Thank you for your nice presentation and it's really a pleasure to be here. Good afternoon to everybody. Good morning from those that are on this side of the day. And thank you for your presentation. It's a challenging situation. I am presenting here something that is much slower than what I've been hearing up to now. So what I will be presenting you is the application of the wonderful presentation that the previous speaker gave us. And it was an interesting talk by Julia who did present the basic points of everything that is fast. Well, we are here in a word that is a slightly slower, but not so slow. But I don't want to dwell in too much of introduction. So the mighty power of photosynthesis is because exactly like any well-being is based on the use of energy resources. Earth is also based on the use of energy resources. The energy is sun. The car is the planet. And of course, engine are plants, the photosynthetic organisms. And photosynthesis has shaped life and the structure of our planet. Since the beginning of the formation of the planet Earth, we know that some microorganisms able to take advantage of solar radiation appeared. And initially Earth was not populated much and was definitely not an oxygenic planet. But then evolution brought in oxygenic species, the so-called oxygenic photosynthetic bacteria that started poisoning the atmosphere, shifting from a reducing atmosphere to an oxygenic one. And actually if you can see this curve here at a certain point, at a certain point, the evolution on Earth of this species, the appearing of new and new photosynthetic species brought us to the Cambrian explosion, where the oxygen level reached roughly 30% of the overall composition of atmosphere. And at that time, the amount of oxygen and the amount, the dimension of animal on Earth, where it was so big that you can see is colopander, which is a small box that's now populating Earth. And they are mostly, at the most five centimeters, were longer than two meters. And dragonfly, you can hold them in a hand and not completely cover them. Well, you know how small dragonfly are today. So, yes, photosynthesis is also responsible, is responsible for shaping the Earth, is also responsible of how we, how to say, how we survive consuming energy, because roughly three to four hundred million years ago, a large number of trees and plants and also animals landed on the floor of, oceans. And then in time, we're covered by sand and silt. And at the end, due to pressure, high temperature, we got oil and natural gases. These two things are directly bound to photosynthesis. And of course, we all know that, and we all know that there is a need, absolutely a need for substituting fossil fuels. And photosynthesis is also involved in this idea of substituting fossil fuels. So, just by quoting Steven Gust, I would say that photosynthesis is arguably the most important biological process on Earth. It's so because the amount of energy that is played in this process, it's humongous. So, theoretical potential of solar power is given by the integral of the flux over the surface of the Earth. And if you just make this nice calculation, you end up with roughly 90 terawatts. Now, this represents the amount, even in an hour, this represents roughly the amount of energy that was used in the entire year of 2001 from all sorts of combined energy. So we have here a powerful energy source and possibly a system to convert it in other forms of energy that would be useful for us. What we need is to understand the mechanism and how to do it. But this will be the second part of the talk. What I want to do now is just introducing you to photosynthesis through its applications by starting with presenting a few molecular aspects of photosynthesis. And these are mostly based on the use of pigments. Pigments are the most important players in photosynthesis. Very important are these pigments based on these two tetrapyros, the chlorine and the bacterial chlorine. The difference by simply one double bond in one of the pyrorines. And these two molecules are the heart of the photosynthetical photochemical machinery that converts solar light into free energy. And this heart is specially formed by the chlorophylls, which are an extension of the chlorins that we saw in the previous transparency. There is some other substituents on the external part of the ring and the Fittil group here on the bottom where bound to the de-cycle of the de-porphyry. And so the Fittil chain is absolutely important because it helps the system to introduce itself inside the proteins. And you will see this in a moment. I just wanted to show you that there is a second here in cycle B. There is a double bond, which can be present or not present. And again, this is the difference between chlorophyll and bacterial chlorophyll. While insisting so much on this molecule, well, because if you look at the absorption of this molecule, you can see that it spans from the entire spectrum, a visible spectrum, starting from the low wavelengths, around 400 nanometers to the high wavelengths. And it spans from roughly 680 nanometers, which is the reddish color, and ends up to 800, 812. Now, this is very, very important because the most important part of photosynthesis is the light goes from 600 to 900 nanometers. And we'll see this little later. On the top of this absorption spectra is the absorption, the flux of photons coming from the sun and eventually being absorbed on earth by photosynthetic corgis. And you can see that most of the absorption of the chlorophylls fall in the red near IR part of the spectrum. There are many different chlorophylls. But together with chlorophylls, we have carotenoids. Now carotenoids fill a hole, which, if we can go back to this transparency, is the hole between 500 and 600 nanometers. And carotenoids are fully colored molecules that are also inserted within the proteins, as we will see in a few minutes. And differently from the chlorophylls, these molecules do not play a central role in the conversion, but do play a role in harvesting light. So we just saw a few pigments, but these pigments that we saw were presented as single pigments in solution, typically organic solution. What happens when they are inserted in biological systems? Well, the differences are striking. Most of the system have their maximum absorption shifted toward the red. And indeed, you can actually reach in some specific microorganism absorption of the bacterial chlorophyll within the protein that reach 100,000, 1100 nanometers. This offers your coverage of the full spectrum from 400 to 1200 nanometers. It's so important because it covers all the visible and infrared light at the most, the largest amount of the photos that reaches Earth. Well, this is just another view of, say, of viewing things and skipping it. So very quickly, who does photosynthesis on Earth? Well, there are, of course, higher and lower plants. We all know the green plants that are surrounding us. But then there are the algae and the bacteria. I will mostly concentrate myself on the bacteria because it's the simplest. And in 30 hours, we cannot have a complete course on photosynthesis. So bacteria are divided into two classes, the one identified by a blue dot and those by a red dot. The difference, the main difference is that the blue dots are typically oxygenic species. So photosynthetic microorganisms that do photosynthesis, oxygenic. So they are appeared later on the planet. And the red dots identify species that do an oxygenic photosynthesis. So the photosynthesis that appeared on Earth more than 3.7 billion years ago. They are all negative, gram-negative bacteria, although there is one gram positive, but none of them is pathogen. So if you look the diversity of the photosynthetic organism, it's very striking that there is only a single mechanism that is able to convert the solar light into other forms of energy. And that is the photochemical mechanism. But of course, this may come as a surprise, but it's not since they all share the same evolutionary path. And the evolutionary path is the best way of converting solar energy into energy, viable for us and for other inhabitants of planet Earth. So I'm just will focus on one single guy. This will be our host, actually our guest, the photosynthetic bacterium rodubactose ferrarius. It's an important bacterium because it's been a model for many, many years, model of photosynthesis for many, many years. And I just wanted to show how it's organized. Biology is important to see how things work and how things are made up. So you can see here an external membrane, an outer membrane that divides the growing milieu from the internal of the cell. Within immediately below there is this internal membrane. In this internal membrane, there are this invagination of the membrane. These are not untouched. They are attached to the upper part of the cell, so they seem to be floating in the cell, but they are not. And these are called interacetoplasmic membrane. Within this interacetoplasmic membrane, they are located the most, actually the incomplete photosynthetic apparatus of the photosynthetic bacterium. And if you take the bacterium and you squeeze it under high pressure and then release it at atmospheric pressure, the bacterium explodes. And those interacetoplasmic membrane break up and then seal again, forming the circular vesicles that are called chromatophores. And the sealed vesicles are formed by four types of protein, five types of protein at the most. So the antenna proteins here shown in green, the second kind of antenna showed is red rings around the central bacteria reaction center, which is this molecule here, protein here in bluet. The BC1, so the counterpart for the establishment of the delta pH across the membrane. And finally the ATPase. Now the ATPase is the important protein that uses the energy converted by the reaction center to synthesize ATP, adenosine triphosphate, which is the exchange money for energy in biological system. If you have ATP, then you can do almost any reaction you can think in a biological system. Now if you open up the vesicle and make it flat, you can see a representation, a simpler representation with the reaction center sitting here. LAC1, which is here represented as a red and shown here as a circular surrounding the reaction center. And then this small molecules that are called LAC2 where LCH says for light harvesting. So this part harvests light and the reaction center instead converts it from photons to charge separated state. We will see this in very, very soon. Now this is the center of the protein portion. And these two are two different enzymes, which are responsible of the conversion, the absorption of the photons and its conversion in charge separated state. On the left hand side, you, you're seeing one that is the first one that was crystallized. It's from a bacteria called blasterchloris viridis. On the left, on the right hand side, you see the one from Rhodobacter spheroidus, our guest, I'd say. And the way it works, light is absorbed by light coming from directly from the sun or from excitation transfer from the antennas arrive to this protein. The system works by circulating electrons within its internal part and then protons get transferred from the inner part. So from the Periplus out on the