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[Assistant] You'll know I'm recovering slowly but surely and maybe next week I'll set my guitar ringing. My voice clears water and everyone's singing, but probably I'll just get up and start grooving. My vocal cords moving.


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[Assistant] Ethic, Hedge, and Adila, the leader of the revolution, plot out how they can steal an artifact called the Node of Power.


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[Assistant] It's being used to run a heavily fortified train that runs all around the country, providing supplies to settlements and facilities.


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[Assistant] This armored behemoth undergoes a complex and unpredictable unloading procedure, a procedure which is displayed in detail on a screen within the engine car.


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[Assistant] Right means the train will go one car length forward, and left means the train will go the same distance backwards. While unloading, the train frequently moves back and forth, so a typical sequence might look like this.


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[Assistant] Also, within the engine car is a button that can only be pressed once.


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[Assistant] When pressed, it lets down the force field over the artifact for 10 seconds.


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[Assistant] The engine car is tiny and designed for a robot. Of your team, only Hedge can fit.


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[Assistant] The members of the resistance have positioned a crane over the train tracks that can pluck the artifact once it's exposed. They'll know when to lower the crane by sight.


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[Assistant] But the only way hedge can determine the train's position and know when to lower the force field is by analyzing the unloading procedure.


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[Assistant] Because he'll be inside the windowless engine car.


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[Assistant] Hedge can't program himself, though, so it's up to Ethic to tell him what to do.


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[Assistant] The artifact is in the car ten positions behind, the one that's directly under the crane at the start.


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[Assistant] What instructions can Ethic give Hedge so that he hits the button at just the right moment?


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[Assistant] The key to this problem, as with many programming challenges, is to reframe the information in a way that a computer can work with. A computer doesn't know what a train is, nor does it need to.


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[Assistant] It can however work with variables. Try making a variable that tracks the train's position. How will it change as the train moves?


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[Assistant] Let's start by breaking this problem into two objectives.


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[Assistant] The first is to know where the train will be as it carries out its instructions.


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[Assistant] The second is to hit the button when the train is in just the right position.


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[Assistant] For the first objective, it'll help to think of the train as a big number line. Let's make 0 the car with the node, 1 the car in front of it, and so on. That means car 10 is under the crane at the start.


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[Assistant] When the train moves one car right, car nine is under the crane. So a right arrow can be thought of as subtract one. And when the train moves left from there, ten is back under the crane, making a left arrow the same as add one.


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[Assistant] Let's set our train position variable to 10, since that's where we start. We can now use a loop to read the instructions one at a time, adding or subtracting as we go to track which car is under the crane.


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[Assistant] The nice thing about setting up the variable this way is that it tells us how far the node is from the crane. So as soon as the variable hits zero, hedge should hit the button. And here's what happens.


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[Assistant] Ethic gets into position on the crane while Hedge rushes off and slips into the engine car unnoticed just before the train lurches to life. It rolls three cars back.


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[Assistant] One forward, another four back, then so far forward, ethic loses track, before it reverses once more.


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[Assistant] When the artifact finally rolls into position, Adila lowers the crane, hoping Ethic and Hedge got it right. At the last possible moment, the force field sputters and falls. Ethic swoops in and lifts the node of power to freedom.


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[Assistant] When Ethic gives the node to Hedge for safekeeping, something incredible happens. The artifact shimmers to life with a vision of the past. When the crystal was unearthed, no one could make the console inside work.


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[Assistant] The government put out a call for people to try their luck with it, one at a time.


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[Assistant] Ethic loved to figure out what made things tick, so she signed up.


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[Assistant] Within moments at the console, something clicked into place, and she created her first robot.


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[Assistant] The government hired Ethic as chief robotics engineer on the spot.


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[Assistant] Within a year, her creations ran almost every aspect of society, and the nation and its people thrived, no longer needing to toil in the fields and factories.


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[Assistant] Continue the adventure in episode 5 of Think Like a Coder.


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[Assistant] Or restart the journey with episode 1. And don't forget to subscribe.


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[Assistant] I granted her wish. She wanted to be the almighty, the unknown. That's what she is. Nobody has ever seen the almighty. She is now unknown to everyone.


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[Assistant] Zero conditional. If you eat too many sweets, you gain weight. If you want to be in good shape, exercise twice a week. First conditional.


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[Assistant] You will not get enough vitamins if you don't eat fresh fruits. If I can wake up early enough, I will come. Second conditional.


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[Assistant] I would have been on time, if the traffic hadn't been so bad.


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[Assistant] If you liked this video, please subscribe to our YouTube channel.


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[Assistant] One of the potential reasons is that bronze medalists might compare their metal to no metal at all, while silver medalists compare theirs to gold, so it could come down to status. Silver medalists are equally one spot away from gold and bronze, and they'd gain much more status moving up to gold than down to bronze. On the other hand, bronze medalists have more to lose than gain. Moving up to silver?


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[Assistant] I'm having such a great time in the summer camp. I'm staying in a beautiful log cabin. We're having so many wonderful adventures. Archery is a wonderful sport.


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[Assistant] We have learned how to shoot arrows at the archery target.


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[Assistant] While doing that, you have to wear a climbing helmet.


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[Assistant] In the evenings, we sit around the campfire, share stories, and roast marshmallows on a stick.


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[Assistant] You're the best tree. I love you.


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[Assistant] Once upon a time in the vast continent of Rolva,


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[Assistant] It is not just our ministers, but everyone in the kingdom has turned into animals.


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[Assistant] Remember Hikachu, your wise advisor.


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[Assistant] The curse has turned our subjects into animals, but it has not taken away the power of human reasoning and speech. They can still talk!


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[Assistant] At least some of them. The king was delighted to hear that.


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[Assistant] Princess Aria called for Hikachiyo, and he came at once.


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[Assistant] At this, King Julian became quiet and sad. What does she want, father?


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[Assistant] The fairies presented Queen Minerva with the king's offer. She smiled. The day has finally come. I accept the invitation.


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[Assistant] Now amongst the participants, the frog, the rabbit, and the grasshopper were considered to be the best jumpers that had ever lived in Meridon.


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[Assistant] The king was quite impressed by the frog's manners.


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[Assistant] The frog stepped onto the stage and got into place. The crowd waited, still. He took a deep breath, and just as he was about to take the leap and jump, a fly came hovering near him. He got distracted and started going after the fly. Boo! Ah! I should have let my little one participate. He would have done a much better job.


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[Assistant] The rabbit too was poised and well mannered, which pleased the king. Not interested.


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[Assistant] Queen Minerva was also amused by the rabbit's jump. She smiled and clapped her hands.


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[Assistant] The grasshopper got into position, and immediately, and just as he was about to jump,


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[Assistant] Thank you for not worrying about the competition and putting your life at risk in order to protect me and your king's reputation. Ask me for anything.


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[Assistant] The queen was surprised by Ragnar's wish. Are you sure that is what you want? I can give you all the riches in the world.


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[Assistant] First, I would like to propose that I adopt Ragnar as my son and heir to my throne. Everyone was shocked, including Ragnar.


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[Assistant] And thus, the rivalry between the two kingdoms ended forever. And everyone lived happily ever after.


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[Assistant] I'm looking for a birthday present for my wife. Can you recommend something?


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[Assistant] That sounds like a very good idea. I would like something simple, nothing too fancy.


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[Assistant] I don't think these would fit her style. They're too sophisticated. Do you have more designs?


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[Assistant] Wow! This is exactly what I'm looking for! How much is it?


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[Assistant] Wonderful! I'll take it! And can you also recommend something for my seven-year-old daughter?


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[Assistant] Hi, I saw your shoe clearance sale ad on the flyer. Yeah, we're offering discounts on all our shoes. It's the best chance to buy your favorite shoes at a low price. What are you interested in buying? I need some comfortable shoes for running. Which shoes would be most suitable? In my opinion, these sneakers would be best for your needs.


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[Assistant] They're great for running lots of miles and they're very comfortable. I like their design. How much are these sneakers?


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[Assistant] Their regular price is $150, but they're on sale for 50% off right now.


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[Assistant] Wow, really? Let me try him on. Do you have a size 8? Let me see. Here you are.


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[Assistant] They're soft and comfortable. They slide off and on easily. They fit me well. I'll buy them.


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[Assistant] Great, I'll pack them up for you and you can pay at the cash register. Thank you for your help. You're very welcome.


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[Assistant] Hello there, how can I help you today? I'm looking to upgrade to a bigger car today.


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[Assistant] My wife and I are expecting our third child and we need a bit more space now.


