while they remain potent they are no longer overpowered in PVP. Two, the mana cast for pyrus blest reflections and infernal hands invocation spars have been significantly increased. Three, exploding bolts and sharing bolts now require more ammunition to use. Four, the usage cost of the corrupted banner javelin has been increased and its damage output has been nerfed. To facilitate this transition we've temporarily reduced the cost of the rillium chunks at the shrine making it easier for players to get their boss weapons from a 5 to a 10 but also to make it easier to try out different weapons and create more varied builds. Our goal is to foster a more varied and enjoyable gameplay experience for all while avoiding overpowered weapons we appreciate your understanding and ongoing support. Wow crazy changes. Okay so on to other tweaks. Additionally we've made these additional adjustments in PVP or for PVP. The host is now unable to return to the main menu while the crimson ritual is in progress. We've made adjustments to the invasion volume boxes increasing the size slightly to help reduce disconnections. This is an ongoing process so you can expect to see further improvements in this patch with additional enhancements planned for next week. We have enhanced the visual feedback for player eliminations in PVP provide a more rewarding experience. Fixed an issue in which the invader could enter the host world with reduced mana ammo or HP if the level disparity between the two players was too high. Okay so on to revenge. We have enhanced the visual feedback when avenging another fallen lamp bearer. Okay so now we move on to bosses. Taught a new trick to the sanctified huntress allowing her to use her dash teleport when cornered against a wall by the player or an NPC helper. Grief pound has been adjusted to be more aggressive in her boss fight as well as her minions. When killing the light reaper at a specific frame of one of his specific attacks it could interrupt his death animation leaving him unanimated for a few frames. We've increased the challenge for a boss at the bottom of a very dark place. The aberration born from love now has higher pacing and a bit more punch. We've intensified the sundered ones aggression and behaviour making him angrier and more formidable despite his sadness. We've noticed that some players have been struggling with Kouranga Guardian for land and his hounds particularly when it comes to his frostbite projectile attack. To help players anticipate this attack more effectively we've enhanced his visual feedback. A Biden defenders now use their abilities more efficiently and frequently making the fight significantly more challenging. Okay so now we move on to AI. The Scarlet Shadow has received a few improvements to make it more dangerous and harder to cheese. Okay the Scarlet Shadow could sometimes receive full damage not anymore. Well the Scarlet Shadow has learned a few new tricks to react to some trolling players. Now you can't hide from him by taking an elevator or get on top of some assets to shoot him without being touched. He's more resourceful. You've been warned. The Scarlet Shadow has now a few more navlings to be able to jump up and down some platforms. Running away from it now is more challenging. Okay fair enough I like a challenge. The AIs have received a pass of additional polish. Additional refinement of enemy spawns in upper caravans. Some in the skin, depth, cistern, fire, mants, path of the ocean, Abbey and Vramis Castle. An additional navling has been added on Skyrest Bridge to help a specific AI navigate the intricate geometry when fighting. An unruly sparrow at Fitzroy's Gorge Cave has had its spawn position adjusted to trigger its jump better. The grand stump animation for deep sparrows has been tweaked to reduce the body's rotation on the ground. Mendacious Visage now has an additional EQS check to find a better path toward hitting the player with its run. It's still avoidable with a dash slash roll. Navimash has been tweaked in Vramis Castle Dungeon to help AIs navigate faster through one of its gates. Now when a deep sparrow attacks a player with its flying attack, it will knock down a player in Umbrell but only do a heavy hit in Axiom. Transitioning to Umbrell is already a significant penalty and sometimes players could fall through a ledge, instantly dying without even seeing the attacking sparrow. Some Umbrell sparrows in the levels had a low lock undisabled when starting their idle breaker animations. It has been reactivated. Tweet the behaviour of Kadrupeds when surrounding the player to look more menacing and cooler. Adjusted AI spawns to leave more space for the flowerbed so they do not attack you if you remain just idle there. Fix a Navimash issue when transitioning from Axiom to Umbrell several times that could block a specific Umbrell zombie in a specific spot in a forsaken fend town. Adjusted existing leashing volumes and added a few more in Upper Cowriff for AIs to pursue the player as long as intended. Additional polish and adjustments for the leashing volumes of AIs in a forsaken fend. Tweaked leashing volumes for all enemy groups and a path of Devotion. Adjusted and added additional leashing volumes to AIs in Upper Cowriff. Tweaked leashing volumes for some enemies in Pilgrim's Perch. Adjusted leashing for some enemies at the entrance of Sunless Skane. Adjusted and added leashing volumes in Red Skull Village. Adjusted leashing for enemies at Fitzroy's Gorge. Okay so now on to balancing. Briarstone's healing speed has been slightly increased to improve their effectiveness in battle. It now takes 12 seconds instead of 20 seconds for the full Briarstone effect to apply. The curse of Adia has seen its duration increase from 10 seconds to 30 seconds and it's damage per second from a 2 to 5. Barrage of Echoes' cost has been increased by around 25% and damage decreased by 20%. Defensive aura has been nerfed by increasing its maintenance cost by 20%. Fixed Holy Slash being easily destroyed upon physical collisions. Fixed Rain of Forns not causing the smite stairs effect sometimes. Also increased damage by almost 50%. It's a great tool to fight abundant regular mumps especially in co-op or when helping other people. Fixed Tick Damage in Runer Ability only following spells. Sliding Sword, Sacred Ground, Dark Mass, Poison Mist, Ombril Mist, Holy Beam and Ombril Nail. Healing aura has been nerfed with a decrease in its base healing per second from 8 to 6.5 which is approximately 20% nerf. Increased Visceral Damage and Multiplayer on Ombril Assassin Swords by 15% to make them a more attractive choice for parry players. Lower the bonus damage from Pendant of Burden from a 0.1 to a 0.07. Stacking status effects are highly efficient and fairly powerful on their own. As such we've selected nerf this Pendant to balance it with other combat options. Monestones, prices have been reduced in vendors. Small from 300 to 200, medium from 600 to 400, large from 900 to 600. Nerfed Enhanced Robles by 30%. Pretty much all of them were over-performing especially enhanced Hammer. Radiant Orb decreased healing and started the acceleration earlier to make it easier to aim for mid-distance. Southern Productor's Ring Poison has been increased from 10 to 25 to boost its effect and make it more attractive to use. Swapped Dunmire's Cane to have in a 3x Meta Ruin Sluts instead of 3x Square Ruin Sluts to treat it like other staves and give it a potential to be more powerful. The Ombril Eye of the Pale butch of Secondary Effect has been changed from Recover Soul Flay while in Ombril to a plus 25% damage to Enemy Soul. So it can be combined with Ombril Eye of Olorun for devastating effects. Pre-Faction Focused Pendants, Faceless Carving, Imperium Pendant and Oroga's Delight are keeping their faction Empowerments but have seen their protection