Well so I'm going to talk about an aspect of an algebraic aspect of perturbative quantum field theory that's probably beneath the radar for many of you because the kind of quantum field theory that this talk is about is the tree level gauge theory amplitudes and the kind of relevant algebraic structures are quite elementary. They're just leap polynomials and cubic trees but it's so nice, the proof in this talk and somehow the subject of this talk which has been explored only really at tree level doesn't really have any nice simple proof in it so I think it's still worth understanding and some of the things in this talk I think are robust enough that they can help point the way to more interesting things at loop level. So the subject of the talk goes back to the KLT relation in the 1980s which related closed string integrals to sums of disc integrals. So this calligraphic A here is a Veneziano amplitude which would normally be written as some sort of disc integral you know z1 less than z2 etc from 0 to 1 of a multi-valued function zij to the minus sij. If you haven't seen string theory before then don't worry but there you go and then immediately after that people realized that a relation of this kind between a closed string amplitude and two to disc integrals like this implied by taking the so-called field theory limit of this string theory. Excuse me, I think no one sees the paper. If you want people to see the paper you're writing on you need to enable the sound with this device so it will be opine. I think we got it sorted sorry I think it's good now. I think I just managed to pin it for everyone sorry for this delay on my part but I understand now everybody can see it clearly. Sorry. I've also changed my microphone and I hope that this Yeah everybody said they can see the paper now so I think we're good sorry for that. Is it fine now? Yes yes it is. Good okay. So all I was saying is that in the 80s string theorists wrote down they said that a relation like this existed amazingly nobody wrote down a formula so this is a relation which suggests that there's an inner product between the disc integrals that gives you this closed string integral which is a very different integral and nobody wrote down a formula for this SAB until 10 years ago and nobody really proved that this was correct until very recently. In any case a relation of this kind at the string theory implies a relation of the following kinds for field theory tree amplitudes. So if Mn here is the gravity n-point tree amplitude then you expect a relation of this form where a Yang-Mills here is say the partial amplitude of Yang-Mills and I'm going to if you don't remember these sorts of physics terms then also don't worry because everything we need I will bring up and do course. So in 2011 various people Byron Ball, Dan Gard, other people worked out a formula for SAB here which is in terms of the which is a function with a certain weight of these variables Sij which are the Mandelstam variables that arise when you compute these abstractions. So the whole point of this talk is to give a very elementary proof of this formula for SAB which occurs in this so-called double copy relation because there's no this is a reasonably important formula but nobody had really written down a direct path to to give you this straight from field theory considerations. So the the plan at the top then is I'm just going to tell you remind you what a partial amplitude is and then remind you of a few very very old you know 50, 60 year old facts about the polynomials and then I will explain the proof. So hopefully I don't labour the point of this slide too much you can compute Yang-Mills using Feynman rules when you do that you write down Feynman graphs and associated to each graph you you have a product of vertex factors and the only reason I wrote this down is to remind you what the vertex factors look like. So you know the trivalent vertex factor is associated to an FABC which is a structure constant of a Lie algebra usually SUM and these lambda a are a basis of the Lie algebra and there's some invariant traits on the Lie algebra and then likewise the quartic vertex in Yang-Mills is a sum of three terms and each term is the product of two structure constants which you can get by taking a trace of a Lie bracketing of some elements in the Lie algebra with some fourth elements of the Lie algebra here and I've drawn the associated trees so I can think of a Lie bracket bracketing like this or an eminomial like this as a tree and so I've drawn where you know each bracket is represented in the tree as a vertex coming together you see okay so the point of this slide is to remind you that if you were going to be you know computing a Yang-Mills amplitude for the first time at an issue what you would actually have to do is write down a lot of terms and each term it corresponds to a cubic tree in some way you first write down the all the Feynman diagrams some of which are not cubic trees because they have quartic vertices but in the ends you get an expression that looks like this where this sum is over cubic trees which I'll say something about the second and another point to emphasize is that for the tree amplitude of almost any gauge theory you're you're going to end up with an expansion of this form so what I'm saying is not specific to Yang-Mills if I start with some other gauge theory then I and I take the Feynman rules and I expand the conventional expression then it reorganizes in this form where C gamma here is a color factor associated to a Lie polynomial in the obvious way so if I have a Lie polynomial one bracket two bracket three like this then I associate