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[Assistant] I completely understand. Are you thinking of a car or an SUV? Or are you interested in a van?


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[Assistant] I think we would like an SUV, but one that isn't too big. And we'd prefer something with decent gas mileage. We have a new hybrid SUV that might be great for your family. Take a look. Wow, this is really nice.


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[Assistant] It has leather interior, a backup camera, video screens for the kids, and optional third row seating. Very nice. How's the gas mileage?


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[Assistant] It gets about 40 miles per gallon. That's incredible. That's better than my current car. How much is it? The price is $40,000. Would you like to try it out? Definitely. Let's take it for a test drive.


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[Assistant] What do you think? It was great. A smooth ride and very comfortable. We have some great financing deals going on right now.


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[Assistant] Sounds good to me. Let's talk out the details. Awesome. Let's head to my office.


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[Assistant] Tell me about the noise. Is it squeaking? Rumbling? Knocking?


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[Assistant] I'm going to take your car for a quick diagnostic test to see if I can determine what is causing the sound.


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[Assistant] The brake pads are worn down, so every time you stop, the metal from the brakes cause a loud noise. I can put new ones on today if you'd like.


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[Assistant] I also noticed that your oil needs changed and your spark plugs need replacing. Would you like me to take care of those as well?


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[Assistant] I'll get everything running smoothly for you. And I'll even run it through the car wash when I'm done.


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[Assistant] I love chocolate, and Allison loves vanilla, so we aren't sure what to order.


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[Assistant] To reach it, Ethic must use three energy streams to climb the tower. As soon as she steps forward, a timer will begin, counting down from 60 seconds.


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[Assistant] At the back of the room, there's a basin made of invisible towers that can hold energy between them.


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[Assistant] During the 60 calm seconds, Ethic and Hedge must decide exactly how many units of energy will fall.


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[Assistant] For each of the three challenges, they must choose the amount that will fill the basin exactly. If they do so, the energy will propel them further upwards. But if they get the amount at all wrong, the energy left will fail, dropping them.


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[Assistant] Diagrams on the walls illustrate some examples. This configuration will capture exactly two units of energy. This configuration will capture four. Three here, and one here. And this one will also capture four, because any energy on the right would spill out.


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[Assistant] The energy will rain down in such a way that it'll only overflow if there's no space that could hold it. Hedge can make one tower of blocks visible at a time and count how tall it is, but he can't look at the whole structure all at once.


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[Assistant] How does ethic program hedge to figure out exactly how much energy each basin can hold? Pause now to figure it out for yourself.


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[Assistant] Each unoccupied cell will hold energy if and only if there is a wall eventually to its left and a wall eventually to its right.


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[Assistant] But it would take a long time for Hedge to check this for each individual cell. So what if he were to consider a whole column of blocks at a time? How many units of energy can this hold, for instance?


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[Assistant] Let's analyze the problem by looking at our example. There are five columns of blocks here. The leftmost one can't hold any energy, because there's nothing higher than it. The second stack can have three units above it, as they would be trapped between these two four-block stacks.


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[Assistant] We get 3 units by taking the height where the energy would level off, 4, and subtracting the height of the stack, so that's 4 minus 1. The third stack is similar, 4 to the left, 4 to the right, and it's 3 high, so it'll hold 4 minus 3 equals 1 unit.


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[Assistant] The fourth stack and fifth stacks have nothing higher than them to the right, so they can't hold any energy.


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[Assistant] We can adapt this idea into an algorithm.


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[Assistant] Considering one column at a time as the point of reference, hedge can look to the left stack by stack to find the height of the tallest one, look to the right to find the height of the tallest one, and take the smaller of the two as the height the energy can fill up to.


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[Assistant] If the result is higher than the column in question, subtract the height of the original column, and the result will be the number of units that column can hold.


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[Assistant] If it's equal to or below the level of the column in question, the energy would spill off. Hedge can apply that to an entire basin with a loop that starts on the leftmost column and moves right, one column at a time.


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[Assistant] For each column, he'll run the same steps. Look all the way left for the tallest, do the same to the right, take the lower height of the two, subtract the original column height, and increase the grand total if that number is positive. His loop will repeat as many times as there are columns.


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[Assistant] That will work, but it'll take a long time for a large basin. At every step, Hedge repeats the action of looking left and looking right. If there are n stacks, he'll look at all n stacks n times. Is there a faster way?


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[Assistant] Here's one time saver. Before doing anything else, hedge can start on the left and keep a running tally of what the highest stack is. Here that would be 2, 2 again since the first was higher, then 4, 4, 4.


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[Assistant] In the end, he'll have a table like this in his memory.


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[Assistant] Now, hedge can take one more pass to calculate how much energy there will be above every stack with the same equation from before. Take the smaller of the stored left and right values and subtract the height of the current tower.


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[Assistant] Instead of looking at n stacks n times, he'll look at n stacks just three times, which is what's called linear time. There are ways to optimize the solution even further, but this is good enough for our heroes. Ethic and hedge work as one.


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[Assistant] The first cascade is a breeze, and they rise up the tower.


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[Assistant] The third is huge, with dozens of stacks of blocks. The timer ticks down towards zero. But Ethic's program is fast. She gets the wheel in position just in time.


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[Assistant] Like the first, it reveals a vision, memories of years gone by.


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[Assistant] The world machine changed everything, and Ethic, in her position as chief robotics engineer, grew troubled by what she saw. When the Brad barrier went up to keep the people in, she knew something was seriously wrong.


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[Assistant] So she created three artifacts with the ability to restore people's power, creativity, and memory, and smuggled them to three communities. Before she could tell people how to use them, the government discovered her efforts and sent bots to arrest her and the other programmers.


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[Assistant] The last thing Ethic used the World Machine to create was a robot that would protect the ancient device from the forces of ignorance by enclosing it in a giant maze. She named her creation Hedge.


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[Assistant] Continue the adventure in episode 8 of Think Like a Coder, or restart the journey with episode 1. And don't forget to subscribe!


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[Assistant] You loved and cared for me all my life. It's my turn now to take care of you. I will work and earn a lot of money. This is a difficult time for us. It will be over soon.


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[Assistant] Me and my daughter will then have the life I always wanted.


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[Assistant] No father, I want to work. Nothing comes out of neglecting our duties. Don't worry, you have taught me well. I know one day my efforts will be rewarded.


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[Assistant] That's alright, I can clean them with some water. You were in need, and I had to help you.


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[Assistant] Uhm, sorry to disturb you, but it's dark outside. Can I stay here for the night? Where are you going? I'm looking for some work. Is that so? Why don't you work here?


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[Assistant] My father taught me to always follow my duty. For as long as I worked here, my duty was to obey you.


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[Assistant] Listen now, you. You have to earn more than her. I got faith in you. She got pearls. You will get me rubies.


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[Assistant] I will not dirty my clean hands and my pretty fit for your dried branches, no matter what.


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[Assistant] Under this burning sun, I will not dirty my clean hands and my pretty feet for your dying roots, no matter what.


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[Assistant] Yes, there were also some strange noises, and it was showing funny colors for a few minutes. Then it just turned off. I planned a little party this evening to watch the soccer game with my friends.


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[Assistant] There are many stores and restaurants surrounding the apartment. I promise you that you will love the location.


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[Assistant] Well, I'll see you at 5pm. Do you know how to get there?


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[Assistant] So, this is the apartment. It has a small kitchen, two bedrooms, and one large bathroom with washer and dryer. Take a look around.


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[Assistant] It's $725 each month and it require a 12 month lease. You'll need to pay the tenancy deposit and the first month's rent.


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[Assistant] Yes, you can, but you shouldn't change the appearance of the property significantly.


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[Assistant] Water, sewage, garbage, and internet are all included in the rent. You have to pay for electricity and cable.


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[Assistant] Of course, but first, let's find out what the problems are.


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[Assistant] Now what's the problem, girls? Why did you want to speak with me?


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[Assistant] Some repair work had to be done on the facade and balconies, and it will certainly improve the overall appearance of the building.


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[Assistant] I'm sorry about that, but the good news is, it won't last forever.


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[Assistant] I do apologize for the inconvenience, but there's nothing I can do about it.


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[Assistant] Perhaps you should contact the management company who is overseeing the repair work.


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[Assistant] You've been lucky to find this apartment with such a cheap rent. I think you should appreciate that.


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[Assistant] I suppose I could offer you a 10% reduction for now until you move out.


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[Assistant] The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free.


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[Assistant] To make a donation or to view additional materials from hundreds of MIT courses.


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[Assistant] Visit MIT OpenCourseWare at ocw.mit.edu.


