I welcome everyone to the 26th meeting of the Health, Social Care and Sport Committee in 2022. I've received apologies for today's meeting from Evelyn Tweed, and one of our members is joining us remotely, that's Gillian Mackay, otherwise everyone's here in person. Our first item on our agenda is to decide whether to take item 4 in private, has everyone agreed? We've agreed, thank you. Our second item today is an evidence session that is part of the committee's pre-budget scrutiny for 2023-24. We have witnesses with us both in person and remotely. In person, we've got Professor David Bell, Professor of Economics in the University of Stirling, thank you for coming along. Lee Johnson, Senior Manager for Performance, Audit and Best Value for Audit Scotland, good afternoon Lee, and we have Professor Raphael Wittenberg, Associate Professorial Research Fellow at the London School of Economic and Political Science, good afternoon to you Professor Wittenberg. I'll start things off, it's a huge area, so forgive us for the wide-ranging questions, I'm asking you the answers not expected to cover everything, but given that we have tremendous pressure on the NHS, obviously not just in Scotland but in the whole of the UK, but obviously we are concerned with the Scottish NHS, given the pressures that are on it from cost of living crisis currently, we've got the fuel costs of running large estates and all demographic factors about staffing, prescribing cost increasing, all these various pressures that are coming, I guess it's if the current plans for spending on the NHS look reasonable, notwithstanding the fact that we've got budget reviews happening both in Westminster and I imagine there's a knock-on effect that will impact on the Scottish Government, but as it stands, can all those pressures, I mean can that the plans for spending be sustained in the face of all these pressures, I'm going to put that to David Bell. Okay thank you for that wide-ranging question, so I guess the question is what can we afford we have resource constraints, clearly we would always have resource constraints and through the last 10 years, although the amount of spend hasn't increased substantially, health has been protected more than most of the other budgets. I guess in my paper that I show that the UK as a whole spends around a kind of average for OECD countries in terms of its spend per head, but it jumped, it really jumped much more than most other countries in terms of what happened during the pandemic. Within the UK, the public expenditure statistical analysis shows that Scotland tends to spend more per head than England, not nearly as much as Northern Ireland or indeed slightly more than Wales, but in the last few years that gap has been narrowing between Scotland and England so that it's now quite small. If those figures are right, there's a set of questions that follow from that, which is that have we noticed that waiting times for hospital appointments, for doctors appointments have got significantly worse relative to the case in England? I'm not clear that that's true, but it seems that what has happened is that spending in England has grown quite a lot, a little bit faster than in Scotland in recent years, but nevertheless its outcomes are well. In some ways, and I'm sure Raphael can talk about social care, are in fact worse than what is the case in Scotland. Looking forward, health and social care will be the largest budget within the Scottish Government's portfolio. It used to be slightly smaller than local government, but over the last 10 years that has turned round. Its projected growth isn't necessarily as big as those in some other of the important areas that spend over a billion, but there's a big change over coming in. You can see that from the spend numbers through to 2022-23 in that the national care service is going to be established and there's a big tranche of extra money going to go to the health budget, but then how that split between local government, which is primarily responsible for social care spend at the moment, and health spend is not entirely clear. If I would add one other thing, which quite a few of the evidence that the committee has received previously, a lot has been made around preventative spend. It's not clear that preventative spend has achieved what was hoped of it with the Christie commission. It's also a question of whether the amount of resource that has been allocated to preventative spend has been sufficient to make a difference. I think that raising levels of activity is a key objective of the Scottish Government, but whether that is being achieved with the kinds of resources that have been allocated in that direction is a question that we need better data on. I guess that I'm saying that there are lots of pressures on the health budget. In demographic terms, we need to be increasing the budget year on year, just simply because the population is aging, but resources are limited. Obviously, there are other calls on the Scottish Government's budget. Again, the limitations arise from how quickly the economy is growing and, therefore, how quickly tax receipts are rising. That's another consideration that has to be borne in mind when you're looking forward. How much it will be possible to allocate to our NHS bodies, be it the territorial boards or the national boards, going forward depends very much on the health of the economy as well as the division of resources within the total government's portfolio. I have just reminded my colleagues online that if you want to come in and add to anything there, then I'll take you. If you just use the chat function and let me know, otherwise I'm going to ask a supplementary question to David Bell, and if you just let me know if you want to come in and anything. I won't go too deep into preventative spend because I have colleagues who want to go into that deeper in the course of this session. It's about quantifying where the other interventions and other spending portfolios have an impact on health. If you're taking money away from an education budget towards health, that could have an ill health impact. If you're putting more money into, for example, a net zero, that has an impact on health as well. You were saying about data and whatever, but are we almost too fixated on the health budget being about health and not about the general budget being having an impact on the nation's health? How difficult is it to quantify that? It's extremely difficult to quantify. I was involved in a conversation this morning at Edinburgh University about whether climate change is going to affect that, on health and what action might be taken to alleviate that, but before that can happen, we need to have some clear evidence around that. That has been part of the problem associated with, to a certain extent, short-term budgets. A lot of the evidence to the committee criticised the extent to which boards can only look ahead for a year. That doesn't create a situation in which the long-term collection of data. A lot of the take-active interventions in education. I was involved in a discussion previous weekend in Helsinki with some experts on dementia. They were considering the question as to whether education is a sort of protector against dementia. If you're going to understand that, you've got to have some idea of, in a sense, people's life histories, because dementia, before the age of 65, is almost unknown, but looking back to their education is a long term before. You've got to have that willingness to approach data in a systematic way. Again, I'm sure that Raphael will know the difficulties that there are, particularly in social care, in getting good data. That's a big problem, because it's a very diverse sector, much more so than the NHS in some ways. There is quite a lot of effort and data, but the question is, does it address the needs, as far as the issues that you're raising around the kinds of spend on housing, education and so on, and what effect those really have on people's health? That also comes back to the issue that's been brought up by Pwetlaw people and they've written the evidence that they gave us around the short-term spending, but also the short-term outcomes of things. There are certain things that, like waiting times, you need to quantify them on a quarterly basis, but the actual health outcomes, that's more difficult to assess. The trouble is that there's a tendency to measure what you can measure, and that's not necessarily the right thing to measure, and waiting times is possibly an example of that. Can I bring in any of your colleagues who want to maybe answer some of those very wide questions that I've put out there to kick us off? Leigh, data's been mentioned and I know that you live and breathe data. Yes, I guess a few things, convener. Obviously, despite the plan budget increases set out in the resource spending review, we've been very clear that health and social care face a uncertain and challenging financial position over the next four years and beyond. We've clearly said in our NHS in Scotland 2021 report this year that the NHS was not financially sustainable even before the pandemic, with boards relying on additional financial support from government and lots of non-recurring savings. Obviously, the pandemic has exacerbated the scale of the financial challenge. NHS boards have been fully funded over the past two years to meet their unachieved savings, but in 2022-23 that will stop and boards are expected to make their planned savings without additional support from the Scottish Government. That will be very challenging given all the pressures that you have outlined in terms of pay costs, inflation and energy costs, as well as on-going operational costs that have already been an issue. It is important that we know that they are. We will have submitted three-year financial plans to the Scottish Government. We have not had a chance to look at those yet, but that will start to give us a better idea of what the forward-looking financial position looks like for NHS boards. We've also been very clear about the pandemic and the impact that it has had on inequalities in terms of health, wealth and education.  