فشرف بل اشتغالي بالعلم ولا تبغي به ما عشت يا دادا دالا وياله من شراف عظيمي الحمد لله رب العالمين له الحمد الحسن والثناء الجميل وشدوى الله إلا الله وحده لا شريك له يقول الحق وهو يهد السبيل وشدوى النسيدنا ونبينا محمد سل الله عليه وعلى آله وأصحابه والتابعين لهم بإحسان إلى يوم الدين أما بعد إن شاء الله تعالى today we are going to carry on من وصايا السلافي للشباب the advice is that the pious predecessors gave to the youth ومن جملة وصايا السلافي للشباب from the advice is that the pious predecessors gave to the youth is ما جا عن جعفر قال that which جعفر said كان ثابت البناني رحمه الله that ثابت البناني who was a slave for Anas ibn Malik رضي الله تعالى عنهم يخرج إلينا وقد جلسنا في القبلة فيقول he came out one day and he sat with us في القبلة إن قتولز قبلة أما إن قبلة فيقول أن he would say يا معشر الشباب or youngsters حلتم بيني وبين ربي أن أزجد له you got between me and Allah for me to prostrate for him and this was that he ثابت البناني indulged in talking and conversing with them that he didn't pray something that the salaf would advise the youth regarding they would come and they would unite and they would meet one another in the masjid but they would spend the time in that masjid by conversing and talking and chit chatting about worldly matters and so they wouldn't read Quran or they wouldn't study or learn or benefit from their time by either praying or by doing dhikr but what they would do is they would have worldly dialogue and worldly conversation so this would get between them and praying it would get in between them and praying so they don't busy themselves with عبادة and they remember and so they leave this so what is required from the youngsters and the youth is that he observes that the house of Allah is a sacred place and what it means to honor the masjid of Allah the house of Allah is that you don't busy yourself in talking about worldly affairs insignificant things that preoccupy you from عان العبادة that he busies you from عبادة tranquility and humility in the prayer especially nowadays when we're all tested with in different forms and shapes is وسائل التصال social media using the telephone so the youngster or the youth he may not even be talking to somebody and he may not be conversing with anybody but what he'd be doing is he'll be on his phone all the time he'll be responding to a people who are searched into social media what's up he'll be on twitter facebook and he'll spend all his time in the masjid sometimes so much so he will open he will basically busy and preoccupy and what do you call it distract when people are in the masjid so they can't even attain ease and quietness from him so that was the 9th advice الوصية العاشرة the 10th advice which is from the advice of the self towards the youth is ما جعن محمد ابن سوقة that which محمد ابن سوقة said he said لقني إلا قياني محمد ابن سوقة said I met ميمون ابن مهران فقلت I sat with ميمون ابن مهران حياك الله ما الله give you life فقاله ستني هذه تحية الشباب this is the greeting of the youngsters and the youth قل بالسلام سيه السلام عليكم also the prophet SAW he said من بدأ بالكلام قبل السلام سيه السلام عليكم anyone who starts speech with you first before greeting you don't respond to them don't respond to them ابن السني narrated this in his كتاب عمل اليوم والليلة وشيخ محمد ناصر الدينة الالباني authenticated it in his كتاب سلسلة أحاديث الصحيحة so what is it that ميمون ابن مهران and saying that the word حياك الله is a kind of greeting that is put forward by the youths and nowadays if you look at the youths today and they are meeting one another they have this own way of speaking to them speaking to each other the way they greet each other and other ways that they greet each other so they've left off the Islamic greeting they've boycotted it and they've made up their own way of speaking to each other so ميمون ابن مهران he advised محمد ابن صوقة to not do this type of greeting and this greeting is nothing wrong about it شرعان which is حياك الله but what does it do what does it do it kind of removes and it makes the individual boycott the prophetic the prophetic the prophetic type of greeting which is السلام وعليكم sometimes a person may even come and they talk to somebody and they converse with somebody and they chat with somebody and then after that they say سلام وعليكم and our messenger عليه الصلاة والسلام he told us that the person who starts talking to you first without any greeting then do not respond to them do not what so it's important that the youngsters in the youth take on board this advice of ميمون ابن مهران in which he gave to محمد ابن صوقة محمد ابن صوقة was a young youth so he said this is the kind of greeting that comes from the youth الوصية الحادي عشرة the eleventh advice it is ما جاعا أبي مليح أبي مليح said قال لنا ميمون ابن مهران ونحن حوله ميمون ابن مهران said we were around him and he said to us يا معشرة الشباب oh youth oh youngsters قواتكم اجعلوها في شبابكم ونشارتكم في طاعة الله يا معشرة الشيوخي حتى متى يا ميمون ابن مهران he said oh youngsters and youth put your power and your effort towards your youth while you're young ونشارتكم في طاعة الله and put your enthusiasm in the obedience of Allah سبحانه وتعالى and then he turned towards the elders and he said يا معشرة الشيوخ oh youth who are elderly in age حتى متى when are you guys gonna go and benefit yourselves in obeying الله سبحانه وتعالى so what is it that he advises here ميمون ابن مهران what he advises here is استغلال قوة الشباب benefiting from the strength and the power that you have when you're a youngster and a youth and the enthusiasm that you have and the energy that you have in what في طاعة الله عز وجلة in the obedience of Allah وما يقرب إليه and that which will bring you and that which will bring you closer to him سبحانه وتعالى so to benefit from your time death does not care about the age of a person and it doesn't bother it doesn't concern him how old you are you can be a young person you can be an elderly person when the day it comes to you death you're gonna go and what's going to be awaiting for you on the other side is the effort and the hard work that you put in so it's to benefit from the age and the youth that you have today that is something إن شاء الله وتعالى that will allow you to grow in positions the day of judgment الوصية التانية عشرة the 12th advice عن الفريابي فريابي يسأل كان سفيان كان سفيان الثوري سفيان الثوري رحمه الله وزوان يصلي ثم يلتفت إلى الشباب فيقول إذا لم تصل اليوم فمتا سفيان الثوري he used to pray and then when he prays what he used to do is يلتفت إلى الشباب he would look at you the youth in the mischief and the youngsters and he would say to them إذا لم تصل اليوم if you guys don't pray today then when are you going to pray this is an advice from to the youngsters in the youth a great advice which is to benefit from this age that they're in شباب if the person does not benefit from if he doesn't benefit from his age of being a youth in what? in prostration then the person will become weak he will grow older his body parts will become weak and he's going to wish that he becomes a young person so he can prostrate as much as he could have so if you don't pray today then when are you going to pray الوصيهة الثالث عشرة the thirteenth advice جاعة ربيعة ابن كلثوم إنه قال نظر إلينا الحسن ونحن حوله شباب فقال ربيعة ابن كلثوم he said حسن البصريه لقتتها إمام حسن البصريه he looked at the youngsters in the youth and he said to them يا معشرة الشباب or youngsters and youth أما تشتاقون إلى حور العين do you not desire and do you not want حور العين the women of jannah and this is very powerful from حسن البصريه he's reminding them the blessings of jannah and the bliss that are in jannah and the things that a person desires ملدات الجنة and that which is from the مصرات of jannah that will bring you joy and happiness especially the fact that these are youngsters in the youths حور العين is something that youngsters and youths would love so this would make them what work hard and make sure that they fulfill their lust and their desires in the heraft as it's better for them than his dunya and that also what you take from حسن البصريه's advice here is that it's about placing hope in the people's hearts and reminding them of the good that they can attain and not scaring people necessarily and making them look forward to something and Allah said in the Quran ومن أراد الآخرة the person who wants the day of judgment he works for the heraft وهو مؤمن and he is in a state of Eman Allah says those ones they are striving is praiseworthy and from the things that you will attain the heraft are the women of jannah the food of jannah and the drinking of jannah الوصية الرابعة عشر the 14th advice is ما جعني الحسن البصريه أيضا حسن البصريه also said يا معشرة الشباب ينكس إياكم