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[Assistant] Australians call them runners. The British know them as trainers. Americans refer to them as tennis shoes or sneakers. Whatever you call them, these rubber-soled casual shoes are worn by billions of people around the world.


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[Assistant] Originally invented in the late 19th century, these simple canvas and rubber creations have changed a lot since they first hit the pavement.


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[Assistant] Today, sneaker consumption is at an all-time high. No country buys more sneakers than the United States, where people purchase three pairs a year on average.


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[Assistant] To meet this demand, roughly 23 billion shoes are produced each year, mostly in factories across China and Southeast Asia. But making shoes has become more complicated, more labor-intensive, and in some ways more dangerous for the workers involved and for our planet.


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[Assistant] Shoe manufacturing accounts for roughly one-fifth of the fashion industry's carbon emissions. Sneakers alone generate 313 million metric tons of carbon dioxide every year.


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[Assistant] Which is equivalent to the annual emissions of 66 million cars. To better understand your shoes carbon footprint, let's dive into the anatomy of a sneaker.


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[Assistant] Mining the fossil fuels that make up these materials emits tons of greenhouse gases, and processing those raw ingredients into synthetic textiles also uses a lot of energy, further compounding that pollution.


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[Assistant] Some sneaker tops are made from natural sources like leather, but tanning this material relies on chromium, a carcinogenic chemical that can damage freshwater ecosystems.


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[Assistant] The outer soles of most shoes are made of rubber that's gone through a process called vulcanization. This technique adds sulfur to superheated raw rubber to create a material that's both elastic and sturdy.


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[Assistant] Until recently, sneakers used natural rubber for this process. But today, most outer soles are made with a synthetic blend of natural rubber and byproducts from coal and oil.


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[Assistant] Producing these materials accounts for 20% of a sneaker's carbon footprint. But more than two-thirds of the shoe's carbon impact comes from the next step— manufacturing.


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[Assistant] A typical sneaker is comprised of 65 discrete parts, each of which is produced by specialized machinery. This means it's cheaper for factories to mass-produce each piece separately rather than manufacturing every part under one roof.


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[Assistant] Once the components arrive at the assembly line, they undergo cutting, pouring, melting, baking, cooling, and gluing before the final products can be stitched together.


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[Assistant] The assembly of a typical sneaker requires more than 360 steps and accounts for the remaining 20% of a sneaker's environmental impact.


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[Assistant] The dispersion of factories fuels another problem as well— labor abuse. Most brands don't own or operate their factories, so the plants they work with are in countries with little to no worker protection laws.


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[Assistant] As a result, many laborers earn below the living wage and are exposed to harmful chemicals like toxic glue fumes.


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[Assistant] When manufacturing is complete, the shoes are packaged and transported to stores around the globe.


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[Assistant] For many, these shoes could last years. But for someone running 20 miles a week, a pair of running shoes will start wearing out after roughly six months. Since the shoes are made of so many different materials, they're almost impossible to break down into recyclable components.


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[Assistant] 20% of these shoes are incinerated, while the rest are tossed into landfills, where they can take up to 1,000 years to degrade.


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[Assistant] Factories need to develop energy-efficient manufacturing processes that consolidate steps and sneaker parts. And consumers should support companies using clean energy and ethical manufacturing processes. We can also buy fewer shoes, wear them for longer, and donate those we no longer need.


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[Assistant] So no matter what your style, we can all take steps towards a sustainable future.


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[Assistant] This episode is sponsored by Wren, a website with a monthly subscription that helps fund projects to combat the climate crisis. Click on the link in the description to learn more about how you can make a monthly contribution to support projects like rainforest protection programs.


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[Assistant] With the climate crisis already causing big problems, scientists are creating new, high-tech solutions that can capture and reuse carbon dioxide. Even better, these new technologies are focused on creating a circular carbon economy. That's where the carbon dioxide that's emitted during a process, like


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[Assistant] manufacturing a shirt or flying a plane is recaptured from the atmosphere and then reused as energy to fuel that process again.


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[Assistant] The goal is to create a carbon-neutral loop, where all of the CO2 that's emitted gets captured and put back into the system. Which is, you know, a lot more sustainable than most of what we're doing right now. A circular carbon economy starts with capturing CO2, and for this, we can turn to an unlikely partner.


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[Assistant] Scientists have been experimenting with using algae to capture carbon for decades. That's because it is great at removing CO2 from the atmosphere. In fact, one kilogram of algae can absorb about 1.8 kilograms of carbon dioxide. But using algae for carbon capture, or sequestration, has been tricky. In the past, algae sequestration has needed lots of land and water to work, and it's required lots of maintenance, too. A study published in 2021 developed a more efficient way to use algae to capture CO2 by making biocomponents.


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[Assistant] Biocomposites are made by combining one natural and one synthetic material to produce a new, better material. In this case, literally a carbon-capturing sheet. Researchers used the microalgae Chlorella vulgaris and coated textiles with it to make a biocomposite. Cotton and polyester, to be exact.


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[Assistant] The fabric gave the algae something to anchor to, so they grow more efficiently and take up more CO2.


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[Assistant] These biocomposites were tested with a mixture of CO2 and air to measure how well they could absorb CO2. The researchers found that their new biocomposites absorbed 3.5 to 14.5 times more CO2 than the control algae that wasn't grown on fabric. Even better, the researchers found that their algae textile biocomposites used less water and were lower maintenance. And they're also hopeful that these biocomposites may help solve another environmental problem as well.


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[Assistant] They want to turn some of that waste into biocomposites so we can keep textiles out of landfills


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[Assistant] By transforming them into slimy carbon catchers. But in order to have a circular carbon economy, we have to do more than just remove CO2 from the atmosphere. We have to transform it into something else.


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[Assistant] Like, fuel. Fuels are substances that react with something else, usually oxygen, to release energy that we can harness to power something, like a jet engine. CO2 is not a fuel, but it does contain the key element that makes up the backbone of most of the fuels we use. Carbon, the problem.


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[Assistant] You have to put energy in to be able to get it back out. One major target for reducing emissions is air travel and the fuel that planes depend on.


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[Assistant] Jet fuel and gasoline are similar, but they're not identical. Both are derived from petroleum, but they're made up of differently-sized molecules. Where gasoline's molecules typically have 7 to 11 carbon atoms, jet fuel has 12 to 15.


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[Assistant] And although jet fuel is not more polluting than gasoline, the amount of fuel that's burned during a flight adds up. A round-trip flight from London to San Francisco emits 879 kilograms of carbon dioxide. To put that into perspective, the CO2 generated by that flight is equal to about 22% of the average person's


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[Assistant] That's a big deal, especially since the Environmental and Energy Study Institute estimates that the emissions from passenger air travel could triple by 2050. So figuring out how to recycle the CO2 generated by planes can make a big dent in emissions. In 2020, researchers developed a process that took carbon dioxide molecules and turned them directly into jet fuel.


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[Assistant] They did this using a special metal-based catalyst, a substance that lowers the energy barrier for a chemical reaction to get going and speeds everything up. Catalysts can be a huge variety of kinds of substances. The only rule here is that they are not used up in the reaction they facilitate, so a small amount can go a long way.


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[Assistant] In this case, the catalyst was made from iron, manganese, and potassium to drive the chemical reaction. To start, scientists infused a stainless steel reactor with carbon dioxide. From there, the researchers added the metal catalyst and 350 degrees of heat.


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[Assistant] And voila! They produced fuel with a similar number of carbon atoms as jet fuel.


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[Assistant] Using a lot less energy, equipment, and space than traditional methods. Since we're using CO2 to make fertilizer anyway, using the same carbon dioxide that's released from the urea to make more urea can help us close the loop and make fertilizing crops


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[Assistant] Especially if the whole process is fueled by renewable energy. And while this technology is new, the researchers want to streamline it so that small farmers around the world can manufacture urea themselves. Which would be good news for farmers and…


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[Assistant] We know that we need to reduce our CO2 emissions to deal with the climate crisis. And one way to do that is by recycling the CO2 we've already released by transforming it into stuff that we are already using, like jet fuel and urea. Or taking old stuff and using it to capture CO2, like with recycled fabric biocomposites. By figuring out how to use the CO2 we've already made.


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[Assistant] We can start taking baby steps toward becoming truly carbon neutral. And when it comes to climate change, every single thing we do to make it better makes it better. This SciShow video is supported by Wren.