It will also have an impact on the outcomes that are set out in the national performance framework. That requires cross-government, cross-public sector, including the third sector, response to try and deal with the inequalities that are so deeply embedded within Scotland to try and help to improve our outcomes. That includes, as we have already talked about, a focus on that preventative spend, although we know that that has been very challenging. It is difficult to know what is being achieved because of the lack of data in certain areas across health and social care, particularly short-term measures that are focused on throughput and output rather than outcomes. There is a need to move towards looking at what outcomes are being achieved by the money that we are spending. A number of our studies, for example, for our children and young people's mental health service study in 2018, found that we could not track the spending and could not tell what difference any of it was making because the outcomes are just not being measured and that is repeated across health and social care. Thank you. I will hand over to my colleagues. Thank you very much for calling on me. I work mainly on social care, as David Ball indicated. My work has been my search mainly on England, but I think that the general points would apply equally to Scotland. I may just make three points if that is okay. One is that the demographic or sociodemographic pressures on social care are rather greater than on the healthcare. For example, among older people, as you know, the fastest growing numbers among those aged 85 plus, a high proportion of those in care homes at 70 per cent have dementia and the average age of one set of dementia is about 83 or 84. The pressure in respect of social care for older people is very considerable because of its concentration on people aged 80 plus and 85 plus. For the younger age group, they have been and are projected to continue to be large increases in the numbers of people with learning disabilities, including moderate to severe learning disabilities, for which social care may be required. In fact, updating work done by the University of Lancaster on this, we are getting not finished yet, but we are getting very similar findings. The very substantial increases in demand for learning disability services, looking at the numbers expected to turn 18 over the coming decade and beyond, potentially. Secondly, a lot does depend when looking forward to what happens for older people, what happens to disability rates, whether those rates will fall or rise, whether they will get a compression or expansion of mobility and disability. We have done quite a bit of work with colleagues in a new capital on that. I think that it is better to say that the jury is out their different views, but it makes over time a very considerable difference to what happens to disability rates in later life and hence, of course, a link with prevention, which has already been raised. I make a third point, which is about rising pay rates in the social care sector. As you know, a high proportion of social care staff, carers and home care and residential care homes are paid at or not much above the national living wage. In our work and our projections, we take account of the increases that the Government has announced up to 2024 and, obviously, for sectors with low wage sector, that too makes a big difference for the coming few years. Beyond that, we assume that wages in the care sector would rise in line with the wider projections of the economy by the Office for Budget Responsibility. However, given the shortages of staff, that may be too low. It may be that wages will have to rise faster in the care sector than in the wider economy in order to recruit and retrain efficient staff and sufficient staff with the skills and the aptitude to work in the care sector. Those are three points that I particularly wanted to highlight. Thank you all, because everything that you have been saying is a really good springboard for deeper questions from my colleagues who want to pick up on quite a few things that you have mentioned. I will go to Tess White first of all, Tess. Could I start off with Professor Bell, please? I declare that I am a fellow of the Institute of Personnel and Development, so I always look at things from that lens first before politics. In terms of two points, the 0.6% increase. We have huge pressures on the NHS and we are talking of such a small increase. Stats showing 63.5% of patients are being seen within four hours, that is the lowest percentage ever recorded. One of the points that you have highlighted is that if you cannot plan more than a year or very short-term planning, then how can you actually deliver any form of workforce plan? I know part of your background you looked at labour sorts of economics. Part of the issue seems to be it is not just the money, it is that this lack and this inability to workforce plan. It seems to me that workforce planning is an essential component of any long-term vision for the NHS. That must be predicated on making, working in the health service or, indeed, as Raphael says, social care and attractive option. Relatively, the wages of any public sector staff in general but NHS staff as well have been falling relative to those in the private sector over the last few years. As a result of that, not surprisingly, it becomes more difficult to recruit. There is a point that Raphael made that touches on your question, which is also worth bringing up. Although it was perhaps an intention of those who supported Brexit that overall levels of migration to the UK would reduce, that is not in fact the case. Net migration to the UK, a huge proportion of which is going into both health and social care, has pretty much stayed the same. It is just that the location of where people are coming from has changed so that, for example, whereas we might have had lots of people from Eastern Europe coming pre-Brexit now, it is India, Nigeria and other countries. That is just the way things have now panned out. There is a reasonable question as to whether that is sustainable in the long run to rely, to a large extent, on migrant labour to be part of your workforce going forward. It reflects the fact that it is difficult to recruit UK-born, Scottish-born people into health and social care and reliance, which has not really changed in a way or perhaps if anything increased in terms of migrant workers. May I ask just one more follow-up, Professor Bell? You can look backwards, but looking forwards, what levers do you think that we can use to pull to change the situation? Well, it seems to me that you have to think very carefully about training, because all of them are effectively professional jobs. How do you make training more accessible and less expensive? That seems to me to be the most obvious route. There is also a weakall route for people who have left, because part of the problem, certainly during the pandemic, has been high levels and, understandably, of people who have withdrawn from the NHS. A thought has to be given as to how you might find incentives to bring them back in again. I do not know if any of our colleagues online want to add to any of Tess's questions, but I can come back. If you get Sandesh Gohani who wants to ask a question as well, if you direct it to whoever you want to answer it, I will bring in Emma Harper. I wanted to ask a follow-up question to Lee when we were talking about data and how you are struggling to find information. A two-part question, would you like outcomes to be explicitly stated when spending in the NHS is announced? If not, or on top of, what can we do to improve data so that we can see what the outcomes are? Let us be honest, outcomes are the most important thing. I would like to comment on whether outcomes should be stated when the funding is announced. What we would like to be able to do is to track the funding to see where it is being spent and to know how the outcomes of those different service areas are being looked at. As I said, I gave the example of our children and adolescent mental health. We could not track where the spending was going and there was very little work into what difference any of the services that were being delivered were making to those children and young people. In our integration report in 2018, you have the health and wellbeing outcomes that were part of that, but they are not reported at a national level. No individual IGBs will talk about those outcomes in their annual performance reports, but it is alongside a lot of indicators that are not telling us a lot about the outcomes. It is important that we can understand that the public sector is about improving outcomes, and it is very important that we can track the spending and understand what difference it is making. As you said, you cannot track the spending, but what would you like to see happen? How can we track that spending? That was my question. What difference can we make to make it easier for you? As I said, as we have commented lots of times, there is just a range of data that is not available. We know very little, for example, about activity and demand in GP practices. Public Health Scotland is working on that, but how can you plan and scrutinise or make decisions when you do not have solid data to base that on in community care and social care, as the other witnesses have talked about? There is very little data, even in workforce. Our workforce data is not as robust and reliable as it could be. The Scottish Government has published their health and social care workforce strategy and has made lots of commitments about improving the data that is available to help to plan our workforce. Again, they promised that in 2018 in the workforce plan. We have seen very little progress, and the same with the GP data. Again, there have been lots of commitments over the years to improve that situation, but progress has been slow. It is about improving the availability of data so that we can actually begin to look at what is being achieved, what impact things are having and the difference the money that we are spending is making to people. The data is one thing, but you have to be able to process it, so making it accessible. There are lots of ethical problems around that, but if those data are made accessible in anonimised way, lots of people can look at it and try to come to the kinds of conclusions about how efficiently the service is running. Emma Harper is on the back of Tess White's question for Professor Bell. I will be quick. It is about recruitment and retention and the plans for clinical training, career pathway for health and social care workers. The Scottish Government has introduced bursaries for nurses in midwifery training and for paramedics now, and there is free university tuition in Scotland. I think that that would help in recruitment as well. I am interested to know if you think that anything else should be done or introduced to support further recruitment, but also retention of some of those people who have left the healthcare environment in addition to the bursaries. Those sorts of measures are obviously the kind of things that you need to get people kicked off into the various professions. It seems to me that you need to really understand why people leave. I guess that the pandemic was a very special time where they were under huge pressure. That pressure has not completely or even partly alleviated yet because of some of the knock-on effects of the pandemic, but there is a clear need to understand why people leave and whether it is financial incentives on the one hand needed to bring them back, or whether it is something about work practices on the other—flexibility, childcare potentially, shift patterns, all of those things. I do not have the answer at the moment, but