 Fe fyddwn i'r yw'r rhagwyr y fwrdd i'r rhaid i yw Ray, y Ryfyrd, am gyfwyrd i'r panffinol a Ddaidol i Carl naffydd, oeddwn i'r Aegean. Mae'n gweithio ar y rhaid i'n gweithio. Mae'n gweithio i'r model spatiol yn ffiannig, ac mae'n gweithio i'r gweithio ar y gweithio ar y gweithio ar y ddysgu archiologifodau bod yma, yn cael ei bod yn cael ei fawr o'r projekte. Mae'r ystyried o'r gweithio'r gweithio sy'n gweld i'r wych yn ei wneud o'r serffynedig. Mae'n mynd i ddim yn ymddi'r ffocor ag yw'r gweithio'r Willan? Dyma'r gweithio'r ffocor yw'r holl ymddi'r prosiect er mwyn i wneud i'r gynghoriad, a'r eich gwrthod o bobl sy'n gweithio'r gwneud o'r llwyllfyn o'r sefylmwynt. Mae'r gweithio'r gweithio'r wneud o'r moddolig. a wneud o'r fath yng Ngharlu'r Gael, ond bynnag oed yn bwysig yna'r gael y gwahanol? Mae'r ddweud yn ysgrifennu i ddweud a'r cyfnodau ar gyfer gwahanol sy'n dweud fel bod yn sefydliad. Yn ymweld, mae'r cwysylltu oherwydd, o'r sefydliad i gael ac yr arddig yn ysgrifennu. Mae'r cwysylltu oherwydd yn ysgrifennu yng Ngharlu'r Gael, dda ni'n meddygau'r ddweud. I personally think there are lots of solutions out there. Archiology has particular challenges, but that doesn't mean that we give up on modelling. I think you just have to work harder. And this is our attempt to begin to show how you could include uncertainty, but the most important thing, whoops, that's gone on, won't do money, oh well, that's, the most important thing is to try and give some sort of measurement of uncertainty, and that's what we try to do here. So, what are the models I'm talking about? Well, these are spatial models, so we've got some sort of set of inputs, which for us will just be the sites. And we're going to try and link those together with distances. So all we're going to include is geography. So all those other factors we're not going to include, we're going to see how far you can go just to geography. And the outputs here will be some sort of flows or interaction strength between the various sites that you have. And what is the, well, this is the study of Rylan Wilson from 1987 to 1991, and they focused on 109 sites from around about 8th century BC in central Greece. And of course, what they're looking for is that all of these sites, which they treated as relatively, well, all identical or equally likely centres for a future development, a question was, try and identify which sites would emerge, surely because of geography in the long run as the dominant sites in their region. Okay. Now they, their analysis in many ways is very straightforward, very simple. So they're putting very little information in and we'll see where we get to. If you need more, that's great. You have to go and do more hard work, but if this is already telling you something interesting, then that's interesting. They just use straight line distances between the different sites and they use what Ray called retail archaeology model because it came out of actually real studies of modern retail economics. Literally this model was used commercially by I think Helen Wilson and others to help supermarkets locate future stores. There are one sense, this is a tried and tested model with real humans, whether or not it's particularly relevant here, I don't know, but this is what you can take. It's a very simple model and has been studied in other archaeological contexts. Now the answer in a sense is very obvious here, which of the sites will emerge to dominate the region but we know the answer. It's picked four of the major ones, the Athens, Corinth, Argos and Thebes and that's what I will focus on. But what particularly attracted our attention was in the original paper that there was no quantitative measure of uncertainty. So we were trying to take this study and it's not that we don't think it's a bad study. We just wondered whether, yeah, how certain could you be that Thebes does emerge as the dominant site up in the ocean. How certain can you be that Athens, just because of geography would always have emerged. There wasn't any measure of that, so we set out to try and do that. Now the way that Rillan Wilson identify their sites, their dominant sites, there's something that they call terminal sites and in their paper you get a picture a bit like this, not exactly a network, but pretty much most sites have a single line for their neighbouring big site and you can see just pictorially that it picks out certainly the four major sites in this case and a few other regional sites like Charkis at the top. And that's great, but this is the sort of answer you would get in their paper. So our question was, how can we measure uncertainty and can we do this for the Rillan Wilson model? So our approach was to take a set of open source data. Well, the data wasn't open source at the time, but I digitised one of their figures, so it's now open source. And we wanted to look at some variations. There is no way that we know exactly how far different sites were. We could do all the GIS in the world and we still know that of course that only captures some aspects of the geology or the geography at the time. So, yeah, let's not worry too much about it, but let's try a few different variations. If any result depends crucially on details like this, then we'd be worried. But if you keep getting the same results coming out, you say, okay, five, 10%, 15% variation in the distances, yeah, we can live with that. That's a sort of error I think is fair. Likewise, when I come on to look at the model, I'll highlight the fact that the model itself has some choices you can make. So I'll look at that. So as I mentioned, I digitised the distances by hand. This is the original figure. I literally