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[Assistant] When you're just beginning your personal battle against climate change, it can be hard to know where to start. So Wren has a carbon footprint calculator to easily figure out your first steps. And Wren makes it easy to see that you're not working on this problem alone. With the help of everyone who subscribes to Wren, they have planted


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[Assistant] Governments to fund these projects, but we can start by crowdfunding them. So SciShow has partnered with Wren to plant 10 extra trees for each of the first 100 people who sign up using the referral link in the description down below. Thanks to Wren for supporting this video, and thank you for watching.


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[Assistant] Okay, now clustering for graphs. So this is, uh,


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[Assistant] A topic, this is one of the important things you can try to do with a graph. So you have a large graph.


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[Assistant] Let me kind of divide it into two clusters.


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[Assistant] So you get a giant graph, and the job is to make some sense out of it. And one possible step is to be able to subdivide it if, as I see here,


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[Assistant] Uh, there's a cut between two reasonably equal parts of the graph, reasonable, reasonably same size.


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[Assistant] And therefore that graph could be studied in two pieces. So the question is how do you find such a cut by a, by a,


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[Assistant] Algorithm. What's an algorithm that would find that cut? So the, so that's the problem.


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[Assistant] Let's say we're looking for two, for, for two, uh, uh, clusters.


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[Assistant] We could look for more clusters, but let's say we want to look for two clusters. So what are we trying to do? We're trying to minimize, uh, so this is the problem then.


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[Assistant] Which will be the center, so to speak, of the, uh, and really it's just these points. Uh, yeaah.


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[Assistant] Uh, so the data is the points and the edges, as always, the nodes and the edges.


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[Assistant] Notice the problem is to find x and y so that to minimize.


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[Assistant] Maybe should emphasize we're in high dimension. Plus the distance.


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[Assistant] From other points, so the ai will be these points, these nodes, and the bi will be these nodes, plus the sum of bi minus y squared.


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[Assistant] And you understand the rule here.


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[Assistant] The A's intersect the B's is empty.


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[Assistant] Just, just what you expect. I'm dividing the A's and the B's into two groups, and I'm picking an X and a Y sort of at the center of those groups so that


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[Assistant] Uh, that, uh, is a minimum. So I want to minimize.


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[Assistant] And also I probably want to impose some condition that the number of A's is reasonably close to the number of B's. In other words, I don't want


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[Assistant] Just that to be the A, and all the rest to be the B's. That would be not a satisfactory, uh, clustering. I'm looking for clusters that are good size clusters. So minimize that. Okay.


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[Assistant] So, there are a lot of different algorithms to do it.


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[Assistant] Some are more directly attacking this problem. Others use matrices that we associate with the graph.


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[Assistant] So let me tell you about two or three of those algorithms. And if you've seen, studied, had a course in graph theory, you may already have seen this problem. First question would be, suppose I decide


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[Assistant] These are the A's and those are the B's or some other decision. Yeah, probably some other decision. God, I don't want to solve the problem before I even start. So some A's and some B's.


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[Assistant] What would be the best choice of the x once you've decided on the a's?


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[Assistant] And what would be the best choice of the y once you've decided on the b's? So, so that, we can answer that question. Just if we knew the, the two groups.


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[Assistant] We could see where they should be centered with the first group centered at x, the second group centered at y, and what does centering mean. So let's just say, uh,


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[Assistant] Let me bring that down a little. So, given the A's,


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[Assistant] Part right. And the answer is, do you know geometrically what x should be here? x is the


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[Assistant] So if I have a bunch of points and I'm looking for the middle of those points,


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[Assistant] The point x, a good point x to say, okay, that's the middle. It'll make the, some of the distances.


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[Assistant] I think squared, I hope I'm right about that. Uh, a minimum. What's the, what is x? It is the,


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[Assistant] Of the, of the A's. And what is the centroid? Let's see. Oh, maybe, I don't know if x and y were a good choice, but, uh, let me see what, uh,


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[Assistant] I guess it's the average A, it's the sum of the A's.


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[Assistant] Of these A's, those are, those are vectors, of course, divided by the number of A's.


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[Assistant] I think, actually, I was just quickly reviewing this morning, so I'm not, uh,


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[Assistant] Totally on top of this centroid. What I'm going to talk, the algorithm that I'm going to talk about is the k, well, k means, it's always called. And here it will be, the k will be 2.


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[Assistant] I just have two partitioning into two sets, A's and B's, so I just, K is just two. Okay, what's the algorithm?


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[Assistant] Partition, the a's and the b's have separated them, then that tells me what the x and the y should be.


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[Assistant] Now what do I do next? So this is going to be a sort of an alternating partition. Now I take those two centroids. So step one is, for a given


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[Assistant] x and y. And that's elementary. Then the second step is, given the centroids,


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[Assistant] x and y, given those positions, given x and y.


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[Assistant] It won't be centroids once, when you see what happens. Given x and y, redo, re, uh, form, form the best


[User] Please transcribe this text

[Assistant] Okay, so step one, we, we, we had a guess at what the best clusters were, and we found their centroids. Now, we start with the centroids, and we form


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[Assistant] New clusters again. And if these clusters are the same as


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[Assistant] The ones we started with, then the algorithm is converged. But probably won't be. These clusters, so you'll have to tell me what I mean by the best clusters. If I've got the two points x and y, I want the points


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[Assistant] I want to separate all the points that cluster around x to the ones that cluster around y. And then they're probably different from my original start. So now I've got new, now I repeat step one.


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[Assistant] Does it go with x, or does it go within the x cluster, or does it go in the cluster around y? So how do I decide that?


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[Assistant] Just whichever one is closer to. So each, each point


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[Assistant] Goes with each node, you should, I could say each node goes with the, the closer


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[Assistant] That are closer to x, now we're going to put them in the cluster around x.


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[Assistant] And does that solve the problem? No, because, well, it might, but it might not. We have to come back to step one.


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[Assistant] We've now changed the clusters. They'll have different centroids.


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[Assistant] So we repeat step one, find the centroids for the two new clusters. Then we come to step two, find the ones that should go with the two centroids, and back and forth. I don't know, I don't think there's a nice theory of


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[Assistant] Convergence or rate of convergence, all the questions that this course is always asking, but it's a very popular algorithm. k means. k would be to have k clusters. Okay. So that's a,


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[Assistant] I'm not going to discuss the, uh, I'd rather discuss some other ways to do this, to solve this problem, but that's one sort of, uh, hack that works quite well. Okay, so second approach is, is what's coming next. Second solution method.


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[Assistant] That's the name of the method. And before I write down what you do, what does the word spectral mean?


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[Assistant] You see spectral graph theory, spectral clustering, and in other parts of mathematics you see that, you see spectral theorem.


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[Assistant] I gave you the most, and I described it as the most important, perhaps.


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[Assistant] Theorem in linear algebra, at least one of the top three is, uh, so I'll write it over here because it's not, it doesn't, this is a, it's the same word, spectral.


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[Assistant] Well, let me ask the question again. What's that word spectral about?


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[Assistant] What does that mean? That means that if I have a matrix and I want to talk about its spectrum, what is the spectrum of the matrix? It is the, the eigenvalues.


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[Assistant] So spectral theory, spectral clustering is, is using the eigenvalues of some matrix. That's what that spectral is telling me.


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[Assistant] Yeah, so the spectral theorem of course is that for a symmetric


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[Assistant] Matrix S, the eigenvalues are real, and the eigenvectors are orthogonal. And don't forget what the real, uh, full statement is here, because there could be repeated real eigenvalues. And what does the spectral theorem tell me? For symmetric matrices,


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[Assistant] If that, if, if lambda equals five is repeated four times, if, if it's a four times, uh, solution of the,


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[Assistant] Equation that gives eigenvalues, then what's the conclusion? Then there are four independent orthogonal eigenvectors to go with it.


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[Assistant] We can't say that about matrices, about all matrices. But we can say it about all symmetric matrices.


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[Assistant] And in fact, those eigenvectors are orthogonal, so we're even saying more. We can find four orthogonal eigenvectors that go with a, with a,


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[Assistant] Multiplicity for eigenvalue. Okay, that's spectral theorem. Spectral clustering, uh, starts with the, uh,


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[Assistant] So that's the key connection of linear algebra to graph theory, is the properties of this graph Laplacian matrix. Okay, so let me say L for Laplacian.


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[Assistant] Where A is the incidence matrix.


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[Assistant] Or another way we'll see is the D, the degree matrix.


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[Assistant] And I'll do an example just to remind you. Minus the, I don't know what I'd call this one.


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[Assistant] Shall I call it B for the moment? And what matrix is B? That's the adjacency matrix.


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[Assistant] Four matrices, they're the key four matrices associated with any graph. The incidence matrix, that's m by n, row, uh, uh, edges and nodes, edges and nodes. So it's rectangular.