والتسويفة stay away from صوفة I will stay away from that صوفة أفعلوا stay away from I will do stay away from that don't have this problem don't have this issue of delaying things صوفة أتوب I will repent صوفة أحفظ على الصلاة I will in the future save God my prayer and make sure I pray correctly صوفة I will I will be obedient towards my parents and upright towards them don't be one who is like that this is called طول الأمل you're giving yourself and you're assuring yourself that you're going to have a long life this concept of a صوفة I will is what really brings about what a person never to do anything and never to hasten and that person will never benefit rather that person will delay and delay and delay and delay that he will never ever come to doing it the قاعدة is don't leave a repentance of today for tomorrow because you're going to have to repent for tomorrow's mistakes as well so today's repentance today's shortcomings and today sins you need to repent for it today not for tomorrow الوصية الخامس عشرة the last and final advice that the pious predecessors gave from the series that we were doing من وصايا السلف للشباب is ما جا عن حفصة بنت سيرين حفصة بنت سيرين the sister of محمد المسيرين أنها قالت she said يا معشر الشباب or youngsters خذوا من أنفسكم وانتم شباب فإني والله ما رأيت العمل إلا في الشباب she said وضي الله تعالى عنها oh youngsters and youth take your affairs whilst you're young فإني والله بايا الله ما رأيت I never saw actions in its complete form إلا في الشباب when you're young والله when you're young and you're a shab it is from من أعظم المراحل it is from the greatest period of time it is called some of the علم I used to call it مرحلة الخيري the stage of good but it's only good in وفق الشباب if the youth Allah gives him the توفق and the ability to benefit from it whereas the other one who jokes around and he plays and he destroys his time he follows his desires and what his nafs is inclined to or he even does that which is حرام العياد بالله he punishes his nafs in committing sins then this person has really caused a great damage to his future he has caused a great damage to his own nafs some of my beloved brothers and sisters may Allah make us those who benefit from this stage that we're in this age that Allah has given us those who recognize its value and its importance may Allah also allow those who are heedless and unaware of the value of what they have right now may Allah allow them to understand and recognize it and to come and to come with it that was all that we could go through and point out وأسأل الله رب العرش العظيمة بأسمائي الحسنة وصيفات العلى أن يوفقنا لما يحبه ويرضى من سديد الأقوال وصالح الأعمال وأن يصلح لنا شأننا كله وأن لا يكلنا إلى أنفسنا طرف تعين وأن يهدينا إلى صراط من مستقيم وصلى الله عليه وسلم على نبينا محمد وعلى آله وصحبه أجمعين وأخر دعوان أن الحمد لله رب العالمين


I'm straight into it. Yes, I was counting on the eye-tracking tool. So I have it running in the local debugging mode and also And I have it as my camera as well, which ways it this way. No, I can't point it. It's like, yeah And it is the same camera Wait, why do I have two cameras running? That's not a good sign It could mean something is wrong Yeah, we we might try the eye-tracking with two cameras at some stage at the moment. There's a problem on the mobile I could not actually reproduce it. So if I go mobile And this is the resolution the dimension of the screen that I have On my mobile device, but it doesn't behave in the same way on my mobile and the video is Well, so it's loading it as a regular website not as a mobile website And that's I think a problem that might be a problem if the width of the This video container in styles as Yeah, this might be This might be an issue The rub flex I'm pretty sure I don't know anything about CSS It's what I have the port for Also the fact that I cannot replicate it Wait, are we calling this CSS correctly? Yeah, so we have one CSS for the entire project So all the website looks more or less the same And then we have another one for a Specific application And I wonder if they sometimes Glash in the actual application. We should not Where is it? Have a video container. Well, wait this Sessions meant to be interactive So if you want to pop your aim Anything in the chat will be more than happy to respond Except questions like where you're from and stuff like that, which yeah, which yeah for some reason some platforms are Encouraging this type of Questions and I don't blame them It's hard to get the engagement And let's check the CSS for Yes, this is the CSS for the whole project Probably be a Minimized Anyway, the main problem is that I can replicate the thing on my in my browser In the browser, it's working. Okay on my phone the overlay They can do like a split view But that that's fine, that's not what's happening what's happening is that the video footage is Is Not starting at zero and then the overlay is Offset I will see. Anyway, we'll see if We did change the code a bit so hopefully just Magically gets fixed Yeah, make sure that the position is the absolute for both the video and the tracking canvas that meant to be Of late it's the of light bit on top. Yeah, but you can change your eye we tied a Height and then the main thing is that the Racial thing Textually makes a lot of difference because it's it's finding the darkest point essentially in that the Region of interest Yes, if you're looking directly at the camera Yeah, it's working better phone for one Then the other And yes, the light in the room will make a lot of difference as well Just do more light and you can actually go Rakes for it Make the ROI smaller She's not looking directly at the camera. That could be a problem as well. Anyway, play around with it And let me know what you think It's on The main page and yes, it's everything all the tools being optimized for desktop not mobile at the moment, so It is work in progress if anyone knows how to optimize for mobile to Let me know as well Last time so we added Yes, we have a bunch of The blogs now it will be good to have this plan out month plot actually display real data Do have just the basic Python code, but that's just generating examples. It's just a random a random stuff a random values We will eventually apply it on to Real e.g. Or e.c.g. Let me know. What do you prefer today? Do more e.g. Or e.c.g stuff Right another thing we were doing yesterday This about section waited a few More pages there's a potential student projects if you have any students that you know or you are a student yourself you want to do a project maybe Send this to your supervisor a One is a many around the doing x AI was explainable AI with biomedical data. No black boxes big no to black boxes explain Everything and know what's inside the box And now project is around visualization which we see can tell highly interested in a Will start doing this resource page. So we actually updated this one a Red window Do some more work on it was actually putting it into a table the table in a sec was called resources HTML it is well run it locally. This was not published yet It's this table that we're still populating yellow the items are unknown even though Should be pretty straightforward to fill the year of release and this has a Data-side comparison thing a number of subjects. Yeah Of course, it's quite important. Some of the subjects are not human. So that's important to mention But yes, obviously once they're not human probably have a Model of some sort of condition a which is You know will require a completely different type of analysis Then we have the data format and yes the math files can be open in Brighton, I do not use muddle up anymore because that's too expensive This one, I don't know why it's unknown a DFS standard format for a AG I Don't know what these ones are If you know what they are Let me know. Yeah, we one big thing is if the And it's quite important to know if the data is raw process pre-processed so on so forth Heavyly process or lightly processed And if there were any additional modalities recorded So we know quite a bit about this neurofist implant data most of the tools on the page From the EEG tools are from that data ECG most of those actually Synthetic a AG like this one Looks real because there's noise added to it, but this is synthetic data. Well, no, maybe it doesn't look real a all the EEG data on the website is this a Neurovist that This essentially publicly available on the EEG org So it's in our website that the old Repos so we have this beat somewhere. Yes, search platforms Is essentially IEG is a search platform It's a It's a rep or not a rep or is it a rep or no, it's a platform and And that's it. Yeah, they just platforms