effects buffed against their respective rival factions. We believe this adapts better to how players are using the strengths and weaknesses of each Magic School. Remove Poison damage from every effect spell such as Graveyard Fog, Putrification and Consecrate to prevent weird looped flinch animations on enemy Rezeal Poison. Swapped a Duplicated Spell, Putrifaction in Revelation Depth with a 3x Poison Salts as this spell can also be retrieved in the Fen. Note that when picking an already earned item you get a reward where we are just granting now a better one. Okay so unto level design, we've polished an Ombril puzzle at the Abbey of the Hollowed Sisters to prevent players from interacting with the Soul Flay from a wrong spot. Added Ombril Flower Signalling and an Ombril Decoration Layer for a new Axiom Wall at Skyrest. A lot of the killing area has been adjusted in Brammer's Castle as we saw some players getting killed without noticing that they were stepping on the lava and that feat will burn for a longer time before getting killed in that corner. Okay so unto collisions, added an additional fail save to an Ombril Wall in an encounter happening at the Abandoned Outpost at Fitzroy Gorge. Being pushed back could block their player inside the wall. Adjusted their Cleric Cape to work in multiplayer. Adjusted Spent 2 Collisions in the Abbey of the Hollowed Sisters to smoothen player navigation. Fixed a collision bug at the ceiling of the Ale House at Lower Carruth that could lead to an unintended B navigation. Fixed a collision near the vestige of the Nunwich in Carruth. Fixed a hole at Brammer's Castle that could lead to a fall if jumping over the Barbican. Fixed a wall in Brammer's Castle that led audio pass through. The walls have ears, don't run, well not anymore. Cool. If the player rolled against two specific beams in Perlman's Perch could sometimes get trapped in a collision with Byron staring at the scene. Removed a collision from a small rock that could prevent players from falling and a sunless skin but no exit was available. We've buffed a part in the Abbey of the Hollowed Sisters so the ray of the abyss now does not go through it so players can hide behind the almighty pot. Collision adjustments in the whole Lower Carruth for smoother navigation of players in AI. A bridge in Lower City could block projectiles on the edges or through visually. It was weird since the only strings on the sides cost them collision added. Fixed some collisions in the Fitzroy Gorge Cave to avoid the player getting stuck under certain circumstances. Adjusted an onboard mesh in Perlman's Perch that had collisions for projectiles in Axiom. Added blocking volumes in Forsaken Fent to prevent players from performing an out of bounds and skipping minibus, fight or getting stuck. Added blocking volumes to prevent the player from getting stuck when attempting to jump up some rocks in Forsaken Fent. Added blocking volumes to prevent the player from climbing a wall in Forsaken Fent. Collision added to prevent escaping the blessed Carrion Knightbus, fog walls. Tweak collisions in two spots at Perlman's Perch to make player movement and camera smoother. Fixed a nav mesh inside Bromis Castle that could prevent a rune from pursuing the player on the whole first floor. Fixed a collision in the Sun and the Ski that could prevent players from falling into the void as intended forcing them to dash to the pit. Fixed a collision to prevent the player from getting stuck with a specific set of crystals at Bromis Castle. After doing a certain action and getting hit by the conflagrant Sia. Adjusted some collisions in the big marketplace plaza at Upper Carroth to better support the big enemy AI there. Cool. Okay so now guys we are onto visuals. Improved the decoration for the last umbral bed flower added underway through the filth. Tankro's chest armour has been tweaked to avoid some visual glitches in extreme player poses. Lowered flail hipstuff slightly as we thought it was a bit too much for the nature of its weapon. Replace two old paintings at the pendant tower and change them for new colour ones. Tweaked a burnt grand tile texture to look better. An umbral giant has been moved for purely cosmetic reasons. Better framing. Done some light improvements in two corners of the scope church. Fixed in two spots. Found by Digital Foundry where GI is barely noticeable. Both process exposure fix for a transition in lower Carroth when exiting a building right before the alehouse. Okay so now guys we're going to move on to cinematics. After last week's optimization on it we've now polished the transition from awakened lamp error into cinematic to in-game. Cleansing the beacon at the tower of pendants now always triggers a proper ombral lamp VFX onto VFX. Completely remove collisions for some cockroaches and back VFX that could block some spell effects. Additional optimization passes on several VFX. Okay so now onto UI. Gamepad could sometimes get out of focus in the UI especially after several alt tabs with added additional failsafe. Sometimes an epic online system pop-up could appear in some loading screens with the activated or non-requested pop-ups from EOS. Lakan was sometimes targeting an AI capsule instead of its centre leading to a slightly displaced Lakan HUD or HOD element. Fixed infinite items stuck in vendors that could not be purchased infinitely. Fixed an issue where the language setting could be set after a game client update. Okay so now guys we move on to the last and final thing audio. We have new update Poe sounds regular and stun based on player feedback. We've also improved stab sounds. And there we have it guys quite a big patch I'm not going to lie how long I've been recording 22 minutes people. But yes this is update version 1.1.282. This is available on all platforms as of right now. This is November 2nd update for Lords of the Fallen. Quite a few changes I'm not going to lie. I'm interested to see how the Red Reaper will perform now when I'm trying to cheese him to get that Viagra but we will see. Guys if you enjoyed the video leaving a like really helps out if you like what you're seeing want to see more be sure to subscribe and hopefully guys I will see you on that next one


Watkins for Villanelle. Approaching the left edge of the penalty area. Stephens in front of him. Stephens gets the block in. It runs loose though. Leon Bailey turning. He's got too much space. Kelly gets the block in. And then tapped in in a six-star box by Douglas Louriz. Early goals conceded by Bournemouth have been a theme, and they've come back to haunt them here. So Lanky onto his right foot. Try to drive it for goal. Straight out, Martina there, she made a bit of a hash of the save. Didn't manage to fumble it behind at the near post, but that's given the Cherries fans a bit of a lift on the far side. They win their first quarter of the game. Fila have the squeeze on. Now Hamid Shru on this dear side. Looking to play in Solankey. What a ball that is. It's put Dominic Solankey through 101. Mings desperately trying to get back, and Solankey took too long. Left side of the penalty area, and in the end Mings slid in and put it behind for a corner. The longer Solankey dwelt on it, the mortar ground that Mings made up. Green number seven comes on the board, and Brooke seven on the back of the AFC Bournemouth shirt. A standing ovation, not only from the Bournemouth supporters, but a rousing reception from all of those around Villa Park as well, which makes the hair stand up on the back of your neck, because after 535 days, and a heroic battle against cancer, David Brooks is back. Here he is now on the pelts, and that's taken Ramsey. Save one net over it, inside left channel, left angle of a six-yard box. That's a lot better. Into the near post, it's an obvious Villa aerial targets. And Villa have a third.