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[Assistant] But I'm forming A transpose A here, so I'm forming a symmetric, positive, semi-definite matrix. So this, this little Gaussian is symmetric, positive, semi-definite.


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[Assistant] Yeah, let me just recall what all these matrices are for a simple graph.


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[Assistant] There are 1, 2, 3, 4, 5 edges, so 5 rows.


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[Assistant] There are four nodes, one, two, three, and four. So four columns. And a typical row would be edge one.


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[Assistant] Going from node 1 to node 2, so it would have a minus 1 and a 1 there. And let me take edge 2, going from 1 to node 3, so it would have a minus 1 and a 1 there. So on. So that's the incidence matrix A.


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[Assistant] Okay, what's the degree matrix? That's simple. The degree matrix. Well, A transpose A.


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[Assistant] And it will tell us the degree of that, which means, which we just count the edges. So it's three edges going in. Node 2, three edges going in. Node 3 has just two edges.


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[Assistant] And node four has just two edges here. So that's the degree matrix.


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[Assistant] And then the adjacency matrix that I've called B is also 4 by 4. And what is it?


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[Assistant] It tells us which node is connected to which node. So, and I don't allow nodes edges


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[Assistant] The connector node to itself, so zeros on the diagonal. How many?


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[Assistant] So which nodes are connected to node 1? Well, all of 2 and 4 and 3 are connected to 1, so I have 1's there.


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[Assistant] All three nodes are connected to node 2, so I'll have no-


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[Assistant] The second column and row will have all three ones.


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[Assistant] How about node three? Okay, only, only edges, only two edges are connected. Only two, only two nodes are, are connected to three. One and two, but not four. So one and two I have, but not four. Okay.


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[Assistant] So that's the adjacency matrix. Is that right? Think so?


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[Assistant] This is the degree matrix. This is the incidence matrix. And that formula gives me the Laplacian. Okay, let's write down the Laplacian.


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[Assistant] So if I use the degree minus b, that, that's easy. The degrees were 3, 3, 2, and 2. Now I have these minuses.


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[Assistant] So that's a positive semi-definite matrix. Is it a positive definite matrix?


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[Assistant] So let me ask, is it singular or is it not singular?


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[Assistant] Is there a vector in its null space or is there not a vector in its null space? Can you solve dx equals all zeros?


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[Assistant] Everybody sees that the vector of all 1's


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[Assistant] Will be, uh, solution to D, to, to, uh, L. I should say, sorry, I should be saying L here.


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[Assistant] It's got one basis vector, 1, 1, 1, 1. And that will always happen with a, with a,


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[Assistant] With the, the graph setup that I've created. Okay, so that's the first fact.


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[Assistant] That this positive semi-definite matrix L has


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[Assistant] C, C, C, C, the one-dimensional eigenspace. Or 1, 1, 1, 1 is a typical eigenvector. OK.


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[Assistant] Now, uh, back to graph clustering.


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[Assistant] The idea of graph clustering is to look at the


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[Assistant] Fiedler eigenvector, this is called x2.


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[Assistant] Next eigenvector is the, is the eigenvector


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[Assistant] The smallest positive eigenvalue for lambda min.


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[Assistant] The smallest eigenvalue and its eigenvector, this is called the Fiedler vector, named after the Czech mathematician.


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[Assistant] A great, a great man in linear algebra. And he studied this factor, this situation. So everybody who knows about


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[Assistant] The graph Laplacian is aware that its first eigenvalue is 0 and that the next eigenvalue is important. Yeah.


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[Assistant] Yeah, that's a good question. So why the word, the name Laplacian?


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[Assistant] The familiar thing, so it connects to Laplace's finite difference equation, because we're talking about matrices here and not derivative, not functions. Uh, so why the word Laplacian?


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[Assistant] So if I have a regular, if my graph is composed of, uh,


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[Assistant] So there's a graph with 25 nodes.


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[Assistant] And, uh, 4 times 5, 20, about 40. This is probably has about 40 edges.


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[Assistant] And of course, I can construct its, uh, graph, all those four matrices for it. It's, uh, incidence matrix, it's degree matrix, so the degree will be four and all these,


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[Assistant] Inside points, the degree will be 3 at these boundary points. The degree will be 2 at these corner points. But the, what will the matrix L look like? So, so, what is L?


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[Assistant] And that will tell you why it has this name Laplacian. So the matrix L,


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[Assistant] We'll have the degree 4, right, we'll be on the diagonal, that's coming from D. The other


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[Assistant] The minus ones that come from B, the adjacency matrix will be associated with those nodes.


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[Assistant] And otherwise all zeroes. So this is a typical row of L. This is a typical row of L centered at that node. So maybe that's node number 5, 10, 13. That's 13 out of 25.


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[Assistant] That would, would show you this. And the, sorry, those are minus 1s. Minus 1s.


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[Assistant] That's the model problem for when the graph is a grid, square grid.


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[Assistant] And you associate that with Laplace's equation. So this is the, this is the reason that the, that Laplace, why, why Laplace gets in it. Uh, because Laplace's equation, the differential equation is second derivative with respect to x squared and the second derivative with respect to y squared is 0. And what we have here is l u equals 0.


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[Assistant] Discrete Laplacian, the vector Laplacian, the graph Laplacian.


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[Assistant] Where the second x derivative is replaced by minus 1, 2, minus 1. And the second y derivative is replaced by minus 1, 2, minus 1. Second differences in the x and the y direction.


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[Assistant] Now, to finish, I have to tell you what the, what clusters


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[Assistant] How do you decide the clusters from L? How does L propose two clusters, the A's and the B's? And here's the answer. They come from this eigenvector, the Fiedler eigenvector. You look at that eigenvector.


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[Assistant] It's got some positive and some negative components. The components with positive numbers.


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[Assistant] Of this eigenvector, so the positive, the positive


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[Assistant] Of, of, sorry, of this, yeaah, of this eigenvector.


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[Assistant] And there are negative components of this eigenvector. And those are the two clusters.


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[Assistant] So, so it's, the cluster is, the two clusters are decided by the eigenvector.


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[Assistant] By the sines, plus or minus sines of the components.


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[Assistant] Plus signs go in one and the minus signs go in another. And you have to experiment to see that that would succeed. I don't know what it would do on this, actually.


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[Assistant] Because that's hardly splits up into two. I suppose maybe the split is along a line like that or something. I don't know what clustering. This is not a graph that is naturally clustered.


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[Assistant] Uh, but you could still do k-means on it. You could still do, uh, spectral clustering.


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[Assistant] And you would find this eigenvector. Now what's the point about this eigenvector? I'll finish in one moment. What do we know about that eigenvector as compared to that one?


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[Assistant] So here was an eigenvector all 1's. Let me just make it all 1. 1, 1, 1, 1.


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[Assistant] In that picture, it's 25, 1.


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[Assistant] Here's the next eigenvector up. And what's the relation between those two eigenvectors of L? They are orthogonal. These are eigenvectors of a symmetric matrix. So they're orthogonal. So that means to be orthogonal to this guy means that your components add to 0, right? A vector is orthogonal to all 1's.


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[Assistant] So we have a bunch of positive components and a bunch of negative components. They have the same sum.


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[Assistant] Because the dot product with that is 0. And those two components, those two sets of components are your two, tell you the two clusters in spectral clustering. So it's a pretty nifty algorithm. It does ask you to compute.


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[Assistant] An eigenvector, and, uh, that of course takes time. And then there's a third more direct, uh, algorithm to, uh, to do this optimization problem. Well, actually there are many.


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[Assistant] This is an important problem, so there are many proposed algorithms.


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[Assistant] Good. Okay, I'm closing up. Final question? Yeaah.


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[Assistant] Well, certainly for k-means. Now if I had to do three clusters with Fiedler,


[User] Please transcribe this text

[Assistant] I would look at the first three eigenvectors, and, well, the first one would be nothing, and I'd look at the next two, and that would be pretty successful.


[User] Please transcribe this text

[Assistant] If I wanted six clusters, it probably would fall off in the quality of the clustering.


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[Assistant] Yeah, but that, that certainly I would look at the lowest six eigenvectors and, uh, get somewhere. Yeah.


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[Assistant] Right, so, uh, okay, so that's, uh,


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[Assistant] A topic, an important topic, a sort of standard topic in, uh, applied graph theory.