a color factor C gamma by taking the Lie polynomial the Lie bracketing of the associated elements of the Lie algebra and tracing it with some fourth fixed element now I can think of this as a sum of the cubic trees because each Lie polynomial corresponds to a cubic tree one subtlety is that you know the Lie polynomial corresponds to the cubic tree or the binary tree only up to sine and so but the sines are important for me because these C gammas you know C of minus gamma is equal to minus C gamma so what I mean by this sum is that for each cubic tree or for each binary tree I choose one of the two Lie monomials gamma or minus gamma and and put it in here now this is not conventionally how physicists starting with the hadronic physics revolution of the 1960s and then the birth of strength there in 1970s this is not how physicists write their amplitudes the way they write their amplitudes is as a sum over permutations so they write them as sum over a where a is a permutation of one through to n minus one and the this coefficient here a a is related to that coefficient there by a sum a gamma C gamma over all cubic trees where this a gamma here is plus or minus one and we'll there's a natural inner product between permutations and and and the monomials as as I'll explain a second but the point of saying all this is that a a here is what is called the partial amplitude and it's those a of a's which which appear in the in the KLT field theory KLT relation so to explain how the properties of these partial amplitudes I'm just going to say a few things about Lie polynomials these are such well-known facts that hopefully we'll have come across them at some point in in their various guises so the the free Lie algebra which I'll write Lie of a I can think of as being a subspace of the free associative algebra if I think of the associative algebra not as an algebra but as a vector space and the the elements of of Lie of a are the primitives in the free associative algebra with respect to the shuffle code product so that that anyways the is probably familiar to most of you in some form or another what this means is that well I still haven't defined this inner product that I'm using but there's a an obvious inner product on on say on the free associative algebra where if I have two words a b in the free monoid on a start on a a some set then the inner product is is one if a equals b or zero otherwise and so what what the statement that what this statement means is that if I have some gamma which is a Lie polynomial then for any two non-empty words a and b this inner product has to be zero so that's that's probably called Ries theorem for many people and what I'm going to do now is restrict to the setting where restrict to the subsets la or subspace la inside Lie which I'll call the multi-linear Lie polynomials and what I mean by a multi-linear Lie polynomial is just it's a Lie polynomial in which for for each it's a Lie polynomial polynomial gamma in which no word has repeated letters so the freely algebra has you know the freely algebra on on some some integers one two three treating the integers as just letters contains things with repeat Lie polynomials with repeated letters like this but that's certainly not what I want because I want to to be using the correspondence with trees where all of the leaves have distinct labels that that's all I that's why I'm just introducing this notation elevate there's there's nothing tricky there and so then in the context in that context Ries theorem if I think of elevators vector space says that elevators the orthogonal space of of the shuffle subspace shuffle inside w where w is the free vector space spanned by the words with no repeating letters and the shuffle subspace is spanned by the expressions a shuffle b where a and b are not the empty word and so the dual statement to to to this is to say that the the dual the vector space dual of elevate is the quotient w by by shuffles and this explains some of the basic facts that are all throughout the physical literature but they're never really prove that sort of their word their sentence sentences which are given to explain some of these things but Ries theorem implies a number of well-known identities that were were conjectured in the 80s so the the partial amplitude of of any any gauge theory as I said before can be written in this form times where the sum here is over some the polynomials gamma these are some coefficients that come from the specific gauge theory that you are studying and it immediately follows from from Ries theorem that for example a the partial amplitude satisfies this identity you see because because if I put a total shuffle here a shuffle b into this formula then by Ries theorem a shuffle b with gamma zero another identity which let's see so this this as a special case has something called the u1 decupting identity where i is a letter and another another conjectured identity is called the class queer identity which which also follows in a in a nice simple way from from Ries theorem and and a statement about bases for the freely algebra so you you might have come across an alternative characterization of the freely algebra as the image of the of the full bracketing map l so l takes any words and and gives you back the limanomial which is a full bracketing a sort of left justified full bracketing of that word but the and and these these monomials are not every limanomial but the dink and stack waiver theorem implies that these monomials span the freely algebra or in my restricted case this this multi-linear component but the the monomials la where a is a word do not form a basis they're not