Family Theater in just a moment, but first an invitation to listen in on Mutual's party line every Saturday night for programs the whole family will enjoy. Comedy of Errors gives you a zany half hour of hilarity as contestants try to spot Jack Bailey's deliberate mix-ups. The favorite parlor quiz, 20 Questions, brings the animal, vegetable, and mineral game, New Sparkle, as the experts and guest Kai Gibi try to identify Bill Slater's subject in only 20 Questions. And Chicago Theater of the Air sends a full hour of the world's favorite music singing your way. For Family Party Night Listening, tune to Mutual every Saturday night for Comedy of Errors, 20 Questions, and Chicago Theater of the Air. Family Theater presents Claudette Colbert, Robert Ryan, and Jane Wyatt. In cooperation with Family Theater presents Robert Ryan and Jane Wyatt in The Lady with a Lamp. To introduce the drama, your hostess, Claudette Colbert. Thank you, Tony LaFranco. Family Theater's only purpose is to bring to everyone's attention a practice that must become an important part of our lives if we are to win peace for ourselves, peace for our families, and peace for the world. Family Theater urges you to pray, pray together as a family. It is to see her. She speaks to one and nods and smiles to many more. But she cannot do it to all, you know. We lay there by hundreds. But we can kiss her shadow as it falls and lay our heads on the pillow again. Content as she passes the lady with a lamp. So long as memory endures, Florence Nightingale will be best remembered by these touching words from a soldier's letter. That she should become a legend is understandable. That a driving spirit possessed her to work until her dreams were realized is perceivable. Now, driving spirits, whatever else they may be, are full of interest. And so it happens that in the real Miss Nightingale, there was even more that was interesting than in the legendary one. Therefore tonight, Family Theater takes great pleasure in bringing you The Lady with the Lamp with Jane Wyatt as Florence Nightingale and Robert Ryan as your narrator. She was born in 1820 in Florence, Italy, while her parents, like so many well-to-do English people of that time, were touring the continent. She was not a beautiful child, but even in the beginning, there was a look of dreaminess about her. Like the daughter of any wealthy Victorian family, Florence received an education to prepare her to take her place in society. Yet whenever she was supposed to be practicing the piano or studying her lessons or taking a dancing lesson, she never could be found. Instead, she would be in the stables with her dog or making a splint for his injured paw or visiting the impoverished and ill, bringing them food and medicine. Florence, where have you been this nearly a dinner time? I've been to one of the poor cottages, Father. A little girl is very sick. But I thought I gave strict orders that you were not to go among the sick. Do you wish to catch something from one of them? Father, as I came from the cottage, a voice whispered a wonderful idea in my ear. You know the house, the country house at Emily. Couldn't we turn it into a hospital? What? It would be heaven itself. And when I'm older, I could be head nurse. Florence, get rid of these queer imaginations immediately. The house at Emily will not become a hospital and you will not become a nurse. But Father, that's what I want to be. My dear, remember, it is your duty to your family, to your state of life, to make a good marriage. In this you will find happiness. I don't think so, Father. Somehow I feel God has called me for something more important. I'm not sure what it is, but this is something I feel here, inside of me. You are much too serious. But come, the dinner bell is ringing and, Flo, forget all this. Some day your Prince Charming will carry you off and then you'll look back and laugh as only one can at dreams. And Florence Nightingale did not forget them. As the years passed, her craving to be doing something useful to help those who needed help and comfort grew and grew until she could think of nothing else. By the time she was 25, she was unhappy and she knew it. Then, as her wretchedness deepened into a morbid melancholy, her family knew it. What Florence needs is a husband.  I am not interested in marriage.  I wish to work in a hospital. Oh, Flo. Then I intend to found a school and train nurses as nurses should be trained. Florence, do you realize what you're saying? That you, a lady of your background, want to make your own living in this world? I do, Father.  A nurse indeed. Perhaps a vacation will bring you to your senses. I think you're old enough now to tour the continent by yourself. But I have no interest in travel. And when you return to England, you had better forget this nursing idea of yours. Or the door to this home will no longer be open to you. Florence visited the art galleries of Paris and the cathedrals of Rome, but soon they bored her to tears. Would she dare while she was on her own visit the hospitals, the schools, the workhouses? So while she wrote letters to her family about exciting travels over the continent, she was in reality devouring reports of medical authorities and studying health conditions everywhere. It was while she was touring Italy that she met Sydney Herbert, minister to England's War Office.  Here in Europe, the only trained nurses are the Sisters of Mercy, except for those at the nursing institution at Kaiserworth, Germany. Now, my ambition is to establish just such an institution. Yes, England needs such a school. What then is holding you back? Duty to my family. No, Mr. Herbert. Now, nothing is holding me back. Nothing. The thing with Sydney Herbert in the experience Florence gained while training at Kaiserworth, and then in an English hospital, was to form the foundation of all her future. But one other trial awaited her. The allurements of the world she had brushed aside, suddenly appeared in the shape of a persistent young man. What was that feeling that swept over her? Could it be love? Oh, I'm dying. I'm dying. Come now, from a broken leg? From want of sympathy. This is a terrible place. The nurses ignore me. One in particular. Alas, I'm a prisoner of fate. Of a polo game, you mean. Furthermore, I was here just a minute ago.  I have 40 other patients. 40 minor details. Is anything paining you? Only my heart. Flo, Flo, where are you going? Back to my duty. Oh, no, no. Oh, my broken leg.  Maybe the pain will go away.  I think you'll care for me a little. But you've made me laugh. It's good to laugh now and then. Why do you take life so seriously, Flo? Do I? Very much. While I lay here in bed, I've been watching. No, no, I've been studying you. Why is it you seem to carry the world on your shoulders? You wouldn't understand. But I want to understand. I want to know all about the things that are important to you. Please tell me. All hidden ambitions. And if I should get to know you better, I will tell you about them. I hope that'll be soon, Flo. Very soon. Oh, there's nothing like a picnic to aid a convalescent. Listen to the birds. I think their song is for us. And the brook. It quietly passes by with so much politeness. Can't you hear it say, forgive me for intruding upon your holiday? Having a good time? A wonderful time. I think any change from the hostel would be wonderful, Flo. Even a bore like myself. You're not a bore. Although sometimes I almost wish that you were. Whatever do you mean by that remark, Flo? Nothing really. You're the strangest woman. I don't think I shall ever get to know you. That chance stopped me from loving you. Embly Park is beautiful, isn't it? Why do you change the subject? I'm not sure. I used to come here when I was a child, during the summer months. And you've not been back here since? No. Not since my family refuses to see me. Your family refuses to see you? Why, Flo? Why? They're against my becoming a nurse. You see, it disgraces them. I'm afraid they have my sympathy. After all, a lady in your station of life can't afford... Brian, you sound exactly like me. You sound exactly like my family. Let's not talk about it, Flo. There's something much more important I want to ask you. What? Will you marry me? Brian.  Brian, knowing you has been wonderful. Something I'll cherish forever. But... What are you trying to tell me, Flo? There's something here inside of me. Something that requires satisfaction. I know that marriage will never give me that satisfaction. I can find it only in nursing, and the two can never meet. And all along I was fooling myself, thinking you love me. I do love you. Probably I shall never love anyone else. But not to become a nurse would be... It would be sheer suicide. Florence, do you realize what you're saying? I do. Perhaps someday I'll regret this decision, but nothing is certain to my venture. But how can it be desirable? Without nursing, I see nothing desirable but death. Years passed, and then in 1854, Florence Nightingale graduated to superintendent of nurses at King's College Hospital. Here she was training nurses on a large scale. This was what she had wanted from the very beginning. And now, her life seemed quite complete. Even her family had forgiven her. And then, England joined France and Turkey in the Crimea. Russian aggression in Europe must be stopped. England was at war. Sydney Urban, war office, London. Dear friend, I have been reading of the dreadful conditions of our military hospitals at Scootery, and wish to render my services, whereby I might take with me, a selected group of nurses. Good to see you. I came just as soon as I received your letter. Oh, you've made very good time here. Have a chair. Thank you. Mr. Herbert, I am most anxious to get down to business. Did you get the appointment? Yes, I have it for you. Oh, good. But, in a sense, that is... What do you mean? The government will give you official permission to work in the army hospital, but they will not give you financial support. I have expected it. But we will get the money somehow. Now, there is much to be done. Committees must be formed to carry out my plans. But first of all, the right nurses must be selected. And that will be difficult. There will not be many who will be willing to accept the horrors or the hardships ahead. Florence, do you feel you yourself are capable of such an undertaking? After all, you're very young, only 34. Mr. Herbert, for years I have been preparing for just such an emergency. If the war had fallen earlier, I would have lacked experience. Later, and I might have been too old. No, Mr. Herbert, I'm ready. What's more, it's my duty. Good. Now, let's say we get to work. In less than one week, Florence Nightingale was ready to sail for Constantinople. 