So, we looked at the various dimensions of the food crisis, we looked at the need for distribution, efficient distribution of food resources and avoidance of waste to make sure that we have adequate food in the present, but in the future we need more food. So, we tried to investigate whether industrial agriculture is the solution and it turns out that according to what facts I have brought to this discussion, it turns out that industrial agriculture may not be the appropriate solution because it may actually lead to an increase in food insecurity. So, then we turn to alternative forms of agriculture and let us try to see if they can help us in this matter. Now, in order to understand why these alternative forms of agriculture actually are important or why they came about or why people develop them, let us compare anthroposystems or human made systems with ecosystems. In anthroposystems generally they are these are also similar to ecosystems, but they are generally more simple, they have they can have about three trophic levels, but they are open systems. So, again recalling from the lecture on sustainable development, we saw how you have resources extracted at one end and then the waste dumped at the other end. So, that is a characteristic of an open system. So, in our usual agricultural systems, they also operate in a linear fashion similarly there is minimal recycling that happens, but the advantage is that there is a high efficiency of transfer of biomass from one trophic level to the other trophic level. In other words, if you are looking at a rice field or a wheat field, let us say 50 percent of the mass of the plant is the food grain, then nearly all of that food grain actually gets consumed, it goes to the next trophic level, which is which is quite remarkable because in if you compare it with ecosystems, you will find in a forest, there is a lot of grass growing, but not all that grass gets even consumed by deer, so by the herbivores. So, that transfer from one level to the other that is very efficient in our anthroposystems, but our anthroposystems are very often they are monocultures and they are highly dense you know growth of one or maximum two or three species. In an ecosystem on the other hand, there are there is high biodiversity and very high density of one species alone is not very common, although there are there are instances of that too. So, what we do is we have some crop plants which we call as crops and then anything else, anything other than that is branded as a weed and it is to be eliminated. So, this is quite different and quite contrary in philosophy to how ecosystems work because in ecosystems there is nothing such as a weed, there is nothing such as there is nothing that is to be eliminated, things keep each other in check, one species will keep another species in check, but there is no need for total elimination. So, our human systems are static and they are quite unstable, so if there are any changes in the weather if the rain falls, either there is too much rainfall or there is too little rainfall or it happens at the wrong time, then your productivity takes a hit. Whereas, ecosystems are generally far stabbler, they are more resilient, they are quite robust, they are adapting and they are continuously evolving, so that thing is not there. So, if we really want to have food security, then we have to pick up some elements from ecosystems to make our systems more stable and more productive. So, I have similar numbers as shared by one of the remote centers from Shastra, I think it was Shastra, where we see that we depend on very few crop plants and although we have many more edible varieties of plants, but we do not depend on them and which is not a great idea and if we depend on very few species of plants, then we are risking, we are putting large populations at risk and the best example of that is the Irish potato famine where in a span of 3 years nearly one people died due to a combination of starvation and disease and why did that happen, it happened because the staple of Ireland was potato and the potato crop caught a disease which led to a collapse in the productivity and which led to starvation and all that. So, at the same time in Peru which was the cradle of the potato plant, they had a lot of diversity in the varieties of potato. In Ireland there were only relatively few varieties of potato and Ireland suffered major losses, but in Peru there were relatively minor losses and this kind of mass starvation never happened during that same period. So, we have several problems in our anthroposystems and we can only turn to nature and natural ecosystems to learn how we can improve our anthroposystems. Now, some things that are very clearly understood are that we need to adopt low input sustainable organic farming methods. Why low input? Because there are organic agriculture methods which require high input such as you need to add lots of manure and maybe some bio pesticide and labour costs are very high. So, such systems even if they are organic are not going to be suitable. So, we need to develop systems that inherently do not require very high inputs. There is another important thing that we need to do is we need to go for indigenous or traditional crop varieties which are locally adapted. The benefit is that if the plant is adapted to the local climate, soil, moisture conditions and including the pests and diseases, then the your agricultural system becomes more self-supporting. You do not have to prop it up with various inputs from outside and then it tends to be more profitable. There is a need to improve farm diversity and if at all required some organic or biological pest management methods can be used. So, we will just take a brief overview of that. So, based on these general principles, many people have developed different varieties of agriculture and they name it differently. So, if a person is more preoccupied with the notion of sustainability, then he will call his farming a sustainable farming. If somebody is develops a farming technique and he is very interested in mimicking nature or something like that then you call it ecological agriculture or things like that. So, there are various types of or various brands of organic or alternative agriculture and all of them have some common features, but then they differ in many other features also. So, I have kind of made a summary of the various features or characteristics of these techniques, what all activities or processes that they have and how each of those activities or processes gives you some environmental benefit. I had a similar table for conventional agriculture where I showed how each of the agricultural processes have got some adverse environmental impact. We are developing alternatives only to remove those adverse environmental impacts. So, some of the characteristics of these farming techniques are listed over here. So, somebody is let us say tomorrow I become an organic farmer, I may choose no till or minimum tillage methods, ground mulching and inter planting. So, my brand of organic farming may include like these two or three features. Somebody else's brand of farming may include some different combination of these. This is what this table actually means. So, among them no till is something that is quite interesting and maybe you can look up on the internet about no till methods of farming, tilling or tillage meaning plowing. So, there are methods by which even without plowing you can get good yields. You would be surprised that in the US roughly 5 percent of agricultural land is under no till cultivation. Now, you may say that it is so good that US agriculture is doing good things, but it turns out that they use copious amounts of herbicide. So, that is not really that good. There are methods of no till agriculture even without herbicides and I am going to show you one such method. Ground mulch is one very important thing that can benefit Indian agriculture in my opinion. Mulching is covering the soil with either living or dead organic matter. So, either you have a green mulch which is living plants covering the soil or you have a brown mulch which is dead organic matter leaf, litter or agricultural residue from the previous crop that can be put on the soil. So, if the soil is covered then it does not get overheated due to sunlight, the UV sunlight does not kill off the beneficial soil biota and the drying out as well as the oxidation of humus is hindered. Moreover, the mulch also provides micro habitats for predators of agricultural pests. Now, there are fears of some diseases also finding that mulch as a fertile breeding ground. If there are adequate quantities of natural predators then it has been observed in many of these organic farms that the pest problem does not become such a severe problem. Moreover, if you mulch the ground adequately then incidence of weeds also reduces because the weeds if the soil is covered by a thick mulch the weed plants cannot sprout up. So, that is one important benefit. Inter planting I think the benefits of inter planting are quite well known in inter planting or inter cropping improves crop diversity and in that in the species that they normally plan it is common to have some leguminous plants to fix nitrogen and that benefits the system. One more feature which is often not given adequate attention is the role of beneficial organisms such as earthworms and bees there are many others there are wasps also. So, these are creatures that actually are our friends and they provide various services such as in the case of bees they pollinate plants even birds do that earthworms you know are very important for the soil the wasps for instance are they feed on the pests of plants. So, if we provide shelters where wasps can have the nests then you are you are building up resistance towards pests in your agricultural system. There are many more points and again as I said each of them is like a hyperlink there is much to learn and much to know about each of them. So, I think teachers should those who are interested should take the time to do that. Farm diversity is very important the indigenous crops with diversity is one of the most important features everything starts with the seed and it is important as Dr. Vandana Shiva explained to us that the seed is the birthright of the farmer and it must always remain in the hands of the farmer and it is the farmers have to develop and maintain their own seeds so that we get good produce. So, there are there are many slides with a lot of detail and I leave that to you I am going to take a few questions that that many people ask about organic or alternative farming methods the first one is that whether it can feed everybody. So, I have taken them one by one and I am I am kind of going to go fast on that the explanations are provided over there, but I will briefly just touch upon them because unless those queries are satisfied we do not we do not feel that it actually is a good solution. So, in the context of future food security I do not think either conventional or organic or any agriculture is by itself going to be enough and the reason I am saying that is if the population continues to rise unabated, if land degradation happens to increase as at the rate at which it is increasing, if climate change also happens and if the water crisis again grows to the proportions that we expected to grow and I do not think any farming method is going to be adequate, but there are there are modeling studies that show that organic agriculture if implemented on a large scale will not reduce the productivity in fact it may increase it in the long run because it will actually slow down each of these problems which I just mentioned except for population it will slow down the others. For instance it may it will slow down land degradation it may even enrich the soil, it organic systems if designed properly not all organic systems, but properly designed organic systems can be designed for low irrigation inputs, still yielding high amount of calories. So, in that sense there is there is lot of promise in organic methods as opposed to the conventional methods where you are assured of land degradation and over exploitation of water resources as well as pollution of the environment and the health effects. So, in order to actually ensure food security we have to work on all these aspects together that this is what I started my first session with sustainable development where I said that in order to solve one problem you must also be working at all the other problems also you cannot expect that only by making some slight modifications in your agricultural systems that you can ensure future food security you have to deal with the water problem also and many other things. So, if all these things are done together then organic farming will actually be more than satisfactory and it will be it will pave the way towards future food security.  