linearly independent because for example the jacobi identity means that you know that that's zero but you can show that a basis for out of a is given by those monomials full bracketing of a where the word a begins with its smallest letter with respect to some ordering some total ordering of a that you can choose and then dual to that is the basis where I just choose the words a where again a begins on on the smallest letter and and it turns out that these are dual bases with respect to the pairing I described earlier and then the the Christquiff relation follows follows from that because there's a nice explicit formula for for the comb operation l of a word if i is the first letter of that word then the full bracketing of that can be written as a sum over bc of b tilde ic where b tilde is minus one and the length of b times the reverse of b so this is the antipode operation on the hop out the hop out group words and then with respect to the pairing the the adjoint of of of this formula tells you that the adjoint of l so the adjoint of l star is explicitly given by a sum that looks like like this and this is tantamount to an identity which was widely used in physics without apparently being proved which is that the partial amplitude b ic is equal to uh minus one to the length of b partial aptitude i uh b b reverse shuffle c so this is some sum of partial aptitudes on the right hand side and you can combine this basis statement with this nice formula for for the full bracketing to to give you this sort of identity um so uh all of that is is is supposed to be just saying uh reminding you of of some classical facts um and explaining that they have an elementary um that they were known by physicists in a very elementary form uh and the reason they the reason that physicists knew about these identities even if they wouldn't know really how to prove them is that uh the physicist is constantly computing with these color factors uh which involve totally practice um and so so now i'm going to uh explain how you can um in a very elementary way just find the the KLT matrix that um uh was was first uh written down at least 10 years ago um um and uh to do that uh uh uh just let um really just a tiny bit more uh notation just so um for for a subset i uh let little s sub i be the mandelstam variable associated to i um and so in uh you know for mandelstam what that meant was that uh uh s sub i was the the rents um norm of the vector uh that you get by summing over the momenta uh case of i inside that subset and so it's clear from that definition that s sub i has an expansion like this um where uh we sum over all pairs ij which which appear in i um and i'm assuming here that the the vectors the momenta ki are uh individually null um and then the kinds of functions that so functions of mandelstams arise in in amplitude computation but the kind of functions that arise are um are the form uh the kinds of functions you expect are in the uh the rom ring with s i uh sub i as the as the variables uh but modulo this relation here um so you don't expect to see functions like one over s12 plus s23 um because s12 plus s23 is not a um uh can't be written as some momentum uh k squared uh that you do expect to see functions uh where you have um one over s123 for example uh and these satisfy uh these relations and in particular the the kinds of functions that we really expect to see are related to to cubic graphs um and so right for for some uh limonomial gamma uh write s gamma for the product of the the s i um where you take each each i which arises as an edge of the corresponding tree so for example um you know one two three is is a is a limon limonomial um um uh actually it's a sort of a too boring one um this is a slightly less boring one uh and the associated tree would be this and you see that there are um there's one two internal edges and i'm going to count the root of the tree also as an internal edge um and the associated subsets to for the for these internal edges are um you know two three for that edge one two three for that edge and then uh one two three four for the root and so associated to this limonomial is the uh is the Mandelstam expression s23 s123 s1234 um and this would be the the product of of of propagator factors that arise if you were computing the the conventional Feynman contribution um from a cubic graph like this uh obviously the so the the propagator contribution would look like one over s gamma and you would add back some i epsilon so so um and then the uh so with that with that notation if the s gamma understood the um klt relation is actually a statement about uh this object here which i'm calling t uh and um which i saw in a talk that Mikhail Kopranov gave uh which he didn't prepare but which he uh he for i don't know how it happened but he stumbled on a room of physicists and had a conversation with a few of them and um and gave a talk on the back of it um and this this object t here is if you like a sort of prototype um of the gravity tree amplitude it might not look like the gravity tree amplitude but the reason it's a prototype is because it has all this it has the same uh pole structure you see because this is a sum over cubic trees again i take each tree each tree i choose either the limonomial gamma or the limonomial minus gamma um and so i i have and these uh one over s gamma factors uh contain all the singularities of the of of a gravity tree amplitude it's just this this numerator uh which doesn't look like the tree amplitude um and so uh because this is some objects then in la tensor la with values in the ring of Mandelstams um but it turns out that there's a um there's some