32 nurses had been selected and trained for military duties, a large sum of money raised, and medical and hospital supplies purchased. Only a handful of people were at the docks to bid farewell to the small, courageous group of women who were giving so much for the cause of their country. Good luck, Florence. Oh, thank you, my friend. You have my greatest appreciation for everything you've done. If there's time, please keep me posted and take care of yourself. Oh, you shall receive a daily confidential report of all activities escalator aid. As for myself? Oh, I'll be too busy for anything to happen to me. God keep you, my dear. Goodbye. Sentiers of Swim, in here! Sorry, Lieutenant, you can't bring him in here. There's no more room. Where can we take them, sir? Everywhere I'm told there is no room. I've got 500 badly wounded men just off the transport. I don't know. Better take them to Barracks Hospital. Right. Have a look. Are your soldiers still walking? Help with the stretchers. Look at those men. Hundreds of them lying on the muddy ground with their wounds undressed. They must have been lying here a long time. Their uniforms are stiff with blood. And they've felt they have starved. Look at that poor fellow. He must be dying. Hey, Lily, ladies, you're blocking the way. Lieutenant, have none of these men had medical attention? That's right, ma'am. Oh, Miss Nightingale, ma'am. Shouldn't we begin at once? We will, shortly. First, we must find our barracks. Unpack our supplies and store them. We can do nothing efficiently until we know our whereabouts. Miss Nightingale? Yes? Welcome to Scootery. I'm Colonel Douglas. Oh, we are glad to see you, Colonel. I'm sorry. Just at the moment of your arrival, there must be so much confusion. You see, these men are being brought in from the Battle of Balaclava. Oh, it's ghastly. Why have they had no medical attention? We're short of doctors. Can't spare a single one for the transport. Well, if you'll tell us where we'll find our barracks, we can unpack and begin immediately to assist you. Your barracks were given over to the wounded. I'm afraid temporarily you and your nurses will have to occupy the kitchen. Nurses, our first duty is to the wounded, to release them from as much pain and suffering as possible. The vermin and filth in this hospital is outrageous. Now, there, nurses, we'll roll up our sleeves, pin up our skirts, and scrub the floors and the walls. This place must be cleaned. Dear Mr. Herbert, the horror of human suffering and scotery is greater than anyone can imagine. Send immediately 3,000 blankets, 2,000... I will assist you, Doctor. Oh, no. An operation room is no place for a woman. It is my wish to assist you, Doctor. All right. I suppose next few women will be wanting to teach the soldiers how to fight. Miss Nightingale, prepare this patient for an immediate operation. Wouldn't it be better to give him chloroform? We have none. Furthermore, it's against regulations. I have chloroform among my medical supplies, Doctor. And you will have a greater chance to save this poor fellow's life. Whatever you say, Miss Nightingale. Whatever you say. Mr. Sydney Herbert, war office, England. Dear friend, I now clothe the British army with supplies you send me. That is, after I eventually receive them. There is much red tape here which I must fight constantly, and it worries me a great deal. Every day a new shipload of wounded arrives. Four of my men, four of my nurses, and seven doctors have died from cholera. I must implore, know, demand that you send me more nurses, more doctors. Come in. You wanted to see me, Miss Nightingale? I'm very busy, Colonel Douglas. Therefore, I will come immediately to the point. Well? Medical supplies, food and clothing, which I ordered sent from England, are waiting to be unpacked in the customs house. The guard there tells me the purveyor cannot unpack these supplies until an official order is given by you. This is correct. Kindly give this order then. My hands are tired until I meet with the board of directors. Officially, the order comes from them. How long will this take? Well, the board will meet again in three weeks. Three weeks? Yes. Do you think I have time for such red tape when the sick and wounded lie half naked, shivering for want of clothing? When men are dying for lack of medical supplies? I'll not wait a day or an hour for anyone. I have not a day or an hour to waste. I'm sorry, but these are army regulations. Colonel Douglas, I will not tolerate this inefficiency. My dear Miss Nightingale, you may not wish to tolerate our inefficiency, as you put it, but I'm afraid there's nothing you can do about it. It goes there. Miss Nightingale, I've come to unpack the medical supplies. You will kindly open the door. Miss Nightingale, I told you I can't tell the provider, says... You will open the door for me, God. Look, ma'am, would you have me court-martialed? I will take entire responsibility if anything comes up. But you have no authority. In that case, I am taking the authority. These supplies will be unpacked today. Now, stand aside. Yes, ma'am. Miss Nightingale, if I may, I would like a word with you. I've been expecting you, Colonel Douglas. Be seated, won't you? Thank you. I... Oh, Colonel, may I offer you my sympathy and the death of your son? If only it could have been brought here to our hospital. Instead of Balaclava, with the help of your medical supplies, our doctors might have saved him. Yes. And if only I had the time to inspect all other hospitals in the Crimea. Miss Nightingale, I didn't realize before how important is your work in what you've done for Scootery. Rest assured in the future, you'll receive all the cooperation I can give you. I too work now to save men's lives that my son may not have died in vain. Night was upon the barracks' hospital, and everyone else had retired. Florence Nightingale, with lamp in hand, would walk through the corridors and wards among the rows and rows of overcrowded beds. Four miles of them. A long walk for the lady-in-chief to make, as she invariably did, night after night. Silently a door opens and a tiny ray of light falls across a soldier's bed. The figure enters and closes the door softly. The figure of a woman, tall and slender, dressed in black with white cap and apron. In her hand, she carries a small lamp.  Slowly the lady with the lamp draws near, stopping beside each kind. Listening to the breathing of one, giving a word of encouragement to another.  He turns and kisses it, and falls happily asleep. To him, she is an angel of mercy. Continue to drive herself on and on. Twenty hours at one time, she would stand on her feet, easing the sufferers, nursing them. Would there be no end to her endurance? Nurse, patient 702 in Ward B must have a change in diet immediately. Three times a day, he is to receive... Miss Nightingale. Ma'am, what is it? What's happened? Oh, here, ma'am, grab my arm. See if you can get me to bed. I think I'm ill with the fever. For twelve days, Florence Nightingale hovered between life and death. The news spread everywhere. She was ill, was dying. When her own hospital learned of it, the sick man turned their faces to the wall and wept. And longed to give their own lives for hers, if only they might. When the truth came to her that she was never going to be strong or well again, from her bedside as now all of her work must be done, came her last demand in connection with the war, the results of which may be seen even today by any who visit that faraway land of the Crimea. On the mountain heights above Scooteray, on a peak not far from the hospital, a large white cross is to be raised, shining like snow against the blue of the sky. This be my tribute to the brave men and devoted nurses who died in this war. May they sleep in peace, knowing that while I live, I fight their cause. What a comfort it is to see her. She speaks to one and nods and smiles to many more. But she cannot do it to all, you know. We lay there by hundreds, but we can kiss her shadow as it falls and lay our heads on the pillow again, content as she passes, the lady with the lamp. This presentation of the life of a great woman. Florence Nightingale's driving courage was a powerful force in building the great profession of nursing. But now I would like to speak of another powerful force, the most powerful force in the world, prayer. Prayer is the reason this program is broadcast throughout the world. For the purpose of family theater is to help restore to homes everywhere the joy, the peace and strength that comes from daily family prayer. It's yours for the taking, so make it a part of your life.  Whatever be your creed, use prayer to strengthen your family circle. Talk to the God who made us all and loves us all. Experience what we mean when we say the family that prays together stays together.  Family Theater has brought you Robert Ryan and Jane Wyatt in The Lady with the Lamp with Claudette Colbert as your hostess. Others in our cast were Charlie He, Irene Tedrow, Francis X Bushman, Herb Rollinson, Tudor Owen and Collins Bain. The script was written by Dale Newton Whitney with music composed and conducted by Harry Zimmerman and was directed for Family Theater by J.F. Mansfield. This is Tony LaFranco expressing the wish of Family Theater that the blessing of God may be upon you and your home and inviting you to be with us next week at this time when Family Theater will present Stephen McNally and Gale Storm in The Foster Story. Join us, won't you? Family Theater is broadcast throughout the world and originates in the Hollywood studios of the world's largest network in the virtual broadcasting system.