Now it turns out they do give high enough yields I have some references over here there are many more and I have spoken to and visited many farms of good organic farmers as I said you have to get it right that applies to anything even I mean it is like saying if you if you drive a car can you can you go fast yes obviously you can go fast, but you have to learn to drive a car if you do not know how to drive a car your car may not even start moving. So, there is an element of learning there is some time that may be required, but once you get it is definitely going to yield high. So, this large survey found that in the case of irrigated lands transitioning from conventional agriculture to organic agriculture gave only a marginal benefit only slight improvement in benefit because the irrigated lands were already operating at high productivity, but in the case of rain fed crops because of water stress and low soil fertility the yields which were very low upon conversion to organic farming the yields increased quite drastically from 50 to 100 percent increase. And that mainly comes from a addition of organic carbon in the soil better availability of nutrients the soil being able to hold more moisture and the diversity that in many projects were was included. So, you had some leguminous plants also in that all these factors contributed to increasing the productivity of rain fed crops. Now, this is very significant because 65 percent of India's arable land is rain fed. So, we need to find a solution for increasing the productivity of those rain fed crops without placing an additional demand on the water on water for irrigation and those crops which are those lands 35 percent which are irrigated they can make do with much less water. So, that water is freed up for other other uses. Now, there is a transitional phase if you are if you have over exploited the land and added lots of chemical fertilizers and the soil quality is very low then maybe it will take 1 to 4 years for the soil and the entire soil ecosystem to kind of rejuvenate during which period there may be slightly reduced yields about 30 percent you may take a hit in the yields in the transitional phase, but after that they will stabilize again to a high productivity level. Now, if those products are organic then in places if they are certified and if there are proper outlets for that they you can command a premium price. Now, that is not always always true because access to such stores and such markets has to be there and some of them require certification which is an extremely tedious process and in fact, it is in my opinion it is unfair because the people who are polluting they do not have to go through this extra exercise, but the people who are doing the right thing they have to go through this enormous pain. Now, there is another factor which I had mentioned in the context of food forests of over yields that take place in polycultures. A polyculture is a system in which you have multiple species that are planted together and the combined output of these multiple species exceeds the monoculture in many cases. So, that is called as an over yield. Now, in the traditional in Mexico they have what are called as the three sisters. So, they do not plant corn, corn is their staple, but they do not plant corn alone. Corn is it is almost like sacred to them they plant the three sisters together and the three sisters are they plant corn they have these mounds of compost and some mulch and in that they plant these three sisters one is corn the second is a variety of beans and the third is a variety of squash. So, the three together give some synergistic effects and the over yields as compared to a monoculture are about 50 percent. So, the reason they give the over yields is the corn plant requires some nitrogen which is fixed by the beans and the bean requires some support. So, it climbs on to the corn the squash prefers the shade and it spreads on the ground since it is covering the ground the ground retains better moisture it is a green mulch kind of. So, the soil remains more fertile and the overall productivity is higher. Now, some studies have even found over yields as high as 150 percent. Another study has found a consistent 15 5 to 15 percent increase in yields due to intercropping. Now, there is a move towards perennial polycultures. So, if you instead of having to do all those agricultural operations starting from ploughing the soil then seeding and then weeding then adding fertilizer and pesticides and all. So, many intensive activities that are conducted in agriculture if we have a perennial system which you do not have to replant it will seed itself or those plants are long lived and you simply go there and you harvest and you take what you need and the system is kind of self-standing. So, you do not have to do all those things. So, there is a land institute in the United States where they are working out various combinations of plants which will remain there perennially. I showed you about one food forest that existed for 300 odd years. I now want to show you a video of how starting from scratch you can start a food forest. So, this is a food forest that will give mainly it will give fruits, but it does not have to be that way you can change the species and you can have it give even vegetables and things like that. So, this is a 7 minute video which is going to show us the various stages in actually making a food forest. Remember that the food forest is a perennial system you do not have to do all those regular operations. In the initial setup phase you may have to do a few operations which are again very easy operations as something as simple as just chopping the plants a little. The reason they chop the you will hear a phrase over there called chop and drop and the principle is that a plant has the roots which are sucking in moisture and the leaves which are transpiring. So, there is a kind of a steady state that is set up.  So, the sap will ooze out. So, in order to prevent that when the shoots are chopped the plant sheds some of the root biomass under the soil it gives up some of the root biomass it reduces the biomass. So, that biomass is added to the soil which starts to decompose and that decomposition process is enabled by soil organisms large numbers of fungi and bacteria actually proliferate over there which enriches the soil. So, when you repeatedly do that the soil gets enriched and kind of a regenerative process sets up. So, exploiting this process and then some other things they are going to actually engineer an artificial ecological succession. People who know about ecology a little bit there are some pioneer species that on a barren or an abandoned land will first strike root over there and grow. They will produce some biomass and improve the soil and these with improved conditions then different species of plants will then find it easy to grow over there. So, the species mix goes on changing as the as the region finally matures into a forest. So, this ecological succession that happens naturally they have tried to engineer it to make a food forest. So, in a short period of about 5 years you can have a nice tall standing food forest. Let us see how. The interesting thing about that it is pretty much self-standing after it is established it does not require any inputs from us as the as I said your input may only be required to increase or to manipulate the production of the various species. He said that there are some what I am talking about such a thing is resilient to climate change because you have woody trees which are which are much more resistant to small spells of drought even if even if the monsoon fails we have in India we have a monsoon climate. So, it is sometimes the monsoon does not provide enough rain and if the monsoon fails then your the regular monoculture crop will suffer very serious problems, but such a forest is more resilient and the species can be determined or can be selected based on the local conditions. So, what grows over there locally is absolutely the starting point for choice of species. Exotics are generally not a good idea, but there are in India I have seen that people who have tried to make this food forest they use some exotic species particularly as the pioneer species and then they gradually eliminate them. So, that is also another approach to take. So, what is the what is the secret profitability of organic systems? See there are see you have the profit is the difference between the two. So, there are two ways either you can increase your output or you can reduce your inputs either way you get profits. So, in organic systems the output actually is high or as we saw in according to some studies it is it improves it is even higher, higher than the regular or the conventional methods using monocultures. So, the outputs are high and the inputs are quite low. So, if you design systems specifically to be low input systems then your inputs will be very low. So, as a result your profit is quite high and then the additional advantage is that the inputs that are required are not external inputs meaning you may be adding some manures, but they may come from the livestock that is already there on your farm not some chemical fertilizers purchased from some multinational company. If you have adequate mulch in your farm then even the weeding labor cost related to weeding and all can come down significantly. So, this is how you can actually ensure that these organic systems are economically feasible. In there is a study which talks about the economic viability of organic cotton and they found that over a period of 6 years in the case of cotton there was a reduction in cost of cultivation and there was an increased gross as there were increased gross and net returns. So, it actually works out in many cases. Now, organic products retain better quality they even post storage they have they retain their quality and the spoilage during storage also is less. There are some people who have argued whether since you are putting manures which come from animal dung or something like that might lead to some diseases or things like that whether they are safe or not, but many studies have found that there is there are no health risks to exposure from microbiological contaminants. Of course, the compost have to be made properly you cannot mismanage things and expect favorable results. So, there are procedures there are there is a good way of doing it and there are bad ways of doing it, but if done properly then that this is not a major concern. In fact, they are quite superior and healthful in on a number of parameters the amounts of vitamins and minerals and things like that they have fewer mycotoxins which can be a major problem. Pest management is again one area where you do not wait for the problem to happen. You start by feeding the soil you make sure that the soil is fertile how do you make sure the soil is fertile? I showed you that video on soil conservation practices. Moreover, we have to cover the soil with mulch make sure there is adequate organic matter the soil should have balanced nutrients. The plants that grow the crop plants that grow in a in healthy soil if they come from good locally adapted indigenous seeds then they will be quite resilient to both climatic variations as well as pest attack. So, such healthy plants will require very little inputs from our side for pest management.  