cytoplasm and can will be used then to synthesize ATP. I added the transparency because I saw that Julia was using so many Nobel prizes in her talk. And we also have our, our, and that's crystallization of the first photosynthetic protein that was awarded to. That is an offer Huber and Artwood Michael in 1988 for crystallizing the first protein on the left, the one, the most complicated one here, the one on the left. So we know we have an hour Nobel Prize. We have very interesting thing because it was showing that they showed for the first time that you can actually crystallize crystallize membrane protein, integral membrane protein. And that's why they won the Nobel Prize, but their work was extremely nice because we have now a precise description of what is the reaction center. The reaction center took his terrible name because the person who first isolated and individuated as a central enzyme for the conversion was a guy called Roderick Clayton who wanted to leave a mark on the, on history and actually he did because it's RC is exactly the words, the letters that form his name and last name. And this molecule here is composed by has a rough weight of 100 kilodalton formed by roughly 1000 amino acids, then it has three sub units, which are here color that three three three different colors. And nine factors that are shown here on the light on the right. For which are bacteria chlorophyll is we saw already color with our chlorophyll is two of them are to bacteria pfio fighting and pfio fighting are just chlorophyll deprived of the center magnesium, then to quinones. Quinones are very important as an electron acceptor we already heard it today and also yesterday in the nice talks and one iron iron not him iron iron that sits here and mostly plays a role in the structure of the system. So, this is how the, the cofatos are organized in the in the reaction center. This is the three sub units. What happens is that along one of the branches that the electron is shuttle from the dimer here, which are two material chlorophyll overlapping one to each other to the quinone. And this overlapping here is actually a pardon this electron transfer here is a hopping between the dimer the bacteria chlorophyll a the bacteria pfio fighting a and the quinone a and finally to the quinone b. Actually the system works like a semiconductor so light is absorbed and promotes electrons from the balance bond to the conduction bond, and then the electrons will reach eventually do catalytic side one you reach in the other. E poor where electron get transferred and moving all the energetic of the system the energetic of the system is so nice, because the engineered system is so well organized that before any charge the combination takes place. Forward electron transfer reaction happens so and the forward electron transfer reaction is at least two three times faster than the back reaction or the fluorescent so from the star which is the dimer excited state chlorophyll electrons get transferred to the bacteria chlorophyll a in 10 to the minus 12 second arrives with the bacteria pfio fighting a and the recombination will be 10 to the minus eight but in 10 to the minus 10 seconds reaches the other. Electron scepter and then again faster than the recombination reaches reaches the last electron scepter so what you actually have done you have moved by roughly. Almost four nanometers the electrons from the position of the dimer to the final position of the quinone and this allows you to move around the protein to move around the. Move around the electron from one side to the other side of the membrane this is amazingly done by the system and is sort of a. A paradise for anyone who won't wishes to do photo chemistry and let study later in class. The optical spectrum of the proton is very important for us and you have several peaks some of them are associated to the dimer 865 nanometers then to bacteria of chlorophylls or bacteria pfio fighting, then you have the second. Q bands of bacteria chlorophyll and bacteria pfio fighting, then the B bands of the bacteria chlorophyll and bacteria pfio fighting a plus the final absorption band that includes quinones and aromatic amino acids, you can use it and have the difference between the. dark and the light spectrum and you can see that they speak, which is at under 65 is complete and at under 65 nanometers is completely bleached when it's illuminated that's because all the electrons get promoted to the. First excited state and you can actually use this ban here to check the. kinetic cover reaction these are very the one I'm talking here is very slow electron transfer reaction that go from milliseconds to. Seconds actually, but they are very, very important because they allow and similar chemistry to take place after the photo chemical acts that generates charge separated state so we're talking about chemical. Time domain that is. Order of magnitude slower than what Julia was showing and but also order of magnitude more efficient in transferring them the charge separated state to chemical reactions. And here is one of the examples that they wanted to give you can see here are two different two different charge recombination experiment, you can see here the red line here as an experimental that was obtained by. shooting a flesh of light here to the system is at 865 nanometers, then the system is fully bleached, and you can follow the charge recombination of the system after the light is being removed in this red trace here is actually. The electric reaction center to which the QB side was removed, so you only had electrons reaching here so the charger combination is faster because has to go from here to here. And then take either another reaction center with the QB or reconstitute the QB functionality. The electron has to travel all the way from the D plus to the QB minus and amazingly enough, there is no electron direct charger combination for QB to D plus but it repopulates. The QA side and then recombines from here so that's you actually see a very slow decay that has an average time between one and 1.2 seconds and of course in one to 1.2 seconds you cannot you can do much much nicer thing than in in chemistry than in. picoseconds and that is the purpose. Of the following presentation but before going to the following presentation just want to indicate and this probably my last but one transparency, the effect of the chemical environment if you look at this graph here, the black line is represented by. Is exactly what we saw in the previous one, so is this one represented here, and then you can actually solubilize this protein in different kind of systems so detergent. Liposomes or liposomes made of negatively charged, negatively charged lipids and you can see that you can slow down the reaction the recombination reaction up to ending up to a recombination reaction that takes about three, four seconds. This is a humongous amount of time for such a system to be used for chemical reaction of course there is trade off the slower the system, the lower the energy story in that system, but you can play with trade off there is always a way to play if you have a trade off. Let me just show you I hope I'm in time, but let me show you just show my very last, my very last transparency, my very last slide sorry, it's half Italian and half English I don't know why, but that's the application of photosynthesis in the living words of today, we can have it in biosensors. Generation from bio biofuels of third or fourth generation production of bio hydrogen bio electricity biosensor cellular in the cellular farm and bio catalysis it's important and growing fields and artificial photosynthesis. You already heard Julia showing some ideas on artificial photosynthesis we will apply this in the next talk, and you can do this kind of things either using the whole organism of portion of the organisms, and to do this you have to be a visionary but as young Sheldon Cooper says there is a fine line between being wrong and being visionary and unfortunately you have to have to be a visionary to see it. I hope I can see it otherwise. It's a bad thing for me. So thank you for your attention and I'm open to question and sorry if I was too long. No, Massimo you were perfectly on time. So we have now a little time for questions so I don't see any question in the chat but you can switch on your microphone and ask Massimo directly if you want just write something in the chat. Too much biology. Too much biology today. I can break the ice possibly asking, you know, having gathered the Julia talk just before your talk. I realize that you have this in this reaction center you have these two branches, very similar to what Julia has in her beautiful molecule. So I'm wondering first, there is a reason for having two branches and not a single branch why nature chooses this complex architecture and then who the one possibly think about an experiment like Julia did putting some vibrational energy or some energy, disturbing one of the two branches. Okay, the answer for the first question is why nature. Made up this thing in this way it's probably was a trial and error way in evolving. And at the end they found out to have a B plan. So, in a photosynthetic organism, something can always go bad and one of the two branches may not work. So you have a backup one that can work so it's evolutionary and struggling for life. Yes, yes, redundancy it's very important biological system there isn't no history of theoretical biology on redundancy. The other one is that, of course you can do this, and there is a fantastic group, there are several groups to do this. The most advanced one is the group by Van Grondel in at the university. What he does is exactly what you represented here I are in in in reaction center and in biology we have the lack of having the possible of making a mutation within a protein so it was not only able to produce the chlorophyll and bacteria chlorophyll within the protein, but also to maintain this molecule and change small amino acid that would move energy around. And he has a so many understanding of this system that it will take like three days only to present his work. Van Grondel is an institution in the bacteria reaction center and fast for the physics and for the chemistry. There is an end rise by Ali. Yes. So, so thanks for your talk. I had a more general broad curiosity about what's understood. You know, you showed these very nice pictures of the photosynthetic system. And, of course, this is a very static picture of, you know, the system and I imagine that there's a lot of conformational heterogeneity dynamics. What's, you know, what's the extent what role does conformational fluctuations play in the various processes of photosynthesis and is this is this under completely understood what are the open questions there. Thank you. This is a very nice question. Saying that something is completely understood is overstating. But in terms of what goes on, what goes on in the very first femtosecond, the fluctuation. That's all within the dimer. So the two bacteria clover facing each other. And what happens is that that if you saw that system, it looks almost symmetric, very symmetric, but that's not exactly true. There is a break in the symmetry particularly around the dimer and the breaking