it is a question of being clear why we have seen this leakage from the system. Before I move on, I will check in with Professor Wittenberg. You have not said that you want to come in on the chat function, but social care has been mentioned in particular relevance to Emma's question about people working in social care. You have mentioned issues around staffing. I am happy to do that. I suppose that there is a big difference between social care and healthcare as far as workforce is concerned. A high proportion of the social care workforce is not professional in the same way of needing degree-level qualifications such as nursing, let alone of course, and medicine, but there are people who can, in a sense, I know that labour force wears competition between the social care providers, the retail sector, the hospitality sector—so a very different type of workforce. Secondly, employers, unlike in healthcare, are mainly not in the public sector. They are mainly private for profit and charitable sector. Therefore, they are one remove, if you like, from the commissioners of the services, the statutory bodies, the IJBs and local authorities in England. That makes a very different situation. There is a lack that is linked to this of career progression for care workers working in care homes or in the home care sector. Some work that we have done using labour force service suggests that those leaving the care sector are carers as opposed to professionals. Those leaving might be moving on to the health service or sometimes other parts of local government. There might be informal career progression, if you like, of people moving from social care into the NHS, perhaps as healthcare assistance and ultimately training. One of the big issues is not just pay, but career progression and career prospects in the social care sector. That prompts the question. I am sorry to butt in before handing it over to my colleagues, but establishment of a national care service is one of the objectives of that very structured career progression. Do you think that that could make a difference in that respect? I am not sure. I am not aware of the evidence as to how much difference it will make, or whether the reforms have not happened yet. I suppose that one would have to maybe look at other countries, and I am sorry that I do not know about what message this one would get from other countries. Can I pass on to Paul Keane? Thank you, convener, and good afternoon to our panel of witnesses. I suppose that I am keen to perhaps build on some of what we heard in that first section about financial sustainability. It strikes me from reading some of the work done by Audit Scotland that there is a requirement for innovation in order to get to a sense of financial sustainability, but perhaps what hampers that progress is the challenges of the NHS facing serious financial challenges pre-pandemic and being exacerbated by the pandemic. To what extent do people feel that enough is being done to try to achieve transformation within the NHS to then lead to financial sustainability? I do not have Professor Bell first, and then we can move to the central one at Scotland. This is not my expert topic, but it seems to me that the last two years or so it has really been about just keeping the head above water. It was pretty difficult to think and understandably so to think about innovation over that period of time. It would be good to think that we now have an opportunity to innovate more. We have to think about where that innovation stems from. To what extent do individual health boards have the freedom to innovate on the one hand relative to innovations being determined from the centre and rolled out? There is a reasonable question as to what is the most effective way to do that. Should we be encouraging NHS boards to look into changing their practices when they might be worried about being singled out if things go wrong? One cannot expect that every innovation will result in a successful outcome, but maybe we should be prepared to allow for some... I understand that it is difficult, but some things may not work, and you have just got to live with that to some extent. Obviously, I think that that point is well made about that level of local innovation, but there are national innovations that I suppose have been waiting on for some time, such as a single patient record and technology and digital. Is your sense that a lot of that has to be driven from the centre across all boards in order to try to make some of that difference? I guess so, and I think that you will get a differential response across boards, because they vary so much in size. The capacities to adopt new practices are inevitably partly determined by the size of the boards because the bigger boards will have that extra leeway, economies of scale argument, to move forward with innovations where the small ones just do not have that freedom. I just wonder if Lee might want to comment. Obviously, my question was partly based around Audit Scotland's analysis of the need for innovation to be sustainable, but then the difficulties of standing still. Yes, absolutely. Again, as we said, I think that we did see some innovation through the pandemic in terms of some of the digital advances, the increase in non-face-to-face consultations. The recovery plan also sets out a number of new ways of delivering services and different patient pathways. For example, the national treatment centres are trying to divert patients away from acute hospitals to increase in-patient and day-case activity. I think that we have to just not lose some of that progress and innovation that happened during the pandemic and just try to advance it. The Scottish Government has also set up the centre for sustainable development, which is trying to share some of the new practice and different ways of doing things across the boards across Scotland. It is just very important that we try and hold on, but there are lots of risks in terms of recovery and redesign going forward. One of them that we have already touched on is about workforce. I think that it is one of the major risks that workforce availability is. One of the other things that the Scottish Government is looking at is how we might use staff differently. Of course, that is still to be developed further. In our NHS in Scotland, we did outline a number of risks around the innovation, and it is important that they are thought about and sought through. However, as part of our next NHS in Scotland report, we are going to look very much in-depth at the backlog of patients and the deliverability of the recovery plan and the progress that is being made with that and the innovations that are outlined in that. That is due in February next year. I think that another interesting point that I picked out of Audit Scotland's submission was around leadership and stability in leadership. Audit Scotland has highlighted a lack of feeble leadership with a high turnover and short tenure, particularly in terms of directives of finance. How much do you think that the lack of the right sort of leadership plays in terms of not being able to achieve that long-term sustainability? It is fair to say that we have seen it stabilising slightly. The turnover has been less in the last year, but there has been a high turnover of senior leadership. Our concern is just about the long-term vision of transformation, but in terms of integration, for example, the ambitions of integrated health and social care services require collaborative leadership. If you have a high turnover, it is based on relationships and building up trust between different partners to progress and advance some of the innovations and ideas and new ways of doing things. Of course, if you have a high turnover at that senior leadership level, then that is very difficult to achieve. However, the other pressing thing right now is that our leaders have been under extreme pressure throughout the pandemic, and now they have recovery and redesign to deal with, but the national care service is also coming into service. Having to manage all that and do it well is very challenging going forward. Emma, you wanted to come in on the supplementary question and Paul's question. Thank you, convener. Just as I am picking up from Dr Bill's paper about the NRAC formula, there is a review that has been undertaken right now, and there are certain recommendations that have been asked for in a way that funding is allocated. I am thinking about rural areas, remote and rural areas, such as Highlands, Islands or the South Scotland area. What do you think needs to be changed in the NRAC formula if anything needs to be changed in the NRAC formula? Basically, the NRAC formula works to allocate money mainly to the territorial boards, which is mainly hospitalisation and GP prescribing. It is driven primarily by population, then by the age, sex structure and then by various indicators of morbidity and mortality. I do not want to prejudge where that might be going in the future. I think that a lot of our discussion today is relevant because, in effect, it is largely about the conditions of demand for health services and how they might be in higher areas where, for example, there are lots of older people. However, we may need to do some more on how easy or difficult it is to attract workforce to different areas. It is not the case that all of Scotland is equally attractive to healthcare professionals. In some areas, we do not have considerable difficulty in recruitment. It is just going back to the overall workforce set of issues. That is me off the cuff suggesting something that might be thought of in relation to the formula going forward. I am sure that more thought has to go into it. I move on to talk about Covid-19 recovery, although we have been skirting around it for the last three quarters of an hour. David Torrance. Good afternoon to panel members. The budget is in 2021 and 2021 has large additional sums to health and social care. Is there a need for continued Covid-19-related spending allocation to health boards? That is a question to which I think there is, as usual, no easy answer. To the extent that the question is how has Covid changed practice, working practice, and, in some sense, they have made things more efficient, as we have heard, with the way that GP practices are using online appointments and so on. However, to the extent that precautions still have to be taken, that adds to cost. To the extent that long Covid is still an issue, that also potentially adds to cost. In relation to what Raphael said earlier, one of the issues that seems to have emerged particularly in the UK is that we have seen a lot of pressure on workforce in all kinds of sectors, hospitality being perhaps the most prominent one. One of the reasons for that is that about half a million people have left the workforce, many of them saying that they are disabled. They were previously working and now saying that they have some kind of problem. Sometimes it is more common now