There is a variety of natural predators that that are found in a in a farm environment some of them are spiders, wasps, frogs, lizards, birds even. So, they are they all feed on the different organisms different insects which are pests we consider as pests they consider that as food. So, the enemy of an enemy is a friend. So, encouraging these organisms now these spiders and wasps they do not feed on your crop there is no need to eliminate them in fact they are beneficial. So, we should encourage them spiders do an important job even if the spider does not have to consume that insect right away many insects get caught in their in their webs. So, they are they are eliminated from your farm. So, giving them good habitat itself is a is a big contribution to the pest management and then in the eventuality that there is some uncontrolled pest attack there are there are alternative organic pesticides such as neem and there are many others many other concoctions that can be made because this kind of intervention should be done at the very last stage the main intervention begins from the soil and choosing the right right crops main protecting the the natural predators of the pests. If these main things are taken care of then with with minor inputs of some organic pesticides the job can be done very easily and at least this is this is how many people have many organic farmers have managed it. Just because you and me who have very little experience if we try to make some experiment and it fails it does not mean that it is it is a failure because there is a learning process and I am I am repeatedly saying that because during my college days I did a number of such farming experiments on my father's farm although very small farm, but I did very good experiments on that I learnt a lot, but I I I actually do not mind sharing this and most of my experiments failed, but it is through the failures that I learnt and success comes only after after many failures, but when it comes you know it really gives you a lot of satisfaction and I will just tell you what what those some of those experiments were in a bit. Organic farming is more environmentally friendly as this review of over 300 published reports says on various parameters organic farming was found to be more environmentally friendly than conventional farming. Now this is important to understand because it is not even organic methods can end up damaging the environment. There are environmental impacts even of organic agriculture methods, but it turns out that they are smaller than the conventional methods. Organic input is very important organic input to the soil there is a lot of surplus biomass and I told in the energy chapter that surplus biomass if there is anything that requires that surplus biomass then it is the soils that require it because the soils are the place from where we get our food. So, the first priority should be given to feeding the soil and if you add the surplus biomass to the soil as mulch you can or in the or after composting as compost. For every ton of carbon added per hectare to a degraded soil it can increase crop yields by 20 to 40 kg per hectare for wheat and 10 to 20 kg per hectare for maize. So, it can it achieves multiple ends you require less external fertilizer you can enrich the soil you can also sequester carbon. So, the soil holds more carbon otherwise that carbon would have oxidized and gone into the atmosphere. No tilling no till methods are probably the best for protecting the soil because every time you run a plow through the soil you damage the roots you compact the soil and all these destructive processes kind of start. This is a 12 minute video that I am going to show you, but I want to save it for the last. So, I want to save the dessert for the last. So, although it is relevant over here this is about a veteran Gandhian organic farmer Mr. Bhaskar Savai who has won several awards he recently passed away but not without contributing immensely to the field of organic agriculture and he is a very, very well respected figure in this area and I was very fortunate to have met him in person I stayed in his house I visited his farm along with a friend of mine. So, watching that video actually gave me very good memories of my college days. So, we will watch that towards the end. Also in this context people who are interested in organic agriculture may be organic gardening I mean you do not have to do it as a profession. I strongly very, very strongly recommend reading this book The One Straw Revolution by Masanubu Fukuoka. He is a Japanese person again he passed away a few years ago, but he is probably can best be described as the grandfather of natural farming. His method is agricultural method is so unique he does not till the soil he does not I mean he makes seed balls. So, he takes a mixture of clay compost and the seeds and he just makes it into a dough and make the mix these maybe a centimeter or size balls and dries them in the shade. And even in that the seeds that he add he adds a mixture of seeds and then he simply tosses it onto the field covers it with the straw of the of the last season and allows the rains to come and then the crop sprouts it grows above the mulch the brown mulch and he also grows among the seeds is also a nitrogen fixing cover crop called as white clover which is very similar to alpha alpha if some of you know about it. So, the cover crop kind of covers the ground and the rice grows up and then he when the rice is about to be harvested maybe a 15 days 2 weeks before that he similarly sprinkles balls of containing wheat or barley seed for the winter season and then he harvests the rice threshes the rice puts the straw back on the field the wheat sprouts through the through the mulch and so basically he has the wheat and rice in succession and the productivities that he has got are just phenomenal. I mean they can compare with the best farms in the world and he absolutely does not add any fertilizers or chemicals there is no weeding his fields have the cover crop in plenty and there are many weeds in his field but they are they are adequately suppressed by the cover crop. So, they do not really compete in a big way with the with the rice crop rice or the winter grain crop. So, it is an awesome book and he talks about many things apart from the actual practices the agricultural practices that he follows he talks about many things related to food agriculture and you know long term food security also. So, it is a must read this book is out of print it has been out of print for decades even when I got it I think 20 years ago it was with great difficulty, but now people have made pdfs of this and this is you just click this link and you will find it a pdf for download. There are many videos related to his farm this 24 minute one is quite a good video you can watch that there is a longer one hour video also available you can search for it on your own and watch that, but definitely it is worth learning for people who are interested. Other important thing which I touched upon and this is a kind of a sensitive area for many many people and they do not want to address this problem they just want to brush it aside or you know pretend as if they did not hear, but I am taking some risk over here and still going to talk about it. It is about vegetarianism and its relevance to the the environmental problem the food problem. It turns out that even the IPCC chairman also made a statement in Geneva that it is vegetarianism is one of the best ways to fight global warming and there is a reason for that. You see that world meat production has increased over the past half century it has increased nearly five fold and as I explained to you based on the trophic pyramids if you instead of being a primary consumer if you are a secondary consumer that is a meat eater then you require much greater land to support you much greater quantity of the autotrophs which are the plants and plants require land area. So, you require much more to feed you now this data is a little out of date when the world population was 6 billion, but at that point the 6 billion humans shared the earth with 1 billion pigs, 3 billion cows, 1.8 billion sheep and goats and 13.5 billion chickens. So, that is 3 heads of livestock per person even now I think the numbers are not going to be any less if at all they might have increased. So, this again shows how meat consumption has increased. So, has human population, but again some of the livestock types like chickens have increased very drastically. If you compare with other countries India is way down as expected the United States is somewhere at the top in meat consumption and India is somewhere at the bottom. So, in that sense that is thanks to a lot of large proportion of Indians who are vegetarian even the people in India who consume meat they do consume significant amounts of vegetarian food and then they have a few non vegetarian dishes which is quite different from the diets in other parts. This talks about the protein intake and you know what is where we source our protein intake. In India we large fraction of our protein intake comes from plant based sources. Meat eating is actually implicated in a number of health problems and even the Chinese government has noticed this problem and there is a call for moving away from particularly from red meats. So, there is nearly literally an explosion in the cardiovascular disease and cancers in the proportion of cardiovascular disease and cancers. There are researchers all over the world other than Indians also who claim that the low quality plant protein which actually allows steady synthesis of new proteins is actually healthier as compared to the high quality animal protein. We all understand that animal protein is considered to be high quality protein compared to plant protein. But it is actually the lower quality which is better because it is consistent with less diseases and longevity also. So, there are these vegetarian based diets which can keep your cholesterol level very low and where the risk of cardiovascular disease is very very small and quite insignificant at least until old age. At the turn of the century heart disease and cancer were very small contributors to death but now they have increased quite drastically which is something to be concerned about. So, according to this scientific American article the best diet for humans for infants it is mother's milk and for adults it is fruits, vegetables, whole grains, pulses and nuts. So, this kind of a diet is the best for humans according to this article and I know many Indians who are claimed vegetarians they are actually the majority of them are lacto vegetarians. So, in other words we consume milk. Milk is not strictly vegetarian but it does not involve killing an animal. So, we kind of associate it with vegetarianism but consuming the quantities of ghee and fried items you know the vegetable oils that we consume you cannot claim that to be a healthy diet. So, although Indian vegetarian diet kind of generally fits in this diet but sometimes the amounts of fried foods and the ghee that some people use is just too much I mean I do not think that can come anywhere close to a healthy diet. So, there are even people are even thinking that there are some studies which