symmetry is exactly in the composition of amino acid that sits with two one chlorophyll on the other one chlorophyll. And that's how nature chooses to use a branches because the energy of the B branches is unfavorable compared to the energy of the B branches because the excited states has the letter and sitting most of the time on the a branch a material chlorophyll of the dimer. So actually that's absolutely true. And this was shown by contemporary experiment by experiment done with the EPR and or and fast fast for the physics and photochemical experiments. And the other thing is that you also have a very nice description of the conformational changes because you can do what is called the time resolved x-ray crystallography. By the advent of free electron lasers as breakthrough from for biology, you throw so much energy that the molecule breaks up, but this happens within a few, almost 10th of picoseconds, but then you can take x-ray images in time between zero and 10 picoseconds and reconstitute the movement of all amino acid before the system explodes. And actually that's that's something that they're doing very nicely in Arizona in Temple University. And there is this group that is building a fellow electron laser x-ray facility. And if it wasn't for pandemic, I would be there since last year, because I got a position there, but they never was never allowed to reach them because of COVID-19 so COVID-19 is a horrible thing. Also for this. Thank you. Thank you very much. Sure. Fascinating. Fascinating. Thank you. Other questions from the audience, please write on the chat or raise your hand. I will try to follow. May I ask a question? Sure. Yeah, that was an excellent talk, Professor Trotter. Thank you. And the direction that you know, in the synthetic or semi-synthetic approach to mimic photosynthesis, one of the challenges that exists. And you know, what constituents of chromophoric systems are required in order to nearly reach there or like have some similarity to what photosynthetic reaction center would do? Well, most of the things were explained extremely carefully and detailed by Julia. Julia showed you that if you take the simple system, then just the model system, the first model system that appeared, the trade-off for having a simple system is that the charger combination has a time that is so fast that you cannot do anything. So if I may say, what is the drawback at the moment to artificial photosynthesis is complexity. The system we are using, although very complex, they are too simple compared to the natural systems. I only showed you a general image of the complexity of this biological system, but you have to imagine that between each step of the electron transfer, there are at least 10 to 15 amino acid involved. So, and that's why the lambda, the reorganization energy that comes in place is so relevant in determining the rate transfer or charge combination or forward electron transfer. So, in one word, it's the lack of complexity, the real drawback at the moment for artificial photosynthesis. Thank you. Once again, I very much enjoyed your talk. Thank you. Thank you. Thank you very happy. I just want to comment on this complexity thing is very, very interesting. So, basically, we have to start to study systems where there are several chromophores because you need this cascading. And most probably also, as also Julia pointed out, you need also vibrational coupling or conformational coupling, call it as you want some relaxation of your system as to avoid going back. Very, very interesting consideration. I was in general. I have more questions, comments. If not, I think we can go straight to the second part of the presentation. And let's see what Massimo has in store for us. In the comment of what Fatima wrote, she said that just the thanks slide strange that even it contains many languages, but it contains Arabic words. Fatima, please send me the Arabic word. I will insert it. I apologize for being so I'm polite to you. If you do send it, the Arabic word that will immediately insert. So please do so. Okay, yeah, let's go to the second part. Okay, I'm sharing the other one. And just anticipate to Fatima will have the same problem in the thank you transparency, also the second part. Coming up, you should see it now. Don't you? Yes, yes. Oh, thank you Fatima. She sent me the word. Okay. Again, applications. I was asked to give a general part general topic and then application of the in my research. Of course, we have to go back to the center for the chemical apparatus which is built as we were saying by a protein scaffolding which the the pigments are inserted that I showed you are only the head of the pigments. I cut away the idrophobic chains because they will confuse the scheme, but each of those pigment has or quinone has a long chain, at least 15 to 50 carbon atoms because these molecules have to be very stably bound to the reaction center but not covalently bound. Now, given that I will just go forward and mention this think of complexity. So solar driven chemistry is the game to play here. Well, as I was saying, one of the very first example of artificial photosynthetic molecules is this triad. And you can see you have a carotenoid on the end, a central porphyrin and a quinone. This is a very bright way of thinking. You can just make up a light absorbing part that distributes excitation to the carotenoid, which gives an electron to the quinone. And of course, if you wait long enough, the electron of the quinone will recombine with a charge left on the carotenoids and the system will go back to the ground state. Well, the point is that the lifetime of the cells and although very high in yield in generating that charge separated state is 60 seconds, 60 per nanoseconds, which is, as I was saying, too short for any ancillary chemistry. And so people understood that there was needed for something else. So they added in a second porphyrin and a second quinone. You can see that the pentad elongates the pathway between the electron donor and the electron receptor. And so, effectively, the charge of combination got much, much longer. The yield was comparable. But still 200 microseconds is too short. So to make this, I was asked this question before. So what is the difference between this natural, the natural system and this system here is complexity and you need complexity exactly as you need complexity in a soccer game. You know, artificial photosynthesis, the system just been played by the two goalkeeper who kicked the ball hoping to make goal and the other to the adversary to the opponent while when and that would be very boring as a game. But then if you had the other players, the complexity of the game increases and we like it more and more, at least I like it more and more. That's exactly the difference between artificial photosynthesis matters for the synthesis at the moment. So artificial photosynthesis adding is adding players but naturally biological photosynthesis has already the players in their plays and they're playing very nice. We were saying that it's so well designed that the forward electron transfer is always faster than the charger combination reaction, and you can actually have a conversion of 100%. So each absorbent photon from the reaction centers is converted in a charge separated state. And that is what we are looking in also natural system that's does not happen. Contemporarily you have high high efficiency conversion and a very slow recombination rate. So these two are typical of photosynthetic natural system. Biological system. And as I mentioned is because of evolution between each electron transfer step we have so many amino acids that have an interplay in the energy distance between the pigments and they may have also an interplay. For example here these are 15 angstrom. There is no way that the electron would rally from here to here just by that simply. There are at least four histidine amino acids here that land their own orbitals to allow the movement of the electrons from one quinoa to another. So complexity is the goal and is what we do and and is what we need. So what we decided to do is to take advantage of the chemical complexity that comes directly from nature and eventually assemble it with some inorganic patterns to to generate the so called hybrid organic biological assembly. And if you look at the energy conversion efficiency. We already mentioned that grows going from artificial to natural system because a structural complexity grows from artificial to natural system. Of course chemical robustness instead decreases. If you increase complexity but that's a trade off the famous trade off we were talking about so for example PS2 which is this for the chemical core that sits in the plants is so efficient in converting that at a certain point is too efficient. And it can't react with oxygen destroying the proteins itself. So in nature this protein is has its own healing mechanism which one part of the protein destroyed by oxygen is discarded and a new piece of protein is up taken synthesize up taken and inserted in these enzymatic system to allow to repeat the photosynthetic to repeat the photosynthetic process and this takes about half an hour you just take and extract this protein after half an hour it just breaks apart you will not work anymore. So there are best practice for RC exploitation this hybrid system, and I will just show you a few example because I have not so much time. And of course if you extract the protein and you want to be sure that whatever you do is useful, you have a fully vectorial you need a fully vectorial arrangement that's because upon the generation of charge separated state. Every protein is possible to be represented as a dipole. And if you do reconstitution for example in on an electrode to take advantage of the charge separated state of the dipole. Then you want to have configuration of the dipole which is this one all oriented in the same direction, so that they all work cooperatively toward one direction. Instead in the lower case you have 50 50 distribution and each dipole will kill the effect of the dipole of the previous one by listening the whatever effect we are doing so. This was the idea that brought us to do what we will show you and together with the fact that you can actually isolate the reaction center reconstitute in lipo some whatever of vesicle of phospholipids and eventually if you look at this photo cycle here you can allow adding external electron donors and electron acceptors here. Queen so external reductant and internal we known what you can do you can shy light and obtain the first charges separated state. Now, the system is organized in such way that if you have an external electron donors before the combination takes place actually before any forward reaction from the q a minus to the q minus takes place. The diamond radical cation can be read reduced and you end up with a radical anion in the molecule that moves and can be doubly. You can do you can repeat the explain with another flesh, obtain again the radical the anion q a minus to be minus and radical cations, the cations get to gain reduced by the external donors. So you end up with a molecular quinoa and if you remember the position is this is the on the be on the be branch. This is a doubly reduced we know that that takes protons from the external water generates a quinoa that leaves the protein and the substituted from external quinoa. So this you can then repeat the photo cycle. And if you look at the actual result of the photo cycle is that protons are up taken from one part and confined and moved to the other part of the photo cycles. So if you actually have a family of oriented reaction centers like we see here. You can do this in a closet vesicle. Ideally, you could have a change in the pH in the internal side of the closet vesicle and an increase of the pH, but lowering in the of the pH within the the cytoplasmic you are of this. Closet vesicle and an increase in the external. Well, actually, that's exactly what we decided that was very, very interesting to do. And what we did is reconstitute the reaction center within those giant vesicle now giant vesicle are lipo sums that can be obtained quite easily. But their size is gigantic. Sadly, they can go from one to 100 microns. So if you imagine one bacteria would measure roughly one microns you can get large amounts of bacteria or whatever it would in the center and you know this giant lipo sums. So what we did is to bind for four to the reaction center reconstitute the vesicle with the reaction center. And you can see the floor force is mostly is almost exclusively bound to the belayer of the giant vesicle. Then you can upload, you can fill the giant vesicle with the pH indicator. It's at the pyramid in this case, and you can see the fluorescence of the pyramid.  