homomorphism from la to uh a space of appropriate functions of of um of Lorentz invariance uh such that n tensor n acts on t to give the gravity amplitude um this is something that is not proved to my satisfaction but is proved to the satisfaction of a number of uh uh so to speak friends of mine and if even even if it's proved or even if they think it's proved i think uh uh everyone agrees that somehow the that map is not very well understood um but this anyway is the prototype of the um uh gravity amplitude and then the prototype of the yang millers amplitude or or the partial amplitudes for any gauge theory um are these t of a here because i can think of t as a map from the uh the dual of the lee lee monomial space elevator uh to elevate um just by taking the inner product with one of these factors uh of t um and so uh yes so so i i obtained this map from h t of a this has the prototype of um a prototype of the partial amplitude uh and the big claim is that t is invertible and the inverse of t is essentially um tantamount to the k l t matrix or in other words tantamount to the k l t relation um and so in order to see that t is invertible uh there's um a really charmingly um simple um uh thing that you can you can show which is that there's a very natural looking lee bracket on the uh dual of the um the dual vector space of the multi-linear the algebra so uh here i'm suppressing that i what i really mean is elevator dual tensor the ring of mandel slums um and there's a lee bracket uh on elevator dual and you define it inductively in the following way so if i have less is i and j then the lee bracket of uh then the the braces of i and j is s i j times i j uh and that might not look symmetric uh but remember that um uh l la dual here is um is is this quotient space by shuffles so in particular i j is equal to minus j i um in in all of a dual so so this is some anti-symmetric bracket uh and you inductively define it uh in this way um and you have a so so here if you have a letter two letters i and j and two words a and b uh then you can expand it like this and there's an analogous relation to b um and so an example would be for a word a uh the curly bracket of of a with i is this sum over the concatenations of the word a where s i c here is the sum of s i j where j is a letter that appears in the word c um and so it's not obvious that this is a lee bracket it's not obvious that this is a bracket you even uh care about yet uh but the the reason you care about it is that it satisfies this very nice property uh which i've put in a box so t of braces a b is the ordinary lee bracket of a and b where t is the is the map i defined on the previous slide uh which goes uh which which is the prototype of of partial gauge theory amplitudes uh in particular i can nest this relation so t of curly one two curly two three sorry three four uh is the lee bracket one two is the limanomial one two three four uh and more generally i can write uh if gamma is a limanomial i can write braces gamma for the uh expression in the uh in in the dual which i obtain by writing gamma as a nested bracketing of commutators and then replacing every commutator by a uh a pair of braces braces instead uh so for example uh going from here to here i can go from there to there by replacing every set of brackets by set of braces and then the claim is that the map which takes a limanomial gamma and returns the uh expression in the dual that you obtain by uh replacing the brackets with braces uh that this turns out to actually define a map from l to its dual uh it's not quite obvious that it defines a map because you don't know that this this this curly lee bracket is a lee bracket and so it's not obvious that um what i've written on the first slide is even well defined um but it turns out that it is the curly braces is a lee bracket and uh s is the inverse of t and in one direction it's easy to see that s is the inverse of t because um uh you know if if i take uh uh t of s of gamma that's just t of the uh gamma with braces in it but just as i wrote on the previous page by nesting this this nice relation which this bracket satisfies um t of that curly gamma gives me back a limanomial gives me back the limanomial i started with but uh you can you can you can go in the in the other direction as well um and then the the um so so this is the main result um and then uh an important mark in fact is that the matrix elements of of this map s are indeed the um so on the first page i i wrote uh the the formula that that had been um uh laboriously arrived at by by this group uh and there there this formula here uh turns out to be a formula for the matrix elements of the map that i've just written down um so to be somewhat precise so uh if i if i take uh the the the full bracketing with the curly braces of of word a uh then that's some expression in the door and so i i can write it in a basis making use of the uh of this particular basis uh where i choose some ordering and then i sum over words b such that they begin with their smallest letter um then these here uh if i write them s a b uh these are the physicists or the the are the sort of uh conjectured formula um that i wrote on the on the previous page and um so so that's the uh that's the first uh thing to say and then the second thing to say about the main result is that uh it implies the the klt relation uh in the following form um which is to say that if i write t again and remember that this is the prototype um gravity amplitude to sum over all cubic trees like this uh then i can write that as a sum over over over ordering to a and b again um restricting to orderings that begin with their smallest