that mental health is signalled as a possible cause for people having left the workforce. That will add to the pressures on the NHS. I am not giving you a definitive answer, but there are quite a lot of pressures going in different directions, it seems to me. I guess also the question is what is your objective in all of this? Is it to return to what might be described as normal levels, which might be 2019, where, as we have already heard, the NHS was struggling to keep its head above water? That is an incomplete answer, but it touches on some of the issues that are very relevant. I think that there will be on-going Covid-19 costs in 2022-23. There are increased infection prevention control measures among many other things, and it is our understanding that NHS boards have been given an individual funding envelope to cover their Covid-19 costs in 2022-23. However, there is an expectation that they will begin to manage those down now and on-going. There are new work practices brought in because of the Covid pandemic. How do we go about designing services and will they bring savings, especially if we are digital or community care or care in the home? The most important thing is how do we get the public to buy them? You mentioned GP practices, and anyone around the table will know that the lack of getting in face-to-face with a GP is probably one of our number of complaints. I guess that the issue is around taking the public with you. If the public are not happy with the kind of service that they think they are getting, you can innovate all you like. It is not going to satisfy what they want. Ultimately, you want the best healthcare that you can facilitate, but that can only happen if the public is happy with the way that it has been delivered, otherwise you end up with unmet need. Unmet need is perhaps a way of describing it. People who do not go to the proper diagnostic services and end up having problems that end up difficult to deal with. I think that the only way is to think about how, if you are changing practices, if you are going to use more data individualised and so on, you have to use whatever means works best to bring the public along with you and get them to form an overall view that this is for the best. This is the best way to proceed. Professor Wittenbergam. I would like to mention that we are doing research in the unit research centre where I work at LSE on a number of the topics that have been discussed in the last few minutes, including for example innovation and adult social care, but also on the current topic of Covid and long Covid. Of course, we do not have the results today, but as we have emerging findings, we would be delighted to make them available in Scotland as in England. On long Covid, we are looking partly at work with NHS England in respect of registries of data, but we are also just starting a project looking at the impact of long Covid and Covid itself on demand for adult social care. That reminds us to raise the issue of the unpaid carers, mainly family members, mainly close family, who provide a great majority of long-term care. One of the issues that we should be looking at in the study that we are starting is about the impact of long Covid potentially on unpaid care, both in respect of carers who may no longer be so easily able to care or people needing care whose condition may be more complex if they have long Covid and other conditions needing care from their family or others. We are looking at some of the topics that have been under discussion and hopefully we will have emerging findings over the next year or two. Thank you. David, have you got any more questions? Audit Scotland. Are management boards or senior managers making the best use of data to recover from Covid-19, or is there a big gap there that stops them doing this? I guess that all I can comment on is the fact that we have been very explicit about the gaps in the data available. It leads you to question how decisions are being made and how performance is being scrutinised. As I said before, when we know very little about GP, for example, demand and activity, we know that we do not have a good understanding of what is going on in the community. Some of our workforce data is not as robust and reliable as it could be and, of course, our social care data as well. We have commented on that many times about the lack of social care data. I am sure that, locally, boards in different areas are collecting their own information, but what we look at is at a national level. It is not available at that national level. I would sometimes question whether there is sufficient data to be planning and making good decisions. I wonder if I could just ask a quick question to Lee Johnson. Recently, it has been mentioned to me that one of our responses to Covid in the hospitals was to increase bed capacity, understandably, and that that has continued. What some of the boards are concerned about is that the staffing was never brought up. We have staffing issues in terms of recruitment, but the full-time equivalent posts are just not there. Possibly running around about 70 per cent of staffing allocation of funding is what was mentioned to me. Is that something that you have picked up on across the board? We have not looked at that in any detail. The only thing that I would comment on is what we do. Obviously, we know that there have been huge staff absences, but there has been a significant increase in the use of agency and local staff. That does not really answer your question, but it shows the pressure that services are under to have sufficient staff in place to meet the needs of their different services, as I have said, in terms of the huge increase in agency costs and the low-come costs. If I wanted to look at bed capacity before and after, who would be the best place to look at that information and what the staffing levels would be around that? I think that it would be a mixture in terms of bed capacity would be for someone like Public Health Scotland and then staffing. It would be NHS Education Scotland, who are now responsible for staffing data, and that is where you would be able to access that. That is helpful. Thank you very much. Emma, you wanted to pick up on something that Lee Johnson said. Yes, thank you, convener. I am sorry to keep coming in, but Lee mentioned that there was data missing from general practice or other information. Why is that, and is there a plan to get that data? Is that something that is in process, as Audit Scotland has highlighted, that that data is missing? We do know that Public Health Scotland is working on trying to improve the situation. I think that it is due to publish some data early to spring time next year. It will be fairly high-level data. I think that I told the committee before that there has been other areas that they have been working on in terms of the SPIR system with NGP practices. It has been patchy in terms of whether practices adopt that or not, so again the data is going to be patchy. As Professor Bell mentioned, there are issues around data protection and the data ethics of some of that data. We can make applications to get some of that data about different specialities or condition-specific data, but we have to go through a long process. Our point is that there is not nationally available data to give us a good insight into activity and demand with NGP practices. However, as I said, Public Health Scotland, as far as we are aware, is working on that and is due to publish data early to spring time next year. Thank you. Talking about pay, we have touched on it quite a lot today already. Since the end of 2019, there has been a significant increase in employment in NHS Scotland. We are looking at 14,000. That is not something that we are expecting to drop off again to pre-pandemic levels, and quite rightly so. We have two really big demands right across health and social care. Number one, increase in pay and especially the high inflation and the expectation that that will rise further. Number two, that demand for additional staff. I am wondering how those two can be balanced. I will ask that to Professor Bill first of all. If you want to increase the complement as far as the different professions within the NHS is concerned, you have to consider the set of issues that attract people to work in the NHS. That will of course include pay, and it also includes conditions. Conditions are a wide set of topics, but clearly you want people to be comfortable within that profession. Pay matters relative to what people's alternative is. It is most obvious in social care that Raphael has said, because the alternative is often retail or hospitality or whatever, because the training requirements are not so high as in the NHS professions. Nevertheless, you can get people withdrawing even looking for other careers. If there is a desire to increase the overall complement and you have to establish that there is a need to do so, I guess that if you are being successful with your prevention strategies, then you might well not need to think about such a large increase. However, if you want to maintain that higher establishment, you cannot ignore pay. It is always about the next best alternative. It looks to me like real pay for most people is going to be falling this year, in the sense that the rate of inflation is going to exceed the increase that is feasible in terms of nominal salaries. It is just the least worst of those options that people may well want to go for. If there is increasing disenchantment with the real levels of pay that people are getting, that means almost redoubling the effort to make sure that conditions are suitable and that, even given the cost of living fall, working in the NHS is still sufficiently attractive to keep people within it. There has been some research on the leap between nurses' pay and the supply of nurses by the Institute for Physical Studies. I am sorry that I do not have the findings in front of me, but I am very happy to send the clerks a note of the reference for it, if that would be helpful. That would be incredibly helpful to have that through there. You have picked up on another point, Professor Bell, on prevention strategies and the difference that that could make. Are they something that you would expect to make quite an impact, going forward? Are there concerns about service delivery, if pay is taken up quite a chunk, on how service delivery might be affected by that, if there is less funding there? It is always a trade-off here. Why, it seems to me that preventative strategies have suffered relatively is that it is so difficult to establish how effective they are. I was in Finland three days ago and learned that Finnish schools all close for a number of days each year and all of the children go out to ski. We have the daily mile in Scotland to get activity levels up. The Minister for Public Health, Marie Todd, is very keen on increasing activity levels. Increased activities—one part of it—reduced smoking, reduced