Beat so that other set platforms and Yeah, I EEG Dot org would be one of those. It should go there It does require a basic A login so that's what we ranking the datasets Yes, we have a data set. Okay. I have a study Okay, you have a device It's because highly convoluted isn't it because we too also have devices So I have a recording device say for EEG then that device could have been used for a specific study that had a certain number of patients and The patients for example were in the different groups or healthy controls and Say epilepsy patients then the same device could be used in multiple studies then you have Potentially the data collected from one study being published in multiple Repositories Yeah, so I have to monitor all this stuff How do we make sense of it? Well, we pop it into GPT-4 What we normally do a optical and the actual HTML that we have Sometimes say refusing to Actually look at the links. Yeah, what I was just starting to Interesting it didn't start from the way from the bottom Yeah, we're showing ads on this page Should be okay. Hopefully getting relevant ads Yeah, we have an overview need to check how it looks like on smaller screens. Who knows Yeah, it doesn't look good How do you show tables on small screens? Do ask To rotate the phone or to deal with this late Right, so some of these links Guess I say this thing goes to a does it the specific does it the description On so forth. It's on the picture And This link however just goes Well because it requires a login so for you It will just go to the website and not the extension with the actual data It's no problem with it's no problem of websites that require login That's why there is no login on On my side So it looks the same for everyone Logins just Yeah, add additional complexities like it. I'm saying is Well because it's a link So because it requires a login it will just go to the general website not where the database is actually stored So should go into Platform. Oh, yes If you go scola and this Dataset was used 300 more than 300 times 400 times yeah, that looks like yeah Quite a good paper Reading it when it came up The war story behind launching a venture to treat epilepsy It's quite a Quite a roller coaster this one. Yeah, the data itself is from 2014 or something It's funny how when you sort by date you only get four results. It's really odd And so by relevancy at four hundred forty two results a Some of this data is on Kegel a kegel as well and my son jumping around but the Jumping around Offlit still makes some sort of sense What what work because we're really running something on it running the eye tracker. Don't we? Well, we don't have to do Dead We're running the eye tracker from Okay, no, they are The one that I'm using this face on is on the website. So it's deployed it's a Should I flask? Yeah flask application, right this one Right, so we have this data set it's currently On kegel this competition.  Yeah quite a big difference In this team Published the solution And I have different members did different things They just took all the models Together so one person was doing a 2d model then why did you need a frequency? transform They all used raw a g interestingly they didn't use the images the spectrogram images That's interesting Because the data Yeah was essentially Yeah, I covered this before Go look at my previous videos Yeah, I have the raw G there what the resolution of this thing is not great And then a spectrum essentially for the spectrum rounds for each recording each from a Quarter of a brain leaderboard Sony interesting say The team that got second place With the public score When to place us down with the private data set Private leaderboard is calculated with approximately 65% of the test data Discomputation is complete the very little water reflects the final so this yeah, so this 65 percent of that was not available to the competitors Kind of important to note That's why it's called private Anyway, interestingly the winning team only looked at the voyage you noted the spectrogram The frequency transform I don't know what they mean by to the model Publish this stuff separately today. No, they did take the spectrogram images Stacks kilogram image Still the same data anyway, the point is That we will try and deploy a You know train a fuzzy logic explainable a I thing on the same model and Then Compare it to a one of those models Obviously one, you know best a first place with a second place Don't worry about the actual H. D. M. L Hey, we want to focus on the table. We want to keep placing all the mentioned and potentially new datasets Into the table and yes, I tell you would like for it to be displayed okay on a mobile phone as well But if it's too hot Don't worry about it. The head around small screens. What why? Especially with mobile responsiveness in mind here are some technical suggestions one responsive design Making tables responsive on mobile devices can be tricky due to their row and column structure One common approach is to reformat the table into a more mobile friendly structure using CSS and sometimes JavaScript Here's a basic CSS only technique CSS at media screen and max width 600 px table with 100% display block why this bot is reading the whole The whole text including the code have another bot And in your HTML it doesn't modify each less than TD greater than to have a data label attribute It doesn't sound that good. Then it can Read Just anything you want really Data-driven approach if the data set is expected to grow or change frequently Consider loading the table data dynamically from a server or a JSON file This will make maintenance easier Pagination or load more if the table gets too long think about implementing pagination or load more functionality to avoid overwhelming mobile users with too much information at once Interactive elements for mobile users ensure interactive elements like links are easily tapable good spacing and larger font sizes help Testing regularly test the table on various devices to ensure compatibility and responsiveness Tools like chrome dev tools can simulate mobile devices for this purpose Accessibility keep accessibility in mind Screen readers interpret tables well, but make sure that any dynamic or responsive features also maintain this accessibility Remember CSS based solutions are often more maintainable and less intrusive than JavaScript based ones especially for something like responsive design The CSS method above keeps your markup clean and relies on CSS for the heavy lifting which is generally a good practice for responsive design And not overwhelming our mobile users sounds like a great idea How do we move the table into a JSON file and Pass it correctly on the page Yes load more For mobile users will be great as well Yep Yep, yep, yep Yep Rather complicated as it seem to become Rather seem to become complicated or come on It seemed to become complicated. Hey, can you generate the whole JSON file and Shall we turn it into a flask application? Because we're already deploying some on our server I mean surely this does not need a back end This is the HTML code that I have so far Turning your HTML table into a dynamic JSON driven flask application can make it more manageable and responsive Especially if the data set is large or frequently updated Here's a step-by-step guide to set this up Step one creating the JSON file You need to convert your table data into JSON format This can be done manually or with a script. But for this example, I'll manually create a JSON structure based on your table Turning your HTML table into a dynamic We're going for flask, are we? Create your flask app in your project directory, create a new Python file e.g.app.py and set up your flask application Link to a JavaScript file in your HTML Add a link to a new JavaScript file that will handle fetching and displaying the data Create a div for the table. In your HTML, replace the existing table with an empty div where the table will be dynamically inserted Sounds like we're going for a full application Run your flask application Ensure that your JSON file and HTML template are in the correct directories Templates for HTML and the root or specified directory for JSON Customize the JavaScript function to format the table as per your design requirements You can expand this setup with pagination or load more button for better performance on mobile devices Okay the question is We've back end Will it be fetching the JSON file from the server every time? Is the option of using a CBN a content delivery network is still available Yep When you use flask as your back end to serve a JSON file by default the server will read the JSON file from the disk Every