letter um uh times times these coefficients s a b um and so and these are the putative uh yang-mills amplitudes um and so this expression is the klt relation and i should say that it's actually slightly stronger than the klt relation as the physicists say that um because these involve words of different lengths so it's um uh a slightly different statement that it implies the physicists statement um and eric stoner's video on which means that i will stop sorry heli i i think you you finished greatly on time thank you thanks heli for the talk um so everybody's invited to ask questions um i i had one which i mean first of all i thank you for this very clear presentation it cleared up a lot of confusion i had from listening to what physicists say sometimes about these things um but i was wondering all the structure that that you that you exposed here um in this tree level case i mean when i think of loop level i still have all this lee algebra as the color structures flying around and there must be a lot of structure in there so i'm just curious uh when you go to loop level what how much of these kind of structures do you think extend in some form or another uh yes i think the the the key thing is um uh the key insight here is that it's interesting to to study these um uh well i i should say first that the the the the algebra uh the the lima lee polynomial story immediately goes away at at uh at further orders in the perturbation series you don't you don't have um the the the color structures don't um uh don't correspond to lee polynomials anymore um but it i think the the story you'll notice doesn't depend on the specifically algebra i'm choosing because i'm i'm just trying to use the uh the nice word combinatorics properties of lee polynomials and there there isn't you could do analogous things at loop level so the main main structure in this story was uh if you like t uh ab i haven't written that in this formula but these are the other if you like sum over all gamma which are compatible with both orderings a and b times one over s gamma and you can consider an analogous object at at all orders in the in the gate theory um uh perturbation series except that there what you're doing is um uh and it takes a while to work through you know it's it's the old story you draw quark graphs with um uh you know ribbon graphs and uh associated to ribbon graphs uh associated fat graphs or surfaces and associated the surfaces uh color structures and so on uh but when you do that you get uh t's labeled by marked surfaces um and these two marked surfaces can have different apologies uh and i i strongly suspect that if you study these t's enough uh you you should be able to formulate nobody's really formulated what this should be uh at all orders so i think the question is how do you formulate it and you can study these which i think is proxy yeah thank you edley um i don't see further questions right at the moment so let's thank edley again


Let me give a quick introduction to the panel and what this is about. This is really talking to the bigger picture on how society will change and open up and what opportunities and challenges lie in this area. Panelists will answer questions from their specific points of view, as managers of large tech organizations, successful open hardware makers and representatives of the community. So thank you very much. I don't know if we can get to the panel in a moment, but by the way, I was wondering what do you think about the music in between? Like do you hear it? Do you like it? Yeah? Thumbs up? Show me thumbs up. Yeah? And who thumbs down? Anyone thumbs down? Really? Seriously? So please talk to me later, William. Yeah? Actually, I wanted to have this music for years. It's Fibucci, yeah? And you can check it out. So later it's a lot related to India, and I like the Indian drum rhythms, so I'm very happy we have it. And yeah, so always related to tech and mathematics, I really like these connections to music, and we also have a lot of connections here in this panel. So thank you for joining the panel to the panelists, and I would like to introduce the panelists. Even some have already been introduced, so the panel is titled Business, Government, Science, What Opportunities Does Open Bring to Society? We really wanted to keep it broad as a topic because there are a lot of different perspectives here in the panel. So next to me is Bunny Huang. Bunny is known for the Xbox originally, but that's actually quite a few years ago already, and we've heard a talk from you today. So you are also a mentor for our community here in First Asia. We always like read you somewhere and try to get some feedback on our projects, so we really appreciate your feedback and the projects that you did, and we heard already a little bit from you. So thank you very much. Then actually I should have done that first, introduce actually Hong-Fuk, because Hong-Fuk is the only lady on the panel. It's not that we are not trying, but we need more ladies in tech, and I'm happy as well. Just like Harish said today that we have more and more ladies joining, but Hong-Fuk, you also have some feedback on this panel because you're not just working with the community here in First Asia, but you also work with companies. For example, last year, there were some engagements here with Daimler, Jonas is here as well, but also with Zalando and other companies that you're working with. So you also have different perspectives to what open means to different players. So thank you very much for joining as well. I think we can also give a round of applause, and also for Bunny, Bunny is also doing good work. Amazing. Thank you very