I feel very honored to be invited here. Thank you very much. I like two, I think I've seen one, maybe two other people with grey hair here. Last talk I gave a few weeks ago was to a meeting of ophthalmologists, and that was a bunch of much older people. Okay. And a homage here to the fifth elephant. This is the novel, the cover of the novel from which it was taken. And well, actually I'm using this as a connection for a little bit of boasting because Terry Pratchett wrote the book. I am a co-author of a co-author of Terry Pratchett. And I actually signed a publisher contract on my 70th birthday a few weeks ago to publish a science fiction novel with Ian Stewart. And I mention that not just as boasting, but okay, this is a data geeks meeting rather than a graphics geeks meeting. But if anybody has graphics enthusiasm, there is all kinds of stuff that would be fun to build for the website that we're putting together for that novel. Strange things happening on that planet and so forth. So do make contact if you're interested in drawing strange and beautiful things because I have some strange and beautiful things to draw and some to interact with. What I don't have is a budget. You have to just like it. Okay, that is pure digression. I was originally a mathematician and that was my PhD. Back before almost anybody here was born. And I've kind of wandered around the world and the sciences and I've turned into some sort of an engineer. But what I'm going to talk about here is the power of particular mathematical point of view which is that numbers are not just numbers. They belong together in shapes. So what are data? Mostly they're numbers. I know they're fields and things. We've been hearing about that. But then you keep counting them. Lots and lots of it is numbers. But are numbers only numbers? Well, no, they gather together in things. They come in patterns. And really big data is all about the arrangements those things make. Just knowing the numbers, you don't know anything. You've got to know how they fit together. Patterns are shapes. So studying shapes, data shapes, any kind of shapes, space-time shapes, that's geometry. But not the kind that I was doing when I was 13 or 14 years old.  But it was all flat in the sand, just like that. And here's Euclid stuff with right-angle triangles and fun things. This I remember as a remarkable theorem that I have never, ever, ever, ever seen a use for. It's weird. It's very much something about the plane. It's strange. And I've never encountered it referred to in anything useful since I left school. It's Dysarg's theorem, which is occasionally useful. But everything's so much in the plane. Data shapes don't live mostly in the plane. Geometry doesn't mean that you replace... Now, this, by the way, is highly superior pointer technology. Much better than those twinkling little red things that you lose track of where it's pointing to. And 10% of your audience can't see red. Now, use something serious. So children think in 3D. They think brilliantly in 3D. They naturally work in 3D. They are connecting how their vision is working with their hands. They can reach out and grab your nose.  It's doing a lot of practice at building a 3D model of the world. And then, and these days, that continues in primary school. 100 years ago. But now primary school is good, but secondary schools suck rocks. It's still, if you get any geometry, it's flat, flat stuff. It can get more and more complicated. Yeah. But I just grabbed that off the web as one particular complicated 2D diagram. But fix your mind in 2D. You get to the point where you can't think, well, are the X and Y axes this way or this way? I found my UCLA students, if I switched drawing on the blackboard from this way to that way because something could be seen better that way, what's going on? They couldn't turn it in their heads. Well, data doesn't live in the plane. It's not flat. If we have three variables, we have three dimensions. That might be how far this way, how far this way, and how far up. And if you're doing graphics, it's three very directly spatial dimensions. But if you've just got numbers about people, I look at everybody here. I know their height. Well, I don't know their height, but you guys do because you're big data guys. Know the height, know the weight, know the age. Three numbers, that's a three-dimensional set. And the pattern that you make, that's three-dimensional geometry. But, of course, you typically have a lot more. So you've got n dimensions, and n can be quite big. So you need to think about n dimensions. And there's two ways to do it. One is to turn it all into algebra, which is what people spend a lot of the time doing. And in this talk, I'm only going to talk linear algebra, which doesn't mean it's the only kind there is, but I've only got a few minutes. So before you can practice thinking in 3D and build up insights that help you very seriously in n-dimensional thinking, I took up carving things when I was a grad student because I realized that my mind had been flattened by my high school and my undergraduate. And, ah! No, I needed to loosen up my mind and think in 3D, so I started using my hands. This is the visual part of the brain, this is the motor part of the brain, and the motor cortex just has to be 3D because you've got to pick things up, you've got to twist them, connect it all up. So seriously, for 3D thinking, take up sculpture. So practice thinking in 3D, and the more 3D you can think, the readyer you are to think in other dimensions, general dimensions, but 2D is not enough. So question for you guys. Most people here have done things, are doing things with matrices sometimes, right? What does a matrix even mean? What's it represented? You have told me the data structure. Yeah, yeah, it's an array, this is the data structure, it's an array this way and this way. But, at the level of algebra and geometry, it's something a bit more. It's something that operates on vectors, it transforms vectors, and in particular, there was a rule that they taught me back, I think, first or second year undergraduate of which way you multiply a matrix and a vector, and I swear to you, it took me a year to remember, when I'm multiplying two matrices, do I go along this way or do I go along that way?  But, trying to avoid spending too much time on this, you do know the rule most of you, and so if you have this 3 by 3 matrix and apply it to this vector, you get this, which is this column. And if you apply to this vector, you get this column. And if you apply to this vector, you get the last column. Now, 1 0 0 means, let's suppose this is the x direction, x this way. It says anything that is purely in the x direction goes to ACF, wherever that is, which is a three-dimensional vector somewhere. Anything that is in the y direction, like 0 1 0, goes to something else. Specifically, it goes to BDG. And anything that starts vertical goes to CEH. So the matrix is actually a list of vectors. It's saying, where does the first one go? Where does the second one go? And where does the third one go? And believe me, if you're doing 3D computer graphics, understanding that point will make it much easier than anything I've ever seen in an open GL manual of what you ought to be doing. They don't explain matrices very well. It's just a list of where these three things go. And in the case of a rotation, that's particularly tidy, right angles, things at right angles go to things at right angles and so on. But not every matrix is doing something as simple as a rotation, unless you're as simple-minded as an IQ theorist, and they rotate things that they know justification doing. If you remember that, you can always clarify, see more definitely what the algebra is doing, and if you know what the algebra is doing, you can make it drive better code. What should the code be doing? So I'm just going to illustrate this point of view with a very top-down glimpse at some of the things that people do when they've got a lot of data. One of them is principal component analysis. Now, this is very sketchy, very, very 2D. I didn't have time to do wonderful 3D animations. I'm sorry. But I've got this variable. I've got this variable. Put them together. I've got data points which are pairs of variables. And roughly speaking, I can say just looking at this, that is this increases, that increases. But if I want to compress my data, then I rotate my axes. I put an axis along this way and another axis along this way. So it's going to be a matrix that says, this guy goes to there, and this guy goes to there. Finding that matrix, there's chunks of algebra not fitting into this time, but that is the idea of principal component analysis. And if you're applying it to a machine that does wobbles here and here and makes squeaks there and all sorts of things, you've got a lot of numbers and you've got to do the algebra a bit more complicatedly than that 2D picture represents, but that is really what's going on. You're finding the way to move your axes and now if you know where you are on this axis, you know most of what you want to know about a data point. Is it here or is it here? One number. How far along it is? And then you say, well you can expect some errors in that direction, whereas in the previous picture you had to know two directions, two numbers. So principal component analysis is a beautiful technique for information compression, reducing the amount of arbitrariness, handling all sorts of things excellently, as long as things are reasonably linear, which is a very, very big if. Small variations, they're more often linear. That's the whole point of the calculus. The calculus is linear approximation of small changes. But larger systems with more variation be wary they're generally not linear. There's an expression nonlinear mathematics, which is a bit like non-elephant biology. You shouldn't be defining everything else by what it isn't, when what it isn't is so special. Yeah, you look to me like an unusual elephant with some missing teeth and going around on two back legs for some reason. That's not really a good starting point for saying what you do. So there is other mathematics than linear, but linear is very powerful, particularly when variation is reasonably small. And that is the whole idea of principal component analysis.  