time a request is made to the endpoint like get underscore datasets in the example This can be inefficient, especially if the file is large or the requests are frequent You can read the JSON file once when the server starts and store its content in memory This way the server will serve the data from memory for each request, which is much faster That's how my server works Don't think it will actually be faster If I keep it in memory all the time If you have static content like JSON files, that doesn't change often using a CDN can be highly beneficial A CDN caches your content in multiple geographic locations close to users reducing the load time Using CDN for static files. You can host your JSON file on a CDN Whenever there's a request for the JSON data the request will be served by the nearest CDN server instead of your flask server Flask class CDN in your flask app You would provide a URL to the CDN hosted JSON file instead of serving it directly from your server In memory caching while faster this approach increases your servers memory usage It's best for files that are not too large and don't change often CDN, this is more scalable and can significantly reduce server load and response times for static content However, there might be costs involved depending on the CDN service you use Both methods have their advantages and can be used in conjunction to improve the performance and scalability of your application Choose based on your specific use case considering factors like data size, update frequency and user geography But if we continue with having everything having the table in a HTML format Would it by default be Using a CDN Hosting static files a CDN is primarily used for hosting static files like CSS JavaScript images and even HTML pages Your HTML file with the table can be hosted on a CDN Faster content delivery the CDN will cache this HTML file in multiple locations globally When a user accesses your page the CDN delivers the content from the nearest server location to the user ensuring faster load times Updating content if you frequently update the HTML file, you need to update the file on the CDN The CDN may have a cache invalidation period during which the old file may still be served to users Dynamic data handling if your table data is dynamic and changes often you might want to consider using Ajax to load the data into the table In this case your HTML file with the static part of your website can still be hosted on a CDN While the data can be fetched from your server or another API endpoint Setting up CDN you typically choose a CDN provider like Cloudflare, AWS Cloudfront, etc Upload your static files there and then update your websites DNS settings to serve files from the CDN Performance, faster loading times due to geographically distributed servers Scalability, better handles high traffic loads Reliability, CDNs often have high uptime and can handle server failures more gracefully Bandwidth reduction, offloads traffic from your primary server Not ideal for rapidly changing data CDNs are great for static content But not ideal if your table data changes frequently unless you employ Ajax to load the data dynamically Complexity and cost, setting up and maintaining a CDN might add complexity and potential costs depending on the service provider In summary, using a CDN for hosting your static HTML file including the table structure is a good practice for performance and scalability If the table data is dynamic consider using Ajax to fetch the data from your server and populate the table while the rest of the static content is served via the CDN Data set, data set, platforms, big share, it's uploaded pretty well Some websites from the Netherlands say 4 to U, research data And we have, well, big share should work, we already tested this thing before Maybe not, I'm just a bit slow to load And those are pre-loaded with the EEG in the search This is a nodal electricity demand in Europe This is the best match, let's try an electron cell of photography Right, this is better, flower electrodes It's from, it's pretty recent, the second one is from 2017 Given that this, okay, that works Try and control, not just F5 It's another, seem to show something useful By the way, if you haven't checked out binarykills.com please go to so You will be supporting this project that way A physio net page not found, what? How do I just do it from the, from the URL? I go physio net data, can't seem to be loading data sets only anyway Those, I will check, it's working okay U, net, EEG Right, then we have the EEG portal that yeah, requires login And Google data set search Right now we actually is, yeah, probably the neurovisual implant Because the, yeah, I already said it like 5 times, 10 times But because it has, it requires a login I cannot have the actual link to the data set It goes to the platform, maybe I can Yeah, it's a bit of a broken website It's just loading forever, is it? Yeah, it's hard to search a general non-pleptic It was a pleptic experiment search Nine items, yeah, subject name and day No, that would be, no, that's the study number That must be subject, that must be day One, two, three, four, six, seven, eight, nine But it's a long term, so there's actually a lot of data And this doesn't have a URL, so it's a problem It's a problem, how this website works I think it's sort of designed quite some time ago Era on the server, that's not good Yeah, it can even view the data from here But I would not attempt it, I think it will not work It's safe to assume it is from one, no, one, two, three, four, five, six, seven, eight Eight dogs, to know, maybe It is stable, it's impossible to work with Your list, eight dogs, that was 31 rats Ten normal 25 with cortical infarction Yeah, do I want to know how that model is actually being achieved Probably not, probably not What else we've got, easy or not, that's not good Check, check this on the original, we need to replace it Let's find it, the html, maplipsid assets Just format this document That way it's a bit weird It's the second one, is it? And the link doesn't work anymore, that's the problem Of some of these data sets, of some of these repositories That data sets just might disappear Just disappear So I'm thinking on a server, shall we Considering they were in the public domain With a creative commons license We should be able to keep a copy, mostly human And let's go physiognatig Just to data Why doesn't it say how many There are, it's possible that there are only three Yeah, one of them is open access This one has quite a lot of tasks for a safe Actuation, music, perfume, coffee For enhancing cognitive states, include subjects, responses, reaction times And physiological data, EDA, HR, PPPG, temperature, accelerometer, EEG All this this one published last year End of last year So like a couple of months ago, it's open access It's interesting, but the one that we were looking for It just disappeared That's not good I'm pretty sure it's been used quite extensively Yeah, there's about almost 3,000 publications They mention it, so it's not going anywhere I'm sure there will be other repositories that have it It's particularly in Google Scholar When you are sold by relevance, it gives you 2,600 results You're sold by date, it gives you 144 One of them is three days ago But we don't want that on the older one It's not very useful What happened to the physio? To the physio.net link It's freely available on physio.net.org Is there a link? There is Yep, good luck Actually, I think I might have a copy of it Locally somewhere Should we start another repo? It's only 2.7 GB How did I manage to compress 2.7 into 500 MB? That's interesting I assume those are subject IDs The data is in CSV files Start time Unix time, I love Unix time CDA, sampling rate Sampling rate could be just a variable You don't need it with every entry Sampling time you again could have just had delta t Essentially your sampling rate Instead of having the actual numbers That do not change Why don't they change? It's a bit odd isn't it? Sorry, for red flags The EDA actually changes That's good It's 0.8, 0.9 somewhere It's quite variable Starting of 0 is a bit odd It's probably the first sample can be ignored Because the EEG EEG Right, only 4 electrodes Time stamps are actually changing It's a good sign It doesn't mean there is inconsistent sampling rate It doesn't mean there is a drift in the times between samples Why this is just not a single variable Then we have 4 electrodes Which might be not enough For most tasks I don't know what state is State sound Auditory So it's a response to sound A problem that could be some sort of artifact Especially if the sound is Yeah, there are