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[Assistant] Okay, so, uh, say you're Wednesday. I'm hoping, I'm hoping on Wednesday, so Professor Edelman has told me a new and optimal way to look at the, the, uh, problem of backpropagation. You remember backpropagation? If you remember the lecture on it, you don't,


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[Assistant] You don't want to remember the lecture on it. It's a tricky, messy thing to explain. But he says,


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[Assistant] If I explain it using Julia in linear algebra, it's clear. So we'll give him a chance on Wednesday to show that revolutionary approach to the explanation of backpropagation.


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[Assistant] I hope for, I told him he could have half an hour and projects would take some time. I hope, now we've had two with wild applause, so I hope we get a couple more in our last class.


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[Assistant] Okay, see you Wednesday and, uh, if you bring, well, if you have projects ready,


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[Assistant] Send them to me online and maybe a printout as well. Uhm, that would be terrific. If you don't have them ready by the hour, they can go, the envelope outside my office would receive them. Good. So I'll see you Wednesday for the final class.


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[Assistant] They have to put it all to the line today. Use your muscles!


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[Assistant] But Count Alaric hadn't even looked at the mighty sun. He was mesmerized with the lady's beauty.


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[Assistant] Her pale skin and bright eyes were all he could see. He instantly fell in love with her. Uh, Miss, are you lost? What's your name?


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[Assistant] Count Alaric knew he had to help her. There was no way he was going to leave her alone in the field. Miss, please come with me to the castle. You will be taken good care of.


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[Assistant] And meanwhile, I will try to find your family.


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[Assistant] Count Alaric was so happy to hear those words, but he couldn't take his gaze off the lady. She seemed to be looking at him, but her eyes were lost, as if she was thinking of something else. Maybe she is scared. I must protect her.


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[Assistant] They rode to the castle. Count Alaric commanded his servants to take special care of his guest. He soon realized that he has to name the beautiful lady. He immediately named her Catherine, for he could not think of a name more suitable.


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[Assistant] She seemed to be thinking of something else. Maybe she is tired.


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[Assistant] I must look after her. Days, weeks, months passed, but there was no news of Catherine's family.


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[Assistant] Nobody even in the neighboring kingdoms had heard of her. The Count desperately wanted to help her. He couldn't bear the look in her eyes. Like there is something she is missing. He wanted to make her happy. What if I ask her to marry me? Will she say yes? I must tell her that I love her. I have everything to keep her happy. The Count immediately asked Catherine to marry him. Catherine smiled.


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[Assistant] After all, the Count was marrying the love of his life. At least a thousand people attended the wedding. He could see the awe on all of their faces.


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[Assistant] The Count smiled, but one look at the Countess and his heart sank a little. My dear, aren't you happy?


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[Assistant] But, there was that look in her eyes again.


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[Assistant] Count Alaric had run out of excuses to comfort himself.


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[Assistant] The kingdom could not have had a better Countess than Catherine. Everybody loved her.


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[Assistant] He knew she didn't wholly belong to him. Each year, the Count threw a ball for his people. Everybody danced their hearts out. Even those who didn't know how to dance. But the Countess was quiet. She was neither dancing nor smiling.


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[Assistant] The look in her eyes killed the count each day.


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[Assistant] He tried asking her several times, but she always held him tight, smiled and said,


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[Assistant] Though she looked at him, the Count knew she was thinking of something else.


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[Assistant] Then, one night, as the Count entered his room, he was surprised to see that Catherine was dancing. Dear, why don't you ever dance with me?


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[Assistant] Oh, my sweetheart. But you were dancing just now when I entered the room. Don't you remember?


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[Assistant] The Count thought of surprising his beloved Countess.


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[Assistant] A night before the anniversary, he rode up to the very field they first met in. Catherine will be so happy! Wait! What is that?


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[Assistant] I have never heard such a beautiful tune in my life!


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[Assistant] He was relieved to see that the Countess was sleeping peacefully in their bedroom.


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[Assistant] Wait, I am not wrong. It was her. Why is she lying to me? She looks so happy there. What do I do now? Only one person can help me. Magda.


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[Assistant] The Count trusted Magda. She knew all the secrets to this world. After traveling for two whole days, he reached a small hut deep inside the jungle.


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[Assistant] It's the Countess, Magda. I need your help. The Count narrated the whole story to Magda.


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[Assistant] That's enough. I will follow her today and show her how much I love her. My love is perfect and I will prove it. That's it. Catherine, it's me, your husband. I have come to take you away. Come with me.


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[Assistant] Don't you remember my love? Come with me!


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[Assistant] Catherine realized that the count was too strong for her. She smiled brightly.


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[Assistant] The Count was happy. I knew my love was perfect. Catherine, are you okay my love? But the Countess didn't speak. She crouched and moaned.


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[Assistant] It killed the count to see his lady unhappy. Catherine? If you stay with me, will you remember your people and be sad?


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[Assistant] And if you went back to your people, would you remember me?


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[Assistant] And he knew she meant it, for her eyes were looking for him and nothing else.


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[Assistant] It was Count Alric's faith and pure love that had brought his lady to him.


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[Assistant] To answer that question, we turn to the written accounts of that time. There are no surviving written accounts from Spartans themselves, as it was forbidden for Spartans to keep records. So we have to rely on those of non-Spartan ancient historians, like Herodotus, Thucydides, and Plutarch.


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[Assistant] Every Spartan, boy or girl, was expected to be physically strong


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[Assistant] This mindset probably made it easier for the Spartan boys, who upon turning seven were sent to the Agogue, a place with one main purpose, to turn a boy into a Spartan warrior through 13 years of relentless, harsh, and often brutal training.


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[Assistant] The Spartans prized physical perfection above all else, and so the students spent a great deal of their time learning how to fight.


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[Assistant] In order to better prepare the boys for the conditions of war, the boys were poorly fed, sometimes even going days without eating.


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[Assistant] During the annual Contest of Endurance in a religious ritual known as the Diomastigosus, teenage boys were whipped in front of an altar at the sanctuary of Artemis Orthia.


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[Assistant] Fortunately, not everything was as brutal as that. Young Spartans were also taught how to read, write, and dance, which taught them graceful control of their movements and helped them in combat.


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[Assistant] Spartan girls lived at home with their mothers as they attended school. Their curriculum included the arts, music, dance, reading, and writing.


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[Assistant] And to stay in peak physical condition, they learned a variety of sports, such as discus, javelin, and horseback riding.


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[Assistant] In Sparta, it was believed that only strong and capable women could bear children that would one day become strong and capable warriors.


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[Assistant] To die for their city-state was seen as the completion of one's duty to Sparta. Upon their death, only men who died in battle and women who died in childbirth were given tombstones. In the eyes of their countrymen, both died so that Sparta could live.


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[Assistant] Yes, that's me. And you must be Thomas from England, right?


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[Assistant] I'm sure you'll fit in nicely. After all, you come highly recommended. Your articles are really good. Thank you.


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[Assistant] Oh, here's Ella. Thomas, this is Ella, the editor in chief of the magazine.


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[Assistant] Let me show you to your office. It's located at the end of the hall.


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[Assistant] Ella insisted that we set you up with all this state of the art equipment.


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[Assistant] From here, you can communicate with any department and get all the information you need.


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[Assistant] Well, here you'll have six people in your team. I'll introduce you to them after lunch.


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[Assistant] Well, there's a meeting every Monday, as well as a meetup with various heads of department on Thursday afternoons. Just so we know what we're doing.


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[Assistant] Other than that, how you organize your time is up to you.


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[Assistant] It's time for lunch now. Let me take you to a nice place. We'll get a chance to get better acquainted with each other.


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[Assistant] No, thank you. I'd like the tuna with a green salad. And for you, sir.


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[Assistant] Well, I know some great musicians. And I also have some contacts in the theater and dance.


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[Assistant] Maybe we could go to a show, and after that you could talk to the actors.


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[Assistant] Walking isn't enough, Thomas. Do you do anything to keep fit?


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[Assistant] Bicycling is permitted on all main and local streets throughout the city.


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[Assistant] We call it apartment here. You can try jogging or running. You know, I go running every morning in Central Park.


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[Assistant] Trainers? You mean sneakers? You can buy some.


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[Assistant] Sure, there's one across the street. I'll come by your place tomorrow morning.


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[Assistant] That's too late, Thomas. Let's make it 7.15.


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[Assistant] It's the restaurants you go to. Why don't you come over to my place after work? I could make you something a little healthier. I'm a very good cook.


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[Assistant] You mean a pharmacy? Yes, it's a three minute walk from here, on your right side.


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[Assistant] What differences have you noticed so far between US and UK, Thomas?


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[Assistant] Thanks for watching, and be sure to subscribe to our YouTube channel for more videos like this.