There's technique, but you need the idea of how it's all working. Okay, so let's try another thing. How many of you have done linear programming? Okay, what is the geometry in linear programming? Because actually the first course I ever gave back when I was a graduate student, I was told teach these economists from this book. And one of the things they were supposed to learn was linear programming, and it was all matrices, and you pivot this and you squiggle that. Is that the kind of linear programming you had? Right, what the matrices do. Yeah, but what's really going on is what the geometry is doing. So first of all, what does this mean? Suppose this was just x, y, and z. If I put equal to zero, that's a plane. I'm positive on one side, negative on another. I say I've got to be positive. So how would I define a cube? I'd say I've got something that's positive on this side of the cube, something that's positive on that side of the cube. Something that's positive as I go down from the top. Something that's positive as I go up from the bottom with six inequalities, I've got a cube. Same idea in n dimensions, but three is plenty for thinking about this one. 2D figures don't give the magic at all of what you need to do, but the 3D problem does. You see, here is where one of those limiting planes is. Here's where another one meets. So they're doing all kinds of things like this. Inside this polyhedron, you're satisfying all of those constraints. Go outside, cross any one of those planes, you're not. And the algebra problem is that the planes meet in a whole lot of places. It looks like a sort of weird three-dimensional, a hedgehoggy thing. This plane and this plane, they don't meet on the surface, but they meet somewhere here. So you want to make sure that you are staying inside this region. So, about 1950, it becomes the simplex method. And that confused me because simplex is a word that mathematicians use differently. How do you find the highest point on that? Or it could be the most this way point or some other objective function. We can rotate it into this. I'm just looking for the highest point. Visually, let me do that. How do you do that? Well, first thing is find a genuine corner. And very, very often, so this is a genuine corner, it's allowed where some of the things meet. Very often, you pick something that you know is going to be a really terrible solution. You only know that it's allowed. Like, if you're deciding in your factory how many of these to make and how many of these to make and how many of these to make when this needs this much time on that machine and this much time on that machine, all sorts of time and resource allocation things. All of those give you constraints. Well, something that meets all the constraints is to produce absolutely nothing and go fishing. So 0, 0, 0 is usually a genuine allowed point. It's not exactly your best point, but it is an allowed point. So that's just how the simplex method usually gets started. And then you look at the edges that happen there and find which one goes vertically up fastest. Just look at the direction, not the length of it immediately. You say, this is shallow, this is tall. Go up this one. Now, then you calculate and say, where does this one first meet another one of these planes? So this one meets that plane. That doesn't mean that this is the fastest way to go because it might be that a shallower one doesn't meet another plane until higher. But it's a way of choosing that only uses the information that you have here. And you know which planes are involved just here, just three of them in this case, usually n in an n-dimensional problem.  And then you do that again. This is the steepest way up from there. And you do that again. And you do that again. And again. And there you are at the top. And worst case analysis says that's an absolutely horrible algorithm but in practice it's pretty good. There are fancier methods but with devious ways of getting faster, but this is not a linear programming class. So this is the example. This is what's going on in Simplex Method. And if you can recognize that in the algebra, then if you're coding Simplex Method, you can see where things are going. So all of that matrix stuff, matrix pivoting and so forth is just playing games with which of the planes you're currently concerning. All of the actual thinking, the hard thinking, the driving idea is geometrical. Okay. So probably more of you use support vector machines and I even saw a wonderful t-shirt this morning said I support vector machines. Okay. Now there are tricks for making the problems of recognizing clusters that don't have linear solutions into problems that do have linear solutions by throwing in a bunch of extra variables, radial basis functions, da, da, da. I won't cover that. I will just talk about the geometrical idea and thinly represent this because I didn't spend the time. I'm sorry, I had a very busy week. I wanted to draw a much more, at least three-dimensional picture, but you have the idea that you want to classify these are the good ones, these are the bad ones. Or the something or other. How do you tell the boys from the girls? Or how do you tell the, you're looking at data about potential immigrants.  So you've got a lot of data and you've got a lot of samples if you've managed to arrest a lot of those guys and you want to be able to predict for a new one, is it in this bunch or is it in this bunch? And I simply grabbed this picture from Wikipedia just to illustrate that the explanations don't do all that well in saying what's actually going on. In particular, they talk about support vectors by which they mean just individual points by saying really what support means. And support, if I've got this bunch of things, then I can take, how many of you know the convex hull of a bunch of data points? Wave your hands. It's not a test, but I'm interested. A lot more of you should know. It's the smallest convex set that you can fit around. So in this 2D case, this would be a polygon like this, like this, like this, like this. This line is a support line, meaning that everything is on one side of that line in this cluster. Nothing is on that. I can't wiggle the line without breaking that. If I move it this way, then I'm catching a bit too much stuff there. If I move it this way, I'm missing something. Now in 3D, that's a support plane, usually. I've got, here's a bunch of points. I don't have a nice flat surface. Imagine my hand is flat. It can bump against three points, or against three points, or against three points. Those are support planes. And if you take all the support planes, you've got a convex object, rather like the polyhedron that I was drawing for, the simplex method. And choosing among support planes when you've got a huge number of variables, this is just two variables, so it's not much of a deal, but if you've got lots and lots, then trying to find a good plane separating them, you've got numerical horrors in just how fast the problem grows. But you can do better with support planes. So you say, oh well, now if I take this one, that's this far away. If I take this one, this far away. If I take this one, I'm not even separating. So there's tricks for finding the best one. You find a good support plane here, a good support plane here, and then take something nice in the middle. And that is the geometry, the core idea of a support vector machine. Plus, as I say, you need to throw in some nonlinear functions, increase your number of variables, and then do the linear stuff just like I was waving my hands at just now. And I'm in the middle of doing this, applying it in the company where I work. We make machines that look deep into your eyes, and they don't tell you anything about your soul, but they say diabetic retinopathy. They say hypertension. But you've got to make the images well. The manufacturing is a tricky production line issue with lots of places where you could make mistakes. So you want to be checking are the images good at each stage, and you want to have a systematic way of doing that, partly because you want to be a good production engineer, and partly because the certifying authorities like UL and the rest of them, they want to see a process. So you want something very systematic. So produce a lot of good pictures and bad pictures, good and bad in different ways, extract some intelligently thought-of features. But isn't Black Box make the neural network think of things that you can't think of, because your neural networks are much smarter than any artificial neural network I've yet seen? Every one of you is smarter than any current artificial intelligence. And you were when you were this big.  