Okay, I think it's time to make a start. My name is Simon Clark, the each use committee program coordinator. And today we're talking vanishing glaciers. What's causing racial males, how it's an impact as humans and what the future glacier might be. So joining us today is Dr. Harry Zachlari, a glitchologist at University Libre Dupercells for the specific interests in the evolution of mountain glaciers and ice caps under changing climate conditions. Harry also engages in outreach programs, such as communicating science at school and through other popular media. So welcome Harry. Thank you. And thank you for the invitation. Yeah, so to kick us off, just could you introduce yourself, tell us a little about your background. So my name is Harry, I'm a glitchologist from Belgium, which is a bit strange because of course there's no glaciers in Belgium. But we have a very keen interest on glaciers in Belgium like the Netherlands, other countries because the glaciers melt sea levels go up, and we are countries that are very close to to the sea level. The coasts. So that's why there's a big interest. Maybe a few words about myself I grew up in Italy, close to the mountains in fact, and I always had this profound interest in mountains and glaciers. And then eventually I ended up doing research in that direction. I did my PhD in Brussels, then I did a two postdocs one in Zurich, and one in Delft, so one in Switzerland and one in the Netherlands, and for now I'm back in Belgium in Brussels, studying glaciers. That's it in a nutshell. And the science always stem from some kind of much younger old childhood interest. I researched eco hydraulics and my background is, I spent a lot of time as a kid in rock balls so I think they're very related. I can say you're a glaciologist but of course I'll say quite a broad discipline, could you perhaps narrow it down a bit for us for what you are your expertise in how how that perhaps differs from other areas of glaciology. So Englishology does people looking at ice, and this can mean very different ways. We're looking at terrestrial ice, so which is typically ice that's at one point in time was snow that compacted and formed into ice. Ice is distributed a bit everywhere on earth, but to give you a broad idea there's two big ice sheets, there's one agreement ice sheets in the northern hemisphere. There's the Antarctic ice sheet in the southern hemisphere. And I'm not really looking at these two big ice sheets, but I'm mostly looking at mountain glaciers. There's about 200,000 of them in the world. And this is one of the things that we are trying to do we're trying to make some projections about how these glaciers will evolve in the future and so I would say, I'm mainly focused on glaciers mountain glaciers and also people doing a lot of observations with satellites remote sensing really trying to to understand what is happening to the glaciers, and we use these kind of observations and we feed them. In fact, into our models, our models which are thousands of lines of codes that we use we press buttons and then we look how glaciers evolve so that's the kind of signs that we're doing here. So, bouncing from that, I think it's good time to kind of trying to frame the context of the discussion. Glacial ice loss. It's a, I think a fairly common feature in the media when it comes to the impacts of climate change. So, how, like, bad is the current ice loss I think that's probably like the key question, like, do you have an idea of how it's changing and how do you have that idea. Well, so we know that glaciers because of all of these observations, we really know that glaciers are dramatically changing. We notice by going in the fields, and if you're just going to feel this probably one of the indicators of changing climatic conditions. There's a lot of nice ways to go to glaciers where they put the steak and they say the glacier was here the front of the glacier was here. 20 years ago and sometimes the glacier is to 300 meters further away so it's really a very visual thing you can really see how glaciers change. And of course we go on glaciers also to measure in detail how much glaciers mouth so we go we plant for instance a steak, which is 200 meters deep into the ice and the next year we come back and if there's only two meters in well then we know that eight meters have melted up. And these are really detailed observations but we're now getting really into an era where we're going to be using or we're using more and more all these remote sensing observation, which means observations my satellites with satellites we can identify in fact, how glaciers have changed and we now have studies that for every glacier on earth. So for every of these 200,000 glaciers on earth they can show us how these glaciers have changed over the past 20 years. And there's a few exceptions but almost everywhere on earth we see that glaciers are are filling. And of course, at the very front of your glacier if your glacier fins and there's no ice left, then you get this effect which looks like if your glacier is retreating which is just because at one point if you have five 10 meters of ice five meters of ice well at one point you have just zero meters of ice and so the glaciers are thinning and are retreating and this is something that we can observe in many kind of ways. So it's, it's not just that the, I suppose, shortening but also that the depth of the ice is also thinning as well. And as definitely so glaciers are really thinning we especially see that the lowest parts of glaciers for mountain glaciers typically the highest part is way higher than the lowest part. For instance a glacier on which I worked a lot during my PhD and on which we did a lot of field work is the multi edge glacier in Switzerland which is very well accessible. And what we see for instance for this particular glacier so for the multi edge glacier we see that the glacier is thinning, but especially at the lowest parts which is around 2000 meters just to give you an idea the highest point of the glacier is around 4000 meters. The lowest one is around 2000 meters in elevation. And there we have some parts where up to 10 years ago it was still 50 meters of ice and there's no ice left now so there's really places where every from year to year we see that the ice is sitting five to 10 meters. So, they're mainly thing and especially in the lowest parts they're very susceptible to changing climatic conditions. Climate change is like the key. I think word here for driving glaciers could you talk to them more about what is driving and like how the glacier mass loss occurs. Yes, so definitely the changing climatic conditions are really driving this these changes in glaciers and what we see in fact is to put it a bit in a in a simplified way. A glacier let's take a healthy glacier so case without climate change a glacier in fact will always become a bit bigger during winter, when there's a lot of snow, and during summer to always lose a bit of of mass. So even a healthy glacier will also lose some mass during summers there's a bit this, there's a bit this expansion of the glacier in winter if you take the total volume, and then in winter and in summer you get this reduction and what we see now with changing climatic conditions. Of course the winter also changes, but the main change that we see is that it still becomes a bit bigger during winter. But during summer it's just going to lose a lot of, of, of mass just because the temperatures are too high so the healthy glacier can compensate the mass loss during summer with what it gains in winter and unhealthy glaciers just using so much during summer, and what it gains during winter is not enough. So, in the end it's just a year by year it's an imbalance and you're just losing more mass than then you're gaining. Maybe another way of seeing it is a glacier typically consists of two parts. There's the highest part where typically you have mass gain at the surface, and there's the lowest part where typically you have mass loss at the surface. The healthy glacier is just going to function because of gravity, you have too much mass in the highest part and that is brought down to the lowest part. And another way of seeing what is happening now is, there's still the two parts of the glacier, there's still the upper part where you gain mass, and there's a lower part where you lose mass, and there's still this this mass transfer so a glacier is something dynamic it moves it brings ice from the highest to the lowest parts, but the mass supply from the highest part is simply just not enough. So there's not enough mass being supplied and as a consequence, your lowest part of the glacier will be thinning thinning, and eventually also retreating. I think one of the key questions that pop up to me when you're discussing, I suppose how much these glaciers are thinning is their sensitivity. I guess in the rates of rich JML doesn't say the same as the climate warms that ice loss will accelerate perhaps. Yes, indeed, so the glaciers are dynamic and they're moving over time and what is in fact happening is a glacier responds pretty slowly to changing climatic conditions. So it means that the changes that we will see for the glaciers in the coming 10 to 20 30 years are in part already driven by the climatic conditions that we've had now. Another way of putting it the glaciers today they're too big for the present day climate. And so what we see when we made these these projections for future glacier changes is that on the one hand there is what we call a kind of a committed loss. So even if we would be able to stop the warming at the present day level, which we can't but if we could have the warming at the present day level, even then glaciers would continue to lose mass. But of course, on top of that we know there's projection that temperatures will keep on increasing. And of course the question is by how much and this will depend on policy decisions. And then of course, everything that has been decided in during the cup in Glasgow all of these elements will will will determine in which direction the climate will evolve. And this will in the this will then eventually also really dictate how much glacier loss we will have but so what is important to keep in mind is the fact that they respond slowly and so that the future evolution is always in part driven by further warming so by their present day imbalance compared to present day conditions, maybe just to give one number to put that a bit in perspective. What we've made we've been making some simulations for all glaciers in European albs that's about 4000 glaciers and about their future evolution. And in these projections in fact we see that over the coming 30 years so between now and 2050 will be losing about 50% of the glacier volume. 