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[Assistant] Lesson 7 – Bats. First listen and then answer the following question. In what way does echolocation in bats play an utilitarian role?


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[Assistant] Not all sounds made by animals serve as language, and we have only to turn to that extraordinary discovery of echolocation in bats to see a case in which the voice plays a strictly utilitarian role


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[Assistant] Everyone knows that if he shouts in the vicinity of a wall or a mountainside, an echo will come back


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[Assistant] The further off this solid obstruction, the longer time will elapse for the return of the echo.


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[Assistant] So was born the echo-sounding apparatus, now in general use in ships


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[Assistant] Every solid object will reflect a sound, varying according to the size and nature of the object.


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[Assistant] A shoal of fish will do this. So it is a comparatively simple step from locating the sea bottom to locating a shoal of fish


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[Assistant] With experience, and with improved apparatus, it is now possible not only to locate a shoal but to tell if it is herring, cod, or other well-known fish, by the pattern of its echo


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[Assistant] It has been found that certain bats emit squeaks and by receiving the echoes, they can locate and steer clear of obstacles, or locate flying insects on which they feed


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[Assistant] This echolocation in bats is often compared with radar, the principle of which is similar


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[Assistant] So the elements are obviously a nice, silky smooth celeriac puree.


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[Assistant] I run kitchen garden program at a school in Ballarat. So what we'll do is we'll take this spinach back to the kitchen and we can make some beautiful toasties out of these. Just pick some off, you can eat it just like that. What do you think?


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[Assistant] Some of these kids have got pretty difficult backgrounds.


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[Assistant] But the student cafe that we run, it's so rewarding for me to see the kids grow in confidence. That's it. Just try and get it all the way. Yeah. Yeah, it's awesome. It's pretty special.


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[Assistant] How good does that look? Would you be happy with that in a restaurant?


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[Assistant] What inspires my cooking is good, honest food, beautiful produce, nothing too fancy.


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[Assistant] You don't have to muck around with it too much. You can just add some flavours and just let the ingredients speak for themselves.


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[Assistant] What do you do, mate? I run the kitchen garden program at a school in Ballarat.


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[Assistant] It's really just a small dream at the moment, but I've got a really


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[Assistant] I know it might sound crazy, but uhm, I was in New York a couple of years ago and there's a little cafe on the Lower East Side and they just do cheesy sandwiches.


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[Assistant] And that's where I thought, geez, I could model that idea and use fresh Ballarat produce. He's my kind of man! Who doesn't love a toastie? I mean, anything's possible. Tell us, what have you cooked? I have cooked pork belly.


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[Assistant] But I really crave the creativity that you get from making food. When I cook, I really feel at peace.


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[Assistant] For the second time, uh, one sister and two sisters.


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[Assistant] I'm saying that this is a scallop dish, but there's actually no scallops in it.


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[Assistant] Kyle. Um, quicker than I would have expected.


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[Assistant] I think that I've just been prodded by my fiancé for a little while and uhm, I think I'm ready.


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[Assistant] King oyster mushroom scallops with edamame puree, tamarind and apple gel around it.


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[Assistant] Uhm, I love vegetables. I just think that they need to be hered a little bit more. You know, they can look beautiful and it's got flavour. And I think that you don't need a big piece of protein or something in the middle.


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[Assistant] Look after the little fawns while Mother Deer was out and help the rabbit cross the river.


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[Assistant] Robbie's home was a big and strong tree, which stood right in the center of the forest.


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[Assistant] It would listen to the tune intently and be happy to have Robbie play it every day.


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[Assistant] Phew. This will take some time. Robbie soon understood what was going on. He quickly hopped down.


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[Assistant] Really? And why is that? Listen.


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[Assistant] And you don't own this tree. Don't waste my time. Robbie was a smart monkey. He decided to scare the woodcutter away.


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[Assistant] Robbie climbed the tree and went straight to the top.


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[Assistant] Just as Robbie was laughing at the woodcutter, the tree came alive! Robbie!


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[Assistant] Robbie ran to call his other friends in the forest.


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[Assistant] Elephant caught a pineapple in his trunk and took a bite while Robbie simply opened his mouth to eat a pear. The animals ate with all their hearts. No need to hunt for fresh fruits anymore. It was true.


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[Assistant] This is selfish, Robbie. There are enough fruits for everyone. You must share.


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[Assistant] Robbie rang the bell, but since all the fruits had already rained down, naturally nothing happened.


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[Assistant] The animals were sad, but nobody doubted the monkey, as they were leaving.


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[Assistant] As Robbie saw his friends leaving, he realized his mistake and began to cry.


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[Assistant] Robbie never used the bell for his own selfish needs again. The end.


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[Assistant] Once in a town not far away from the city lived Coco. He was a smart little boy.


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[Assistant] Coco's father owned a big shop of hats right in the center of the city. Although Coco was only a child,


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[Assistant] His father would often leave him in charge in his absence. Coco was a good salesperson, and he was also good in maths.


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[Assistant] He often made good sales and made a decent profit. Coco's father too admired his skill, but he was also worried about his son.


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[Assistant] Dear, Coco told me about the prophet made today. He's doing well, isn't he?


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[Assistant] What arrogance! He is good at sales, that's all. You worry too much.


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[Assistant] He wanted his son to think before he acts. The star heard his wishes. That night, Coco had a dream.


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[Assistant] He hurriedly placed it on his head again and took it off. There it was, another gold coin.


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[Assistant] Coco very well remembered what the fairy had said to him.


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[Assistant] Coco carefully kept his cap in the closet and went ahead with his daily activities. He felt very happy.


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[Assistant] But he constantly kept thinking about the cap in the closet. No matter what he did, he could not take it off his mind.


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[Assistant] Without thinking about the result, Coco went on taking out money from the cap. And soon there was a heap of gold.


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[Assistant] But Coco hadn't realized one thing. Huh? Oh no! It had taken years for Coco to grow tall, and he traded it away in minutes.


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[Assistant] When he stood up, he realized that he was back in his old tall body. Just then, the doorbell rang. He ran to open it.


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[Assistant] Coco held his father tight and promised to never act without thinking about the future. The end.


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[Assistant] When we see the world, our eyes send around 60 images or flashes per second to the brain. Our brain then combines these images, helping us see like this.


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[Assistant] Hence, when its brain combines 250 images, one second feels much longer. Making the fly see in slow motion and allowing it to react much quicker than us.


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[Assistant] Now, when we move our hand to swat a sitting fly, our action seems like a super quick single action to us. However,


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[Assistant] Owing to the fly's ability to see our action in slow motion, it gets enough time to fly away, even as we are just in the middle of the action.


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[Assistant] How is coffee decaffeinated? Using a vacuum cleaner.


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[Assistant] Oh. Nah. Coffee contains caffeine. Caffeine boosts our energy and keeps us focused for a short duration.


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[Assistant] However, caffeine can also cause headaches, nervousness, etc. Hence, decaffeinated coffee is a very good alternative. Now, there are various methods to decaffeinate coffee. One of them is solvent based method. In this, green coffee beans are first soaked in hot water for several hours.


[User] Please transcribe this text

[Assistant] Because they wear anti-freezing socks. Nah. Penguins live in very cold climates and walk on ice. Hence, penguins have developed certain adaptations to avoid losing body heat and to protect their feet from freezing. One of the adaptations includes a mechanism called countercurrent heat exchange. What is that?


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[Assistant] Now, when warm blood flows through the arteries to the feet, much of the heat from the warm blood gets transferred to the cold blood in veins, which is carrying blood away from the feet.


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[Assistant] So, do they use a mini vacuum cleaner to absorb oxygen from water? No. To absorb oxygen from water, fish use special organs called gills. Gills are full of blood vessels. Also, the walls of the gills and blood vessels are very thin.


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[Assistant] Now, during breathing, fish take in water through their mouth and forcefully push it through their gills. When the water moves through the gills, the dissolved oxygen from the water passes through the thin walls of gills and blood vessels and enters the blood.


[User] Please transcribe this text

[Assistant] Apart from this, the waste carbon dioxide present in the blood passes into the water, thus helping fish to breathe underwater. Eventually, the carbon dioxide-rich water is given out from gills.


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[Assistant] So, imagine you're cast away on the MasterChef Desert Island. You can only cook one thing to eat every day for the rest of your life. That's what we want you to cook us today. It's your Desert Island dish.


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[Assistant] I had no idea it was going to look as, well like this. It calls out for you to grab a chop and dredge it through everything and eat it. And I think that's really exciting. There you go.


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[Assistant] Tasting the dish, I can absolutely see why you picked this for this challenge. There's real potential there.