say that the meat industry is actually a drain on the American economy because they consume so much of meat it just turns out that the sales of meat in US are almost equivalent to the healthcare costs in the US. So, there appears to be a relation between the two that you eat more and more meat and you spend money in the hospital for treatment of cancer and cardiovascular diseases. It is quite likely that there is a possibility that it is a net drain on the American economy and why America because they consume more meat. So, the effects are obvious in that. When so many people are starving is it yesterday in the last session there were some discussions about ethical issues being part of the sustainability discussion or the sustainability discourse and these ethical issues come in the choice of food that we have in the consumption of various resources, in the consumption of energy, in the choice of energy sources that we choose. Ethical issues are come up everywhere and particularly when we are faced with so many starvation deaths to divert some of the food that is available to cattle feed definitely is an ethical problem and we need to address that. What is the problem? You may say that I am diverting some grain or to feed the animal and then we are getting the meat from the animal. So, that does not work out as easily as that because for getting 1 kg of meat you have to spend 7 kgs of grain, but those 7 kgs of grain could have directly fed many more people. With 1 kg of meat you can feed fewer people, but with 7 kilograms of grain if cooked you can feed many more people. So, if the food grain that is diverted towards livestock is actually taken up by humans it can either completely feed everybody or at least to a large extent. So, these are some kind of interesting numbers if an American reduced his meat consumption only by 5 percent then he would end up feeding all the hungry people in the US and if he reduces it by maybe 50 percent then maybe he can feed all the poor people in maybe few other countries also. So, this talks about 6 kgs of plant protein is being required to create 1 kilogram of high quality animal protein whereas that 6 kgs of plant protein if directly given to humans then it will actually satisfy the requirement. Now, meat eaters contribute to greater energy use as compared to vegetarians because meat consumption requires 20 times as much energy to produce 1 calorie of animal food. So, this tabulates the energy consumption of so, how much energy is put in and how much energy do you get. So, you have to put in 4 units of energy to get 1 unit of energy through meat, chicken. In the case of beef you have to put in 54 units to get 1 unit of energy and in the case of grains this is a little surprising and there is a reason to for that for grains it appears as if you have to put 3 units to get 1 unit that is not entirely correct because that may be so for industrial agriculture where there are lots of fossil fuels that are used to given energy. But the traditional food production systems and particularly the polyculture and the no-till natural farming methods of Okuoka they are they require an insignificant amount of energy to be put in and you actually get energy and farming or any growing plant should not require energy inputs to give you energy output because it is taking energy from the sun. The energy that we put in is really not even required for natural ecosystems. They take all their energy from the sun which is not factored in this calculation. So, really speaking no energy from human being should be required but nevertheless we do have our agricultural systems which require some human labor or some things. So, some small quantities of energy alone will be required. The factory farms of livestock they actually contribute to lot of methane emissions. They consume huge quantities of water to produce one pound of beef some 5 tons of water is used and for lettuce and tomatoes and all these vegetables very very small quantities of water is used to create one pound of food. So, water consumption again is energy consumption is high for meat water consumption is also very high for meat. If you pass up one hamburger then you would have saved water enough for taking 40 showers with a low flow shower head. So, even if you are consuming meat then shifting from pork to chicken will require half the grain and half as much of water. But in reality these livestock farms are so big and they are even increasing that the waste from these farms has become a problem. In fact, there is this pig farm somewhere in Utah which produces more sewage than the city of Los Angeles and Los Angeles is among the largest cities in the world. So, this one pig farm over 50,000 acres produces more sewage than the city of Los Angeles and livestock in the US produces 130 times as much waste as humans. Land requirements again you require much more land if you are dependent on beef and other forms of meat, but you require less land if you are vegetarian. So, the graph over here shows that the calorific needs of how many people can be satisfied on 2.5 acres of land. So, if you have beef then you would satisfy only one person, but if you are eating getting all your calorie inputs through cabbage then maybe 23 people can be supported on 2.5 acres. A similar calculation is made by Fukuoka in 1985. So, when the world population was 5 billion. So, he said that if everybody is consuming grains alone as their main diet then you could support 60 times the world population at that time meaning 60 times 5 billion. So, many humans could be supported on the earth's land area and if everybody ate potatoes then it would be 20 times if everybody ate beef then it would be only 5 billion that can be supported. Okay, topsoil loss again over grazing leads to topsoil loss this is a major problem. Again the most uncomfortable topic in this context of vegetarianism is animal slaughter. Some even in the United States alone some 9 billion animals are killed for food each year and all this is when plenty of vegetarian food is available for Americans. So, the same applies to urban Indians there is no shortage of vegetarian food in the urban places. So, when that is the case it is clearly a choice a preference it is not a matter of need there is no need for consuming non-vegetarian food it is only a it is a matter of your tongue and for that for the sake of that if so many animals are killed how can we run away from the ethical aspect of this issue. So, many people have on on spiritual or similar philosophical grounds have favored vegetarianism including Gandhi and many other followers of Gandhi and there are there is the Jain community in India which is very vehement about vegetarianism and so definitely some of their arguments are worth taking into consideration. Reducing meat is actually a win-win situation because you will if you reduce meat not only will your health improve the environment will also benefit and it is also more ethical. So, in all contexts actually reducing meat is good it is very much possible with a vegetarian diet to live a very happy healthy life free of disease meat is absolutely not compulsory. So, and again some animal protein that is required can be taken through by way of milk products. So, a lacto-vegetarian diet seems to be a good balance. I am not saying that there are no ethical issues with dairy farming there are ethical issues nobody is exempt from those issues. There are unethical practices that happen even in dairy farming, but it does not mean that since some unethical issues are unavoidable therefore, you do a massacre of 9 million animals it is that is not justified. The unethical issues that happen in the dairy industry should also be eliminated that is my stand on it. So, what can you personally do to alleviate this problem? I have a long list of things support local produce grow your own food urban gardens rooftop gardens. If you have some land somewhere in your native place you can try to move to organic farming support local farmers and consumers sometimes when they have excess production you can take it up that time you need not I know everybody is entitled to their choice of what they want to purchase for food, but if there are local farmers and if they have surplus production we can accommodate them if you accommodate them then spoilage of food is reduced and it helps the environment helps the farmer. MNC marketed GM crops can be a problem and they should be avoided if whenever possible home cooked food is best preserved food has got lots of embodied energy and it is not even as healthy. So, that can also be avoided those who are vegetarian great those who are not vegetarian can consider sparing some of the grain and some of the arable land for feeding poor people and reducing their meat consumption. Lokmanya Tilak in this context made a very interesting statement he was writing a letter to his nephew who was going to the west to UK for higher studies. So, he gave his very fatherly oncular advice to his nephew and he basically all the good things you know that hold on to your values all that glitters is not gold you have to work hard and things like that all good things and in that he even made a statement which can roughly be translated like this in the letter was in Marathi, but can be roughly translated like this don't turn your stomach into a graveyard for unfortunate dead animals. This was one of the advices that Tilak gave his nephew. So, we have so many things that we can actually do for this and we have come to the end of this session. I want to end with this beautiful video of Shri Bhaskar Save who is a Gandhian organic agricultureist in South Gujarat the Maharashtra border very close to a place called Dhanu the actual village is Umbergao. So, let us watch this video it's a very nice video there are some interviews with him in which he speaks in Hindi, but there are English subtitles. So, if there are people who are sitting at the back of seminar hall I request you to please come up front so that you can read the subtitles in case you do not understand Hindi. So, the video is actually a documentary in English, but there are some interviews that are in Hindi. I visited his farm when I was in college I really enjoyed it it was such a great experience the discussions that I had with him and they kind of molded my thinking in many ways. And one interesting thing he makes he has Chiku achhats Chiku sapota and some of the sweetest and the most delicious Chikus that I have ever eaten pure sugar they are so sweet and so tasty I cannot forget that I just thought I would share it with you. I hope everyone enjoyed this movie I wanted to keep this for the last like a dessert. I hope that in these all these sessions starting on Tuesday from the sustainability talk and the talk on water and energy and this one on food. I have tried to share many different perspectives with this huge audience of all teachers. This is I think what I have shown are these are some pointers to the best of my understanding now there is no guarantee that that is the best or that is the only perspective there are many more perspectives. But I feel that some of the things that that are shared over here are definitely worth further investigation. And all of us are very qualified very mature people. So we are capable of doing that inquiry of investigating further and taking this forward and to make it very meaningful personally to ourselves as well as our students. So if I would say that really we need to only open our eyes around there are natural places you can learn directly from nature you can learn from people who have learnt about nature such as this great gentleman we saw on the video. So that is all I have to share with you and this completes my set of sessions that I will be sharing with you. Okay so with this I take your leave thank you very much for hearing me out.