50% and most of this mass loss is not due to the additional warming that also plays a role but most of this past loss is really due to the present day imbalance so the just effect of the glacier still need to adapt to the past conditions. So I suppose a key aspect of that is that even if we stopped emissions now. There will be some level of warming, at least if you stop the increase in emissions that we saw the level of warming. So the future is that even are really optimistic curves in emission reduction is this still going to be huge, huge impact on glacial melt. I think that's what I'm getting from your description of how less and how sensitive they are. So there will be a big loss anyway but maybe a thing that is really important to stress is that the future loss will really be dictated by what we're doing today. So if we take this example again of the glaciers in European albs, where I told you in the coming 30 years we lose 50% of their volume, but we show that in 2100 it really depends on which emission scenario will be following. And there, I mean the situation is pretty grim for glaciers in European albs because they're pretty sensitive. They're in a region that is fast warming but in a good case, we think we could still save one third of the present day mass. So this is in a case where think of Paris Agreement, which means where we'll be able to get the warming that's on a global scale compared to pre industrial levels around plus 1.5 to plus two degrees. If we were able to get this, we could still save one third of the volume I mean it's still not a lot, but just to give you the bad side or if you really would, if emissions would really go through the roof or stay at present day levels and we do not invest in new energies and we stay away from the Paris Agreement. In that case there's almost no ice left so we lose more than 90% of the total volume that's for the European albs but these these these numbers I think you. They're generally general for other regions to of course typically they will have less loss, but this idea that the present day actions that we take and the amount of warming that will have in the coming decades to century will really have a big influence on how much ice will be left in the different regions around the world. So what optimistic scenario would see two thirds of the current alpine glacial mass to peer. Is that yours. Yes, for the European alps yes but then just to put it in perspective if we take that. So that's 4,000 glaciers if we take this 200,000 glaciers around the world the situation is less crim because European alps are relatively low in elevation compared to other mountain ranges, and we see that in other places like in high mountain Asia or places where typically glaciers are much higher elevation. They're typically the most lesser also the Arctic regions where there's also a lot of glaciers except for the ice sheets, think of Arctic Canada Alaska and others. And that's our projected to be losing a bit less but nevertheless, there will be still be important mass losses, especially under under a high warming. But for European alps, even in a good scenario will be losing about two thirds at least that's what our model says and models are also tools and there's also uncertainties related to these models. Our numerical simulations do. Maybe something to explain it more a bit in general because it seems a bit like a black box like something we put stuff in and then it projects something. What we always try to do with these these models, these long codes is what we try to do is we know how glaciers changed in the past. What we typically try to do is also first as a kind of a check to see does our model work is we're also going to try to first reproduce what happened in the past and that gives us some confidence in the fact that our model is able to reproduce past changes. We can also use to tune some some parameters in our model. And then once this is done, we make projections and these projections for wonder worth. They're telling us that for the European alps you could be losing two thirds of their mass, even in a in a pretty good case. So, these, the models you use them are basically using historical data aspect like perhaps pay you data as well. To test and train models which use them for predicting future ice loss. That correct. Yes, correct. It really depends on which time skills we're looking at. In fact, I told you glacial responding responding slowly, but compared to ice sheets are responding really fast. Typically when we try to to simulate how glaciers evolve. We're looking at typically observations from what we call the satellite era so from the 1980s and beyond and typically this is what we tune our models to and then and then and we look if they work well and then we use them to make projections but if you would, you would be talking now about glacier, someone working on glaciers that someone working on ice sheets, then the ice sheet person will probably tell you yeah we're using paleo data so they're probably going to be using a lot of old moraine extent or other reconstructions of how the ice sheet looked in the past. And they'll, the first thing they'll try to do typically is to reproduce these past observations and, in fact, the principle is the same you use past observations, the time scale is just very different then it's maybe over thousands of years. Well, glaciers respond slowly, slowly in the order of decades, but in the order of decades is still fast compared to the millennia millennial time skills on which the two big ice sheets respond. So, being such dynamic. I suppose landscape features, the really kind of renders glaciers as a potential are useful indicators of climate change, we don't see that's an accurate thing just. I think part of the reason that pop pop is my head was, there's such a huge media discussion around glacial ice losses, I think COP26. I think Glasgow, one of the universities in Glasgow and watch our common remember which one named a glacier in Antarctica as Glasgow as a kind of symbol of hope that something will come out of the COP26. I think glaciers are a sort of indicator of climate change in this case. So I think they're really symbols of climate change, and because they're really showing if you have someone who doesn't believe in climate change and that things are changing well I think if you bring them to a glacier. At one point you showed them pictures have I would look before it's it's very confronting so I think they're, they're a bit, they're a bit symbols of changing climatic conditions are some of the clearest indicators I mean people if temperatures rise one or two degrees will not immediately notice this but a glacier that changes can be used as well to communicate science and to really also show to visualize changing climatic conditions. But they're also really used for scientific purposes that's I think pretty interesting there are some studies and then it's on slightly longer time scales and typically for big glaciers. And sometimes we also have something in between glaciers and ice sheets which we refer to as ice caps ice caps cover the landscape, but they're not as big as the ice sheets so typically in Iceland now you have ice caps. And in other Arctic regions, and for instance there's also studies which use ice caps, and we know how these ice caps behaved in the past, and then you can in fact change the situation around so you're not going to be putting some climate in the glacier evolves. The question is how where the climate conditions in the past, we know how the glacier was. So you have different pieces of the puzzle. And so what you try to do in fact is you try to reproduce how you we know that the glacier or the ice kept was in the past and based on this you can say, Well, this was only possible if temperatures were three degrees colder or if precipitation was so much higher So we can really use also glaciers and past glacier reconstruction so the so called paleo reconstructions. We can use these really also to say something about the climate of the past which is, I think quite fascinating it's always a puzzle and you try to solve it. And sometimes you don't know what the glacier evolution is but you know what the temperature is, and then you solve it that way but in other cases you think you know at least how the glacier was in the past but you wonder well, how was the temperature and so that's with these models. So how do you do to glue that all together. Staying on to because of your of your approach to research. And suppose in the theme of dynamic feedback looks affecting of ice loss. So ice loss also affects a glitch logical research as well then if the thing that's been studied is disappearing dramatically does that impact how you approach the work. Does it perhaps matter less when things become more digital. Oh, no, it does matter because, as I explained to you we need a lot of different types of observations for our work and a lot of it is done with remote sensing switch means from distance, which is to be done with satellites but also more and more by flying with drones over glaciers, but we also need to really go in the fields to measure things really in detail. And just from a practical point of view some of these glaciers to which I used to go 10 years ago before starting my PhD and if I go back to them now we cannot take the same routes that we took to go up the glacier just because the glacier is less accessible and has retreated up so from this perspective just from a purely practical perspective, it is sometimes challenging. Of course we also know that in mountain regions, there's more risks, it's not only related to glaciers but also the fact that there's a lot of permafrost which means it's like frozen frozen soils and rocks and others and of course if it warms you get more rockfall from a physical perspective it plays a role. And then it depends what you're willing to collect when you're on the glacier some people take these ice cores from glaciers, for instance to say something about past climatic conditions, you can look at the air that is trapped within this ice and you can look at some relationships which are in there. Isotopic relationship, which means in fact is the types of ice which are in there, and these types of ice in fact can tell you something about the climate of the past in that particular region. And so, the reason why I'm explaining this so that people are going there to collecting ice well in some places this ice is super valuable because it gives you indications about past climatic conditions. Because once this ice is gone you will not know what the climate of the past is there, and maybe there are iconic example there is on Kilimanjaro in Africa. And Kilimanjaro in Africa there's there's still ice but not a lot on top of Mount Kilimanjaro and we know if we go there now we can still extract these cores but it may be that in 2030 years, this ice is gone. This is very valuable indicator of past climatic conditions may also be begun. So, there's a lot of impacts of climate change on research both the practical way of going there but also what we want to collect can really be affected. So, with more warming, there's going to be a loss of these data archives and also accessing these data archives in a form of ice also becomes more difficult, basically. Yes. So, staying on the theme of impacts but perhaps they taking a step back a bit is, could you tell us a bit more about how glacial ice loss might impact humans. Absolutely, so glacier changes has effects on our, well, on many different scales and my skills I mean on also on spatial scales and depending on where you are. First of all glaciers react everywhere in the world on raising rising temperatures which are typically caused by people who don't particularly live close to the glaciers just by getting additional CO2 in the air temperatures rise and temperatures rising we see that glaciers are affected everywhere. And also the same the other way around also when glaciers change they can also have effects on people which live really far away. I think maybe one of the important examples and I've already been mentioning this in the introduction is sea level rise. These glaciers these mountain glaciers they don't contain that much ice you would think at first. To put that in perspective, the Antarctic ice sheets contains more than 50 meters of sea level rise of the whole Antarctic ice sheet would melt sea levels would go by 50 meters that's globally. If green and ice sheet would melt sea levels would go by seven meters, which is less but still substantial. If all these 200,000 glaciers when I'm mainly talking about today if these 200,000 glaciers would melt sea levels would go by 30 to 40 centimeters. And at first you could be thinking of okay that maybe