just took the figure, took a screenshot. That's all online. The most interesting part for us, and this is I think one of only two or three equations we're going to show, but we don't pay much attention to them. This is the retail archaeology model that I mentioned at the beginning. This is what we actually used. So you put the sight sizes in. They're all equal here. This is the later sight size, if you like the emergent size. This is an output from the model. These are the flows, and I said all spatial models give you, but the flows tell you the effective size later. And this whole model just runs around and finds the best possible solution, given this very limited amount of information. And the one place where distance, if you like geography comes in, is here. So this, what I call the distance to cost function, this potential here, is some sort of function you have to tell me, you have to give it to me, typically all your distances, so this is the distance between two sites, I and J, a scale relative to one parameter, which I call big P, the distance scale. So if you're interested in working on a 10-kilometre scale, let me say that to 10-kilometres, if it's 100-kilometres, 100. So for instance in the work I've done in the Aegean, in the Carl, 10-kilometres might be a good scale for sort of rowing in the early Bronze Age, but maybe when you've got a sale, 100-kilometres is roughly right. I'll come back to that in a little bit. The form of the distance function, though, of this function of cost, the distance, that's the thing that there's a wide amount of choice in. Although there's a typical distance scale to the big P parameter in the problem, you can choose different shapes. You imagine that the further you go, the less likely you are to have flow between two sites, the costs get higher, so that this is going to suppress, you want these functions to fall away, to get to larger and larger distances, but the precise shape, of course, we don't know. If you don't know whether the cost is true, our time to make the journey, whether it's got something to do with a social or political cost, a lot of that information's lost. You could add that in if you have it, but let's suppose we don't have it, you would want some general shape looking like this. But we don't know exactly what shape, so what we did, we took several different examples. Financial form is the one that Willow-Milton used. This is a bit of a disaster. This is an early version of my talk. So this has finished. Oops, I'm afraid I've copied the wrong version. Let's see if I've gone back to the beginning. Is it going to go to the square? Yes, but I've got a feeling that's an earlier version. Let me see if I can just find the conclusions, cos I'm nearly finished, as it is. Final slides. OK, let me show you the result. This is the main result from our shift F5. So what do we do at the end of this? Well, we managed to end up with... This is two sets of results. The coloured ones ignore. Let's look at the grey one. So Ribbon-Wilson came up with very definite results. They found that these four sites continually appeared again and again and again, whatever they did, at least according to the paper. We've now introduced more variation. What you can see from these dark sites is that when you've asked for eight dominant sites in your region, emerging purely because of geography, these are the sorts of sites you get. You don't get a single site, you get a set of sites. So, for instance, down here is Argos, number 101, but we found two or three other sites would pick up in the same area, and these regions are typically about 10km wide. The exception was Athens. At least when we were working at Arlo, Athens continually turned up again and again and again as a unique answer. So when you're asking how certain can you be, we could be pretty certain that actually geography according to this model is always, always going to pick Athens as a dominant site. Whereas Thebes, the question I put in the title up here, you're much less certain, okay, if not Thebes, it'll be a village within about 10, 5km. So that if you imagine a sort of process of agglomeration where certain sites are slowly growing and becoming more dominant, if you looked at an era when you had eight sites, the grey circles, then you could see the Athens-Argos current emerging as part of that. Another conclusion, though, was that if you then pushed it on and said, what if this model picked out three sites, then you do get another arty. You still find Athens emerging consistently. Now feeds it's much less clear that the circle is bigger. There are more sites we keep finding. But there's a real problem down here and the Corinth and Argos, neither of them are picked out as the dominant site. So if this model is telling us anything, either geography is working in some cases, working up to an arrow of 10, 15km up here, but failing down here, something else is needed, or perhaps what happens is you agglomerate it into eight or so dominant sites and then different processes other than geography were needed to understand what happened later. In this case these two cities remained dominant powers. OK, so that'll do me for now. Conclusions, last word. Conclusions we reached were that you need to include uncertainty whenever you do modelling and we've shown various ways you could do it in this case. For this particular example, geography can go a long way to explaining some of the patterns we see and where you find a failure in our very simple model. That's when we suggest you need to go away and start adding in more, either using agent-based models or a more sophisticated model. OK, thank you. Sorry for the...