Well, welcome everyone, it's a pleasure for me to introduce Professor Fernando Llegas. He will talk about Bled, a mathematical puzzle. Thank you. So, this is a puzzle that I worked on many years ago with two of my colleagues at the time and UT Austin, Lorenzo Sadun and Felipe Voloch. And if you are worried or curious about the name, you see there my daughter Malena is being thanked for providing the name and it's a complicated story why that happened. This puzzle, we were pleased with my colleagues at the time, made it to this website, puzzles.com. They even made this little logo, but anyway, what I'd like to tell you is some mathematics that's behind it. This was part of a course that I taught in Austin where the, with the excuse of discussing various puzzles, I discussed some mathematics behind them. So this is one, probably the more sophisticated in the sense of what mathematics it involves. So let me first tell you what the puzzle is then. You start with a sequence of A pairs A and B arranged in a circle, say N is the number of A's and B's, going to be an even number. And this is the starting configuration and there's two rules that you can use. If you see a pattern of the form A, B, A, then you can change it to the pattern B, A, B. And conversely, if you see the pattern B, A, B, you can convert it to, to change it to the, to the A, to A, B, A. And the, so this is the allowable moves and the goal is to maximize the number of A's or maximize the number of B's or maximize, minimize either one because it's, it's all very symmetrical. And this is a clear direction in which goes towards your goal. If you see a pattern of the form B, A, B, this has only one A and if you change it by the pattern A, B, A, now you have two A's. So this direction is the, is the greedy direction that will increase the number of A's. And this puzzle, I don't think or claim to be particularly interesting in itself. I mean, and if the only interesting I have, if you actually try it on your own a little bit and see what is behind it, but unfortunately then that would mean that I couldn't give the talk. So I'll spoil the little fun there might be and tell you what's behind it myself. But it's an illustration of this problem that greed is not the answer, typically. Because if we have an implementation that I, I'm not sure I'll be able to show you right now, but so an implementation just to illustrate has N equals 28, so you, you click, so one way to think of this is that you can click on such a pattern on the B and it converts it into this or you click on this pattern on the A and it gets you the other one. So that's an implementation of this idea. And if you're greedy, you only get the number of A's to go to 21, but in fact the maximum possible is 23. So this, let me just say a little bit about the, the type of problem. Okay so first, first of all, I don't know if you, if you seen, you must have seen something like this. This is peg solitaire and the, this is sort of a similar type of idea. So you can say that this puzzles are all involved replacing a pattern by another one following specific rules. So if you think of peg solitaire is, if you have this A's now correspond to two pegs in blue and B a blank. So you can move this peg over to the blank and take this blue one in the middle out. So it goes from B, A, A, B to B, B, A. But this, in this puzzle, you only go in one direction. You can't go back. Once you do a move, you're done. You can't undo it. And here the goal is also similar is to minimize the number of A's which would be the number of blue pegs and in this game you can actually achieve one. It's one of those things that I played this when I was a kid about 10 and I managed to be able to solve it. And then later on I got interested in this type of connection between mathematics and puzzles and I even had a book in John Conway of Cambridge is famous in many, many aspects and one of them is interesting this type of stuff. And as soon as he wrote a really nice book which I refused to read until I could solve the puzzle again and I just never could. So I don't know, progress it doesn't seem to always go with age. So in any case the issue here is we have a space of possibilities, yes? What is not allowed? You can only change this pattern to this one or backwards. In the other game you only find the sun correctly. You just do the puzzles the way the pegs, the way I illustrated. If you have two blues with a space ahead then you can move one peg over the other one and remove the one in the middle. That's all you can do. You can do it horizontally or vertically. And the idea is every time you do this you have one lead speg and you have to keep doing this and the goal is to get to just one peg at the end which of course you cannot take because there's no other move possible. And if you try this you'll quickly find out that to get to one peg is not completely trivial at all. So the general picture here is that we have some kind of space of configurations which is typically very big. In something like this I haven't been able to recall how many, I have computed how many of these configurations possible there were but it's some big number of states and we are sort of navigating through this to try to minimize some functions. So we try to minimize a function on a discrete space and that's a difficult problem. There's no calculus here to help us. So let me just say a little bit about the question of minimizing discrete functions which is again I view this as an excuse to discuss this topic. And when I first started with this puzzle I used this method to try to understand what was happening before we eventually found with my colleagues a solution. So this is in a sense unusual typically if you have a problem of this kind there wouldn't necessarily be a way to actually solve it completely which is what we have in this case which in a sense is the topic of the talk. But let me take a parenthesis and discuss very, very superficially this question of maximizing or let's say minimizing a discrete function. By that I mean I have a large discrete set and some function on that set that we want to find a minimum value of. So to just schematically let's think of the X variables which are the possibilities in our space. I think of it just to do a graph as a one dimensional thing but you should think of this as some big space and then we have a function which from the point of view physics would be energy so call it E and then the graph may look like this and what we're trying to do is find the minimum values or one minimum value let's say it's only one so we're trying to reach this point by moving in this space. So we don't really have much way to guide us as to you can't quite see as this is the minimum this is where we should be going. So let's say you start at some point or maybe the point is given to you and this is where you should start and so what we could do is so schematically let's think of the state that you're at X zero here then you make some move towards a neighboring point which you could do perhaps randomly and what you do is you compare the energy at the neighboring point and the energy at the point you were at and if the energy at the neighboring point is smaller than the one you're at then you're happy because that's a better point and so you take it it's typical this is one up one way to do it and now the question becomes what happens if you, if the point that you pick is actually worse well if you are greedy you always want to go down and you will only take it in this case and in this case you just don't take it and try a new one so what happens with that idea of greedy is that for example if you start here and you keep moving then you're gonna get stuck at this point so greedy may result in stuck at local minima. You take not a random point but a neighboring point the move you think of it as something that is sort of nearby yeah but even then yeah so yeah you should think that the moves is something that takes you reasonably close by you do a small modification of your problem like here you can have you sort of think of this is a huge circle they do a tiny modification you move to a neighboring configuration so the idea that comes from from physics is resulted in an algorithm in this in a sort of vague sense not not too specific got the name of simulated annealing so when you annealing is a process where you take a say a metal and you heat it to a high high temperature and then you let it cool very very slowly okay and so the heating kind of freeze the atoms to do whatever they want and the cooling kind of lets them sit and arrange themselves in a better way that they were before you heated it up very very simply explained so you do something similar here and the idea is okay we take it if we if we are have an advantage but if we have a disadvantage that looks like this is a bad thing to be doing you take it with a certain probability so in a certain sense you flip a coin and you say okay look this looks like a bad move but I'll take it anyway and so if you stuck at this local minima then if you allow yourself to take some steps in the sort of wrong direction maybe you will climb out of the local minima and fall in to the next one and so this is a very basic idea that resulted in a very useful very interesting algorithms to minimize discrete functions so as I said this is a tangent it's not quite how we going to discuss this puzzle but it was how I came up with some ideas about it so let me show you an example so this is an example so there is a probability and the probability you can the sophisticated way to think of this is that the probability will change with the iterations so you think of a of temperature as something that you have at your disposal in this in the sense of annealing so if you have very large temperature then basically you take anything you like you just go anywhere and if you cool off you then are becoming much more greedy if the temperature was zero you're totally greedy and you let the temperature kind of slowly low slow down so at first you basically move around randomly completely with any no control and then you slowly cool down so this is an example of this and here the energy is measured let me just say that what you will want to see at the end are black and white strips one next to each other because you measure whether the guys vertically are of your same color and the guys on the on the sides are the opposite color and so this wonderful simulation lets you do this and there's a cooling rate which is how is the temperature going to be slowly decreasing so we're going to see in this graph global energy this energy measure then it should be going down and we'll see the temperature starting at one and going down to zero okay well we didn't quite get white black white black strips but for many purposes that result is good enough no there's a probability involved in the temperature so the temperature there's a cooling rate here this is a cooling rate tells you how the temperature is going to change and here's the temperature we start at temperature one I haven't explained but it basically measures how good your configuration is by measuring what your vertical neighbors look like and how you horizontal neighbors look like so you so if if you if you were in exactly the position all white and black strips one next to each other the 10 the energy would be zero okay so we are in that kind of picture with with a met and with a measure that is that the only solution to it is this black and white strips one next to each other okay so it's I don't know exactly I don't want to get too much into it but some some sort of switching of of the colors of the neighbors some particular exchange of of white and black yeah the radius is is how far how around it are you supposed to I think it's just a swap of of black and white neighbors it precise neighbors I just wanted to show you the picture the one I get too much into the specifics of this example but anyway let's write again so this clearly doesn't look like white and black strips so we didn't we don't like this and what looks like a reasonably small amount of iterations it produces something that at least you probably can live with okay and you see how the energy has gone down to what looks like is not going to come down from that anymore yeah is what sorry yeah I mean I the talk is not about the system it's just I wanted to just uses an excuse to bring this up and hopefully it will entice you to to explore it on your own I mean you probably can teach it but others have seen it before so it's just that I want to put the the puzzle itself in the in a context but what we're gonna do now is something that sort of appeals at least to me mathematician of wanting precise answers that in this particular instance that I'm erasing we have a way to understand this minimum quite precisely and that's really the topic of the talk so what I'm gonna do then is and try to understand this maximization problem in in this bled puzzle by relating the question to something else so we started with this cycle of a's and b's but let me sort of cut it out and think of a string and now let's take w to be any string any string of word in a and b and I will associate to this a certain path in the plane so this will be a polygonal path z squared in the lattice and this also somehow has to do with physics and it was suggested to me by Harald Skarky and so what I'm going to do is describe the motion by this this a's and b's are going to be instructions for something to move in the plane apart I think of a particle moving in the plane and there'll be two variables and perversely the physicist is called q the position which I'll try to remember to use the right letters and p the momentum and there will be at any given time there'll be two two vectors that tell you where the particle is and what would be the next thing it would do and there's two ways that this will move there'll be an a and a b will will correspond to that if we do an a will be to actually move one step in the direction of the momentum and keep the momentum as it is and a b will be keep the position as it is and change the momentum already miss this up keep the position as it is and change the momentum by minus one unit of the position okay and so here's an implementation of this idea I will start my initial state would be that I start at the vector one zero I think I'll use row vectors so it's one zero and the momentum is zero one so you see the red arrow is the position and the blue arrow is the momentum so if I do an a I just moved in one one step in the direction of the blue arrow if I now do a b then I change my momentum vector by minus one unit of the position okay so it was up here and now is it was pointing up to here now it's pointing this way so if I do a and b and I repeat this these are vectors I have two vectors at every time two two two dimensional vectors and my moves are for a I change the red vector by one by adding one blue vector and in this case I change the blue vector by subtracting one red vector well they keep moving I start here and they'll be whatever they are we'll explore and see what what happens so let me do a and b and I'll iterate it that I have to put it here okay so this is what happens if you iterate a and b let's try a b b see I think maybe a a b so let's just get a sense of this so somebody give me a string some short string and iterate and see what we get a a a you're never turning right you have to use a b b is changing the velocities if you never turn this will just keep going up okay