for sea level rise we shouldn't care about these glaciers compared to the ice sheets. But that's really not true because these glaciers, if you remember from what I said before they really react way faster. So in fact we see that from the present day sea level rise. A lot of this in fact is caused by mountain glaciers. Kind of as a rough to put it in a rough pictures we have about three to four millimeters of sea level rise every year, right now, and that is three to four centimeters. Sorry millimeters three to four millimeters a year, luckily not centimeters three to four millimeters a year, and out of the street to four millimeters. We see that in fact 25 to 30% of this around one millimeter is caused by these 200,000 glaciers. And there again a sea level rise of 10 or 20 centimeters may not seem a lot to people but that's already huge it's huge for people who live in coastal regions, because there will be more erosion of the coastal regions but there's also way bigger risk of having inundations. At one point of sea levels really go up a lot will have to build new defense mechanisms. Maybe a different perspective of looking at it is always when infrastructure is built to defend the coast of course it cannot be built to defend the biggest storms which will ever come so for instance, infrastructure which now works for a storm which occurs. And with this with this with the with the sea that goes inland which, which can protect it against an event which occurs every thousand years. Well if your sea levels are 10 or 20 cm higher. This event will not occur every thousand years but it may be occurring every century or even every, every decade for instance. There's so many examples but one of them why glaciers matter, at least on the on the global scale is really related to sea level rise. I don't know if I can continue to give other examples because I think also locally there's some interesting ones but maybe you want to add something there or ask some questions here. Yeah, sure I think that's, that is super interesting I think just summarizing your point really is that perhaps the, the greater dynamism of mounting glaciers means there's a faster injection of that not water into the ocean, which introduces a lot of certainty for people looking into coastal protections. I think an example of that, I think from what you said about storms for example is a certainty surrounding the costs and height of flood defences, an extra few meters on top of a storm surge which is already above expected, perhaps an expected high wave storm like this may not come alongside a hurricane or something. And it could be enough to overtop a barrier or something so there's, yeah there's a lot more. And this has to introduce I think by the rapid inclusion of glacial meltwater. Yeah, I think my next question to refer was to ask about the local impacts of glaciers as well so authentic of our time I'll just let you go on to the next point had a mind that's okay. Yeah, the local side and there again there's many sides of ice as I explained glaciers are changing. So they're going to be changing the landscape but one of the things that places are wonderful at doing is providing water to people living close to them or at least in the valleys downstream of glaciers. And in some regions in the world are extremely important when we're thinking of high mountain Asia. There's really a lot of people living in big basins like into Skanges Brahmaputra where there's tends to hundreds of millions of people living. And these people are very relying on water from glaciers, and the way that this works a bit is before I was explaining how a glacier a healthy one so let's take a case without climate change but a healthy one would always become a bit bigger during winter and would melt a bit during summer. But wait because that's just when people need water most it's typically during the hottest and driest periods of the year, your glacier which is in fact up there in the mountain will be providing water to you so that's really the time of the year when you need it most. So in fact a glacier is a natural water resource waiting for you in the mountains and giving water. And what will happen if climatic conditions change. It's a bit two folds. At first of course there's even more water coming during summer. So typically, in the coming decades also people living in this plains in high mountain Asia where, where this is all the water coming from the glaciers at first it will have enough water because there's these glaciers are melting too much because of climate change and so to still be getting a lot of water during summer when they need its most. However, on the longer term once your glacier has disappeared your natural water resources gone up in the nonsense. And if you don't have a natural water resource in the mountains, you're just not going to be getting the water that you need from the glaciers so people will during the time of the year when they need its most in summer, there will be less water coming from these glaciers. And this depends a bit. So there's, there's going to be a peak in the water in summer and then we're going to go to a level which is in fact lower than than your baseline. So this is a bit unearthed where we are to see to see where we are in this in this peak concept. So just to put it in perspective in the European house we think that we have reached the peak water now. So we're now expecting to getting to be getting less and less water during summer, which is problematic but on the other hand, the glaciers in European alps are not the main water provisions is also the snow and there's others so they play a role but over the whole concept they're they're not as important for instance as in high mountain Asia where really are people are really very defending on them. And there we see for instance that in high mountain Asia it seems that the for now the water levels that we're getting or that people are getting in summer still rising so they're still, there's a buffer now now we're in a situation which is okay. That's of course only temporary and at one point will reach what we call the peak water. So the point where people will be getting most water during summer and then we'll get a decline and this will be problematic, especially during the second part of the 21st century for people living in high mountains in Asia and it's because these these regions are so heavily populated also that they're this water is really really important. If now you have a water quantity that you're getting during summer but if in 50 years from now you only could be getting half. That's huge because you need that water for agriculture for well for everything for your household. And so this this may cause severe problems. Yeah, so in addition to perhaps increasing risk to coastal issues on a global level on a local scale is also a resource issue really. So you could also have numerous knock on effects, which I think we're more physical than sociological but you also mentioned there would be a peak during the summer. Where to be a lot more water released. Relate to further responsibility. Well, there's always this water coming from the glaciers and this one is especially important. The moment during the year when they're the most important is towards the end of summer because first there's all the water also coming from snow. The snow that always melts every year but that comes in that melts every year so these are places where there's no glaciers that will be formed. The main peak that you get where there's really a lot of water coming so now I'm speaking about peak throughout a year is typically more depending on the regions that is typically more towards the end of spring early summer. And it's only during the second part of summer typically that glaciers are really important in their water provision. And so there the quantity of water that will be getting from the glaciers will be higher than the baseline, but not at a point of causing floods or orders that's not really what we're expecting. It's mostly the fact that it's already not that much water at this present day levels and if even that level which already is not so high or which is maybe now slightly higher, because there's a melt. Well, we're mainly afraid about the moment when this these levels will be will be dropping dramatically. Sure. So I suppose that one of the key taking messages is even though I suppose for example, the Alps looks to be one of the more badly affected collections of glaciers communities of glaciers perhaps the impact of its lack of available. And so the reduced water resource is actually going to be bigger in like power nations. So, there's an equal distribution of the impacts of glacial loss basically from glacial melting. Correct, correct. So in fact, there was a very interesting study which which appeared one years ago by colleagues who was led by colleagues from the university in the Netherlands and which they showed. They were really referring to these glaciers as water towers and what they made is a water tower index. So they're going to, they said for every mountain region in the world where there's glaciers they said how important are they as water towers and what they did in fact is they they showed in fact that it depends on two different things. It depends really not it depends on how much water they're providing study these these water towers. It depends on how much water they're able to provide but it also really depends on the people who live there. So, then it's to really look at how the impacts are you need to look at the whole socio economic structure of, of the, of the system. So in fact, there's a kind of there's a supply index there's how much supply and then there's also the demands. There's, it's a bit like economic market but there's a supply and there's the demand. And of course in places where the supply is at risk and where the demand is very high. Well there it's clear of course that the glaciers are very important as water towers today, it would score high on a water tower index. And this means really that well these regions will be really strongly affected. In other case, if you go somewhere in a high Arctic, they may also be big changes in the water provisions but if there's not that many people living there the impact will be will be more limited to its. I think that's quite fascinating about this research it's a bit putting everything together it's not only the purely understanding and mounding how the system Earth will change but it's also of course taking into account. Yeah, how societies will evolve and what the economic realities there for what water is needed but also taking into account political tension and all of these aspects. But I would say yes, the high mountain Asia and the end these I didn't mention the end these but also the end is in South America definitely two regions where glacier loss will have a big impact, at least from a water supply perspective for people. Thanks for the answer. I just want to perhaps move away from the impacts of English loss on humans and think about it more from a perspective perhaps that's more geophysical so would the loss of mountain glaciers also feedback into climate change perhaps or perhaps impacts to more political development I mean the cove. Through cove values over centuries of thousands of years, where the loss of these glaciers have effects. These systems. Yes, so so glacier changes, you can really see them very clearly in landscapes, and not only for big ice sheets but also glaciers typically when they advance and when they reach a maximum they form a so called moraine which is like, like this kind of a bulldozer which is advancing taking the landscape and depositing it at a given place so of course, there's these moraines in the landscape