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[Assistant] The colour of those prawn tails, with the chilli and the tomato and the broth, bam bam bam. Could you eat this every day? I could.


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[Assistant] We asked you to bring us a dish that you loved, a dish that you could eat every day for the rest of your life. And four of you did just that. If I call your name, please step forward.


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[Assistant] Hey, I haven't seen you in a while. Where were you?


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[Assistant] Really? That's so interesting! What did you do there other than studying?


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[Assistant] Wow! Did you have any problems during your stay there?


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[Assistant] Well, the first job that I can remember was in high school. I had a part-time job working at a fast food restaurant. Really? Yeaah. I started out as a cashier and mostly on the weekends. And after a couple of years I got to be manager. So all the way through university I worked there.


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[Assistant] Yes, a lot of my friends were working there, so that made it a lot of fun. But when I graduated from university,


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[Assistant] I really wanted to get a job in my field so I got a job as an economist after that. An economist?


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[Assistant] Yeah, I worked as an economist for a little over two years, and uh, I didn't really like that job. It was so boring.


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[Assistant] On top of that, I didn't get along with my boss. He was always asking me to work overtime.


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[Assistant] I didn't really like the atmosphere there, so I quit. What did you do after that? After that, I wasn't sure what to do. I went back to Phoenix and stayed with my parents for awhile.


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[Assistant] I only got the job because I was broke and needed a little dough to live on before moving on.


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[Assistant] I thought it was hilarious that this grocery store maybe goes through some lengthy training and orientation.


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[Assistant] So I could stock dairy and do super basic customer service. Was it full time? Yeah, it was full time.


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[Assistant] In the meantime, I went back to university and I got my master's degree in English.


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[Assistant] I read in a magazine about a job teaching English overseas in Thailand.


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[Assistant] Uhm, yeaah. That was a very interesting job.


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[Assistant] I mean, it was my first time overseas and it was my first time teaching.


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[Assistant] But I just had a one year contract and certain aspects of living in Thailand were difficult.


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[Assistant] So after my contract was finished, I came back to the US and continued to teach English here.


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[Assistant] I needed to try and fail to figure out what I'm good at and what I like. The more experiences I was exposed to, the more I learned.


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[Assistant] Sam, have you heard Ron might be fired soon? No, I had no idea. I wonder what happened. Have you ever worked with him?


[User] Please transcribe this text

[Assistant] Yes, I worked with him last year, and I've heard stories about him for years.


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[Assistant] I've never worked with him directly, but I know people that have.


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[Assistant] She had this idea for a project and she brought it up at a meeting and he liked it. He made her do all the work planning it. Then when the project actually got started, Martha was left out of it and her name was not mentioned anywhere.


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[Assistant] I heard the project won an award because it was brilliant. That's right.


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[Assistant] Martha saw red when she heard about the award, because she didn't get the credit she deserved.


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[Assistant] But she couldn't do anything. Her hands were tied.


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[Assistant] Yeah, Ron would have fired her if she had dared to report him. It must be a really bad feeling to have your ideas stolen. How did you find working with him? It was a nightmare, because he was very tough.


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[Assistant] Nobody dared to contradict him for fear they might lose their job. People were genuinely afraid of him. I heard many people had a hard time working with him. Were you on good terms with him?


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[Assistant] Yes, I did my best to stay in his good books because I needed this job. And I was lucky I didn't have that much contact with him myself. They're doing a full investigation.


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[Assistant] So I suppose a lot of these stories are going to come to light. I hope so. I really hope he's not coming back.


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[Assistant] We know about our universe's past. The Big Bang Theory predicts that all matter, time, and space began in an incredibly tiny, compact state about 14 billion years ago.


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[Assistant] Cosmologists have three possible answers for this question, called the big freeze, the big rip, and the big crunch.


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[Assistant] To understand these three scenarios, imagine two objects representing galaxies. A short, tight rubber band is holding them together. That's the attractive force of gravity.


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[Assistant] Copy the system over and over again, and you have something approximating the real universe. The outcome of the battle between these two opposing forces determines how the end of the universe will play out.


[User] Please transcribe this text

[Assistant] The big freeze scenario is what happens if the force pulling the objects apart is just strong enough to stretch the rubber band until it loses its elasticity. The expansion wouldn't be able to accelerate anymore, but the universe would keep getting bigger. Clusters of galaxies would separate.


[User] Please transcribe this text

[Assistant] The light they emit would be redshifted to long wavelengths with very low, faint energies, and the gas emanating from them would be too thin to create new stars.


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[Assistant] The universe would become darker and colder, approaching a frozen state also known as the Big Chill or the Heat Death of the universe.


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[Assistant] What if the repulsive force is so strong that it stretches the rubber band past its elastic limit?


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[Assistant] As a result, the matter that makes up stars breaks into tiny pieces. Even atoms and subatomic particles will be destroyed. That's the Big Rip.


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[Assistant] That corresponds to a possible future in which the force of gravity brings the universe's expansion to a halt and then reverses it.


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[Assistant] Galaxies would start rushing towards each other, and as they clumped together, their gravitational pull would get even stronger.


[User] Please transcribe this text

[Assistant] Stars too would hurdle together and collide. Temperatures would rise as space would get tighter and tighter. The size of the universe would plummet until everything compressed into such a small space that even atoms and subatomic particles would have to crunch together.


[User] Please transcribe this text

[Assistant] Could this tiny point of matter explode in another big bang? Could the universe expand and contract over and over again, repeating its entire history?


[User] Please transcribe this text

[Assistant] The theory describing such a universe is known as the Big Bounce. In fact, there's no way to tell how many bounces could have already happened, or how many might happen in the future.


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[Assistant] Each bounce would wipe away any record of the universe's previous history.


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[Assistant] Which one of these scenarios will be the real one? The answer depends on the exact shape of the universe, the amount of dark energy it holds, and changes in its expansion rate. As of now, our observation suggests that we're headed for a big freeze.


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[Assistant] But the good news is that we've probably got about 10 to the 100th power years before the chill sets in. So don't start stocking up on mittens just yet.


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[Assistant] Anxious about how to spend your time between now and the end of the universe? Check out our video on time management to help you tackle your to-dos.


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[Assistant] Magic Treehouse Merlin Missions Book Number 25, Shadow of the Shark. This is Mary Pope Osborne.


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[Assistant] Did you see anything amazing? Annie asked Jack.


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[Assistant] They were standing on the warm sunny shore of Frog Creek Lake, packing up their new swimming gear. Flippers, masks, snorkels, and red life vests. Not really, said Jack, weeds and rocks. Same here, said Annie. How was your new mask?


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[Assistant] Cool, said Jack as he put his glasses back on. It didn't leak or fog up at all.


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[Assistant] Jack picked up the waterproof swim bag with all their gear and they headed to the bike rack.


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[Assistant] I'd love to snorkel around a coral reef someday, he said. Me too, said Annie.


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[Assistant] Jack strapped the bulky bag to the rack over his back wheel.


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[Assistant] He and Annie pulled on their helmets and pedaled out of the lake parking lot.


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[Assistant] Remember when Randy and Jenny snorkeled around a coral reef last spring? Jack said.


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[Assistant] Oh right, they went to a place called Cozumel with their parents, Annie said. They did all kinds of cool stuff.


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[Assistant] Hey, should we call them? They said they'd be back from their aunt's house by two. Sure, said Jack. Hold on, stop, said Annie.


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[Assistant] Jack and Annie pull their bikes over to the side of the quiet road.


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[Assistant] Annie reached into her handlebar bag and took out the old cell phone their dad had given them when he had gotten the newer model. Hey, we have a text from Randy. She read the message.


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[Assistant] Darn, he says they're not coming back until tomorrow.


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[Assistant] That's okay, let's just go home then, said Jack.


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[Assistant] He started pedaling again and turned at the corner. He started up their street heading for their house. Jack, stop. Annie called from behind him. Jack stopped his bike and looked back. Annie was speeding after him. What's wrong? He called. She screeched to a halt. We have a message from Teddy.


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[Assistant] She cried, waving a yellow piece of paper.


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[Assistant] When I put the phone away, I noticed this in my handlebar bag. How did it get there? said Jack. I don't know said Annie.


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[Assistant] Teddy must have put it there when we were snorkeling. Or maybe when my bike was in our yard. Or parked at the library. Or maybe-


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[Assistant] Okay, okay, just read it to me, said Jack. Annie read breathlessly. Jack and Annie.


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[Assistant] Please meet me at the tree house as soon as possible. Teddy. Let's go, said Jack.