alcohol are also both parts of it. It is very difficult to show what the difference is because the difference is going to come years later. What we do know is that Scotland's life expectancy is low compared with European countries. Its healthy life expectancy is low relative to other European countries. What we are spending on the NHS is not making that difference. We are spending about the same, but in those overall terms the outcomes are certainly not that good. It is the difficulty again of short-term budgeting. Putting in place the long-term strategies that I was speaking to someone this morning, I am very glad that the daily mile, which was a Scottish invention, seems to be pretty much established. Selling those at the sharp end when there are real problems about healthcare delivery systems through the NHS or through the social care system is extremely difficult. It would be good if Professor Inberg is able to comment on that. The impact of preventative measures in having a bit of protection, if you like, but I had asked about service delivery, too. If there are increasing demands for staff pay and therefore less money, to be spent on service delivery and the concerns around that and how it might tackle them. On prevention, in the field of social care and the sense of preventing the onset of disability or the worsening of disability, the evidence is, unfortunately, rather limited. We did some work with colleagues in other European countries. It is only really in very particular areas, like falls prevention, that there is firm evidence. One of the challenges is lack of evidence in terms of preventing disability in later life. As David Ballas indicated, it would not be easy to generate that evidence because of the long time lags between intervention and the desired outcome. One area that I have worked with colleagues on is prevention of dementia. In that field, there is even a shortage of information among the public that Alzheimer's disease, Alzheimer's dementia, is in part preventable—at least a third of it is preventable—to various reduction or various risk factors. Partly the ones that have already been mentioned relating to smoking, physical activity and also to controlling blood pressure, for example, in middle age, which we have shown is cost effective even if one looks only at the dementia outcome. Others may be less well known, like the use of hearing aids. There is now evidence that hearing loss—if it is not corrected using hearing aids—is a risk factor for dementia. There may be some new fields where there could be interventions that would be helpful, but the evidence is, as David Ballas indicated, part of the challenge. Moving on to discussing the national care service, which we are about to scrutinise in stage 1 in coming months, I will hand over to Sandesh Gohani. Thank you. Just on that last comment, I think that I might email you outside, because I have not heard that before for hearing aids. But no, definitely something that I might do. But just on the national care service, if we move on to the theme that I have, I was looking through the call for evidence and I saw a lot of respondents when it came to the financial memorandum. That was presented just before the summer recess. I will give you an example. West Lothian integration joint board said that there is so little detail provided in the financial memorandum as to the basis of the cost that it is impossible to say if the costs included are reasonable and accurate. I suppose that my question to David Ballas is whether you share those concerns. To a certain extent, I haven't been closely involved. I did speak to Derek Feeley in the course of his inquiry, but I haven't been closely concerned with the implementation. I have to say that I am not clear exactly how the additional money is going to be allocated. Adding extra money to the NHS is reasonably straightforward. Adding it to the care services is such a complex sector between voluntary private providers and unpaid carers. There are a host of actors in this particular area. How you provide additional resources and what that means at the national level seems to me to be a big challenge. Rafael mentioned the possibility of having a better career structure for carers. If that was part of the new care service, that would be a plus. However, it seems to me that there are a lot of unknowns around how it might affect local delivery. I am reserving judgment at the moment to see how it further develops. Again, we have submitted a response to the consultation around the bill. Given the details of the arrangements that have yet to be finalised and determined, the scale of the costs involved in the financial memorandum are estimates with a lot of caveats. Our take is that the affordability of the vision set out is not certain, given that the actual scale of the costs are not yet clear. That would be our take on that. Local authorities and other stakeholders are also very concerned about the administrative and structural costs of establishing the national care service. Do you share their concerns that a high administrative cost will lead to a less financial resource for service delivery? There will have to be some sort of administrative overhead to the associated with the national care service. We have seen similar things in relation to, for example, Social Security Scotland. I have to say that I am unclear at the moment as to what that might mean and what the trade-off there might be between additional efficiency savings at the local level compared with the administrative costs at the national level. I really do not feel that I can comment on that, because it is not clear how the size of the administrative overhead is going to be, and then how efficiencies might be gained at the local level. Given, as I have said already, it is a much more diverse sector than the national health service. You are clear about that. What can we do to make that data available to make it clearer as to what is happening? Part of it is around where local authorities are going to stand in the future in relation to the provision of care services. There is clearly a potential gain through improved interaction, fewer delayed discharges, improved interaction with the health service, I should say, and fewer delayed discharges. We seem to be getting to a good place as far as delayed discharges were concerned around 2018 or thereabouts, but with the difficulties that the pandemic caused in the care home service, those successes have, to some extent, been wiped out. All that I am doing is conveying uncertainty here. I think that it will be important for the committee to understand more clearly than I think is possible at the moment how exactly the implementation will run through what the administrative costs are, how it will affect local authorities and the interaction between local authorities and the NHS and all the separate providers around there. We largely adopt the same charging structure that is run in England with slight variations, but not massive variations around when you become self-funding, for example, in social care. Will there be changes around those asset-based tests as to whether people become self-funding or not? Thank you. I have been doing a bit of reading since we got our papers last week about the NHS state and sustainability and how the NHS can become Achieve net zero by 2040. I am interested in what the panel might think about. The issue of 20 million miles per annum has been saved by the implementation of near me during the pandemic, so that shows that mileage reduction can be achieved. I thought that that was a hefty figure, which, when calculated into CO2 emissions, is in the billions of milligrams of CO2 saved. There was another issue about remote clinics or virtual clinics and using telemedicine so that blood pressures can be obtained remotely and then analysed by a GP to see the results without seeing a patient. I am interested in what the panel will think about. How do we get the biggest bang for our buck in saving on emissions in our NHS state? I suppose that we will go to Professor Bell first since you are in front of me. That is not my specialist subject. Clearly, there have been a lot of innovations that have been moving in the right direction. The use of drones is another area for delivering medicines. It is another area that has been explored. I guess that the issue is that a lot of the state is not that efficient in terms of its annual usage of CO2, the actual state. Transport is very important, but it is the physical buildings. The question around what are the levels of investment needed to convert those to being more sustainable? For some, that will be a big challenge. It seems to me around hospitals, for example. Progress can only be made if the investments are made. Learning is shared across different parts of the NHS, and the willingness to do that is very important. Would either of our remote colleagues like to come in? I could see you nodding along as David Bell was speaking. Would you like to come in? I agree with Professor Bell, but it is not an area that we have done a huge amount of work in. We identified the net zero requirements as adding a challenge to the NHS recovery process and the fact that it will need additional investment in the already pressured budget. We agree that it is vital that NHS make the most of the opportunities arising during the pandemic to reduce carbon emissions, for example, from the things that Professor Bell talked about and near me. It is not just about the reduced travel, but it was reduced PPE and things like that, which all contribute towards it. Climate change is in our work programme. We will do more work in this area, but it is not an area that we have done an extensive or in-depth look at the NHS at this point. Back to Lee, we still need to make journeys as part of the NHS travel. The Scottish Government has a switched on fleets fund, which is £20 million, and NHS Lothian and Aberdainshire Council have added 20 new zero emission vehicles using the Scottish Government funding. I think that you can measure the journeys. We know the mileage if NHS employees are making a travel distance, but I am thinking about dialysis patients and very predictable journeys if they are using taxi vehicles, which many do. You know where the start point is, you know the end point, Monday, Wednesday, Friday, Tuesday, Thursday, Saturday—same patients, same appointments every week. That would be very measurable if Audit Scotland is looking for data on how we can measure emissions reductions by replacing the vehicles that are diesel-driven with electric vehicles. Is that something that we should be looking at? Is that something where we can get a big win if we rapidly adopt electric vehicles for the likes of those patient journeys that we can measure and demonstrate emissions reduction? That is a set. I just have not done enough work in this area to really know whether that is, but it is something that I can flag to our climate change team. We