which which reflects that's a direct influence on the landscape there's these moraines. There's also the way that material is eroded under glaciers which typically of course, when we're looking at the way that this will be changing the landscape that's on longer time skills. We're thinking about the sediment inputs which comes into reverse and which then has a lot of effects also for people downstream or for hydropower companies well of course these will all change under if glaciers change. So, also from a geophysical perspective, yes, they're they're forming the landscape and they will have also impacts. Yeah, more directly. Also, maybe a bit at the interface between this and hydrology is also glacier lakes. We know that a lot of glaciers by advancing and by by the way that the ice moves. In fact that they have over deepening in the bedrock which means that over deepening is really kind of a depression in the bedrock so in the rocks which are underneath the glacier and of course if your glacier retreats, we can get huge lakes so the glacier lakes which are in front of glaciers. There's also other lakes which are potentially dangerous and these are just some superglacial lakes but especially also ice dam lakes, so which quite often form in between a glacier and the surrounding mountains and of course if your glacier retreats. So we're going to get more of these sudden events in which a lot of water is released. These are so called gloves, these are major lakes outburst floods. And there's, there's also some research being done whether these would also be increasing under changing climatic conditions or not. So that's another risk then is potentially low frequency, high impacts flood events on these arise dam futures. Yeah, so just, I think the final few minutes as we focus kind of on the future bit more. So the question is, I suppose the key question is like what does the future of glaciers look like? Are we going towards a glacier or an ice free world as people like to put it? Well, it will really depends on how the climate will evolve. And so it's really going to be depending on the actions that we as a society are will be taking today. Under a bad case or better case with a lot of warming, which used to be referred to sometimes before as business as usual. Nowadays it's recommended to not refer to this as business as usual and work is luckily. We think that we're not going to be ending up in that very high case, but if we would keep the emissions levels at the extremely high level and then we get warming, which can globally be globally be in the order of three four or five degrees by the end of the by the way, you should always keep in mind all these numbers but warming plus one plus two plus three that's always on a global average and mountain regions and polar regions tend to tend more than the average. So typically that means that even stronger warming for mountain regions for glaciers. Well, if we would end up in such a case and of course it will be almost no ice left in the coming centuries. I think there's, there's, there's hopeful signs that there's good signs that we're not going to be heading in that direction so I think normally going towards the ice free world I don't think so but of course that we see that if you want to limit the warming levels to plus one point five or plus two degrees on average. We need to make a lot of investments and there's a lot which needs to happen today and it's clear and I think you're also for everything we've been seeing in the news. That's unfortunately also from what came out of Glasgow there's some things were reached, but there's always the question about how fast are we, how fast are we getting there and it's, I think for glaciers at least every year or every decade plays a big role for the warming so likely not in the ice free world, but the question whether we'll be having 3040 5060 70% of the ice mass left so that's not for European alps but globally. Well this will really be determined by the policy actions they can take it now. And from what you said earlier. It sounds like I think you mentioned the glacier ice loss is potentially accelerating as well. So really this this time of making decisions on climate change is critical for mountain glaciers especially, which I suppose increases the vulnerability of those people you mentioned before who are most affected by it. I suppose it's coming to my final question. And it's, what was the key takeaway message from the audience, I guess as you started approaching talking about decision making around COP26 and the potential impacts on policies you make is perhaps it's a key point to conclude a webinar was your thought. The takeaway points I think is that glaciers and of course, I'm very narrow minded and I really like glaciers I've been talking a lot about glaciers, but I think a lot of things that I've been telling today about glaciers also apply to other systems. If you would talk to someone who's working on oceans, or someone who specifically looking at the atmosphere and the levels of warming looking at at forest. I think there will be a lot of different examples. So what what I've been talking about today was very much focused on glaciers of course, but I think for glaciers. Yeah, just the fact that they respond slowly. And it's always a question what is slow, they're fast compared to big ice sheets that respond slowly. And so that's today's action will have a big effects under under future evolution. And it mean, I think the impact I just highlighted a few, but just to give you an idea is many more impacts even of changing glaciers so there's this. There's the sea level rise there's the water provision, but they're also really important I mean if they cause natural hazards, then this this can have huge effects. And glaciers are also also have a quite important touristic value in Europe and also in other regions, where a lot of people depend also on gracious being there. They're important also from a water perspective for instance there's countries like Switzerland which generates a lot of their electricity with hydropower, and this hydropower is also impart related to how much water comes from glaciers if your glaciers change. This may affect how much electricity you can produce through hydropower so there's just really, really plenty of effects and what we try to do is really make the best simulations that we can we try to make some good predictions and I find that really fascinating because we really try to explain system earth everything is connected all of these concepts that I've explained with changing temperatures and how your glaciers change. It's not that a happens and this has an effect on be in system earth typically a happens this has an effect on be which but see also had an effect on a which affect the, and of course we, we can think about this but our human mind at one point cannot make all these connections and so maybe to to to visualize this to people to explain to what them do when I tell them I do thousands of lines of codes where I'm sitting behind my PC impressing on all buttons. Well these lines of code they try to connect all these systems in the, the determine how a glacier evolves. It's, it's something fascinating to do. On the one hand it's it's sometimes frustrating and it's, it's sad to see how glaciers evolve but I mean the work in itself I think is really interesting and I think or I hope that we're able to make better and better projections for how glaciers evolve in the future. Thank you. So, now we'll move on to the audience Q&A. I thought if you sent in to me. I want to say if you're watching right now you can enter a question in the Q&A box at the bottom of the screen. Just type in there and then we can answer it. Yes, sure. So I've got a few questions sent in already. One is talking about artificial glaciers. Do you think glaciers should be preserved like they do for example skiing etc. Or is it like a waste of resources. It's a very good question and it's one that isn't easy to answer. I think that we can, on a very small scale at least we could protect glaciers and there's different ways of doing this but the most classic way of doing this is putting something very white on top of the glaciers so typically a white blanket. And if your surface is white of course more of the incoming solar energy will be reflected. So you get less loss. So in say it sounds like an amazing idea why not cover all glaciers. Well, it's totally not feasible because it's extremely expensive to do so. It's very labor intensive to do so. And you can also only cover very small parts of glaciers with this in the end. It's very expensive. It's also probably not that good for the environment because it's typically done with plastics and others which then also break off and there's also this micro plastics which are everywhere in the environment so from that perspective, but nevertheless in some cases, people, I think it is worth to do so and it works I mean there's some skiing areas where so that people could ski longer during years typically when you ski in European alps most of the time you will not be skiing on a glacier but in a skiing area you could also be skiing on a glacier. Well, if you have a bigger glacier you can have people also skiing for longer during the season so there's at small scales. There's people putting blankets on glaciers. Another example is a rune glacier in Switzerland which is one of the most visited glaciers it's very well accessible and they have also ice cave where you can really go in the glacier on the side. And there they also put blankets to really protect the glacier so it works well, but I think it's totally unfeasible at the large scale also, not only practically but also economically it's, it would cost really really a lot and so the only way to save glaciers in the world is to try to get the temperature at a given level. And there's some crazy ideas about also putting a lot of snow on glaciers on this mortgage glacier which I explained before. But we have been doing some some some studies on this also really to see whether it would really be feasible and it seems to be very very hard to do, and it would cost not in the order of millions but really hundreds of millions of euros to maybe have to do that instead of retreating three kilometers over a given time spent with only retreat one or two. So, it's not the way to go but it's, it is of course something. Well, not the way to go that's my opinion but it's, I think there's really some challenges linked to that and on the on the bigger, in the bigger frame the only way to do so is to limit levels of warming. And that's the best way to save glaciers. It's useful for a local short term business solution but not really the outside to vanishing resources. Okay, so another question, which is more on your outreach work. And it's as someone who engages the public on science, how do you handle communicating on such heated issues like ice melt and climate change. It is it is a fun it is definitely a heat addition. Typically, what I what I try to do when talking about this when going in schools of course is. I try to get people excited for the topic it's of course different if you talk to school kids to adults who are ready maybe sometimes skeptical from before the conversation starts. And I try to get them excited to show where the also the cool side, also a fun to the of being a glaciologist and, and going on the field and flying with a helicopter to remote place where we will be dreading suit to get them excited and then really to show them I think one of the easy things for me to communicate about glaciers for instance, would I have to do compared to oceanographer who's talking about changing oceans or someone talking about another aspect of system Earth is that they're