what else b a b one more a a b b that's yeah a b b so it's not always the case that this thing closes up yeah okay I'm gonna come back to this so then associated to a sequence a word in a b we have a path in the plane what we could do so to keep track of what's happening we let the matrix mk be the matrix where these are the rows we start with m zero as the initial state as the identity matrix and then doing a is nothing but multiplying by the matrix 1 1 0 1 and doing b multiplying by the matrix 1 0 minus 1 1 so you can call these the state matrices and the path that we see is the what we the queues are the positions so if we look at our matrices what we see are the the first rows are the positions but we also have the second rows which are the momentum and they move themselves and then their own copy of z squared so let's do an example let me do this so for example I can we can get something with five vertices to do a b a b a a b a b b a b b a b so so what we see is this so these are what we're seeing here the dots here correspond to the q vectors the positions but there is a corresponding picture for the piece and the piece we can read off by looking at the tangents so if I start here I mean there's some ambiguity what I start but say let's say we start here so the first vector is 1 0 or actually they start the same place so we the first vector is vertical so I have a 1 0 1 there then is horizontal to the left and you keep following this and you see that this is the path that the piece do so this is some path gamma and this is some path we can call the dual and they both come from projecting this path of matrices to the first row and the second row the key observation first key observation that will allow us to understand this minimum on this game is to notice the following if we look at the length of this path by which I mean how many dots there are on the path 5 and I look at the length of the dual there's 7 and 7 plus 5 is 12 and one of the theorems of math method theories of mathematics is that all the 12 are the same and in fact any path they do will have the same statement so any path that you construct out of following these rules will produce a dual path that has a number of dots in it which is complementary to 12 from the one you start so what's this what is the smallest path you can do how many is the smallest number of dots you could have is 3 yeah and the dual of this will have 9 which is the biggest you can have the dual will be we can get it this way oops missed up enjoy the time no I sort of been an a and then you get this big triangle so this is a theorem that we proved with Bjorn Poonen and maybe Don will recognize this 12 of having to do with the delta function he just talked spoke about a year about a half an hour ago the proof that we gave of the statement is in fact using the delta function of Ramanujan but the statement in general is the following if you count the number of points in the path plus the number of points in the dual you get 12 times the winding number of either one of them so by the one day number I mean how many times it goes around which could be any any integer we're moving always count a clockwise so what this amounts to is so what we see here so let me maybe you should write this pentagon again a b a b a b b a b so the word in question is in this example is a b a b b a b b a b so if we look at the a's those are exactly the five of them that's exactly the number of dots on the path gamma and the number of bees is 7 is the number of points on the dual is every time you do an a you change your position and that creates one more dot in your path and on the b side if you use a b you creating you changing the momentum exactly by adding one more point and so what this says is if you want something that close around only once you'll you will have to use 12 letters and so it's a theorem of Scott so what other properties I mean what kind of properties those these paths that we see they're not completely random things that we see so how would you characterize what these paths are that I get by playing this game this particular game this a and b story if they close they close once what about the area well it what is a little misleading is this looks like we're talking about an equidium problem but it's not an euclidean problem it's more than a hyperbolic problem and so things that are really the same in the sudden have will have will look very different because the group that we're using here is SL 2 z not not not preserving distances so what what the condition turns out to be is the gammas that we see contain a unique only the origin as a lattice point internal lattice point and it turns out this is almost caught that if in any dimension if you fix a polyhedron convex polyhedron with lattice points at the vertices and you you require that it has a certain number of number of points inside a positive number of points then there's finally many possible such polytopes up to the group of a change of variables so let me show you what happens in the case of two dimensions there's a 16 of them and this is these are all up to changes of coordinates so they may look like different if you look if you do this yourself or you do you look somewhere else but this is an example of this these are all distinct I think up to SL 2 and so these are all paths all the paths that contain exactly one interior point and you see there's a guy here with nine as the biggest guy and this the corresponding dual up in the top left corner which is the one that has exactly three points so how do you prove this theorem well I mean for when the number one you just check one by one which be a pretty silly proof and that's what I was my original proof is just noticed that this statement seemed to always hold now if you want to do this for a higher winding number of course then you have there'll be finally many for a given one number but that will not allow you to find a proof for all cases and so you'll have to do something else and and as I said the proof that we have in the paper with your opponent uses the eta function of that again okay so this will turn out to be the key ingredient to bound the maximum or the minimum number of a some bees you can have in this game so let me a sketch for you how that goes so what is the key fact well one other key fact recall that we had those matrices a and b there you can check for yourself very easily that the matrices a and b satisfy this so what will happen is that the paths that you get by using this rule in the game will look different but they will all lead to the same final state matrix and so this will allow us to get the bounce that I'm going to tell you now so the theorem is the following then suppose that gamma our path is eventually closed by which I mean that as we were trying to do some examples in this simulation you have a string and if you repeated a certain number of times it will give you a path that comes back exactly the same initial state both the momentum and the position are exactly the same so this as we saw an example not always happens and in fact if you start typing randomly a's and b's in this you will get past the do not close so suppose the gamma is eventually closed then the number of a's let's call la the number of a's in the path and the word that corresponds to the path and L the total number of letters is bounded above and below by 1 6 and 5 6 so this is for a but this is all very symmetrical so this and holds for b so this will put a limit on the possible number of a's that you can have because the path that we have in our game is a path that is eventually closed so note a b a b n times is eventually closed because a b done six times as we saw is closed that gives you a hexagon yeah so let's do it again so we do a b well let's iterate this six times okay so the pair a b repeated six times is closed so the pair a b is eventually closed and so the pair a b to the n or the n over 2 rather if I do this six times this is the same as a b to the 6 n over 2 times and a b to the 6 is closed so the path that we're talking about is closed is eventually closed so it will this statement will apply and it limits how many a's of b's you can have because any modification by the rule of the game as I said will change the path itself but it won't change the fact that he's eventually closed because the end point remains the same okay so let's let's see how we can prove that I'll come back to that let me let me first prove this well the final state matrix a word is a series of instructions so if you follow all of them there's a final state you know let me sketch the proof of this which is I like because it uses the geometry of this path I mean a priori we start with the game would seem like a completely discrete thing not connected to anything else but with this path business now it becomes something we can use some elementary geometry for so the first observation so let's let's say let's say that gamma itself is closed the idea then will be more or less the same and let v1 to vr be the vertices okay by vertex I mean a corner so in this case there's six but we saw squares other things so the number of vertices is not the same as the number of ASOB's in fact what is a corner a corner in this path is a place where instead of moving forward we decided to change the momentum so it has to correspond to a bee at least one bee so in fact the vertices correspond exactly to blocks of bees now let's look at the vertex so we're coming in from here coming out there and let's define the exterior angle to be the angle here and one small thing to convince yourself is that the sum of these angles is equal to what well if we went around one time it should be 2 pi if we went twice it would be 2 pi times 2 and so on it's 2 pi 2 pi times the winding number but by this theorem that I erased the winding number is the number of a's plus the number of bees divided by 12 so that means that this is pi times the length over 6 and on the other hand the number this theta's each angle is at most pi and each vertex corresponds to blocks of bees and each block of bee has to have at least a bee so this is majorized by pi and bee so we get that yeah so it's strictly bigger so we get that lb over l is bigger than 1 6 and now we do this symmetrically with this with the a's and you get that is less than 5 6 so it's just a quick idea but but the key thing is to use the geometry of this path to understand how many possible bees in this setting there can be because the bees correspond to vertices and vertices are where you turn and so there's an angle involved and there's a limitation for those angles anyway I understand it's quicker than it could have been but I want to get to to the final point so what I was saying before about being eventually closed is that so let me use a little notation so we have a word consisting of a's and b's so a word in in a a and b and we can let me define row of w to be the state matrix at the end if I were to do it in that thing I will look at the string and click as many times as these letters indicate and at the end I'll be somewhere with some red vector some blue vector that's my state matrix M yes that's what I do yes and then take the product yeah indeed yeah I just look at the string and now replace as Don says the letters by the matrices and that's take the product of all of those and that's indeed and so the point is that the this thing is the identity and there's a little bit of work to do but I think I'll skip it that if you modify so let's say w prime is a modification of w by the games rule then if one of them is eventually closed then so is the other so in the initial word w consists of a b a b a b that's eventually closed and so the theorem applies and because of this statement every other sequence that comes from having done a modification to the original game starting point is also eventually closed and therefore the theorem applies for it sorry yes in fact it is yes yes indeed yeah that's maybe even better clearly just because the matrices themselves satisfy the the rules of the game so in a certain sense if you think back to the original question I mean you can take this puzzle as being okay there's some configurations of that you're allowed to change by another one and you can imagine zillions of puzzles of this kind and this one happens to be analyzable in this form because this replacement rule is exactly something that is has is very tied to this particular geometry of this group and just I want to say just a couple last things what is the geometric meaning of doing the rule well let's just do a small the justice case a b a itself so we go up then we turn and then we go so an a b portion if we started from the beginning will look like this and the corresponding replacement a b a a b a b will be we first turn then we move and then we turn again so what happens is in general what you'll see is that one of the paths w might have a piece like this and w prime will have be replaced by that so one way to interpret what this rule of the game is is that in the path you can chop off a corner but the corner has to be such that there is no other lattice point involved and so I'll finish with this example should have done something with this so let's do a b b a b b a b a a so here's a an example and if we look just at the at the path there's only one corner we can chop off which is down here here every other corner will necessarily have either goes through the middle or something's wrong yeah that's all there is there's no other corner we can chop off without sort of including one extra lattice point and if we look at the at this at the string here there's only one string a b a that we can actually change to the b a b which is right here at the bottom no there should be only one is it where they can last no this one you cannot join to that one no but that's just a segment no I think I think this is the only one so let me do this let me replace the a b a by b a b now run it again and we get the same thing with the corner chopped off so if you look at these pictures what there's the greedy algorithm will be to always chop corners off what we would like to do is to get this to be as small as possible and what we found well maybe in the case of only one turn there's so few things that you don't really see it but if you add more you will not be able to chop it off to the smallest possible way by just always chop it in corners sometimes you have to add a corner which would be the inverse of this and to to cut a corner somewhere else so yeah so this was this puzzle that I wanted to discuss which I kind of think of it as a puzzle with a moral the greed doesn't always you should not have you should not cut corners good point but or you should cut the good corners and greed may not always lead you to what you want so thank you


Okay, welcome back, like to call everybody back in as we get ready for our next panel. First of all, one bit of housekeeping, the innovation showcase will be open until about 7 p.m. tonight, so if you didn't get a chance to get around to all the companies you wanted to see, you will have another opportunity to do that. I'm Mike Morgan, by the way, it is my great pleasure to introduce our next panel. We are turning now to the global part of the Global Energy Forum. Next with a session on the Middle East and then moving to North America, and chairing our session on the Middle East is Secretary Rice and then Ambassador Abdullah Al Mualimi, who is the permanent representative of Saudi Arabia to the United Nations. Thank you both.