This is the actual view of the giant vesicle in microscope and this is a fluorescence microscope and you can see there is a lot of variety in the dimension but we set up to choose the dimension of roughly 20 microns. So this is a fast representation of the giant vesicle in which roughly 90% of the reaction center is reconstituted with the dimer, which is this flat part here exposed to the external and the quinone exposed to the internal. There are some that are opposite but they are cancelled out. And if you just look at the photochemistry that I showed you, you can have the electron traveling from the quinone from the dimer to the final quinone. You can re-reduce the reaction center dimer using cytochrome and again cycle the cytochrome from 3 to plus, from 3 plus to 2 plus using ferrocyanide. So you have a full cycle that can be driven by illumination and electrons will be picked up by the from the internal solution from the inside of the vesicle. You can actually show that this is actually taking place by measuring the charge recombination of this charges separated state here and you can see that in absence of cytochrome you have a full recombination rate while the recombination rate dies out if you add cytochrome. That's because this is re-reduced and there is no way that electron can go back to D plus because we have no more D plus. So we showed the orientation, we show that the orientation is corrected for us and then in time we illuminated in 15 minutes we illuminated the different vesicles. These are three different giant vesicles and you can see that the pH inside changes because the pyranine become more and more brilliant and the fluorescence of the pyranine increases because the pH internal pH increases. And you can do this also by showing the change of the pH in time by plotting the intensity of the fluorescence calibrated toward the internal vesicle pH and you can see there is a linear behavior between the amount of light that actually reaches the giant vesicles and the delta pH. So this is important because we were able to obtain a fully oriented system that can be used to re-photochemistry in a closed vesicle. You can imagine this is a very powerful system. The other thing that we showed that was that the other important thing is that we want to increase cross section. As I mentioned, the reaction center is surrounded by light harvesting complexes. These light harvesting complexes are proteins that are generally very tend to degrade under harsh conditions where the reaction center is much more stable. So we like to take them away during isolation and end up only with the reaction center. But that cuts the cross section of the system, so less light is absorbed and the system is less efficient in long accumulation. So what we did is as a principle, we just took this nice molecule that was taken from the lab for organic chemistry. It is built to be a very, very efficient fluorophore. It has two triple bonds that are conjugated to two benzines and there is a central core here that is very fluorescent. This central core here you can play around to have also bound some exigroup that will allow to stay within the membrane since we are thinking to bind it to the reaction center. And then here is the system that we use to conjugate to the license of the reaction center by by conjugation to the via Succinimidil ester. What we do is just we take the spectra of the reaction center in black here, the spectra of the molecule, the one we saw before. This is the fluorescence of the molecule. So, if you look at the peak of the absorption and generate this band of the eye, then you see that there is no absorb correspondence absorption of the reaction center. And so you actually extended the ability to absorb light. But would this be efficient in generating charge separated state? Well, we thought yes, because the emission peak corresponds to one of the absorption peak of the reaction center. So when we do bioconjugation, we actually see that shining light where only the fluorescent molecule absorbs, then you have an increase of five times in the charge separation state production, compared to the native reaction centers at one that lacks the artificial antenna. And similarly, we can drive the photo cycle that I showed in the first in the first transparency in the first slide. And you can see that there is a three to four times increase in the rate of the photo cycle, because the artificial antenna is driving faster and faster the electron, the energy transfer from the 2D reaction center. Well, you can also have some structural information, and we try to have the crystal structure, but since the system is quite disordered, we could only see one binding point to the leasing M1110, sorry, which is close enough to the, but anyway, this shows that the binding molecule is close enough to the pigments to ensure the forced electron energy transfer from the fluorophore to the pigments, explaining why we have such a good converse, such a good increase in the charge separated state. We also then we decided to team up with this organic chemistry group, and you can see here all the molecules that they did for us, and many of them they're used and improved in different way the charge, the yield of the charge separation state. So we actually are also able to, we were also able to increase the yield of conversion in different part of the spectrum. The other application I wanted to show you is that this is probably the most, well very interesting for me, I don't want to say the most interesting. As I was saying earlier in the first part of the talk, we have this closed vesicles, and this is the entire photosynthetic apparatus and you see here the ATP synthase. The ATP synthase, as I mentioned, is the molecule that produces ATP, which is the exchange coin, the exchange currency for energy in biological system. If you have a way to producing ATP, you can drive most of the biological reaction. What we tried to do was to use again giant vesicles, you'll see here this large giant vesicle, isolate the chromatophores, which are naturally organized to have all the photosynthetic apparatus already well ordered in its belayer, and having the ATP synthase protruding towards the outside of the vesicle. You can see here how it works, light, then combining the entire photosynthetic cycle, and finally the synthesis of ATP in yellow here, as molecule that produces energy. If you reconstitute the vesicle called chromatophore within the giant vesicle, then you have a photosynthetic way to produce ATP within a giant vesicle. And if you can have a T7 RNA polymerase, and a template RNA, you can actually synthesize mRNA, just shining light on the system. And you can actually look at the formation of mRNA by looking the fluorescence of the amino-acrydena complex, showing that the entire system can be considered as a minimal cell for biosynthesis of mRNA or proteins or whatever you can think of. Well, this is a proof of concept, so you can think of something that's not sure that we can do, but I have to say so to be cool. Anyway, this is an experimental part, this is the way we isolate the chromatophores, they're all picked at the dimension of 100 nanometers. And if you look here at the microscope, you can see these are time images, you can see here the curvature of the giant vesicle. Here is the chromatophores, some are open, some are broken, but mostly are open, so broken, broken, closed, sealed, sealed. Now, if you take these yellow parts and zoom it out, you can see that in the top part, you have a bubble here that you can look more carefully and reconstitute and recognize as the RTP synthase. So, we know you have sealed the chromatophores showing the ATP and you can use this to synthesize ATP, showing the ATPase and you can use this to synthesize ATP. So, if you do some tricks, you can also, the same trick of the cytochrome I showed before, you can show that roughly 70% of the chromatophores are sealed and functional, so in this fashion here. And if you shine light on the system and you have your amino-acridine channel open, you can see that shining light for longer and longer time increases the fluorescence of the amino-acridine, which binds to the, which is presented within the sealed vesicle and binds to the mRNA as soon as it's formed. So, in time, what you're seeing is that fluorescence increases and if you do this in a calibrated way, you can measure the amount of RNA that comes directly from the fluorescence of the amino-acridine orange, the amount of ATP that increases and then decreases. Increases as is formed by the chromatophore, chromatophores and then decreases because it's consumed during the reaction of the synthesis of the mRNA and of course the decrease in the ADP, which is the substrate for the ATP synthesis. Now, I hope I didn't go too long again, but here it is, my terrible transparencies again apologize to everybody whose language is not here and thank you for your attention. Thank you Massimo, you stayed on time perfectly, we have time for two questions depending. This one raised the end from Eric Ottunson, please switch on your microphone and ask a question. No, perhaps I was wrong, it was just. Yeah, it was just an applaud. Okay. Okay, thank you. Any other questions, comments? Or any other applause. I don't see any questions for now. I have a, well, perhaps not nice question, nasty question. Let's put this way. I appreciate your idea that borrowing from nature allows you to go towards complexity much easier than going in the chemical lab. The question is, the nasty question is how expensive it is extracting this structure from nature. And if you compare with the cost of chemical reactions and things like that, how difficult it is, how expensive it is. Thank you for the