so extremely visual that there's so many of these images where you see the glacier 1850 which was huge covering a whole valley and you see the, or even with timeframes you see the between you really see how these glaciers have massively changed. So that is something that I typically try to do. And then what I always try to do is really let the science talk for for it's like I'm not the one advocating exactly what needs to happen and I'm not saying that we should stop warming. And you need to do all of these things. What I'm trying to do is really let the science talk and say well if levels of warming will be very high well this will happen with glaciers, if we were able to to limit the levels well this will happen with patients I let to, I try to let the science and a bit almost to put it in a blunt way because of course it's not always that black and white but almost try to be really the nerdy scientist who does the numbers and then gives it to someone else. And that person then then can make decisions the policy maker others that's that's a bit the approach that I try to take really apply maths and physics through these models on system Earth on glaciers and try to make as good predictions as possible. Yeah, sure. So, when it comes to communication the public. Obviously, keeping it simple, but also try and I guess let the public come to their own conclusion from the sciences as you have really. As a scientist that's the best we can do of course, at one point there's a question should we as scientists really be engaged and also be the one saying that we need to do is or not and I think there's different opinions and I think there's pros and cons to being more reserved and giving numbers are also really trying to say well we need to act upon this. And let the science speak for it is always it's always very strong, of course, if you can just make projections and then just just show what will happen with glaciers under changing climatic conditions. I think it's time for a couple more questions. And one is it's still to make gains in glacial in glaciers so I guess what they mean is, I guess we've talked about glacial loss and vanishing in the morning climate as a possibility of it. Going back. So the question is whether it's a possibility of glaciers growing back or to the question is, is it possible that there might be glacial gains and I'm assuming. potential for glaciers going back. Yes. So glaciers can typically grow back I mean if you put in colder climatic conditions again, the unlikely case that we're able to limit the levels of warming at one level and then put them back down again or that they evolve to that way down glaciers will eventually with some delayed response but will eventually start growing again. So for most glaciers this works for ice sheets it's a bit more complicated because ice sheets are so big so that this ice sheet agreement and the one in Antarctica. They're so big that sometimes you have to 3000 meters of ice. And of course if you melt all that ice away, and you would then put the same colder conditions back it may not be regrowing to the same state. And that is simply just because you're 2000 meters lower because you've lost this. So then not that it's not the climate signal but it's just the fact that you're lower. And of course the lower you are in the atmosphere the warmer it is, and then sometimes this is the so called, or one of the so called points of no return where, for instance, but it doesn't really apply to glaciers it's more for ice sheets, because glaciers are way thinner but some ice sheets may really be at a point where, at one point, they start losing and losing mass. And then, even if you would put the conditions which are now here to get the glacier this level, sorry the ice sheet, it will not be able to to regrow anymore. But in say glaciers, if you wait long enough, so the order of decades to centuries because they respond slowly but eventually a glacier which is retreating now if you put in some colder climatic conditions. And it will eventually then read bonds. Yes. So if we get into a negative emission scenarios soon glaciers should be bouncing back the next century, hopefully is, is what might expect. Well it depends on which, on which levels will get a stabilization of temperature but let's take the best case where we can get this around plus 1.5 degree, compared to pre industrial levels. So we're getting glaciers which are approximately today's size are even smaller still that today because they're still we're still responding and we're now about plus one plus 1.1 degrees compared to pre industrial temperatures so even in the best case where we would end up at plus 1.5 degrees glaciers will be smaller than they are today. And just one final question. You mentioned point of no returns. Do they exist for these features then, or are they useful. A useful communication tool I guess to describe these dynamics as having points of no return. We think that they do exist. Of course it's always difficult because these are things that we model we simulate and we try to put all these elements together. I mean I'm not an expert in working on these so called tipping points and points of no returns for ice sheets I wouldn't venture too far in that direction to answer that question that there's strong there's strong evidence at least from a modeling perspective that indeed the ice sheets may at the front due to dynamics. This is one concept that I explained before about the fact that temperatures are lower at high elevation that if you lose your mass, it doesn't come back, but your strengths for the Antarctic ice sheet. We know that a lot of these glaciers which are in contact with the oceans, they're on retroglades slopes for the bedrock, and due to this without going to details, this is just very unfortunate and means that sometimes just by losing a bit of mass at the front of the Antarctic ice sheet, you can get huge retreats, which could not have effect on the inland ice so I think there is definitely some some of these points of no return do exist. And of course this is something we're learning more and more about by making simulations and making better projections and it is there are things that we need to take into account also and try to understand. Thank you. So we're just about our time. So I'm going to conclude the webinar, like say, thank you, Harry for joining us today. Thank you everyone who has enjoyed and yes, have a good day. Goodbye for now. Bye bye.


So, I'm going to be talking about simple number theory in Perle-6. Number theory, the fundamental branch of mathematics, studying properties of integers, it is certainly fundamental in modern cryptography. Perle-6, I don't really need to talk a lot about what Perle-6 is here, sister language to Perle-5. A lot of this is conference-driven development, that is I've done a little bit of work with Perle-6 and wanted to do some more, so this is a way to force myself to do that. So I am Dana Jacobson, I'm coming from Portland, Oregon, the United States, come to Fostom a couple of times, love it here. Number theory for me is a hobby that got out of hand, I imagine lots of you guys have had something similar. So nice things about Perle-6. I've all heard there's lots of ways to do something in Perle-5, there's more than one way to do it. Perle-6, here's this, laughs, hold my drink, I'll tell you. Perle-6 has so many ways to do things, a lot of them are really nice. For me, everyone's going to have a different set of features they like, Damian Conway talked about how he just loves using Unicode characters in his programs. I'm from the United States, I don't know what he's talking about. So Jeff and some other people, Brian, are looking at grammars, I haven't looked at grammars, but it has something for everybody. I love big ins, native to Perle-6. In C code and in Perle code, you're constantly fighting with this issue of when my numbers start getting large, weird things start happening. We have rationals, I don't actually care so much about them, I know a lot of people love having the idea of rationals where I can just maintain this idea of it's 1 over 3, not immediately turn that into 0.333, something not 3. Junctions are pretty cool, EXP mod is a wonderful feature, it's a function I end up writing in every other language because when you want to raise A to the kth power, mod n, that's a terrible way to do it if you actually raise A to the kth power. And then mod n, because you end up with the humongous number and there are much faster ways to do it. Perle-6 has it completely built in. Perle-6 also decided that hey, this idea of is a number prime is pretty fundamental and people keep writing it in every language, so we're just going to toss it in. That's nice.  Pick is surprisingly useful, you take a list and just say give me a random element from it, it has lots of variations, it is used all over the place. So let me start with this very simple RSA example, we're going to generate a key. So we want to generate a couple random primes and as the product of the two, I think, yeah, so we choose, take the LCM of the totions, which because their prime is very easy, we choose an E, we get our D, let me go through the Perle-6 code for this. And random primes, it's really, really simple except my is prime ran off the screen there. So we just take, we have a number of bits, we just keep taking random numbers until it's prime. And there we go, now we can fill up P and Q very easily. These are very simple, oh wait, but Perle-6 has LCM built in, the least common multiple. So I want to choose an E, there's a different way to do this, if you want you could just pick an E that's coprime, this is a different way to do it, you go ahead and pick a random one. And we get to use our GCD function and again our pick just says, just give me a random value from that, we do it until it's coprime. So now we want D which is going to be our private key, we want the inverse of that. The idea is D times E ends up being one mod phi. So how do we do that in other languages? Well we get to write a routine to do it, but in Perle-6, well we have this exp mod, just give it minus one, it'll give you the inverse. It's surprisingly handy, this is really short code compared to what we end up with writing in other languages. And we decided to use 1024 bits, Perle-6 has no problem with this whatsoever. My talk is not going to be about cryptography so I'm going to leave aside all of the math reasons why and the boilerplate code you would normally add to actually make this a useful routine, you can look that up. So binomial is very common, we want to find the number of combinations, taking 50 items for instance, I want 50 items and I want to choose combinations of 10 of those. How many do I have? I add dot elements and I get this humongous number. Well I'm sure I'm glad I didn't iterate over that, Perle-6 is very clever and knows that in fact you're just asking for the number of elements, you didn't want me to create this huge list with this many items in it, you didn't want an iterator, you just wanted the number of elements. So Perle-6 gives that to me. This is a formula for how you calculate that. If you dig through the Perle-6 internals, this is the product of n times n minus one, n minus two and so on, we divide by factorial of k, if you dig through the Perle-6 code you find basically this in Perle-6. First we have n down to zero, this is a zip operator, so we're going to take this second list which has a little optimization in it for the minimum and we do the divides. And finally we get to reduce it, we just say star here, it says multiply everything together. Now in these, these ended up being rationals. So in most languages you end up having to write a whole lot of code to deal with this, it's not complicated