So apply your intelligence, bring it in. But we extract a bunch of things about contrast and texture measures and entropy and so forth, extract a lot of numbers from a picture, and then we can say, oh yeah, this one belongs in the bad focus area, that one belongs in the uneven illumination area, and so on, and we can give feedback on quality of that image and manage our process much better. So classification is a very, very nice thing, and this is one of the cute ways to do it. And the way that it was invented and the way that it is guided, code doesn't tell you geometry, but the idea driving everything is geometry. The geometry drives the algebra. Yeah. That was the question I just answered. I got out of phase with my clicks and you kind of roll around and it's not too different in feeling from the simplex method. So geometry organizes what the algebra needs to solve, needs to do. The algebra on its own is a tool that geometry sets the tasks. Algebra, which often means linear algebra, but don't fall into the trap of thinking everything is linear just because that was what your classes were in, it organizes what the code needs to do. And planning your code needs algebra. I mean algebraic understanding. What are you trying to do? Computers don't... Well, they don't think actually. I mean, I know some of you guys are saying artificial intelligence and they're getting a little closer to thinking, but in particular, they think very, very poorly about shapes. And shapes... Well, sorry, I'm a geometer. Some of my best friends are algebraists but I wouldn't want my wife to marry one. To me, mathematics begins with a sense of shape. Back before we were humans, we were aware of round things and long things, long time before we were counting things. Deep in our brain is geometry and I don't mean that everything is set theory. I mean everything is shape and we have shape recognizers in here. It's driven by geometry and early mathematics was highly geometrical. I know that more about the Greeks than I know about the Vedic mathematics but there was plenty, plenty there. Then it turned into algebra and Vedic is very algorithmic whereas the Greeks like to prove that something is always true but the geometry comes first. Then the algebra manages what the geometry needs to do and bugs... Now, some bugs come because you have done something that at the coding level is dumb. Well, no, let me change pronoun. Bugs come because something I have done at the coding level is dumb. I'm very good at programming errors. And also there is a private belief of mine which I don't require you to accept. In fact, I don't require to accept any of this but I have a private belief.   Well, let's try this, try that... I don't see what... Eventually you say pasta! I can't do any more of this today. I'm done. I spent four hours fighting this what should be a tiny bug and you cannot get it to do right now.  Well, it's the stupidity field seeping into you, right? You need to get out of it sometimes and even if you don't believe in the stupidity field you should take a programming break now and then. So some bugs come from coding wrong as such but some bugs come from what you're implementing at the algebraic level has a mistake in the algebra. So to get it to work right you need to understand the algebra and some bugs come because you got the geometry right and turned the geometry wrong and turned that into algebra correctly but it's not the right answer because you got the geometry wrong. So there's no guarantee where your problem is there's all sorts of things of chasing it but you have to try to think at all these different levels plus of course all the stuff that this conference is mostly about which is how do you manage just humongous collections of data and so forth I'm not trying to claim that this is the core of all packing and data management things but I'm saying this is a part of all this that you need to be thinking about or at least somebody needs to be thinking about this is what teams are about I know user interaction needs thinking about how is the user feeling about this what's the user's workflow what's the user's mind flow and some people are good at that some people are bad at that that's cool you can be good at different things but when somebody who really believes that zeros and ones are easier to understand than people gets the job of designing a front end for a web application you're not going to get a good web application you need a good designer that doesn't mean necessarily somebody with a qualification in UI design some people are just naturally good at it but some people they should be doing the back end and they may be genius at doing the back end if the spec of what is to be supported has been worked out by somebody thinking at the human end there's a nice story of pretty much the original personal digital assistant the nouns are escaping me I seriously will forget my own name next anyway PDA and it'll come back to me just too late and what he did to design it was to make himself a piece of wood about the shape of the instrument that he wanted a bit like a modern smartphone but a bit heavier he walks around carrying this piece of wood and pretending that he had an electronic digital instrument and imagining his own interaction with it what did he want to do, how did he want to do it and after imaginatively getting himself into that for two weeks he sat down and wrote a spec and told the engineers he was CEO so he could tell them that make it like this and so they sat down and of course coming back to him all the time saying hey wouldn't it be cool to have this feature wouldn't it be neat if we could do this and he said no do it like I said because that massive features each individual feature might be wonderful but the mass will confuse the user here's a thing from medical software there's all kinds of stuff for looking at medical images and dealing with medical data and it usually comes with a manual now what happens when this first gets installed somewhere is one brave doctor plays with it understands the manual as best he can or she can figures out yes I can do this that I want to do if I do x y I can do this if I do y z and writes down a cheat sheet this is how you do this, this is how you do that this is how you do that and shares it and that replaces the manual for most users they just have do this, don't know why it works but somebody figured out and it does produce the effect even if it's the equivalent of standing on one leg while singing but getting a transparent easy user interface is a special skill so not everybody has to do everything because some people are better at one kind of stuff than others but between you you should be thinking at all levels so if you're a brilliant coder but you don't find yourself thinking geometrically try and get a team member who thinks more at the mathematical level if you're like me I do think geometrically and I can handle algebra as long as I give it a geometric meaning but I am one of the world's worst programmers so I work with people who code much better than I do make teams and learn just enough at least to identify if you're mainly a coder who are good at the mathematical end of thinking or if you're more of the theoretician, more of the abstract nature of the information thinker learn who's a good coder and respect them so either as an individual or as a constructed team think at all these different levels and plus all of the stuff that has been and is being mentioned in these three days honor to the fifth elephant Thank you. Do we have any questions? Tim, I think the name you were trying to recall was Jeff Hawkins I'm sorry? The name you were trying to recall the inventor of the PDA, Jeff Hawkins, right? You were trying to recall his name? Ah, sorry Yes, you say? The inventor of the PDA, Jeff Hawkins Yeah, and what was the PDA's The Palm Pilot? Palm Pilot, yes Yeah, this is one of the well, actually I got into mathematics because I had a lousy memory in the first place I mean that quite seriously at high school, I was always fascinated in science when I was this big I had fantasies about extracting colored paint from rainbows and other practical ideas and I had a chemistry set when I was a bit bigger and you could pour this colorless liquid into that colorless liquid and oh, it turned blue but now why did it turn blue? My chemistry set little book didn't tell me anything it just said you can do this, you can do this why, kind of