question. That's not a nasty question. In the sense that we ask ourselves, it is worth doing or it is not. At the moment we are playing with the proof of concepts and it's always worth it. The fact that we were published by PMS was really worth it. Sorry about that. Okay. But if you actually think to this proof of concept, what we are trying to do is making this thing simpler and simpler. So we want to use this technique, for example, of ATP synthase in the next step by using the whole bacterium. Now, this is expensive in terms, mostly in manpower because of, because all the isolation, the control, the system that rebuilding is really time expensive and you have to be very careful. So you need fantastic students and postdocs. The thing is that if you can do this with an entire bug, that would be perfect, I imagine. The problem is that entire bugs wants to stay alive. And so the first thing that happens when you have a bacteria within a giant vesicle and that bacteria start to eat the bilayer of that giant vesicle because sees it as food. So that's what we are trying to, we might have the same results in a system formed by a giant vesicle and a bacteria, but we have to try to find a way to avoid bacteria eating up the giant vesicle. That's, and that's, that's the last question. So, yes, when we'll be able to do it, hopefully before retirement. Okay, thank you. I have a question. Must you are good or whatever. Hi, Massimo, I thank for the talk. I have a question actually curiosity. I remember somehow from other sources that the overall efficiency of photosynthesis is not that great, but today I was happy to hear from you that actually in the separation in the process of separate creation of, of charge separated state is very efficient. So it's like 100%. But so where is then the bottleneck. If you might say something about this if there is one or maybe I'm wrong. No, no, you remember very well so it efficiency as a way to measure the capability of our system to convert one thing into the other. So the trick to having the highest figure is to take the right conversion reaction. So if you look at the charge separation that's 100%. If you look at proton transfer, it dropped to 60% because there are a lot of other processes that gets into the way. If you look at the synthesis of carbohydrate, then you drop below 1%. So you're right photosynthesis in its absolute so for example the conversion to from from light to come to carbohydrate is below 1% and that's definitely a non efficient way of of working. So everything depends on when you start to intercept your electrons to make a good use of them. The entire story is that you have to do it before they get converted. So you should intercept your electrons once they're producing from the photosynthetic apparatus and before they go in any further metabolism and for example, throw them out to an electrode. But of course in doing so you don't have to kill the bacteria or the plant or the of the algae, because otherwise it will last a very short time. So what this, I don't know if this makes sense to you but what you're trying to do the community of bio hybrid photosynthesis is to play with the photosynthetic apparatus within the organism in such a way to extract half of the electron from the metabolism and live in the other half for the metabolism. In this way, our idea is to eventually be able to convert sunlight in energy with efficiency of 50%, which is of course not as good as the initial one, but still very good in terms of a system that has a very should be ideally very sustainable for the energy conversion. Hope I did answer your question. Yeah, yes, yes, thank you. I was just thinking that nature, I mean, it's interesting to think that nature did very well on one part, which is the first one and then was not probably, I mean, there must be some reason why the second part is definitely harder to achieve, but I guess this discussion. Yeah, there's a huge field in the theoretical biology that asks why nature is not so good as in photosynthesis, but we could go through it, but I'm sure that there is time for more stuff to come in your lecture, so I will avoid to waste your time. Thank you very much. Thank you. Thank you. There are other questions. It seems not that I guess Massimo will be happy to answer any question. Of course. And so we can thank Massimo again. And close this session, this part of the session, we have a small break for 15 minutes, so we reconvene at 45. No, at 12, sorry, at 12. We did contribute. So thank you.


Today, ITU, the oldest agency in the UN family, turns 150. Happy birthday, ITU! Happy birthday, ITU. Happy birthday, ITU. Happy birthday, ITU. Czech-Native-Chiklarozignan, ITU. Happy birthday, ITU. What we need today is to bring people together, and that's exactly what ITU is doing for the last 150 years. Happy birthday, ITU. Happy birthday, ITU. Happy birthday, ITU. Happy birthday, ITU. It gives me great pleasure to wish our very good neighbor, the International Telecommunications Union, a very happy 150th anniversary. Happy birthday, ITU. Happy birthday, ITU. Thank you very much, ITU. Happy birthday, ITU. I would really like to thank the UN for this exceptional cooperation that we have for more than 140 years. Happy birthday, ITU. Happy 150th anniversary to ITU. Congratulations. Happy 150th anniversary, ITU. Happy 150th anniversary. We celebrate the 150th anniversary of the International Telecommunications Union. Happy 150th birthday to ITU. This is a letter from here from Australia. Happy birthday and have a great 150th anniversary. Congratulations. Happy birthday, ITU. And I'm watching you, ITU.


Hi, this is George cow and I'm here with Michael stone one of the members of my master heart group coaching program It's great to have him here. He's gonna be sharing with us some wonderful deep wise lessons from his journey of Developing a business Michael great to have you here. It's great to be here George. Thanks for inviting me. Yeah, thanks for being here So let me read your bio to everybody first and give people some context for what work you do And then we'll go into some of the sharing and learnings you can you can share with us I've got my cat here in case anybody's wondering. I'm always a little distracted sometimes. He's like trying to bite my cords Okay, so let me let me read your bio here So Michael stone is a shamanic practitioner teacher mentor Journalist and the host and producer of the shift networks shaman shamanism global summit and KVMR Conversations KVMR is I guess a radio show that you do he interviews leading edge thinkers authors and Activists in the areas of environmental restoration social justice and spiritual fulfillment Michael spent most of his vocational life as a corporate organizational development consultant communication specialists and leadership trainer and now you're bringing some of the work that you've been doing with Shamanic, you know wisdom into into the corporate world as well. So we could talk about that later full circle. Yeah, full circle Yeah, no, that's good. So one of the lessons you learned, you know in our conversation earlier was About fear. So maybe maybe you can start there. What I think that's something many of us entrepreneurs experience you know, I think it is and It's a major issue right now with the Change environmental social justice economic You know, there's so much uncertainty and we have a desire to try to get it right get it perfect and That loses the opportunity to really meet fear as an ally Because when we try to get rid of fear or we try to suppress fear if you're really present you realize in the moment Fear is your ally. It is it is frozen power and the more we try to suppress it the stronger it gets So there's not You know people and that that's the same with anger or any emotion that rather than resisting it Which causes its persistence? We embrace it and open to it and so fear Whatever you're afraid of is really your soul's calling wanting to emerge These are the things that your soul is saying hey work on this stuff confront this Walk into the fear and open your field of awareness to a greater perspective and so You know, that's that's a huge issue for people we we look at things from a Deterministic view that there's a cause and effect, but quantum physics is really Breaking up our worldview, even though it's been around a hundred years. It's just starting to impact that and it It teaches us some pretty important rules. One of them is that we're not separate there is no such thing as separation in the entire universe and At the heart of our suffering is this belief in separation most of my career has been in organizational settings and My evocation working with the mystical world and and and studying physics, but this idea that I am in this body I have a Reality-centric to a self called form reality and that means I'm an object in a world of objects of the old Newtonian Cartesian paradigm well, all that has changed and There is clearly no separation So when we go from this form consciousness into actually being embodied And and into the cellular nature We realize that we've got 70 trillion cells each one has over a hundred trillion atoms Each atom has a proton and neutron and an electrical field Which is producing light and heat out to the edges of the universe We are not in any way separate and so much of my career has been to work with Interrupting that belief because our our beliefs Shape our perception and our perception shapes our reality so that brings us to a place of really questioning our beliefs and to do that we need to be present and You know, we are so fragmented and frazzled with the computer a world of social media the constant bombardment of information and most people have a hard time being still and Stillness is really also one of the lessons that we need to learn. We need to remove ourselves from the constant activity still the mind and get embodied and begin to recognize that not only is Unseparable in separable, but we can never have certainty In a subjective world. We think it's an objective world. There's no such thing as certainty, but Looking for certainty causes us huge anxiety So a big part of the work I do is about embracing uncertainty to find the lessons within and when we do that We go into one of the third principles of physics and that's potentiality We unlock the wave collapse where we made a story up about something that happened in the past and when we Actually recognize that it isn't the thing from the past like, you know, our mother did this or our father or some Somebody did this to me that incident you already survived that but you're still living in a story from the past that protects you That's why it's so important just to come around full circle to embrace your fear and honor your fear as a great teacher a soul teacher Long answer for a short Fantastic. It's there's a lot there that but that I'd like to unpack. What I mean Certainty is One of those things that entrepreneurs year and for Businesses Basically, I mean, this is how the economy works, right? You you need to keep growing at a steady pace and that presumes certainty and So let's let's talk about this a little bit I mean particularly when it comes to and what I call building an authentic business, which by definition is Not