code but you have to keep in mind oh wait I have to make sure those divides are all integers. In Perle-6 we don't really care, we just write the routine just like we would like to. Here's binomial in C, this is a pretty standard way to do it, Mark Jason Dominus had this on his blog in 2007, well not this, but something like it and said this is how you should do binomial, it has no overflow problems, it's great, except it does overflow. Someone found a, he posted this on Reddit and someone said oh actually it does overflow. Now probably most of you will see the obvious way to fix it. So this is how you fix it in C, it's actually very fast, it's clear, everybody would do this and you completely understand why this works until you realize this is still only for 64 bit. If I go past 64 bit I have to start getting into big ant libraries and portability issues and so on, Perle-6 solves it all. So now I'm going to talk a little bit about primes, why primes, well okay some of you who know me are wondering have you ever given a talk where you did not say the word prime and yes but it was about a decade ago. Primes are really important, in number theory they are the atoms for the integers, if you will, there are a lot of algorithms, in fact the binomial algorithm you can do faster, if you say well I don't actually have to denote all the numbers up to n, I can just go over the primes so I can speed things up. There are a lot of algorithms in number theory where it turns out you don't actually have to go up for instance solve to n, you can factor n, perform your operations on the prime factors and then combine them and you come up with much faster ways. So there are three things we generally want to do, generate primes, recognize primes and factor integers, we don't factor primes. So the usual way of generating primes is the Seaf of Eratosthenes who wrote about this in about 250 BC, he was the chief librarian of Alexandria, he wrote in all sorts of different areas, he contributed to many many many fields, unfortunately all his works were lost when the library burned but lots of people wrote about the things he did including this algorithm and interestingly there are some new sieves that have come out in the 20th century, they are all slower than this, they have some interesting properties, the Seaf of Atkin actually is slower than the Seaf of Eratosthenes, I'm going to talk about just the very basic monolithic non-segmented sieve, you can get complicated, start adding optimizations like everything you can spend a year adding optimizations. So very simply we enumerate all our numbers from 2 to n, I've chosen 120, we pick the first one and say that one's prime, because they all kind of look prime right now and we actually we know that 3 is as well because we know everything up to 2 squared is prime and we just mark all the evens because we know they're all multiples of 2. So then we can move on to the next one which is 3, we're going to mark all the multiples of 3 because I've chosen 15 here, they're all going to line up, we can do the same thing for fives, notice that I don't, I start at 5 squared because everything up to that it's already been marked, we go up to 7 and it turns out at that point we're done because 11 squared is 121, so there wasn't a whole lot of operation going on to generate these primes. On Wikipedia you'll find the pseudocode, which it turns out seems to be remarkably hard for people to implement, it's four lines, we go up to the square root of n, we ask if it's prime, if this number's prime so far we go from i squared up county by n. So there's an operation that is not done in here, which is remainder or divide, it's a very efficient algorithm because the only thing going on is marking and adding. So in C, we're not going to go over this very long but basically it's exactly the same thing as the C, here's our four lines we can argue about i times i versus taking the integer square root, but there's your four lines and then we go through and we can do that. Pearl 5, in this case I've done an additional optimization of only going through the odds, that is we saw most of that work was at the very beginning where we had to mark all the odds, well after two we know we don't have to deal with them at all, so we're just going to ignore them. So here's, this is not very pearly code but it is exactly the same as that C code or the Wikipedia but in this case we get to go, we skip the odds. There is a bit of wonkiness at the end where we're doing a map and grep to turn those odds back into the numbers we care about. So we use half the memory by doing this. So on Rosetta code, I looked last year, it was partly the reason for this, I said there are three examples of the sieve of veritastins on Rosetta code and all of them are wrong. So they start out okay, they say zero and one, not prime, everything else looks prime so far. We do a gather, this is a cool feature where we take the key value, we just say I want the actual number and then I want the value that's in that array. So I can get them both at the same time and then we do, oh well if it looks prime then take the number but wait what is this doing? That's a mod operator. So for every number from n squared up to n, I'm going and checking the divisibility. I'm basically doing trial division on every number repeatedly. So there's a simple solution, now we have the sieve of veritastins in pearl six. Looks exactly like the C code or like the pearl five code or the Wikipedia pseudocode and it runs significantly faster. So pearl six has a lot of different ways to do these things. We can try doing it using a set, this is something someone put on Rosetta code as well. Doing it with a set, we have our multiples, we're going to gather unless multiples contains the number, we take it and we do a set union. You can use fancy unicode characters for the contains and union. Basically we're making a new set with number squared, that plus number and so on, which is exactly what we wanted from that pseudocode. You could change it to is the number an element of the set, is the number intersected with the set, we can go straight to exists key, lots of ways to do it. We also have this is prime operator so we could just do, well I'm just going to walk all the numbers and ask if it's a prime. That's not a sieve but is prime is built in so maybe that's fast and certainly easy. It's so easy you could just do basically grep is prime through a list. So the set operator, so that code has some significant problems with it and also pearl six's sets haven't been optimized entirely so we're going to ignore that. But here's our trial division. It took four hundred and one seconds to generate the primes to one million, which is absurdly slow. So we know doing trial division basically the incorrect sieve of veritostin is the wrong way to do it. Here's the is prime version. Okay, so I wrote a new version of is prime. I went to more VM and started writing C code and so there's a new version of is prime and I'll talk about that more later, which is significantly faster and it's faster at all sizes. So hopefully I will actually get that pushed out soon. So our sieve actually when you fix the sieve instead of doing this kind of broken sieve you do the real one it's looking pretty good. You can do odds only. I didn't show that example but you can speed that up some more. That's looking good if you increase this it would start looking better. Pearl five has had what twenty something years of additional optimization and we're marking and adding this is absolutely what C loves to do. So this is a little bit of an unfair example here because this is so simple but we've chosen something very very simple to try out and see there are lots of ways to do it in pearl six and you can speed it up and in fact you can certainly call C code from pearl six if you wanted to. So we're moving on to the next one how do we recognize a prime? Well we can do trial division which is actually really good for numbers up to you know a thousand or a million but if I give you a 64-bit number and say hey try dividing by all the numbers up to the square root of n or if I give you a thousand digit number you're never going to finish it's really slow. Miller came up with this method in about 1975 which is very efficient and answers the question entirely of whether a number is prime. It's a bit of a problem. Step one prove the Riemann hypothesis. So this has been giving us a bit of a bother for the last 150 years so that doesn't really work very well. We can do special forms. Mersin numbers or proth numbers that is numbers that are two to the n minus one or two to the k times two to the n plus one we have some really efficient ways to do it but that only works for numbers of that sort if you like to finding large Mersin primes then that's nice but that's not very useful for most people. We can do partial factoring methods this is really what was used up to well in the 1800s 1900s up to 1980s where I take n minus one I want to find out if n is prime I take n minus one or n plus one and I perform some factoring on it. I don't have to completely factor the number but I have to do some factoring. It turns out we did primality fairly well that method works quite well up to about 40 digits starts getting slower and eventually you just can't find factors. So in the 1990s there were a couple methods. They're quite efficient APRCL and ECPP. APRCL are the initials of the people who created the algorithm. ECPP is elliptic curve primality proving. I think there are two reasons people normally don't use these. One is computer programmers don't usually know that they exist and two is they're complicated. Perl 5 has one of the in the n-3 module has one of the only implementations of ECPP out there this open source certainly the vastest and hopefully Perl 6 will get one soon. So because these are hard we come up with this idea of a probable prime. So what to do to find a probable prime you find some property that all primes have and that most composites don't have well if lots of composites have it then it's not a very useful test but if all primes have this property and very few composites have this is actually fairly useful and this is quite commonly used. So the common return values are zero definitely composite one is probably prime sometimes will add something for definitely prime and minus one is the if these are your only responses and you have for instance you're doing a Lecaux Limer test and it's not Lecaux Limer scene number well you can't return anything here it's the wrong form you don't know what it is. No small divisors we're going to give some little little Perl 6 code here this is a particularly bad one this just says are you visible by two or three if not you look kind of prime most humans go something like this they might go with five as well do something like this I don't know it looks kind of prime so this is kind of neat these junctions where we can basically just instead of saying n equals two or or n equals three or and so on we get to just say n equals two or three here's the mod 30 version of it all primes past five are going to have this property this gets kind of messy in most languages junctions make this really simple and easy to read oh if the remainder after 30 is this great so from all I was just in France and they were telling me yes it is from all and look ah in the United States it's either from all or format if I said look ah in the United States no one would have a clue who I was talking about it's a Lucas there but so from all came up with this little theorem which says if we take an a between two and p minus one and we raised to p minus one power if p is prime it's one mod p all primes have this property some composites do most don't so here in pearl six