mine? So the secondary school I went to went for the interview there and I said oh, chemilabs, I'm going to learn chemistry I'm going to learn this stuff benches and these graceful taps they have in their chemistry labs and then the entire first year at that school they weren't actually teaching me chemistry so I started in the next year so I kept on going past the chemilabs and then it started and they wanted me to remember the difference between ferrous iron and ferric iron which have different valences they wanted me to remember this and this and this and this which was as difficult as remembering the date of the battle of Pondicherry or if you forgot it, not a hope but at the same time they started to teach me some physics and I discovered that in physics I could remember a bit less and think through a bit more and then gradually realized that this was actually all about the mathematics and in the mathematics I could remember least and think most like that weird formula cosine of x plus y is equal to cos cos minus sine sine took me a ridiculous amount of time to learn that and I had to revise it because I knew it was going to be an exam where I couldn't have my book now I realized that all it really means it's the component parts the sine and cosine addition formulas they're the parts of rotate through x rotate through y gives you the same result as rotating through x plus y and if you understand what the matrices are doing what I was telling you where does the vector go all of this is obvious so I can rebuild it in my head so you're looking at somebody who had a memory leak 50 years ago and I don't think I've got early onset Alzheimer's but certainly I'm getting the typically aging effect of it is getting harder and harder I remember substantive nouns even in my own area of expertise so I just have to face the embarrassment of that and thank you very much yes palm pilot and Jeff Hawkins thank you I have a question the multi here the multidimensional the multidimensional model in the data warehouse in a data warehouse multidimensional cube is that what you're talking about the geometry in data so it's arbitrarily many dimensions a dimension just means something you can measure if you identify as a mathematician in social life then at parties well actually at parties in India people will ask you what you think about Vedic mathematics it's the default question to mathematicians but anywhere else in the world they will say what is the fourth dimension and well I have a short answer if I'm trying to get to the food and a longer answer if I think this person looks interesting to talk to the first answer short one is I will point in the direction of the first dimension if you point in the direction of the first they don't come numbered it's just how many different ways can something vary and the mechanical engineering usage of the word this is a dimension of the object and this is a dimension of the object and the diameter of this hole through it is a dimension of the object so you get 10 numbers specifying it 10 dimensions to the perfectly reasonable engineer usage of that word but then if the person is more attractive interesting or you want to learn something about them in other ways you say well the first dimension is waste measurement the example I gave you could have height and weight then you make a scatterplot everybody's done scatterplots right so you got the planar scatterplot height against weight and they roughly go together although you can have the same height and different weights or you could have the same weight and be different heights but they sort of go together then with age in there let's take say age against height then okay age this way height this way everybody starts fairly small in both ones so you've got a cloud of point coming up like this increasing age increasing height it levels off and you've got a cloud that goes like this and if you've got a population like say South Korea where in the last half a century nutrition has gone up then you find oh the older people are pretty small the older people are foot taller the younger people are foot taller than the really old ones but if it's a static population it looks more like this it's a cloud in 2D at weight becomes cloud in 3D you have age you have height and you have weight and this cloud comes up they all three increased together now you've got somebody about 20 they're not getting any taller they are getting older and they get most of them get steadily heavier so the cloud goes out that way but it's got thickness in all directions and by the way it's non-linear it's going up and then it's going along another thing so three dimensional situation okay now I collect one more number I bring along a tape measure I put it around you I get a rather small number I would guess that's a fourth way to vary but it's exactly the same sort of thing I've got a collection of four tuples of numbers that is a four dimensional space so in that one the fourth dimension is not time it's not anything mystical it's just how many centimeters around the middle of you four dimensional means something much more than oh wow I've got an extra direction four dimensional is how the shapes go three dimensional is can I turn in more ways than just going plane geometry leads you to wrong insights not that they're wrong about plane geometry but expecting relationships to look like pictures in the plane misleads you as to what relationships between data can be you need to think in at least three dimensions and you need to take up 3D thinking as a kind of this is the closest you can get to thinking in 4D or 70 or 500 dimensions because you've got that many numbers thank you so well we'll stop whenever the question stop coming one addition to what you said and one question the addition is that again I started off most of the young engineers here not liking the math or I started hating the math at one point when the algebra got to me and I couldn't make sense of it and today I do computer vision as a living and I do 3D geometry or all things related to those things and even graphs and whole bunch of things and today but I see it in a completely different light and I given those intuitions I'm able to connect to the equation so I guess what I want to leave the thought here is if there are people here who are afraid of the math there are more interesting things that you can come back and connect so don't worry about it and please meet people like Tim or others and online courses maybe in order to go ahead the second I guess is a question this is regarding again about programming you were saying you know there are three levels of debugging you know from specific things going all the way broader now in that context I guess I'm curious to know what your thought process is on how say categories as in category theory connects to programming especially given the connections of you know connections of category theory into programming languages like Haskell or other functional programming which is used today well I cannot speak well for the big data language manipulation things I have not built experience in that but let me give you an example from a simulation problem somebody a student at University of Singapore working on a thread manipulation simulator for doing virtual surgery so you have forceps and you're pulling this fine nylon thread around and how does that shape go it's very tricky to do this game in real life because you're trying with one pair of forceps often with very tiny little threads you're trying to tie a knot in it so you've got to make a loop happen and then pull something through so it's not just how do you make it go through the flesh it's how do you make it how do you make the nylon dance and she was getting places where the algorithm went unstable and she was trying different things at the coding level and I looked at that and I said you are in a place where you're going to get a zero eigenvalue one year close to it how many of you heard of eigenvalues okay how many of you feel you can explain eigenvalues okay but that would take another talk we don't have time but the thing is that I know because of my mathematics and I mentioned Ian Stewart my co-author of the science fiction thing the book that we published a long time ago it's called catastrophe theory about how you connect calculus of things that are changing in nonlinear ways and suddenly jump to you could recognize yeah here is the direction in the linear approximation to the nonlinear thing that is going on and where this becomes degenerate you can expect other things to happen and but if you look carefully along that direction you can write a very economical algebraic algorithm that you can then code run in real time enough for haptics force feedback which needs 1000 returns per second so your calculations are better be fast the theory got rid of that oscillation it was not at the coding level it was at the level of understanding the mathematics of elasticity and the nature of how that looking for what the equilibrium would be actually worked I can't give you an example from everybody's field but that's one from my own personal experience