have a team working on this at Audit Scotland who will be looking at the different ways that we can look at how progress is being made in the public sector to meet some of the commitments and targets that have been set going forward. I will pass that on to that team. I will halt there because I am giving out homework. Can I move on to discussing, in more detail, preventative spend? I have some questions from Gillian Mackay. Thanks, convener. Good afternoon to the panel. In the panel's opinion, given the increased pressure from Covid-19 on waiting times in other areas in the NHS, is it realistic to move towards greater preventative spend in the medium time? Who would you like to address that to, first of all, Gillian Mackay? Can I maybe go to Lee first? Thank you. Again, the focus is on recovery. Obviously, there is a backlog, and that is very important to our communities out there. However, one of the other things that we identified in our NHS in Scotland report that was published in February is that one of the risks with recovery is that we lose sight of prevention and early intervention. It is still key to reducing our inequalities as well as equitable access to services. However, as we have said many times, we know that that is not an easy task. It is very difficult to achieve anywhere else. We have found that moving resources towards prevention and early intervention often requires a significant change in how services are delivered. It may involve reducing budgets in some areas and increasing others and targeting resources to specific groups of people. We know that certain areas in our community planning partnerships and integration authorities have started to explore small-scale preventative projects, but a significant scaling up of that activity is needed. However, that will require difficult local choices in terms of what we prioritise, but a stronger shared strategic planning across an area for prevention. As we have already discussed earlier, I do not think that it is just about health. Health cannot do it on its own. It has to be across Government, across public sector and across third sector initiative, if you like, to try to implement that. I will go back to Lee again for the question. Is there an argument in the first instance, which we have touched on earlier, that preventative measures should be taken in areas with higher excess mortality or in areas where the number of healthy years of a person's life is expected to be lower? I do not know if I have a particular view on that. I would argue that it is important across the board that it has to be thought about in all areas, if you like, but, as I have said, there are specific groups of people who perhaps need resources targeted towards them in that early intervention prevention space. You mentioned it in the call for evidence that the care and wellbeing portfolio that the Scottish Government is implementing is at an early stage of development, but it is one of its problems around preventative and proactive care. Within that, I guess that the Government is committed to designing a new, coherent and sustainable system that is focused on reducing inequality, prioritising prevention and early intervention and improving health and wellbeing outcomes. Its objectives as part of that include a decision-making framework that prioritises prevention and early intervention, which, I guess we would say, is promising, but we need more detail. We have not got enough detail that is still in the development and in the early stages. It does sound promising, but we really need to see more detail around that, so it will be interesting to see how that develops and what possibilities it brings, I guess. Gillian David Bell would like to add to that. Hi. I am actually on the advisory board for an investigation into health inequalities in Scotland that the health foundation is carrying out. It may be of interest to the committee to hear that report once it is available, which should be towards the end of the year. Coming after our report next week. We are well aware of how health foundations work on this as well. I guess I would say that there is a case for targeting preventative measures on those areas that have the lowest healthy life expectancy. I know that some areas are starting to think about things such as social prescribing. I know that bodies such as the RNA are buying up golf courses in deprived parts of Glasgow. I am trying to make that particular activity a more accessible activity for people from more deprived backgrounds. In general, I guess that sport that has done most is probably football in terms of providing facilities, encouraging people in deprived areas to get involved. That, at the end of the day, is the sort of thing that helps increased activity levels. We are pretty clear that increased activity is a thing that leads to better health outcomes in the long run, but again it is in the long run. We have got to understand how big that effect is. Thank you, Gillian. Do you have any more questions? No, that is me, convener. Thank you. Thank you very much. I have a final line of question on this. Sorry, Stephanie. Do you want to come in? Yes, please. If I could. Of course you can. I am wondering as well. The national care service is very much, we are talking about focusing on what it is that matters to individuals. It is about supporting people to achieve the outcomes that they want to achieve. My thinking is that it is very much about their health and wellbeing. They feel better. It is likely to improve their wellbeing, which can have a huge impact on health as well. That seems to be quite at the heart in the national care service. I am wondering how much do you feel that the preventative impact of that, for example, falls into the bigger picture, if you like. I do not know that, but I have explained that particularly. A number of different things jumped into my mind. When you said about people's choices, one of the things that I should have said that I am not really clear about is how self-directed support will fit into the new national care service and how, indeed, that links up with the payments that are being made through Social Security Scotland in relation to disability, because all those things are linked together. Achieving outcomes that relate to people's personal wishes in relation to health and wellbeing, there is a big question about the extent to which those are determined by people's own choices, rather than what professionals think is good for them. I am not taking a view here about that, but that is something that has to be part of the consideration of the design of the national care service. It seems to me to make sure that there is no double counting in relation to the support that is being given to people. Self-directed support took off pretty slowly, but it is now reasonably well embedded across quite a lot of local authorities. What role will that play? I have to say that I am not clear about that. I am just wondering whether there is a place for an individual action plan that people have that they share with different health, different social care providers and so on that keeps centering things back to their own priorities, because it could be quite easy when they are having those conversations or when they are getting limited options. Is that something that could really help, or does that fly in the face of things that are being based on data, evidence and so on? Not really. With healthcare interventions, there usually is no choice. If you have appendicitis, you need an appendectomy. However, if you need social care, the options are much wider about how that could best be achieved. It makes sense that the individual receiving the care or their representative, their guardian, helps to make those decisions. It seems to me to be important that the national care service takes account of that. I am sure that that is part of the thinking, but exactly how it is done will be important for the overall level of satisfaction that there is with that development. On the previous discussion, I took part on an evaluation of the Well London programme, which was about prevention in deprived areas of East London. The outcomes were rather mixed, but if that was of interest to the committee, again, I could send the links to that. On the current topic of cash for care, my understanding of such evidence as there is is that there is a big difference between different groups of service users that is much more attractive for, say, younger disabled people who may welcome the opportunity to employ their own care or to be in control of the care that they receive. For older people, it has been rather less acceptable. Indeed, anecdotally, I can remember speaking to a group of older service users who said that they just saw it as a mechanism for the statutory authorities to transfer the burden of organisation for the service user away from the authority. I think that it does depend on the user group, but it may also be that, for example, for older people that support services in the actual use of the cash for care direct payments, it may therefore be very important from such evidence as I am aware of. A final line of questioning is on health and social care outcomes. Of course, this is a thread that has been going through everything, but, Tess, you have some questions. I do, thank you convener. I think that this is one for the panel, but if I can start off with Professor Bell. It is a question around conflicting priorities and balancing outcomes. You have got increased labour costs, increased drug costs in terms of capital costs, but also an immediate need to reduce waiting times and improve treatment times. So, how do you balance those immediate needs and those immediate outcomes with the longer term outcomes? That is a very difficult question. Because effectively rationing short term supply of healthcare is extremely unpopular, saying that we have to look to the long term is extremely unpopular, what it does do is it perhaps drives some people to the private sector. I think that that is increasingly the case at the moment that that is happening. Ultimately, I suppose that the Government should be driven by what works or what is the best outcome among the conflicting alternatives. However, it is very difficult for Governments to avoid responding to short term requests, it seems to me. Unless you are prepared to count on some different funding mechanism, it seems to me that the probability is that it will be the short term measures that win out. We push further and further into the future, the kind of long term strategies that we spent a lot of time this afternoon talking about. I think that, in the end, much of this is about really a policy decision rather than one that is readily amenable to analysis. In pure theory, I could probably imagine analysis that looked at the gain in quality-adjusted life years from short term measures and from long term measures and tried to compare them. First of all, one is up against real