this is a bunch of boilerplate mainly having to do with small numbers and I'm gonna you could add restrictions for making sure your base doesn't exceed it doesn't go out of range I've decided to try to make that work it's kind of irrelevant wow that's easy the XP mod so there is a problem Carmichael came up it said hey there's this class of numbers where this is true for composite some composites this is true for every base so you will never be able to figure out those numbers are prime or composite because they look prime based on this test so Euler published a few papers and one of the things he came up with was well we can improve this test so we're gonna have now it is p minus one divided by two is plus or minus one and same boilerplate but there we go note the shift operator is plus the bitwise shift operator plus greater than we use our junction again very easy Euler also went and said you know it's not just plus or minus one it's equal to the Jacobi symbol what's the Jacobi symbol so Legendre came up with this idea even earlier and said well this symbol and surprisingly useful number theory is zero if it evenly divides P it is one if it is a quadratic residue that is if there is a number that exists that it's a square mod P and minus one otherwise so here's a crazy version of Legendre symbol in Pearl six we've used an infix operator with a special pipe we've made Damian happy by using italicized characters and their sigilists and we're using a given one so unfortunately this particular form doesn't help us much because we're already going through the same operation the Jacobi symbol is basically the product of that for factors but you don't have to factor and you can do this is kind of ugly code but it exists you'll see the same code in lots of languages so now once we have that very simple Euler Jacobi in Pearl six we mod n because we're going to get back a one or minus one so this is a simple way to do it and all of a sudden our kind Michael go numbers go away this test if you run random a values it turns out that no more than half of the a values are going to work for any composite so Solovey and Strossen made this a primality test you probably heard of Miller Rabin test this came first and now we'll go to Miller Rabin you may have seen this before we take n minus one basically take out the odd part and run this routine I'm not going to go over the math behind it but that one also has no Carmichael numbers is is classically used this looks exactly like C code you'll find everywhere for this so in Pearl six with this idea that will the chance of being a composite passing this test is one quarter if you use random bases then your chance is four to the minus K which goes very small very quickly in Pearl six says we'll use a hundred bases for this is a great idea no so the reason why this is not a good idea is actually two-fold the number one is in more vm it uses Lib Tom math and Lib Tom math does not use random bases is the first 100 prime bases which sounds great until you find out that in 1994 someone published a paper which showed you how to generate counter examples to this so this is a particular number that he published there's an algorithm to generate these and Pearl six will tell you that this is prime it is not prime there are ways to fix this we'll talk about that in a minute the other thing is using a hundred of these tests is significant overkill we don't need to do that any tests so that's a performance issues and this was a common method in the 1980s early 90s some people published papers and said you know this is really problematic for a number of reasons so Pearl six used to have in the language specification that is prime took a parameter of the number of trials for Miller Abin which I particularly disliked because it put implementation details into the language itself fortunately that was all removed before the language came out so we can apply better methods without changing the API as long as we do the right thing so the BPSW test is the way that most people have standardized on you do a single Miller Abin test and you do a look at test hopefully a strong test this is my wall of text that I should not do in talks it was published in 1980 it is deterministic for all 64 bit in numbers no counter examples have been found there are at least two theses where people worked hard on trying to find counter examples using very clever math to say well I'm sure that this set contains it the only problem is the set is of size two to the one thousand something and so one of those numbers in that set might be a counter example so we haven't found that yet almost all math programs use this and go Julia and Python modules have all started moving to this so I have an implementation in more VM for this and it should be pretty easy to put in JVM as well and it's faster so you know a couple methods for factoring I'm not going to talk about all of these trial division very straightforward for Ma busy guy also came up with a method for factoring Pollard has his row method and P minus one very common square form factorization ECM quadratic sieve and NFS are all commonly used NFS is generally a PhD level pro I think there are two implementations out there certainly I'm not going to show you an implementation it would be tens of thousands of lines so child division Damian showed an example in his talk the primary difference here is just that when you find a factor you need just your new composite you need to start looking less I guess I should say a lot of the examples do not do this test of redoing the limit and so they do a lot more work this this is useful for small numbers for Ma we do basically we're looking for differences of squares all odd numbers can be represented as differences of squares from all said hey if there are two factors are close to each other we can find this fairly quickly we have this is perfect square predicate so how do you find perfect squares that is a number that is s times s equals n is any perfect square so you think oh well I can just write it like this I have big big numbers so big it's great I just take the square root of n turn that into an integer and see if that returns that but we then realize Pearl 6 does not have big floating point numbers so that actually doesn't work so the right thing to do is write a integer square root routine I did not do that yet about 64 or 53 bits this starts failing it's just like see just like Pearl 5 this is a way to solve the problem it's not ever it's fine for 64 bit it gets very very slow this is the wrong way to do it or it's an inefficient way to do it so some other people have said you can actually do some tests you can actually quickly look at a number and find out for some simple properties is this is it possible this is a perfect square so we can run that final test less often if square root is really expensive you can do some very simple math to avoid it you can also be clever with bits and do it notice the shifting the bitwise and is a little different in Pearl 6 you can go totally crazy if square roots are really expensive and you can continue this process these are using bloom filters which are basically a way of filtering out anything that isn't going to be possible using different simple divisors so Pollard row Damien showed this example this is with Brent's cycle optimization Damien said that this was called the row algorithm because it uses a variable called row it doesn't use a variable called row and that's not at all the reason why that's named that it's a really fuzzy image the idea is we're trying to use the birthday paradox to find examples where we can find a collision so we have two processes running one going slow one going fast and the idea is when can we find an example where they correspond and if you graph this out somebody said well it looks kind of like a row simple and that's why it's called Pollard's row and it is really really fast at finding small factors when I say small I mean say eight digit ten digits it doesn't matter how big your number is if it has a small factor you know under ten digits this is going to be extremely fast at finding it so it's not useful for solving RSA cryptography if your keys were generated correctly you have two very very large factors not going to work at all but for small factors this is really common and this is Pollard's P-1 algorithm was trivial to write straight from Wikipedia into Pearl 6 it basically says well maybe I'm having a hard time factoring n but what if n minus 1 has a lot of small factors and if it does we can factor n very quickly and that pretty much concludes my talk on Pearl 6 and number theory


Everybody forced here ripping the sports card Almanac ultra high-end multi sport volume 9 case break number 7 case break number 7 Let's go over a few things before we do our randoms. We're gonna random first to See which case number we're gonna have you have four cases remaining And then we'll do the random for the draft order the draft order random is going to be names and numbers Which I represent the pick the pick number We'll put the randomized them both put them side by side. That's how we know Whose pick is whose Before we get to it though Please respect the draft. That's the first rule is no influencing the draft the second rule is no discussing card values Those are pretty similar rules Just wait till after the drafts. You can say great hit you can say all those good things.  I got the time on my phone I'll be typing in chat. I'll be looking at YouTube and Twitch chat. I'm gonna drop the latent sports cards at Gmail Email address right there. I will check the email if I end up having to probably make a pick for somebody I will look at that before I actually have make the pick two minutes. I'll be typing in chat twitching YouTube I'll be verbalizing if you cannot attend the drafts We we will have to pick best available for you based on values of the best of the breakers ability, which is me But again, I don't know your PC. I don't know what you prefer if it's for sport or whatever So, yeah, we always encourage people to be here Let's see. Let's see. I think that's about it. You guys Again, this is case break number seven Yeah, let's do some randoms So we'll roll the diet one the dice one once here just to the the case number random No, we roll for the The the draft order randoms seven times whichever case number is up top seven times Seven isn't it isn't it for number seven one two three four five six and seven I told y'all ha ha Seven seven one more. Yeah, that's a jackpot, right? All right Reroll now and we got names and numbers again. We're randomizing both same amount of times put them side by side That is your pick number Whatever you end up next to Good luck. We'll randomize both of these ten times One two three four five six seven eight nine ten Steve oh down to Linnea C and And ten times on the numbers everybody one two three four five six seven eight nine and good luck Ten eight down to two There you go Steve. Oh with pick eight Eric W has the first pick send Victor with the third pick Eric W with the fifth pick as well great random for Eric W Dean. I number six Brandon a number four Scott and Nine Cheyenne with ten Jim D seven and Linnea with pick number two these results will be posted to latent sports cards comms results tab Let's get to it And that is your draft order. I'm gonna give you a link so you can just get again if you need to Okay, number seven you guys anyone feeling lucky Eric has hit many big cards of us Eric had the 2021 national almanac spot Chromo win thing He's had a lot of big cards with us, man. Thanks for joining Eric. Thanks for joining everybody else as well We do appreciate you guys And if it's your first time watching almanac Let's have some fun Let's have some fun. Sean. Are