no problems with sound Being played that could be Actually interfering The EEG electrodes could be picking up The sound Especially if coming through Ear buds that have a magnet But I don't know anything about it It would be interesting to have a look at it Considering it was published recently It's open source Creative commons license So we could look at that Yeah, it's a shame that some data sets just disappear From the public domain It's not good We'll see if we can find it somewhere else I think we actually might have a copy Of the data set ourselves Because all these papers that mention it Yeah, how many papers mention This link 87 Yeah The data set is gonski That's not good Might add Regulation Might add This data set to the mix Can we ask We might continue with the HTML Format for now Can you add the following data set Into the table Sure, let's add the specified data set to your HTML table You'll insert a new row into the existing table structure with the details of the data set Here's how you can modify the table in your HTML You can place this less than tr greater than table row Tag inside your existing less than table greater than tag in the HTML file Following the structure of the other data set entries This will add a new row to your data set table Remember to replace placeholder text like, unknown, with the actual information if you have it The description I provided is based on your link and might need to be adjusted based on more detailed information about the data set Yeah, did you actually Look At the link Rain verbal monitoring experiment Why is it experiment A1? How do you know the quality? How do you know the quality is high? 2020, no, it's 2023. Where did you get 2020 from? Yeah, we need to add the if it's a each I don't think you actually looked At the link Great Let's add this specific data set to your HTML table I'll create a new table row for rain wearable monitoring experiment one a one data set You can insert this less than tr greater than into your existing less than table greater than structure in the HTML The details are based on a general understanding of the data set from the provided link But you should just the specifics like the number of subjects exact data formats, etc. Is necessary to match the data sets actual properties Go back and something Use this link instead Sure, let's add the new data set to your HTML table Yeah, that's more like you will need to append a new road to the table with the details of the data set Here's the updated part of your HTML with the new data set added Insert this row in the appropriate place in your table If you have specific information about the number of subjects data format year of release quality accessibility score data processing or additional modalities You should replace the unknown placeholders with this information Remember for maintainability and scalability Consider the dynamic loading of this data using a back end service or JavaScript as discussed earlier Especially if the data set is large or frequently updated Do I do a scraping like automated scraping Probably not allowed. Okay, we'll do it manually Can we like semi Can we semi automate the scraping of this website can actually look at the website Don't think you are Why there's conflict of interest Rose T. Faggy and MD Raffiol Armina co-inventors of a patent application filed by the University of Houston related to this research to The rest of the authors have no conflicts of interest to declare that are relevant to the content of this article It might finish now, might continue this Hopefully tomorrow or next time Let's just check it there Any questions Facebook Someone watching on Twitch No questions Supposedly nine People probably zoned out On LinkedIn Don't think there are questions Sometimes the platform is just quite bad Anyway, I can't see any YouTube Haven't actually monitored YouTube No, there's nothing in the chat So, yeah, I'll see you next time. Thanks for watching. Don't forget to check out Let me know what you think


Okay, so we finished last time where just about pushed through the calculation of what L squared is as a differential operator, which we did, if you recall, by multiplying the ladder operators L minus and L plus together, and it was rather a tedious calculation, at the end of the day with luck we ended up with this. And we should recognize that this L squared is minus this combination of partial derivatives vector theta and phi is the, it's minus R squared times the angular part of, of del squared, the Laplacian when looked in, when put into spherical polar coordinates. So if you take, if you take this thing and put it here, this minus sign cancels that minus sign and we get a one over R squared sine theta d with theta sine theta, et cetera, which I hope you recognize as, as del squared. So, so you might ask yourself, so physically what's happening? We have that the kinetic energy operator, i.e., so we've got this, this h sub k, which means p squared over 2m, where this is px squared plus py squared plus pz squared, is also minus h bar squared over 2m times del squared. So in the position representation, this operator becomes this, right? Because p is minus ih bar times gradient. And classically, we have that L is equal to v tangential times the radius. So L squared is v tangential squared times radius squared, L squared over R squared is equal to v tangential squared. So we have, we have that hk is equal to, well, sorry, that's suggestive something, isn't it? That this, this nabla squared can be written in terms of some radial derivative plus, so we could say that, yeah, sorry, we could say that hk is equal to some radial minus h bar squared over 2m, 1 over R squared d by dr, R squared d by dr. And then we're going to have plus h bar squared L squared over R squared, I think, just by substituting into there over 2m, sorry, over 2m. And what's this going to be? We've defined the angular momentum operator L squared to be dimensionless. So putting an h bar in front of it, h bar L is the classical animal, right? So h bar operator is the analog, I shouldn't say it's equal to, it's the analog of classical angular momentum, total angular momentum. So this that you have here has the dimensions of total angular momentum squared, it's the classically understood thing, so this term here is, looks, is looking awfully like v tangential squared, sorry, I need a mass here, right? So the classical angular momentum is m v tangential R. So the square is m squared v tangential squared R squared. Move the R squared down here and this is the classical relationship that L squared over R squared is m squared v tangential squared. So this is looking like, this in the back here is looking like half m v tangential squared. That's what this suggests to us. This is a quantum mechanical formula which is correct, but it's suggesting to us that it's this, the sort of natural translation in classical physics is this, and this is clearly the tangential kinetic energy. So this is the k, the tangential kinetic energy associated with tangential motion which suggests that this here should be the kinetic energy associated with radial motion and that's what we want now to put on a firm intellectual footing. So we're going to show that this thing is minus h bar squared over 2m times pr squared where pr is the radial momentum. So the question we want to address now is what is the radial momentum operator? We found the tangential operator, we found it in some sense the tangential momentum operator in the sense L, now we want to find the radial one. So classically momentum is a vector and we can say that the radial momentum is simply r dot p over r. In other words the unit vector r dotted into p must surely be radial momentum, momentum in the radial direction. But there's a problem with this from the perspective of quantum mechanics because this operator doesn't commute with this operator. So it's, well what does that mean? This thing r, so in qm r dot p over r is not Hermitian. Let me prove that to you. It's easier to prove that in general than in particular.  