formulaic But it is an expression a spontaneous expression oftentimes of what is real for ourselves in the moment So certainty if you want to really look George at certainty it's not possible and Anything that you're certain about can only come from experiences from the past So what you lose by trying to find certainty constantly try to get it, right? Find certainty first of all you create enormous anxiety and stress for yourself but secondly you miss the opportunity to discover what you don't know that you don't know and Open into the field of potentiality the observer effect Heisenberg's observer effect You know says that when you look at a wave it it turns into a particle Well, that's when you make up a story about something it turns into a particle You're you're imprisoned by the beliefs that you have and that's way more important Than genetics because right now epigenetics is completely Debunking the whole theory of genetics and we and we realize that our beliefs actually change our genetics and and it's very much proven that that happened so we By going into these news areas and and seeing the beliefs that are shaping our reality We get to see the stories that are shaping the belief When we deconstruct them we realize that they're just stories from events that happened long ago And then we can reauthor our own life and and reauthoring you rewrite your life And then there's two major things you have to embody that and live that and create practices consistent with the new story But one of the things that most people don't get at is the community field the community field is We've trained all the people around us to respond to us Based on the things that have come out of our mouth our story and so people know us to be you know Michaels this way George is this way and then when you start to change number one people don't want you to change because they know you a certain way and it threatens their own Reality and the facade that they live in the story of themselves the self-centric reality It starts to break that down So it's a threat to them because people especially an organization say I won't call you on your you know What if you don't call me on mine? It's a conspiracy that Is in our world? It's not just the corporate world. It's everywhere in our friends and so You really need to watch the field because it's like when a drug addict goes 90 days clean and sober and comes back He goes to see his friends. She goes to see her friends with 24 to 48 hours They're using again because they've gotten themselves back into the field of conversations, you know And one of the things that people Think in this embodied in this form consciousness is that my brain lives inside this box how it ever got relegated to that is a story of the last 300 years but More and more research is sowing that there's a field of consciousness And the most important thing we can do is begin to tap into the field which taps us into the unlimited potentiality that's fantastic and Tapping into that field is partly what shamanism has been about right So so make that connection for us I mean you're you're you have had so many conversations of various shamanic teachers You do you teach it yourself. You do your journeys. How does that connect to the modern science of quantum? It's totally connects to it I mean the mystics have been saying forever and shamanism for a hundred thousand years that we're all connected But it's become a bumper sticker. You know, we're all one well That's true, but that's not how we're living and we're looking at the world from a skin encapsulated ego That's based on our past experiences. So so Shamanism has been saying that everything is connected and everything affects everything else and that's what physics is saying embracing uncertainty has been the magic of shamanism in that we look at and In an animistic way and of thing in other words everything has a soul everything is alive Then we recognize that we're part of a living changing Massive organism called the universe and we're inseparable from that so very much what physics is saying and and doing in terms of potentiality if our word is Our power in which I which I that's a whole deep long conversation we'll get into it, but When we name things in quantum physics, they call it a wave collapse when you Look at a wave and it becomes a particle, but it's the same thing In shamanism they call it soul loss It's exactly the same thing. So they're very much aligned a very much connected and when you break up those Beliefs you begin to see that there's inseparability that there's uncertainty in this potentiality and then there's coherence and coherence is a key thing Both in shamanism and in the world of physics because it says You need to be in a line with the larger systems of which you were apart Shamans get their power from what the mountains the apples the water the waterfalls the land they don't think You know, they're particularly powerful. They get their power from the largest Larger systems in which they are apart. So we're going from a system that's that's Objects in a world of objects to one that's all connected and all of these things are being proven every day by Coherence just being coherent with ourself and listening to our inner voice is coherence Doing things in the world that that recognize our inseparability Gives us power and most people think that power is force or control or manipulation or guns or money or whatever But really power is the ability to be present and to be conscious of Consciousness and how it affects us and how it affects the field that we're in and the people that we meet and the people that meet us We're always being affected by them So Getting out of the remembered past and the imagined future and getting ourselves Right in the middle where we have a stimulus and the old story wants to come up But we have a gap with a choice point where we can choose a new story Brilliant so you are Creating a course right now called the quantum power course Yeah, tell us about that because you've been giving us some of these concepts that are surrounding this idea of quantum power Yeah, well like I mentioned in the beginning people right now. I've never in my 73 years of being on the planet seen so much Fear and so much People feeling powerless with the magnitude and complexity of the changes that are happening in the world and We are not going to fix those things that are broken in the world with more stuff that comes from here That is not gonna happen. What's predictable is that we continue to you know, it's Einstein's if we continue to Do things from the way that they were originally discovered they will not be any better That's a terrible paraphrasing, but you get the idea so the opportunity to to Really see where we give up way power and by the way, I have a power Assessment tool that I've created and I would love to share that with people. Can I tell them how to get that please? Yeah, yeah, you just write to support at well of light dot com That's well Oh, F light.com. I also have my consulting Website which it's it's also available and you can Go there and request and it's a power assessment tool for people What's your consulting website? Do you want to give us the link? Yes quantum consulting group Dot org Yeah, and I will be sure to link that in the notes of the video for those who are looking for it Thanks George. Thank you. Yeah, so I'm doing this course with another woman who's an amazing belief change person she's worked a lot with Bruce Lipton and Sandra Wallin also does equine therapy working with leaders to understand Their nature through being with horses and it's a really brilliant thing. I've done it with PTSD people also and it's amazing so that starts on Let's see what date October 2nd and then it's three Wednesdays at from noon to 1 30 and there'll be a lot of very practical hands-on work So this is a this is an opening for Possibility for anyone who's feeling powerless in any way and we give our power away to the experts we give our power away to You know our identity we give our power away to our fear There's one of the things you'll see when you take the questionnaire the assessment tool Is all the areas where we have power loss because they're all embedded in the questions Yeah, beautiful. That's great and the the work that you're doing with with companies Tell us what kind of company would benefit most from this kind of work and well, I've worked with everyone from the European Union the EPA to Boeing Microsoft Prudential You know, I've I've worked with all different mostly large-scale Organizations in Europe and North America mmm, and What kind of work are you bringing now to to these kinds of companies that we were talking about this quantum power? But what what what shift? Can be expected or yeah, yeah, yeah That's a great question. So one of the things that that When people get to this place of presence and I teach presence power and performance courses for leadership When they get to that place they renew their creativity their flexibility their ability to focus and Their ability to be with people in an intimate way Intimate and authentic and I know intimate is usually not used in the corporate world But I'm really talking about a level of connection that builds trust that creates Integrated teams. So that's that's the kind of work that I do in the corporate world You know my company that I started in oh my gosh I guess either late 70s or early 80s when I actually started mastery of management international our our motto was bringing heart and meaning into the workplace and That hasn't really changed but it kind of sounds a little new AG but it's really about connecting people and the ability to have a Successful organization or business is directly proportionate to our ability to relate with and inspire Others through very much like what you do George you you talk about authentic marketing and and People know the difference between the you know jack them up glaze them over and tell them they can't live without this there's a way we give up our power and people who were really there in service to each other and I love organizations because there's such a breeding ground of consciousness and And they also want results and I think that's a really important thing You know all of these concepts are fine But the reason shamanism has lasted a hundred thousand years is it produces results So they've gone through burning of the state genocide, you know Colonialism and there's still Shamanism is stronger than it's ever been in the world right now and it's because it produces results That's wonderful great great background for us So Michael, thank you for being on this on this interview and is there anything else you want to share parting words of wisdom as we Complete I just want to share, you know, you are such a shining example of Operating with integrity with authenticity And I know you're a tireless work. You put out so much work for so many people and I just want to thank you For that George because you're back there just cranking it out with people and and always available It's it's truly amazing the work that you do and You know for for somebody who wants a reel with a capital r coach talk to George cow Thank you, Michael. I really appreciate that Well, I have the links in the notes of the video so those of you who want to connect with Michael and The quantum power course or anything that you're and the also the quantum power assessment Be sure to check out the links below and connect with Michael there So thank you Michael for the work that you're doing I know that you're about to go on a vision quest And right after this power course, we're gonna head to the healer wilderness for 10 days of vision quest and then You know just I think and I think it's really important Just the last word is that we take care of ourselves, you know I can I can really easily with the excitement around my work Not take care of myself and we really need time for stillness and that's what mariela and I are Are going to do is take time to be still and see what wants to emerge In this world that's that's here now Oh, I look forward to hearing how it goes So thank you, Michael and I'm sure we'll connect again soon I hope so. Thank you, george