you ready? Sean thinks he's ready. You hear that guy. I Don't know if I'm ready There's still a card out there that I am so excited to see the reaction to I know it's out there I didn't pull it. What a start dude. Wow Bat barrel auto one-of-one Paul Goldschmidt Are you serious? From 2021 top sterling baseball What a start That's insane dude love the bat barrel nameplate one-of-one auto Goldie. He is very good at baseball He's building a Hall of Fame case you guys if he might win MVP right here probably should He's building a Hall of Fame case Very quietly too. He's been so good for like a decade now Geez man, what a start they're getting no hit tonight They're not losing though So hey, there's that no hits with the same score as the other team That's a that's a pretty classic Carter there will be 2017 Don Russo optic hollow rated rookie Patrick Mahomes the second nine five gem mint Beckett grade there Corners got a nine everything else a nine five centering edges and surface Hollow rated rookie Patrick Mahomes the second Good at football Good at football Beautiful man. Hollow rated rookie optic Patty Mahomes Probably about once a month maybe once every two months frosty It's been a little while since our last one, but that's because during the summer We have a lot going on with like the the national and all that But we'll have a little more frequently than that We have different price points. We sometimes you do single-sport almanacs like last year We did a baseball almanac and a football almanac We've done like like Pokemon almanacs on the on our late in gaming site as well So we do a lot. All right moving right along Okay, that's a 2021 rookie quarterback Holy cow one of one from 2021 XR football rookie triple tag auto trey lands Goodness gracious do a laundry tag and then the swoosh from the laundry tag as well sweet sassy molassy That is pretty insane. We have some cases here guys. We got some case right now Also good at football. Maybe not as good as Mahomes, but we'll see we'll see Got that starting gig His now At least good is he great to be determined to be determined All right. All right. I feel a PSA slab So this is a 2020 select football Xrc Joe burrow PSA 10 on it PSA 10 on it Joe burrow Xrc Man, the football is hot right now Three straight rookie quarterback cards big ones to beautiful man What do you guys think the 2020 Xrc design of the 2021 Xrc design? Very different very different designs. Oh Joe. Shiesty crazy, right? Football case. So if I know Lane, I'm not expecting a whole lot more football in this then We'll see though Lane Lane's always got surprises and almanac always Or 2019 sorry, I said 2020 select is a 2019 select 2020 Xrc.   He's man. It's four straight rookie cards K7 Ring on the heat See what else it has in store Lipsquiff Mother's Day pink 2022 tops rookie wander Bronco Gemmin 10 Dude 46 of 50. Oh My goodness the Mother's Day pink Gemmin 10 wander. Oh This is a big-time rookie case Holy cow, dude Amazing grade on that Man Wander Mother's Day pink rookie. That's a biggin.   Maybe we'll see some legends here. I don't know more orange Oreos That's a good call Vaughn. I'm gonna have to get some tomorrow.  Oh I think this was the preview Blue 2018 Optic rated rookie Josh Allen nine five Gemmins The color match Ten on the edges nine on the surface nine five centering in corners. Oh my god Over 500 viewers hit the like button, please everybody. Thank you very much the color match blue rated rookie Josh Allen serial number 56 of 149 95 Gemmins Yeah, dude This one feels thick. What is this Beckett slab? Yeah, Beckett slab back at slab down on it. Oh I forgot this one was in there LeBron James Vince Carter 0607 upper deck black all-star jersey auto Holy cow four out of five LeBron and Vince Sanity are you serious? eight five Ten on the auto eight nine five centering nine edges corners eight surface eight five Good God Holy cow This is freaking bonkers dude case seven I guess was the lucky number the gold ink on those autos as well.    It's 2021 I think we should get to the draft. I think we should Take a deep breath and get to the draft Did the quarterback case for real? That You know critics call that case a tour to force Two thumbs way up Game informer ten out of ten. Oh my god. I don't know you guys that case has rattled me Uh, Eric W has the first pick one sec guys. Let me get my timer ready No discussing values. No influence in the half. Please. Let's cut the chatter down focus on on the draft now Oh, yeah, oh my god, man four or five Dual Jersey LeBron and Vince Carter. It is 0607 upper deck black Jersey auto dual Carter and James 8 5 here sub grades again 9 5 Centering 9 edges 8 corners 8 5 surface and the autos were 10s LeBron and Vince Carter Says game one, right? Yep, both all game use on these Gold ink sticker autos on this card Upper deck black 0607. He'll he'll say he'll say something else. Yeah Luca rookie. There's a bunch of quarterback rookies here. Goodness gracious, man How many one-of-ones three one-of-ones good God 90 seconds Eric. I started timer just a bit late 90 seconds. Yeah, we need to get like a You need to get a little stand back there. I mentioned that last time chat. I think we just forgot But I mean the you can find the bro fairly easily. I would think in the and then the homes I'll show the back Eric's first pick is pick one. Yep going with the Herbert Grads Eric. He's going to 2021 second-year flawless underdink auto one-of-one Justin Herbert Sick card Eric. Congratulations Sick card Yeah, serious. Congrats to super tough choice. Well in ASC pick two Good luck when they are Timers starting now Yeah, very tough choice, but hey, like I said, that's how it should be, right? You have to think about it. It's got that Lucas Spector rookie Jersey auto one-of-one Lance from XR the XRC burrow 10 the hollow Mahomes 9 5 The wander mother's day Crazy CP 3 right there the blue Josh Allen 9 5 rated rookie bat barrel auto This is the second one of the night rich His number seven Linnea see one minute Linnea you want to see something up close, please. Let me know Oh very official, I like it selects the beautiful LeBron Vince Carter. I like the idea. So official. It was awesome. We like it. We like our own noise Not the NFL draft Norse the NBA draft was your own noise Fantastic pick LeBron and Carter Congrats Linnea. Congrats huge card beautiful card Thank you for joining Thank you and Steven both for joining All right, send Victor Troublemakers pick yeah two minutes for you send Victor Yeah, I don't on ban now It does not get easier when another card gets picked either the tough the choices still states off Yeah, he's a mod somehow. I don't know how we manage that Who would mod that guy? Oh Whoever that breaker is deserves a swift kick in the rear end, yeah Never be me. All right, send Victor 90 seconds Probably that was like three minutes 30 seconds to type out. She knew her pick all along. She was just typing it out Luka Trey the Allen is out of 150 That's a 149 D1 better 56 of 149 There's a sub grades again nine on the surface ten on the edges corners and centering nine five makes it a nine five Yep, so hollow rated Ricky Mahomes 2017 Don Ross optic Hollows non-numbered, but you got a nine five gem mint grade nine corners nine five centering edges and surface Few more seconds in Victor. I have a good one Peter. Thanks for watching buddy. See you Peter All right, so Victor the timer is up. So give you just a few more seconds Just a few more seconds and then just your zipper order number with What to pick two? Who's Invictus go with the wander? That's a really nice pick Mother's Day pink Order number uh I need a number not not a 46 of 50 2022 tops wonder for dude Mother's Day pink is just sick PSA 10 No matter what will be super low pop down. All right, we'll wait for him to get his order number, but he's gonna take that I know it's Invictus. I just want to follow the rules Or is it whichever one you want whichever one's better for you before we move on. I just make sure let me confirm that for him It's a secret Oh, yeah, yeah, yeah, yeah, yeah, cool. Thank you. Thank you confirmed congrats on the wander pick four is Brandon a Start your timer now Brandon Still got a bunch of rookie quarterbacks Got that CP three and Luca those really nice patch autos for basketball and then a bad barrel auto Paul Goldschmidt Brandon a pick four, you know what we need a sound effect for this This is it right here You know buddy rookie quarterback or rookie quarterback cards there No, as long as you have the correct zip and you know the name on the order then I think I think you're fine No, let's make sure you're ready to go with the zip code and order number. You should be good We've had other people pick for others before they were like designated people because they wouldn't be able to make it so Not uncommon Brandon a got about 45 seconds Congrats Brandon He's I forgot what he got last case. I know it was pretty safe 153 299 rookie Jersey auto from spectra Luca Donchich.  We've got number was it five Two picks in the top five Eric. Wow, man All right, Eric your second pick of the break I Tell you what dude Eric's crush There's going to Josh Allen Congrats on that buddy. Thank you again. Appreciate you Eric We're doing well Dean. I have now Do you know snap calls rifle? Sometimes it happens man.  I See people snap call a not an obvious choice You never know what people PC or what they want or what who they think what card is going to go up What so it's right? Yep? One of one from 2021 XR football trey Lance Got two regular looking laundry tags and the shield tag here is a one-of-one But it's a shield. Oh swoosh. I'm clearly a swoosh Certainly not a shield going with the burrow XRC great pick Congrats Dean PSA 10 Number seven now is Jim D Jim D CP3 Goldschmidt my home is in the Lance Who's it gonna be? I? Don't even know what I would pick honestly three different sports left Really different cards here to like very different. Yeah, right Dario. That's exactly what I was thinking when I said that it's just It's really tough to choose on a lot of these picks I'm surprised that Chris Paul fell so far Good I can grad Jim. I'm honest his prizes fell As far as it did that's freaking sick. It's was a collection 15 or 35 CP 3 8 5 10 with just a just a silly patch just for crazy There were three Steve. Oh Steve oh grass everybody in their picks up for all great picks so far. Yes I Was taking the Tray Lance XR had a great design this year nice Lance triple laundry tag with the swoosh not a shield as Some fool would say Congrats Steve. Oh final pick Scott in Yeah, that's that is a beauty of it at least when you're picking towards the back end. You know, you it's not ideal But it's narrow down for you Yeah, very true Still solid Everybody picked on the strap so far. Yeah, it's awesome. So we get Scott to pick it Yeah, seriously, man, if he has a big year that card's worth a lot I mean the wonder there's so many of these rookie cards all these guys are still playing at least in this case. So Really Scott and pick number nine Yeah, it was like sometimes there's like There's that some people see something like that and like I don't have that or I'll take it But sometimes things like that don't because I already have one I've seen that before someone passed at Jordan Fleer. You're like, I have I have that, you know Can you give us your Man right there Scott ends going to Mahomes hollow rated Ricky Mahomes nine five Congrats Scott's Great card number nine good Cheyenne get this bad barrel auto one of one Paul Goldschmidt That is freaking awesome that is freaking awesome insane last card love That'll do it for case break number seven guys you've got case number eight coming next what a case dude Wow


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