Hello everyone! I want to say you two and today I'm at the International Airport of Sydney I have my own bag the red bag as you probably already know it's mine I can't put the envelope but I put everything else and there's my wife she's still in her phone and now we're going to the big ports to go to the main part of the airport so we just passed the security of the airport and now we're at the main part of the airport and I still have to wait for the day so we just exchanged our Australian dollars for Indonesian dollars and I just found that in Indonesia if you want to buy a cup of coffee you need to spend 20,000 dollars Indonesian so we're now in a very long corridor waiting for the permission to go to the airport and I just thought that this situation would be terrible if the zombies suddenly disappeared so now we're in Bali we just arrived and according to the Australian weather it's one day after midnight but according to the Bali weather it's now the next night so now we have to go to the airport and then find a taxi so we just arrived at our hotel and now we're recording it and soon we can go to our room so now we're at our hotel and actually my wife chose this hotel and now I want to show it to you so now when you're in Bali you can't drink straight from the screen we can do that in Australia but not here so now we have water bottles and this is the chef's room I'm sorry because it's not very good it's night now so there's the bed and in fact I want to see it because I haven't seen it yet I haven't seen it yet here's my beautiful bed here it is yes pardon me say hello say hello say hello say hello good and here's our hotel you can't see it very well but tomorrow I'll show it to you and our room or the room in fact it's two meters so say hello to everyone again it's the next morning as you can see I'm in two rooms but soon we'll go to eat and start to see Bali so I'm very excited and I want you to come with me and of course I can't shoot the movie here at night it's too early so I just want to say sorry for that and now I want to show you my father's design so come with me it's too early how beautiful you are so we'll stay in the room in the room two if you want to visit me I don't know how big that room is so I have to wait 30 minutes before I can eat so I decided that I just want to eat and you can come with me because I want to tell you about something that happened last night and I didn't film so last night when we went to the hotel of course we were in the taxi but as soon as we wanted to go the hotel there was a garden and the garden came to it and it started to control the taxi for bombs it had that mirror where you put under the car and it simply controlled it for bombs so I thought what the hell is that mirror because I know that I thought that probably many years ago there was a big terrorist attack here in Bali and a long time later Australians didn't want to come here as you can understand because more than 100 people died I believe in death so I I'm happy that they have that now because I can be something certain about my security but yes that's simply something scary at that time so I just took a shower because now I want to go and eat but I want to show you something new look at this it's simply a mirror in my room but no it's the mirror of the ship itself I really like that so I can go from here to throw away my investments and jump into the ship straight into my room what's so scary about that hi Uleto my name is Jasibu Dia I'm your god so the breakfast is ready and I can finally eat what did you eat or actually we didn't eat it's just part of our hotel hotel so now me and my wife are going to eat here in Bali we just want to see the local landscapes and as you can see our truck just arrived so we just arrived at our first temple in Bali it's pretty hot here I almost can't see but the light is there so yes, here's the first temple and what? I want to show it to you so we just arrived at our this is the chief temple and in every house in every house there's a temple every house has a temple so we're now on the beach as you can see we're very high because we're on a bridge and as you can see the mountain is black because it's actually the volcanic stone and they mince it and use it to construct temples and other constructions here so we decided to go to the beach because we just want to see the landscapes here so my wife just said that she wants to buy a jewellery I don't know how to say that in Esperanto maybe you can tell me in the comment below because it's very expensive and you can't see it but it's very smelly when you want to eat it so my wife all alone just want to eat the whole jewellery do you like it? no do you like it? the most terrible part about tropic insults for me is that I'm the most white white in the world so when I hear I shudder look at my hair I'm outside the car for 5 minutes and I'm almost red so we just arrived at Balia cafe boutique here we can try different types of coffee you just saw how we make coffee they shudder the seeds and then here's the coffee that just came so we can try different types so we just decided to buy 3 packages of coffee and I decided to buy chocolate coffee because it tastes good I've never really liked coffee there are two seeds hello seeds how are you? here's the first time in my whole life I've seen seeds what are we doing? can I touch you? yes hmm? don't you want to touch my hand? no, she doesn't like it we almost reached the top of the mountain where the temple is located as you can see I almost died and I just wanted to take it and film it and go because it's really hot and maybe you can see and my hat is running and that's not because of my team but because I almost died so now I'm home now at least I'm at the hotel and tomorrow I'll film elephants and I'll take a boat and I'll do a lot more and I just wanted to say that last time I lost a few subscribers so if you like my channel and the way I do there's a link in the description you can help me one dollar a month it's enough and that's all if you like this film like it, share it, subscribe to my channel if you haven't subscribed and I'll see you in the next film don't be there now I suppose that I'll find you after my trip in Bali and Indonesia and I'll do a lot of things for you but now I can't think of it probably I'll write it in a reply and I'll feel that for you and as always I want to thank my subscribers for Patreon because without them I can't upload this channel they are the best of this channel and as always thanks for watching see you in the next film


My name is Lieutenant Michael Ray, the Assistant Director of Medical Operations and Planning. And here in Cambodia, in addition to that, I was also the Assistant Officer in charge of MedCAP3. We had four MedCAPs in Cambodia comprised of 50 personnel each. MedCAP3, we actually had eight additional host nation medical defense representatives to help us out. We were spread geographically across Cambodia, and we saw about 12,000 patients between the four different MedCAP sites. Every MedCAP is provided in four categories, adult medicine, pediatrics, dental, and optometry. And depending on the site and the way their day goes, they're going to see anywhere between 500 and 1,000 patients a day. We actually had one site that saw 1,114 in one day. I think the mission in Cambodia was a huge success, partly because of the vast number of patients that had access to care and only wouldn't have it, and just the things that they were able to talk about, see with U.S. physicians and our counterparts, was access that they wouldn't have anywhere else. And the Civic Partnership brings that to these countries, and I think that's a good thing. Hi, my name is Chief Scotty Baylis. I'm here with the CEL and Echelon CBs from ACB1. While we're in Cambodia, we worked on one four-bedroom maternity clinic and two four-bedroom maternity clinics and three different locations throughout Cambodia. I think anytime that you can go into a country, build a building and pass it on to the locals so that they have something that they can use to benefit the local populace, is great. And it's great to be able to go in and actually see the product that we're doing from the start to finish. You know, a lot of the other stuff that we do on this mission, you know, you don't get to actually see what you're doing right in front of you, you see the completion of it and how it affects the people. My name is Helu Husko. I'm a Danish veterinarian. I'm the team lead for a world that's volunteer. In Cambodia, we had two different vet caps. The first vet cap was a great vet cap where we had nine local veterinarians involved and trained them to vaccinate their cattle and to train them into doing surgery and doxing cats. And the second vet cap was divided into two. So half of the team would have a surgical clinic every day and the rest of the team would have a remote clinic that would go around to treat the cattle and doxing cats. It was definitely a success because we strengthened their capabilities here in the country. Hi, I'm Hospital Corpsman Third Class Stephen Matthews. I'm a surgical tech here on the U.S. and S. Mercy. We just finished up here in Cambodia. We accomplished approximately 219 surgical cases and treated hundreds of patients here at our surge caps. I believe our time here in Cambodia was a success because working together with our host nations, NGOs, and our medical students, all our training really worked well together. You can see how even though different countries may separate us, that our training is all the same and that when put together, we can accomplish the mission.