Then let's look at a b dagger. If I multiply these together, what is, I get an operator a b, is this operator Hermitian? Find out. That's b dagger a dagger because the rule for taking Hermitian adjoint is you reverse the order and dagger the individual bits. But b is b dagger and a is a dagger so this is equal to ba. So is this equal to ab? Well clearly it is if and only if b and a commute. So this is only if, whoops, a comma b equals naught. In words the product of two Hermitian operators is itself Hermitian only if those two operators commute. If and only if those two operators commute. So this r dot p which is shorthand of course for x px plus y p y plus z p z would be Hermitian, could be Hermitian only if x and p x commuted, y and p y commuted. Well they don't. Therefore this is not a Hermitian therefore this is not an observable. So it can't be what we're looking for. We're looking for something, the momentum in the radial direction which is, which is observable-ish. All right, well there's a fix to this problem. There's a general fix and we're going to use it but if we do a half of ab plus ba, this is Hermitian, right? Because if you take the dagger of this, this one, we've just proved the dagger of this one is that and the dagger of that one is this so this thing, the dagger of this bracket is itself. So when you've got two non-Hermitian operators, sorry, you've got two Hermitian operators that don't commute and you want to make the product the way to go is to, is to take the average of them, you know, it's a really naive thing to do. So let's do that. So let's, so we try, let's have a look at the Hermitian operator pr which we're going to define to be a half of r dot p over r where it's important that this r here is in front of the pr plus p dot r over r. So this thing here will be Hermitian and I'm going to show that it is what we require. So in the position representation, so we, we, you can do this calculation in the abstract, not in the position representation, but it's easiest in position representation, so that's how we'll do it. So pr is equal to, so this p gets replaced by minus i h bar grad, right? So this is going to be minus i h bar over two common factor, we're going to have r dot grad over r, that's, this of course is the scalar r, plus the divergence of r over r. Well, now the issue is this, when, what, this isn't quite the divergence of this, what this means is, is, this is remember an operator, it's waiting for a wave function to come and stand in front and get operated on, right? So this differential operator operates on everything to its right, it operates on this and it operates on these two. This here, this differential operator operates on everything to its right, which is only the psi. So we have to, we, we, when we, when we expand this out, we're going to get three terms because we're going to get this thing operating on this, that, that's standing idly by, this thing operating on this with this and this standing idly by, and this thing operating on this with these two standing idly by, which is the same as that. So this is going to be minus i h bar r dot grad over r, right? So I'm taking this one that I've got and the one that I'm promised at the end of all this reduction here, so that's where the two went to. So that's, that's those two and now I've got these two bits minus i h bar brackets, we're going to have over two, sorry, that's this factor here, then I'm going to have this thing operating on this, the divergence of r is three and then I've got this thing operating on that, it's going to be r dotted into the gradient of one over r. So that's going to be minus r dotted into the gradient of one over r, the gradient of one over r has to be, oh well, it is the vector r over r squared. This minus sign comes from the differentiating of the one over r, right? Because I'm reminding you of prelims maths now, the gradient of r itself is the, is the vector r divided by r, this is a dimensionless animal because that has dimensions of one over length, that has dimensions of length, so it's the vector, it's the unit vector r and that's what we've been using. Oops, excuse me, so I made a mistake, this should be r cubed, maybe we need to do this, sorry. So what, what, just to fill in here, so the gradient of one over r is equal by the ordinary rules of differentiation minus one over r squared times the gradient of r. But the gradient of r, I've just said, is the vector r divided by r, hence the r cubed. These two dot together make an r squared, which cancel most of those, so, so this minus sign, these two can be combined to a two over r, the twos go away and guess what we end up with is minus i h bar r dot grad over r plus one over r. So that's what this, this stuff reduces to. What we next want to know is, so what is r dot gradient? Well, I want to know what this is in spherical polar coordinates. Well, the thing to do is just to write down, let's write down r d by dr. It's easy to see that that is going to be x, d, well, let's, let's do it, r, then we're going to have, by the chain rule, dx by dr d by dx plus dy by dr d by dy plus dz by dr d by dz. That's just the chain rule. But, but what is dx by dr? You know, x is equal to r sine theta cos phi, so dx by dr is equal to x over r, and for the same reason, dy by dr is equal to y over r and so on and so forth. So this is equal to x d by dx plus y d by dy plus z d by dz, because this is x over r, but this r cancels the r on the bottom, y over r, r cancels what's on the bottom. And what's this, this is a vector product of x comma y comma z with nabla, d by dx, d by dy, d by dz. In other words, this is, this is the animal that we're interested in, r dot grad. So I have now that pr is equal to minus i h bar, r dot grad, we've just agreed is r d by dr, so those r's go away, and we have d by dr plus 1 over r. So we have an interesting result, we have the momentum associated with the radius is not simply d by d radius, like the momentum associated with x is d by dx, there's also this additional term in here. But just to convince you this really is the momentum associated with radius, let's for fun calculate r comma pr. So what is that? That is minus i h bar of r d by dr plus 1, which is r times pr minus d by dr of r minus 1. Yeah, right? Yes, sorry, I mean danger of getting zero on time, that's the trouble.  Yes, yes, yes, yes, sorry, sorry, yes, yes, yes, yes, yes, it's perfectly correct. Okay, so the ones go away, this sort of thing is confusing. Right, now as I say, what does this mean? This means d by dr of everything to its right, and there's a phantom wave function here waiting to be operated on. So this is the derivative of r of psi. When we take the derivative of the r, we get one times of psi, and then the r stands idly by and we do the gradient of psi. The second term cancels on this because r times the gradient of psi is occurring here with a plus sign, and there it will be occurring with a minus sign. So what we're left with is the d by dr times of psi, the d by dr which makes one. So this is equal to plus because there's a minus sign coming here, i h bar, so that it's these two operators satisfy the canonical commutation relations, right, canonical commutation relation. So pr really is the momentum associated with r. Okay, so what what are we really trying to do here, we're trying to show that that one over r squared d by dr of r squared d by dr is essentially pr squared. So let's calculate pr squared. Pr squared is going to be minus h bar squared because there'll be two, there'll be two minus i h bars, and then it's d by dr plus one over r brackets d by dr plus one over r, which is equal to minus h bar squared. Obviously this on this is d two by dr squared. We will get this differential operator, we'll differentiate that and reduce a minus one over r squared. We will otherwise get a one over r d by dr and also a one over r d by dr. So we'll get two of one over r d by dr, and sorry and I haven't finished, and I also get this thing on this thing is a plus one over r squared. So these two terms, these two terms cancel and we're left staring at this. I should have had two of these terms. I think I said I was going to get two terms because I have a one over r d by dr, and I have a one over r d by dr. After this operator, when this operator works on this, it reduces that, but also it works on the phantom wave function sitting over here without standing idly by, so we get two of these. I think I said that but I didn't write it, I'm not sure. So we have a minus h bar squared d two by dr squared plus two over r d by dr, which can also be written as minus h bar squared over r squared d by dr of r squared d by dr.  So yeah, this term here, we've now shown that hk, the momentum operator, which is minus h bar squared over two m del squared is also minus h bar squared over two m of, sorry, of, well, let's leave that outside. Let's take the h bar squared into the bracket. We're going to have a one over r squared d by dr all that stuff, which we've just shown is pr squared. And then, whoops, there was a minus sign, so that soaks up this minus sign, a pr squared.  