Let F be a field and let C be some number in that field. We call that number C a root, or some people like to call it a zero of a polynomial F of X, which I should mention F of X belongs to the polynomial ring F of join X, right? So C is a root of the polynomial F of X if the polynomial evaluated at the number C is equal to zero. This is also why people sometimes call these zeros of the polynomial. I'm personally not a big fan of that because I mean, zero is a number and that number actually could be a root. And so to say things like, oh, seven is a zero. It just seems a little bit confusing language. Don't get me wrong. In mathematics, we abuse notation and overload jargon all the time. But I feel like if it can be avoided, that can be done. And that's why I personally prefer the word root in this situation. Some people might call that a next intercept because we often think of F here as a function of real value function, maybe. F as a function from the real numbers to the real numbers. And so if you were to graph that function, the number C would in fact, then be an X intercept of the graph. But as we're not taking this analytic geometry approach, we're gonna avoid that terminology because after all F here is an arbitrary field. It could be a finite field for all we care. And this notion of a root still makes sense in that setting. So the roots of a polynomial are those numbers which evaluate the polynomial to be zero, okay? And so the main result from this video of lecture 20 that I want to present here is the so-called factor theorem, which actually tells us that there's a correspondence, a one-to-one correspondence between the factors of a polynomial and the roots of the polynomial because our interest in lecture 20 here is to explore factorizations of polynomials over an arbitrary field. In which case finding the roots coincides with finding linear factors. And therefore it's important to consider the search of roots of the polynomial as we try to factor polynomials.  Then the factor, well, sorry, excuse me, that the polynomial X minus C is a factor of F of X if and only if F of C equals zero. So in other words, X minus C is a factor of a polynomial if and only if C is a root of the polynomial. So there is this one-to-one correspondence between linear factors and roots of polynomials. This is what I was alluding to just a moment ago. And this is gonna be a consequence of the remainder theorem. But we'll see that one just a second. So suppose that X minus C is a factor of F. Thus, there exists some polynomial Q such that F of X equals X minus C times Q of X. Now, I wanna be aware that this statement right here is not utilizing, this is not utilizing the division algorithm of any kind. It's just, hey, if you have a factor X minus C, this is what a factorization means. You could factor F to be X minus C times something. Now, if you evaluate this equation at the number C, well, the left-hand side is obviously F of C. The right-hand side, you're gonna get C minus C times Q of C. Don't care where Q of C is because C minus C is zero. Anything times zero is zero. So I want you to be aware what we have here. If X minus C is a factor, then C is a root. That will be true for any ring whatsoever. No comment is necessary about whether it's a field or a domain or anything. If you have a root of a polynomial, that produces a factorization of the polynomial, okay? Now, conversely, suppose we have a root. Now, in this setting, we're gonna use the remainder theorem. The remainder theorem told us, just as a reminder, the remainder theorem told us that if you divide a polynomial by the divisor X minus C, then the remainder in that division will then be the evaluation of the polynomial. Therefore, F of X, which will equal X minus C times Q of X plus F of C, right? So the remainder is the function evaluation in this setting. But since we're assuming that C is a root, the remainder will be zero, and therefore we have a factorization. So by the remainder theorem, we get the other direction as well, which the remainder theorem did actually use the fact that F is a field. Perhaps we could have had a somewhat weaker setting there, but as we get to Gauss's limit, which is the titular topic of this lecture, we'll see that how to relax this condition about a field. It doesn't necessarily have to be a field. A domain is actually a pretty good setting, and Bo will explain more about that, of course, in the next video. Now, before we close this video, I wanted to present a very important corollary of the factor theorem, and it's important enough that I'm actually not gonna call it corollary, I'm gonna call it a theorem, the so-called number of roots theorem. And so this is something you would have seen in like math 1050, college algebra, or your equivalent of what that would have been. This would have been done over like the real numbers or the complex numbers, but we can actually do this over any field this is just a consequence of the factor theorem which we just saw. So if you take a polynomial over the, if you take a polynomial whose coefficients come from some field F, then the number of roots of that polynomial is no more than the degree of the polynomial. Now, you can actually have different roots, right? So if you have something like X minus one times X minus two times X minus three, if this is your polynomial, let's say this is over the real numbers, right? Then clearly we can see that X equals one, two, and three are roots of the polynomial. This is a degree three polynomial, you can see when you multiply out the X's, you get X cubed there. This theorem is telling us that all of the roots are now accommodated, there's only three roots, there's not something else happening in this situation. But you don't have to have this maximal number of roots. For example, what if you took the polynomial X minus one squared, also viewed as a real polynomial, of course.  It's degree two polynomial, but the only root is X equals one. This case has a repeated root, and so when you count the multiplicities, you get all of the roots, you get one and one, so you count it twice, but we're not gonna engage in this conversation about repeated roots yet. That's something we'll have to talk about in a future, in a future video because for rings, I should say fields of positive characteristic, this can get a little bit more confusing. The real numbers, of course, are characteristic zero. So again, I will postpone that conversation for a little bit later.  Because if your polynomial f of X is equal to zero, if it's a zero polynomial, then you can evaluate at any number R and you end up with zero still. So every number in the field is a root of the zero polynomial, which is very likely that's gonna be a lot of numbers, right? But the zero polynomial, it doesn't have a degree, right? We did sometimes say, oh, the degree is negative infinity, but that was more of just a cave out, a cop out so that we could talk about formulas and such. Zero doesn't have a degree attached to it. When we talk about norms of domains, we don't define a norm for zero. And so zero, we don't have to talk about because even though it has every number as a root, it doesn't have a degree, so it's not a counter-example to this. So we do consider only non-zero polynomials. Let me first consider the situation where f is a constant polynomial, AKA a degree zero polynomial.  If I evaluate that at some number R, you're still gonna get the C. And since this is not the zero polynomial, f of R is never equal to zero, it has no roots. And so that matches with the formula, okay? Now let's assume that the degree of f is a positive integer. So it's one, two, three, four, or something bigger, but it's gonna be a positive integer. And so now let's apply the factor theorem here. The factor theorem tells us that if R is a root of the polynomial, because maybe there's no roots, right? I mean, that seems kind of silly, but at the moment in the development of our theory, maybe there's no roots to the polynomial.  There is no real number whose square is equal to negative one. The complex numbers include a root, but the real numbers don't. And so this is gonna lead to this idea of extension fields that we will talk about later on in this lecture series, but in that situation, it's degree two, but the number of roots is zero, and zero is in fact less than two. It's in accordance with this theorem that we're talking about right here. So if the polynomial has a root R, that is F of R equals zero, then the factor theorem applies and we can factor it as F of X equals X minus R times Q of X here, which necessarily the degree of Q is gonna have the N minus one, okay, by the additivity of degrees. Now, if that was the only root, then we'd be fine, because remember, we're assuming N is a positive integer and therefore one is less than or equal to N. If R was the only root, we'd be done, we were great. What if there's another root, say S? Well, if we utilize this factorization, then F of S is gonna look like S minus R times Q of S, and that's equal to zero because S is a root right here. But looking at the factorization, S minus R times Q of S equals zero. Now, since F is an integral domain, that means F of joint X is also an integral domain. We've talked about this already. And so the only way a product of two quantities can be zero is if one of the factors is zero. Well, could it be the first factor? Well, R is not equal to S, which means S minus R is not equal to zero, so it's not that one. So the fact that F of joint X is a domain would then force it so that Q of S equals zero. But Q of S has strictly smaller degree than F of X here. And therefore, we can then invoke induction here. So the induction of hypothesis would be like, oh, it worked for everything smaller. So the inductive hypothesis would tell us that Q of X has less than, it has in minus one or fewer many roots. Well, if you would join the one root we had from before, that means that F of X will have in minus one plus one, here's a secret for everyone, that's equal to N, and that's then gonna be upper bound on the number of roots that one has. And so this is a pretty nice result here that over polynomials whose coefficients come from a field, the degree gives you an upper bound on the number of roots. And this is then a very nice corollary of the factor theorem.