difficulties about the evidence. Secondly, one cannot really escape the issue about how to discount the futures against the present. As you know, Treasury guidance is that future costs and benefits should be discounted, regardless of whether they are less valuable than short-term ones. In the end, there is an element of judgment in that. My feeling is that it is to give a pure lease of health economics, analytical answer, would be probably not realistic. In the end, a lot of it comes down to policy judgments. I do not think that I have much to add. As we have already talked about, the health and social care financial position is very challenging going forward. Across Scottish Government, not just in health and social care, there will be some difficult decisions to be made going forward, but that is for Government to decide and not something that we would comment on, on where those decisions should be made. I do not know if I have read correctly or heard correctly. It is almost as though the balance between the decision to put the wheels on the bus, because the bus is not moving, or to decide strategically where that bus is going. Is that correct? There certainly is a bit of that. It is a political choice. Thank you, Tess. I have a final question to Emma, unless I have other people want to come in in the last couple of minutes. Emma, it is over to you. It is going around like we are talking about preventative spending, we are talking about better outcomes, we are talking about better health overall. I am thinking of one example of keeping people out of hospital from asthma attack or COPD exacerbation. Overnight stay in hospital is minimum 1,100 quid, but if somebody was having their annual asthma plan reviewed and they are taking their inhalers appropriately, whether it is COPD or asthma, that helps to keep people out of hospital. In order to support the practice nurse, the specialist in airway management or respiratory, that means that that has to be done in primary care, but that means then, do we take money away from secondary care and give it to primary care, or do we have to figure out, do we get an extra pot of money from somewhere, and then how do we have a wee borrow in pot? Oh no, because we cannot borrow money in Scotland. What is the best way to take a pot of money and divvy it up in the best way possible? You could, as Raphael said, do the sort of calculation and perhaps that kind of calculation would be more appropriate in this context, because it is not really one that has big political overtones, but it is one that is possible to figure out, which is going to give you the most bang for your back in terms of, well, the technical term is quality adjusted life years, but the issue then is the division of resource between hospitals on the one hand and primary care on the other, and there there is a question about how effectively primary care's case is being made for it when the division comes up in budgetary terms, and if programmes like that are deemed to be sufficiently important to warrant that kind of intervention. Again, we are going back to data and the presentation of evidence as to how our overall budget should be allocated as between on the one hand hospitals in this case and primary care on the other. Thank you. I want to thank three panellists for giving us so much food for thought as we approach our budget scrutiny and for all their very helpful pointers, particularly as we approach national care service scrutiny as well. That's all we've got time for in this particular panel, so I thank you to you all. Members, we have got one final item in our agenda, and that is consideration of our negative instrument, and that instrument is the general pharmaceutical council amendment rules order of council 2022. The Delegated Powers and Law Reform Committee considers that instrument at its meeting on 6 September, and it made no recommendations. The purpose of the instrument is to allow the appeals and fitness practice committees of the general pharmaceutical council to hold meetings or hearings using audio or video conferencing facilities on a permanent basis. In addition, in-person meetings and hearings will also continue to be available, and no motion to a null has been received in relation to this instrument. Do any members have any comments in relation to the instrument? Don't? Nobody does, thank you. I propose therefore that the committee does not make any recommendations in relation to this negative instrument. Any member disagree with that? Thank you, colleagues, so we are agreed. Our next meeting, the committee will take evidence on winter planning for the NHS and social care, but that concludes the public part of our meeting today. Thank you all.


Some formulas from yesterday so if you remember this was the the energy we are looking at and It was pointed out to me by a good year last night. I used them The same letter for two different things yesterday, which was very bad And so I'm going to fix this by defining the energy with a curly H here Okay, and we have a splitting of this That we proved yesterday of this form Mu V is the equilibrium measure Zeta is this sort of effective confining potential and then yesterday I introduced the potential generated by the fluctuation measure and So this one should be a H with straight straight H So it's the integral of G of X minus Y It depends on X and of course it depends on the configuration So for each configuration you have a given a given function okay, so this is the This is the potential and if you remember it says minus Laplace H n equals sum of Dirac minus n mu V and the the point was to try to prove that this Next-order energy can be expressed with this electric potential Let me Stop here for two to talk about what's happening in the one dimensional logarithmic situation because you remember that in 1d the logarithm is not the coolant kernel So I cannot write this however. It's easy to generalize these formulas by thinking that The real line are Can be embedded in the plane So usually people do it in the complex plane, but let's embed it in R2 and so each point X i you can view it as X i comma 0 And then this function H n you can view it as defined over R2 So now X is in R2 It's going to be integral of minus log X minus Y the sum of the Dirac masses at these X i 0 Minus n and mu V is a function of the real line only so Let's write it X sorry y1 for the force coordinate And here d y right but of course mu V of y1 I can also Think of this as a measure in the plane with density mu V of y1 times Delta R of y So I write here Delta R to denote the sort of Dirac on the real line right, it's the it's the uniform measure on the real line and it takes you When you integrate a function Against Delta R Say X1 X2 It just integrates With zero for the second coordinate okay, so Once you view H n as an as a function on R2 this way It's simply the potential generated by the configuration the distribution of charges at X i 0 minus n mu V times the Dirac mass on the real line and then you can write That this holds true In R2 okay, so this is a sort of trick That allows to see The logarithm interaction in 1d has a sort of restriction of a 2d interaction For measures supported on the real line and then you can continue the calculations in the same way as if you were in R2 For specialists and when you do When you look at log gases or random matrices on the real line you compute the silt still ts transform It's it's exactly the same procedure. So you view things in the upper complex plane It's the same thing as expanding this and computing the gradient of age So it's essentially the same as the still ts transform Okay, so now I want to give a rigorous meaning to the computations. I was doing yesterday about computing f n mu V of Xn and relating it to integral of gradient H n Squared and so in order to do that I'm going to have to introduce a truncation procedure For these Potentials H n which are singular at each charge right so H n you remember blows up like the Coulomb kernel Near every point of the configuration So I define I'm given Give myself some eta which is just a vector of numbers It's a one eta n and think of them as small numbers and I define H n comma eta To be H n It's the same as the function H n minus the sum of G of X minus X I Minus G of eta I Positive part, okay So you see if you remember H n near X Near each X I is going to blow up exactly like G of X minus X I So this thing is removing the singular parts and Replacing it by G of eta I which is a constant right, so effectively it's the same as Saying you have a you have a function whose graph is going to look like this and you replace this graph by the truncated version where you truncate at The value G of eta I so eta I is this little radius and you're just going to chop off all the peaks You're all the points you chop them off at distance eta I Okay, so this is this is a formula that does this All right, and now You can try to compute the laplacian of this guy So what are you going to find? Well, it's going to be the same as the laplacian of H n except in the ball Centered of at X I and radius eta and there instead of having a Dirac mass at X I you're replacing it by the laplacian of the function whose Graph is like this So let's say this is the function f eta of X. It's just G of X Minus G of eta positive part Okay, so what this what does this function do? It's zero Outside of a ball of radius eta it has this infinite peak And then it stops here When you reach G of eta Okay, what is the laplacian of this guy? It's the Dirac at the origin There's the CD everywhere So it's the Dirac at the origin minus What I will call? Dirac zero eta Or Dirac zero eta or Dirac p eta is a measure of mass one on The sphere of radius eta Normalized to have total mass one. Okay, so why is this true? It's a computation, but the other way to see it is This thing is a radial so the laplacian of f eta has to be something radial and so it's natural then that would be a uniform measure well because This laplacian is just simply the jump of The normal derivatives when you reach the boundary of the ball right so it's supported on the boundary of the ball and Then by symmetry it has to be uniform and the fact that it's total mass one It's easy to check because the total mass here has to integrate to zero All right, so another way of saying all this is that this truncation procedure What it does it removes the Dirac mass and replace it by replaces it by a smeared Dirac mass Which is just smeared on the sphere of radius eta All right, so when I go to compute the laplacian here Every time I had a Dirac mass I replace it by a Dirac mass smears smeared radius eta I And then nothing changes the rest is the same, okay so it's one way of regularizing these Potentials that are singular and what what's convenient with this way is that it's completely explicit and it's it's fairly straightforward. It's just these truncations Okay, so with that I can proceed to computing And what I'm going to prove