Let's see what transpires here tonight in what is the Wanderers. 200s a league match. Raw's need, arguably the greater yet to win under Fowler. It's slow starts, doing that Achilles heel that, and a lack of goals. It's a clever dummy by Invan, gets the return from O'Donovan. Small promising for Brisbane Raw. Invan looking to curl it, and it's pushed away by Lopar.  He did well perhaps not to parm it, straight back into the path of an attacker. Sandwich over the top by Backus, perhaps will do the trick for Maier. Slung into the box by Wilburing, and Crokem stretching. Jorgeski, it's a really good save by the goalkeeper. Stuck out a strong arm and deflected it over the top for a corner. The Wanderers' best moment of the game so far. Donovan did well to control that, and find more. Can they're building again here, Brisbane? It's J.O.Shay, beaten away by Lopar again. Brett Inventrona, follow in. Couldn't put the ball into the back of an ad. It's a good play from Brisbane there, down the right-hand side. He's been quite happy, creative. A number of opportunities down the other end, and you've seen them in the last couple of games that they... Well, error here. Chance for Alex Maier. Saved by Crokem, but it's Kwame Yabba. And Brisbane scramble. Well, still not away. Costa-Grozas has elapsed it, but couldn't make contact. And they find some reward for this pressure. J.O.Shay with the corner. And Gillespie's header, it's off the line, and then Lopar keeps it out somehow. The Wanderers survive. Miraculously so. But it's still not clear. Back in by Steffen. Maier can glance just wide by Roy O'Donovan. And they cannot believe that they don't lead in this game, Brisbane. Well, there was a wonderful clearance off the line there. And you thought for all money, as the ball falls down, that they're going to tuck it away. Great save from Lopar. And as it comes back in again, Roy O'Donovan at that near post, a free header just looking to glance it into that far corner, just not getting enough. There's German at that back post. A little drop here for Kiado Bacchus. That was not far off. And he timed that terrifically well on the volley. Touch of Paolo DiCanio about that, the scissor kick on the edge of the box. And when he scored like he did the other week, there's no reason why he shouldn't be shooting from there. It's a good effort. Again, the option-wide rights. Even go with O'Shea. Come back for the Irishman. Good football, that's by Brisbane. It's off the head of Mordekutis. Only for Scott Neville who'll drive on. It's pushed away by Lopar. And it caught up Mardi Holloway totally unaware. It's still the wondrous pen in. It's with balls. O'Shea should be the goalkeepers. It brings matters to a close. And at least you could say the atmosphere will be all between Messas, Barble and Fowler. The two Liverpool teammates in the post-match. They end all square. Brisbane are still looking for their first win of the new season. The wondrous 100% record is over. Although they do return to the top of the league ahead of Sydney FC.


Hello and this is Shivani, welcome to Sistweek. In this video I will tell you how you can speed up your slow running Mac. If you do these activities regularly, you won't have to worry about the need to speed up your Mac again. So, here are some quick tips on how to speed up your Mac. Keep your data organized. To check the storage space, click the Apple menu, select about this Mac and look under the storage heading. If you find your Mac loaded, then you have to free up space to make the system run faster. Click on manage, sort out the files and delete the unwanted large size files. Second is clean up your Mac with tune up my Mac. Tune up my Mac is an easy to use tool and has clutter free interface. It enables you to clean system and user cache and log files in a single click. It removes the redundant parts of applications along with the unneeded languages of localized applications. Moreover, it also helps find duplicate files with its duplicate finder feature and recovers disk space. List out the memory hogging process. To monitor and find out the process hogging your device, open activity monitor. To open it, press command plus spacebar together to open spotlight. And type activity monitor and press enter. Once it is up, click on CPU tab to check which applications are using what percentage of CPU. To force quit a process, select it and click close X button on the toolbar. If you are not sure about the process, you are about to end, try to close the application normally. If this doesn't work, don't worry, click view menu and select all processes to check all the processes running on your Mac. Cover to the memory section to check a process using a major amount of memory and also check the disk section too as a process using a major part of the disk as these could also cause your Mac to run slow. Close applications. To check what apps are running, look for the applications mark with a dot on your dog. Make a right click or control click on their icons and select quit. To manage login items, open system preferences, go to Apple icon and select system preferences. Click the users and group icon, select your current user account and click login items. If you want any program to start automatically or remove it from the list, then click the plus or minus to add or remove startup apps. So to speed up your slow Mac, try to reduce the number of browser extensions and open fewer tabs at once to save CPU and memory resources. Moreover try to use native browser apps Safari as it also good for your battery power. Reduce transparency and animations. Open the system preferences, go to Apple icon and select system preferences. Click accessibility then click display and choose reduce transparencies.  So these are the best ways to speed up your Mac. Try them and let us know in the comment section and for more such videos, subscribe to our channel. Thank you.


Jacob Elordi in Del Toro Monster Mash. I cannot wait for this movie. Del Toro is the perfect person to bring Frankenstein to the screen in this day and age. Let's jump right to that part then. Jacob Elordi put this up. This is him in the makeup. He just posted this. Which I'm not a huge fan of Jacob. He's hit or miss for me. I was very excited because originally it was supposed to be Andrew Garfield and he dropped up and was replaced by Jacob.  I watched Euphoria. I thought he was great in there. Elvis was pretty good. So I would be very excited to see how his portray of Frankenstein. Lily? I mean, yeah, I've been impressed with him. Like I said, I just kind of saw him. Everyone was making a big deal out of him.  But then I started watching a lot of his work and I was like, oh, okay, I get it. Which makes me feel bad because he played Elvis in Priscilla and Austin played Elvis and Elvis. And now I'm like, oh no, I can't pick. Like, well, obviously it's going to be Austin, but yeah, I'm excited. I really want to see him in this. Here's mad respect I have for Jacob because this guy is a beef cake, handsome boy. And he's doing the monster. He's like, Del Toro movie, sign me up. What, I got to be the monster? Sure, I'll do that. He's got really good, great built for it. Del Toro after he started the month of February sharing on his ex account, pictures of his scouting, frozen Canada for his own adaptation of Mary Shelley's Frankenstein this past week, made waves in social media. Jacob posted this image of in makeup of the story's monster. Del Toro's Frankenstein is currently in production in Toronto and Ontario, Canada. It also stars Mia got Oscar Isaacs as Dr. Frankenstein and Christoph Waltz as Dr. Pretoria. Here's what I did not know. His character, which is wishes to continue the experiments started by Frankenstein 40 years after the story's main events. What do you think of that? This is not, this is not the first Frankenstein iteration. It's going to be 40 years after that. That's kind of interesting. I think it's a good idea for, I hate the word this word, modern day audience because this book has been adapted multiple times to screens, I completely trust Del Toro in this. I've not been disappointed by any of his movies whatsoever. I mean, one of them is probably in my top five is Pan's Labyrinth, it's something. And his ability to make monsters seem beautiful and have humanity to them, I think he's perfect in it. And I'm okay with it being set 40 years after where the original book has taken place. Nicely said, how about you, Lily? What do you think of it being 40 years after the fact? And this cast is insane. Stack. I'm glad they did that too, because every single time we get like a classic story, they always want to start it from the beginning and it's always the same thing. And we're like, we already know this part of it. Give me something new that you're going to add to it. And it's perfect that, yeah, Del Toro's the one that's doing this, because oh my gosh, I cannot wait to see how it actually looks too. How he, all the elements he's going to bring in to set the tone with the movie, because oh my gosh, a lot of his sets in his movies are just beautiful, like the lighting that he chooses, like everything has some kind of like symbol in it. I can't wait, I'm so excited for this. I want to add one more thing about this. Everybody's focused on Jacob, but Mia Goff, I think a lot of people don't give her credit. She's fantastic, especially in the horror genre with Pearl X. I think it's Maxine coming out. Maxine's coming out. Yeah, yeah. I think people don't give her enough credit because we have, this is a fully stacked cast. Obviously Oscar Isaac, Jacob, they're a little bit bigger than she is in the mainstream news, but I think a lot of people are going to underestimate Mia. Mia's really great at what she does. Well, and she's, I totally, first of all, I totally agree, we're huge fans of Mia Goff here. We've gone to seeing her movies in the theater. She's always present, always committed.  So that, that's, you know. That helps. And it's built all, it's like, whoa, this is fantastic. So yeah, that's the news there. We've given our little opinions. What do you guys think? Let us know, comment, all that good jazz.