This is a very important formula that we will need when doing hydrogen, and therefore fundamental to, so it's expressing your kinetic energy in terms of your radial kinetic energy and your tangential kinetic energy. And that's one of the reasons why the total orbital angular momentum operator is important because it encodes your sort of energy of going around and around. So with that, we are now finished with, we can mercifully finish with orbital angular momentum and we can get on to spin. And this is somewhat more interesting in the sense that it's quantum mechanics says more remarkable things to say and it's less tedious because all that stuff with those partial differential operators, d by d theta and stuff is not much fun, it has to be said. All right, so we have identified two types of generators of rotations. The total angular momentum operators and they generate, we introduce them in order to generate complete rotations. So u of alpha being e to the minus i alpha dot j rotates system as on a turntable. So it moves, it moves your system around the origin, if you put your system, it's as if you put your system on a turntable, centered at the origin with its axis at the origin and you turn the turntable around, your system moves through space and it rotates simultaneously, whatever internal structure it has. But we also have shown that Li, the orbital angular momentum, moves system on circles. So it moves it around, physically it translates it around the origin, but it does not rotate it at the same time, it leaves its orientation fixed. And we have some, well okay, so we found the commutation relations here, we found that J i comma J j is equal to i sum over k epsilon i J k J k and we found that it was also true that Li Lj was equal to i summed over k epsilon i J k Lk. They had the same commutation relations amongst themselves, these operators, which is why we could use the work we did demonstrating what the eigenvalues of these could be. Also down here, this implied that M, that J squared has i values J J plus one, for J is nothing a half, one, three halves, etc. And from these commutation relations, we inferred that those are possible values for the eigenvalues of these operators, but we also had the principle that if we wrote, if we translated something completely around the origin, we proved that that was the identity transformation. So we concluded that L, L plus one had to be L equals, L equals naught one two integers only allowed in this case. What we're now going to do is introduce S i is by definition J i minus L i. It's the difference between these two. What does that mean physically? It means that S i is going to be the generator of rotations of a thing about its own axis. So we're not going to be, this rotates it on a turntable, so it rotates it and moves it. This simply moves it around a circle. So this is going to only rotate it on its own axis. It's not going to move it. It's only going to rotate it. That's what we expect to happen, but we'll have to be guided to some extent by the mathematics. Well, it is what is going to happen. Right, so what about the, so what we want to, having introduced these newfangled operators, it's important to figure out what the commutation relations are going to be. Now S i comma S j is going to be J i minus L i comma J i minus, sorry, J j minus L j. We're going to get this, commuting with this, so we're going to get I summed over K epsilon i J k. This commuting with this will produce a J k. This commuting with this will produce an L k. This commuting with this, now we didn't write that down, but J i commuting with L k, this is a vector operator and therefore this thing, when you, when it commutes with this always produces the missing component of this vector. So this is going to be minus L k and similarly this thing on this thing is going to produce, swap them over and you're going to, well there are several signs here that we could hound down, but this thing is, we're looking fundamentally at the same thing as the commutator of this on this. We're looking at minus L i comma J j is equal to, is equal to obviously J j L i is equal to i epsilon J i k L k is equal to minus i epsilon, that's summed over K, this is summed over K of epsilon i J k L k. So, all right, J i, J i k and, but I would like to have this in the order i J k, so I swap those two over and introduce the minus sign to compensate and then at the end and then you can see that this thing including that minus sign is the same thing as this thing including that minus sign, so we have a minus another L k, so this is the justification for that last term there. So what do we end up with at the end of the day, these three L k's collapse into just one L k, it's going to be J k minus L k, in other words this is going to be i summed over K epsilon i J k S k. So these spin operators, sorry did I say that they're going to be the, we call them the spin operators, they have exactly the same commutation relations as the J, therefore we know what their eigenvalues are, so this implies that the eigenvalues of S squared, which is of course S, which is S x squared plus S y squared plus S z squared are S, S plus 1 where S is equal to a half, sorry nothing a half, 1, 3 halves blah blah blah, okay, because these results follow nearly from the fact of having the commutation relations S i comma S j is i epsilon i J k S k. Are the half integer values allowed? Answer, you will have a half integer when J does because L does not, all right, why is that? That's because S z is equal to J z minus L z and J z comma S z equals nothing, which is also the same as L z comma J z, etc. All these three operators commute with each other, so there's a complete set of mutual eigenstates, and if, so we can now see that if this has half integer, this is using half integer eigenvalues, so the eigenvalues of this are going to be, are going to be the difference between the eigenvalues of this and the eigenvalues of this, so if this has half integer eigenvalues, therefore this will have to have half integer eigenvalues because this one has integer eigenvalues, so if J has half integer eigenvalues then S does, correspondingly if J doesn't, S doesn't, it just tags along behind J, and indeed that's how we tend to think about it, we tend to think that the integer amounts of angular momentum come from orbital motion L z and the half integer values, if present, come from S z and that's why J has half integer values, that's how we tend to think about it. And I think I've claimed a few times that spin is something to do with, spin is something to do with the orientation of our system and now is time to make good this claim that the eigenvalues of the spin operator or your response to the spin operators encodes how a particle is oriented, and this is a strange area, a very quantum mechanical area. Okay, so in general the internal configuration of a system could be written, we could write psi is equal to the sum of S m psi S m, we got a complete set of mutual eigenstates of S squared and S z, right, so this is the, so we're saying that S squared on S m is equal to S S plus one, whoops, one of S m, and we're saying that S z on S m is equal to m S m, and there should be a complete set of eigenstates of this, of these, mutual eigenstates of these operators, so I should be able to expand any state as a linear combination of these states, and what are we going to have to sum over, we're going to have to sum over S is equal to naught, a half, you know, and we're going to have to sum over m is in modulus less than or equal to S. This should be a generally valid statement, but for the wave functions or the states of real occurring systems in the laboratory, the good news is, you don't, you only have to, there's only one value of S will occur in this sum, so this is, this would be generally the case, but for systems in the lab, for microscopic systems, this wouldn't be true, so if we were talking about a cricket ball, we would need to do a sum over all of these things, up to 10 to the 40 or something, but if we're dealing with an electron or an atom or whatever, we don't have to sum over all these things, we only, only one value of S has non-vanishing amplitudes, so this is going to vanish for real systems except when S takes one particular value, so for real, for microscopic, microscopic, only one value of S occurs, non-vanishing S, M, psi. In other words, this, we can say at the outset that the amplitude to find a value of S other than a value that's peculiar to the system is zero, so we just don't need to consider it, so we're able to, so we're able to write that psi is equal to the sum from M equals minus S to S of S M psi S M. That means, what does that mean? We're encoding, well the state of the system is described by these numbers here, there will be two S plus one complex