is the following proposition that f n Mu v so let's say for any new mu This next order energy which if you remember was defined by I'm going to write it here Fn of xn Respect to mu Is equal to the double integral on the complement of the diagonal of this fluctuation against itself okay, so the Proposition is that this is always greater Than 1 over cd the integral of gradient h and eta squared minus The sum of g of eta i plus error terms Which are small essentially so I Will control these error terms by the sum of eta i squared Let me check c times n times this So the idea is that later. I will choose this eta i properly this eta i is properly In such a way to make these error terms Small enough Okay, and There is this inequality With equality that's important if all the balls Bxi eta i or disjoint So it will be sometimes useful to choose the eta i so that the balls are disjoint. Okay, so this Formula is doing what I was promising. It's it's making rigorous this this relation By saying well instead of having this integral that's divergent we're going to compute the integral of the truncated The quantity for the truncated potentials this one now is finite and convergent, but we have to remove a certain divergent Quantity which is exactly the the energy that the tip carries so you If you look at what happens when eta goes to zero this thing Tends to infinity again, but this thing subtracts off exactly the divergent behavior And in effect you are computing things in finite parts right Okay, so let me explain roughly how This can be proved so the first step the first step consists in studying these energy of this truncated potential and showing that this is roughly It's actually equal to CD the double integral of G of X minus Y so this the into the Coulomb interaction of the smeared Dirac's with themselves Okay, so this This is what this is the computation I was doing yesterday Except now for the truncated guys. It's it's legal. You don't have to worry about the diagonal anymore The integral is convergent So basically you look at this formula you multiply the formula by You integrate it against the same right-hand side and Then you integrate by parts and you find this okay, so this is the the legal version of it Okay, and now what we have to do is we have to compare this and this Okay, so these two Quantities sort of look the same except I have the Dirac's here and I have the truncated Dirac's there and here of course I can remove the diagonal by writing that I Have diagonal terms first So what is the diagonal? I'm integrated G of X minus Y the Dirac on Smirred on the ball radius eta. This can be computed. It's going to give you just G of eta I for each For each point so this is the diagonal term and so I'm writing that this is roughly equal to this plus CD The double integral on the complements now of the diagonal And I do the same. I have the smeared Dirac's and the smeared Dirac's here Okay, and so now when I make when I subtract this Minus that I have this term Which is not formally very much equivalent to this term. Yeah When I equals J here Right so when X equals Y or when I correspond to Y equals J So it's the interaction of the point with itself so if it was a True Dirac the interaction of the Dirac with itself. It's infinite. You don't want to see that But when it's a smeared Dirac, it's okay. It's a finite quantity. You can compute it And it gives you this right so this is the integral of G of X minus Y Delta X I eta I of X Delta X I eta I of Y All right, so this is an explicit computation. It's all radial. It's easy to compute So it's the self interaction of a smear charge and it blows up of course when eta goes to zero You should expect that it behaves like this All right, so now my my task is to prove that this quantity is bigger than this quantity up to error terms And that there is equality if the balls are disjoint and so that It's based on the following argument So I'm just going to look at the terms that correspond to the interaction of the charges So these these types of terms X I eta I X J It's I J and now I is different from J Because I've taken into account the terms for which I is equal to I okay so now let's look at a function like this G of X minus Y Delta X I of Y For example, this is the potential generated by a Dirac at X I We know what it looks like. It's just G of X I minus X but if you think of it as You can view it as the solution to minus Laplace H equals CD Delta X I So it's a function which is harmonic away from X I And otherwise, it's always super harmonic So H is super harmonic So here we use the Coulomb nature of the interaction we're this is really where it comes to play a role and If I do the same with eta I The same is true, so it's super harmonic and it's harmonic Away from B X I eta I Okay, not too hard Now, you know something that's called the maximum principle right maximum principle tells you that if you take a harmonic function and if you Average it over a sphere It's the same as taking the value at the center of the sphere Right the average is equal to the value at the center so if I take this function if it's harmonic and Now I average it on some other Sphere, so I take this whole thing and I average it It's the same as if I take The same thing against the Dirac mass Right, it's this is the maximum principle the average is equal to the value at the point But that's going to be true only if I'm In the zone where the function is harmonic, so this is okay If I'm away from B X I eta I so if B X J eta J Does not see B X I eta I Then this is true because I'm in the region where it's completely harmonic And so I can replace the function the average by the value Okay, but the maximum principle also holds for super harmonic functions with an inequality It tells you that if you have a super harmonic function, and if you take averages Over a sphere the answer is going to be smaller than the value at the point So in any case I always have an inequality Which is true? Okay, and so when I put all that together I find that The integral of G of X minus Y Delta X I eta Delta X J eta That's less Then the integral Sorry, so this is eta I eta J Eta I so here I can replace by the value at the center and Then I can exchange the roles of I and J and I can do the same again Okay, so you find that Basically, this is telling you that the interaction energy between two smeared Charges is smaller Than the original interaction energies that you had before smearing Okay, so this is an effect of The Coulomb nature of the interaction moreover All the inequalities here are equalities if the balls are disjoint And so if I put all that together It proves my proposition So there is just some error terms that come from dealing with the mu V here What I see when I have mu V and I like I change delta X I by the smeared by the smear charge, but since mu V is a nice Measure with the density it will create error terms that are proportional to the Radius of the of the spheres So this is how you get these these types of terms Okay, so now With this proposition I Want to show you that we've already obtained some interesting information so we have a way of re-expressing the this total pair wise Coulomb energy of the system That's composed of the neutral system that's composed of positive charges and a negative background We have a way of re-expressing it in terms of these integrals Right and the idea is that these integrals are going to be extensive in space and scale like Essentially like the volume of the area in which you integrate them So as a corollary we have a Lower bound for Fn Which is valid for any configuration of points Take it up So you take it Equals for every eye Okay, you want to find the right value of eta i that you should plug in there The idea is you want eta i to be small so that these error terms are small But you also don't want it to be Too large too small because otherwise these terms will become very negative and you're looking for a lower bound So if you optimize those two things you find out the right eta i that you should take Is n to the minus one over D And that should not come really as a surprise because this is the natural Length scale Which we expect to be the distance between two points right the distance between a point and it's nearest neighbor We expect it to be of that order and so we are truncating here at an order that's comparable to the Distance between the points I could take here any small constant in front. It would not make any difference Okay, so if I plug that in what do I get? The idea is I'm going to take Fn of Xn. I have a Lower bound here and this term is obviously positive so I can just discard it And so I find minus So I'm going to have n identical terms Equal to this. This is the choice of eta i and the error terms I Bound them below by Cn The eta i squared will give me n to the minus 2 over D and I have n terms so I have a 2 Okay, and so now let's compute what this is So you have to distinguish two cases in the log cases Then G is minus log right so what you find here And I have Sorry, there is a plus. It's a plus No, it's a minus okay, so it's G is minus log so it's a plus and then there's a minus So I get minus n over D log n minus C and To the 2 minus 2 over D This is good and then in the other cases Because I have to assume that the error term has the bad The wrong sign right I have to assume that it's bad for me. I Want a bound from below. I don't know the sign of the error term So if I want a bound from below I put it with a negative a Negative constant. This is the worst case scenario My lower bound is very low Okay, so in the other cases G is n to the power sorry G is R to the power 2 minus D if you remember And so I put that in factor Get n to the minus 1 over D to the power 2 minus D and if you believe me It's going to give you minus C and 2 minus 2 over D okay, so the logarithmic cases are a little bit different because you get these terms that Pop out which you don't get in the other Coulomb cases Okay, I think I made a mistake somewhere Okay, so for example in dimension 2 You see that this lower bound is of order n and is this is actually the idea is that this lower bound is actually optimal it gives you the right order and Proving that of course is It's a more difficult endeavor and so once you have a lower bound for the energy You can obtain easily an upper bound for the partition function. So now let's think We're in the situation with temperature and we're looking at the probability density of this form Now we have a lower bound for hn this curly hn because we have this splitting formula And we have a lower bound for fn And so naturally this gives us an upper bound For Z because Z Okay, it's the integral of this The xn So let's input The lower bound that we just found Into the the integral Okay, so Sort of obvious computations, but everything is going to come out of the integral and You're going to get Say n squared IV of mu V if you remember well then these terms are going to come out so I add a plus beta