In Galileo's doomed experiment at the Leaning Tower, it turns out he was right all along. Different masses should indeed fall at the same rate, or have the same acceleration, in the absence of air resistance. The spectators completely misunderstood the true reason why the feather fell slower, which was because of air resistance and not because it had a smaller mass. Scenes at the church and at the Leaning Tower. Mention is made of Aristotle's law of nature. What is it and why is it incorrect? Can you think of any better laws? I'll give you a clue. One character in the film can't stop going on about them. Aristotle's law of nature says that heavy objects fall faster than light ones. Although our everyday experience seems to suggest this, in fact careful experiments easily disprove it. So Aristotle's law is a bad law or not a true law of nature at all. Newton's laws however are better because they explain many different things. Can be tested and make successful predictions. But on earth they're not common sense. Things just don't keep moving in a straight line at constant speed without a source of power.  The balls would be moving slower, so surely it would be easier to see what was happening. What are the pros and cons about doing it this way? Think about what's actually happening when the ball is rolling instead of free falling. Have a go yourself to find out.  I'll be using a ruler to start them off together. How about that Amy? When the balls roll down the slope, some of the energy of the ball that would normally make it accelerate fast is being used to make it rotate. So the effect is the ball rolls slower, or more precisely it accelerates slower. If we were to use say a can of drink and a can of solid food, we might even bear to tell the difference between the two. But overall we can conclude that this experiment definitely shows that Galileo was right. Different masses roll down the slope at the same rate. To improve on Galileo's experiments of dropping weights with all modern day technology at our disposal, how could we actually measure acceleration, rather than just showing that different balls of different mass reach the ground at the same time? Today we could use electronic timing to improve upon matters in Galileo's time, or perhaps a very high-speed video camera. However, for this demonstration, we're actually going to use something a little different. We call this machine Sparky because with the aid of a power source over here and a metal ball, we're going to be able to create sparks between this wire and a length of special paper. These sparks will be made 50 times a second. Now that means to say that when we examine the paper trail after the ball has landed, every spark will have been separated by a time of one-fiftieth of a second, and by making measurements with a ruler we can determine the acceleration of the ball. Okay, let's give it a go. First start the sparks, press the button. How about that then? What would have been the results if Galileo had dropped his weights under feather on the moon? There are two differences, Amy. They both fall together on the moon because they have the same acceleration. That's because there's no air resistance, but they are both much slower than on earth because of the lower gravity. A very similar experiment has actually been carried out and filmed on the moon by the Apollo 15 astronauts. They used a hammer and a feather. Well, in my left hand I have a feather, in my right hand a hammer, and I guess one of the reasons we got here today was because of a gentleman named Galileo a long time ago who made a rather significant discovery about falling objects in gravity fields. And we thought that where would be a better place to confirm his findings and on the moon? And so we thought we'd try it here for you. The feather happens to be appropriately a falcon feather for our falcon. And I'll drop the two of them here and hopefully they'll hit the ground at the same time. How about that? Well, we knew that Mr. Galileo was correct in his findings.


I'm doing another test here with the Intelligent Auto. We're just doing a video with the 8218 and now I'm using the 12-60 Leica lens and these are the Superstar lenses for the GH5. I love the fact that you call them Superstar lenses. These are the ones that we're proud of, these ones that we love to talk about. We've got the 12-35 f2.8, my personal go-to lens. I use it for street photography a lot so that even if I'm doing portrait shoots I can sometimes get away with this one.  This one has the most beautiful bokeh in the world. Yeah, absolutely stunning. If you haven't gone in then you should buy it. It's because of the glass in the lens. Absolutely beautiful. The 12-60 you're shooting on at the moment so that's the new Leica 12-60. It's the most popular one that goes with the GH5 currently and then obviously we've got the 8-18 that we've been speaking about which again like I say is the premier for here. All on the GH5 but we don't just do it's changeable lens. You'll notice in the end here we've got the FZ2000 so people that want to do video but don't want it to change the lens. We've got the FZ2000 which is basically very similar to a GH4 with a fixed lens. Inbuilt ND filters, 4k shooting, really really nice piece of kit. So people are excited about this for video because what is it? It has a great lens. It's a GH4 with a fixed lens is the beauty of it so if you want to get into videography but you don't want to have to change your lenses then primarily this is going to win because you've got a huge zoom, you've got a larger sensor, so one inch sensor, inbuilt ND filters and the ability to shoot 4k video. Let's see how big the zoom lens goes. So what you'll notice is even when I'm zooming okay it's non-trompony so that'll give you a really smooth zoom. It's really nice. I can zoom on the ring, I can zoom on the camera itself but it's non-trompony so I can get a really smooth zoom in and out. Stabilization, it's fantastic even at the long end, really handy piece of kit. Nice. All these cameras, does this one also use the same battery as the GH4 GH5? We use the same battery as the GH4 GH5 but what we try not to do is change our batteries. So what you'll find here is this is a BL12 so if anyone's got a GX8 they'll have a BL12 battery so we don't change them hugely. If you've got a G7 you'll have a BL12 battery so primarily you've got a kit already they just drop straight in and it also means that the charges are also interchangeable. Nice but when you look at this one you'd recommend people buy them all the lenses? Nothing makes us happier than someone coming in and saying I'll have all the lenses. That's what it means right? Panasonic Lumix G is get more lenses. Right there. I mean the thing is that's you know the best way isn't to have a lens that will do everything is to have a lens for that specific job and you really will notice the difference in the results. When you go to the premium lenses in the X-series lens and the Leica lenses you do absolutely notice the difference in the quality of image that you get. These feel cold. This one is not as cold? Yep it's because these are metal-bodied so what you'll find is they absorb any cold that's in the air but they're all weather-sealed and they're also dust resistant so wherever you want to use them you can. So this one these two have dual IS too? Correct. But these two don't? Nope. So the Leica basically what you'll find is that this is using the body stabilisation on the sensor and that's all it needs. If it needed dual IS and we couldn't get away with it we would fit dual IS however on this focal though we don't need it because the body stabilisation is good enough as it is. It's so wide you don't need it right there maybe it wouldn't even be possible because it's so special in there. Yeah yeah I mean to be fair everything's possible but it's about size and weight so for example you know we could make it a constant f2.8 but it makes it bigger and heavier. We could give it dual IS but it makes it bigger and heavier. All right what makes what makes quality of the image glass? The glass. So what you've always got to remember is the sensor captures the image. So when you're talking about glass anything you're going to put in front of that sensor any kind of glass is going to either deteriorate or improve the image. I think this is one of the things that people kind of misunderstand is without good quality glass you're always going to sacrifice the image quality. You know the investment should always be in really good glass. But the GH5 sensor and all that technology is doing all kinds of stuff. Yeah absolutely so the sensor will do great work but if you put something that's not as good as the sensor in front of it you're going to hamper that sensor. So to make the very best you have to have the best glass. And these dual IS too lenses have a new technology, new chip, new kind of technology that does this. So the new algorithm is to work with the dual IS. So that's why you would change if you're going to do video or anything else you do benefit from the dual IS. All right and which of these are in kits? So basically the Leica 12 to 60 is in the GH5 kit or you can get the standard 12 to 60 which is on here in the GH5. You can't get the kit with the Mk2? Nope. Nope. So you buy them separate. So you just buy it separate as a little treat to yourself at the weekend.


Welcome to the GVSU Calculus Screencasts. In this edition, we'll talk about equilibrium solutions to autonomous differential equations. Recall that a differential equation is autonomous if it's of the form dy dt is f of y, where y is a function of y alone, not t at all. So in this screencast, we'll discuss what's meant by equilibrium solutions of autonomous differential equations. Let's consider an example. Let's take the differential equation dy dt is y times y minus 3. Now an important solution to this differential equation is one in which the solution is constant, when things don't change, or when we think of things as being in equilibrium. Now a function is constant when its derivative is 0, so the constant solutions to our differential equation will occur when dy dt is 0. Pause the video for a moment and determine those constant solutions to this differential equation. Resume when you're ready. On our example, we will have constant solutions when dy dt is 0. That's when y times y minus 3 is 0. And this occurs when y equals 0 or when y equals 3. So y equals 0 is a constant solution to this differential equation, and y equals 3 is a constant solution to this differential equation. And we can see these solutions pretty clearly, these constant solutions. When we look at our slope field, it looks pretty clear that there is a constant solution y equals 3 and a constant solution y equals 0 to this differential equation. Now if we examine that slope field a little bit more closely, we can see that there are really two different kinds of behaviors for solutions to this differential equation that depend on the initial condition. Notice that we have an initial condition where y is bigger than 3, say, oh, right here maybe. Then when y is bigger than 3, dy dt is positive, and that forces the solution to our differential equation to drift away from that equilibrium solution y equals 3. Equilibrium solutions that are like this are said to be unstable or repelling. The solutions are repelled away from that equilibrium solution. On the other hand, if we have an initial condition where y is less than 0, say, right here maybe, then dy dt is positive, and that forces our solution to move toward the equilibrium solution. Similarly, if we start with a point where y is between 0 and 3, say maybe right here, then dy dt is negative, and that forces our solution to be attracted toward that equilibrium solution y equals 0. And equilibrium solutions like this are said to be stable or attracting, because they attract nearby solutions. To summarize, an equilibrium solution to an autonomous differential equation is a solution where the derivative is 0. So equilibrium solutions are constant solutions. They have 0 derivative. And if we have a system that's modeled by our differential equation, that system is said to be in equilibrium because nothing changes. An equilibrium solution is stable if nearby solutions are attracted to it. And an equilibrium solution is unstable if nearby solutions are repelled away from it. That concludes our screencast on equilibrium solutions to autonomous differential equations. Please come back soon.