numbers, these numbers here, and they're telling us they're encoding somehow the way the system is oriented, so this is two S plus one complex numbers encoding, encoding orientation, and what we want to do now is get some feel for how this encoding works in simple cases. How would you encode the orientation of a macroscopic body? Well the traditional procedure is you use Euler angles, you write down three angles, we should describe how you get some axis in the body, which way it points with respect to the z axis of some fixed coordinates and then how it rotates around that, so you usually encode the orientation of a body in three Euler angles for a classical system. For a quantum mechanical system you encode it in a certain number of complex amplitudes, the amplitudes defined it in various orientations, but it's carrying the same information, right, in a very funny way. Okay, so let's consider the various cases, the case S equals naught, in other words if the only occurring thing here is naught, there's basically no information, there's only one amplitude, naught, the state of your system, and also if you rotate your system, you try and rotate system with u alpha, which is e to the minus i alpha dot s, this is the, so s is the generator of rotations of the system around its own axis, right, so I've written down the unitary rotation that makes me a new system, which is rotated around the axis alpha by the magnitude of alpha, then if I use this u alpha on psi, what do I get? I get, using that expansion, I get nothing, nothing psi times u alpha on nothing, nothing, well let me replace this by e to the minus i alpha dot s, when this operator sees this ket it thinks, you know, nothing doing zero, right, you simply get all of these things, that becomes nothing, so we have e to the nothing, which is one, so this goes back to itself, which is the same thing as psi, in other words when s is one, you can't tell the difference between the system before you rotate it and after you rotate it, it's like an absolutely immaculate and perfect sphere, if you rotate it it stays the same, so a particle that does this, that has s equals naught, so no spin implies same after rotation, so if you like, for a classical animal we would say this is spherically symmetric and there's only one amplitude we need to bother with, so we say it's a scalar, so the simplest particles are spin zero particles, there's just one amplitude which is used to say what the energy is or to say what the location is, because there's no issue of how is it oriented, it's a silly question, how is it oriented, it doesn't have an orientation, you can't tell it, well it doesn't have an orientation, that's the best thing to say, nothing changes if you try and reorient it, and because of the one amplitude business you say it's a scalar particle, right so that's s equals naught, next in the hierarchy and for an example a pion is an elementary particle which is a scalar particle, right let's do s equals a half, so unfortunately there are not many particles, there's not much in physics that's a scalar particle or a scalar field, this is a rare case, the really important cases are s equals one and s equals a half and s equals one and we're all built out of s equals a half particles, right, so this is electrons, protons, quarks, therefore neutrons, a wide range of things, anything made out of an odd number of quarks will be an s equals a half particle, we'll prove that later on, okay so this is the really big class, we have that the state of the system can now be written as, there's going to be a half, a half of psi plus a half minus a half, oh sorry I need to times a half plus psi times a half minus a half, so any state of the system of this particle can be written as a linear combination of this state which is to say that m is, you know, you're guaranteed to get the answer half if you measure sz and a linear combination of this, so we now have a non-trivial linear combination with two possibilities, this is a very cumbersome notation so people don't use it, they either write that this is plus psi plus plus minus psi minus, that's a handy notation, right, there's really no point in writing down this half because the first half we know for certain will always be there and instead of writing a half we write plus a half and minus short n for minus a half or since this is only a boring complex number we often write a plus plus b minus, so any state is a linear combination of these two basis states where we're guaranteed to get plus a half for s or minus a half for s and there are amplitudes so this is the amplitude, it's mod square gives you the probability if you would measure the z components of spin of this particle you would get a half and b is obviously the amplitude mod square of that would be the probability that you've got, sz was minus a half, so let's do some stuff with spin of half particles, so if I take an arbitrary spin operator, well so let that be the, this is the spin component along the unit vector, what is it mathematically it's n dot s in other words it's nx sx plus ny sy plus nz sz this wouldn't this this that I've just written down would apply for any spin not just spin a half and I would like to to do calculations like if I do sn on a psi what do I get I get some new state phi say all right this is an operator I use it on a state I get a new state I want to be able to to do calculations like this we will we'll find this is crucial now we know that this everything every one of these states can be written as a linear combination of plus and minus so this can be written as c plus plus d minus here's sn and this can be written as a linear combination of a plus plus b minus and the name of the game is given the numbers a and b which characterize that to calculate the numbers c and d which characterize that we need an apparatus that does that for us and that's easily obtained what we do to find c of course is we bra through with plus and then on the left we get c plus nothing so we find that c is equal to plus sn plus times a plus uh plus sn minus times b and brawing through by minus we get an equation which tells us the value of d which is equal to minus sn plus a plus minus sn minus b and there's a handier way of writing this we write this as c d is equal to a matrix right this is just a boring complex number plus sn plus that's a boring complex number minus sn plus plus sn minus minus sn minus and that's operating on the column vector ab so here we have a concrete apparatus this is a matrix a two by two matrix of complex numbers working on the given complex numbers that characterize psi which gives us the two complex numbers that characterize phi so for example uh suppose we take just got time to do this suppose we take uh n is equal to is equal to nothing comma nothing comma one then this becomes sz and this becomes s i mean all these sns become sz and then sz on plus is a half of plus so this number evaluates to a half then c d is equal to uh half sz on minus is minus a half times minus but minus is orthogonal to this so we get a nothing nothing and sz on this is minus minus so this one evaluates minus a half of minus so this thing evaluates to minus a half so in this particular case it evaluates to this which people write as a half of sigma z ab a column b where sigma z is the power matrix one minus one nothing nothing a power matrix so these matrices we really want these matrices but it's handy to take the half outside of the matrix uh and write them in terms of these well this is anic this is the first of them and if we had time which we haven't now we'll have to do it tomorrow we will derive what sigma x is and sigma y are the three power matrices that enable us then to write the matrix belonging to any one of these spin operators and then do calculations uh on these so it's it's time to stop


Well, like me, I come from a travelling family. There was six of us in an 18-foot caravan, about six foot wide. You know, we had no room water, no electricity. We washed outside.  And one old lady changed my life forever. Freezing cold day. Come in the sun, she said. I was about 12. Come in, it's very cold. I went into our drawer in room, she had a lovely big drawer in fire. The place was lovely and warm, cosy. I thought, why can't we live like this? I said, what is this? I put my hand on these radiator tights. I didn't even know what they was then. So why is that hot? I thought, why is the side of this house hot? But it wasn't, it was a radiator. But I didn't know. You know, just another machine I'd not seen. And I thought, I want to be warm in the winter months. I want to do this. I want to do that. And if she can do it, I can do it.