much. And then we have Shankar V. Selva-Durai. I'm always getting Indian names wrong, but you told me before, we talked before, so I hope I got it right. And Shankar is the Vice President and CEO of Cloud and Cognitive Software of IBM. And you lead the technical organization that helps clients across Asia Pacific to explore and co-create cloud-based solutions that leverage data, analytics and AI capabilities to deliver better decisions and outcomes. So I noted it down here for me. So while leading teams varying in size from six to over a thousand, I think very different kind of style, you have to work with different teams. And you did this in North America, Europe and Asia, so a global citizen. You also told me that you were born originally in Malaysia, but then grew up in the UK. And then almost you have a very long story, so I think you have the chance to tell us about this a little bit later, but you also hold a Bachelor of Science and a Master of Business Administration. So even here, you also combine different roles. Thank you very much for joining. And we have Dr. Graham Williams here. Master of Data Science at Microsoft. And Graham has been an open-source developer since the 1980s, with early contributions to Emacs, Tech, Debian also. So I guess you know Martin, yeah, and R. And you are the developer of various machine learning toolkits. He remains a strong advocate for open-source and is a practitioner, researcher and educator in AI. And his current role with Microsoft, he leads a team of data scientists working with business to implement machine learning solutions and to drive open-source product development. And you are also an adjunct professor at the UC in Canberra, Australia, and have written many books on the AI topic. So thank you very much for joining. And finally, Carsten Heitzler. So probably many know you, like many who have been to the first Asia summit before, but also to other events. We can meet you at many events. And you worked in Linux and open-source industries for 20 years, more than 20 years. But you also started originally actually as a community contributor to the Enlightenment Desktop and Window Manager project. And you have written lots of graphics-related code for X11. And that's 20 years of programming mostly in C and assembly on top of Linux, shipping in, now listen, 100 million devices around the globe. That's something. So big round of applause. So we see already that we have different perspectives. And for me, the perspective was in 2009, President Obama said that openness prevails. So I don't know if anyone was here in 2009 and remembers how the time was. It was all about openness. There was the Freedom of Information Act at that time. And it was the time when First Asia was founded. So it just fitted perfectly into that time. And a lot of politicians were talking about this. And for us, as an open-tech community, it was just natural. It was just logic that we should have open-source software, but also like information about how the government is doing, about open science and so on. Things should be accessible. And not just out of a theory, because actually out of a collaboration model. We just heard the talk, how in Debian, it's not mainly only a software project, it's like a global community. You have connections everywhere, you have friends everywhere. So this is very natural for us. And the question now is like, what does this panel have, like, how is the background of this panel? So openness for us is not just an idea, it is the basis for collaboration in the false community. For example, imagine we all have to sign NDAs. We all have to sign copyright agreements. Would we have ever worked together? Maybe many wouldn't have. It would just be too complicated and it would cause a lot of overhead. So it really enables us to collaborate. So in this panel now, I have a few questions. And I would like to get insights into how this idea of openness changes your daily work and changes the work in your organization, or in your community, or in your life. How it changes your development, your communications, tools and technologies, and how you work together. So I think we have the biggest contrast here, right next to us. Bunny comes from a very open model, then also going into business areas. I saw some of your projects on crowd supply. And we have another area here, which is more from a corporate perspective. And I really don't know who to start with first. But as you haven't had the chance to say anything today, I would like to give Shankar here the opportunity to say something first. So about openness in IBM. I think that microphone should work. Yeah. Yes. Yes. Yeah. Is it working? Yeah. Can we switch on the other mic? Yeah. No. No, no. Is it working? Okay. Sorry about that. That's all right. You guys can hear me? Yeah. Well, thanks. Thanks for the opportunity. Before I start, I just wanted to do a quick poll here. Can you put up your hands? How many of you are aware of IBM's involvement in open source? Okay. So 50%. Okay. That's pretty good. I was expecting lower than that. Some people may be thinking that I'm here representing IBM because we recently announced the acquisition rate had. That's a relationship. But actually, I just want to put in context, right? So IBM has been involved in open source way, way before it was cool or lots of people were talking about it. So this was probably 20 years, more than 20 years ago. In the 90s when we helped establish the Apache Foundation and then the Eclipse Foundation and then the Linux Foundation, right? And when we did that, right, how we supported the communities and projects was that, first we either committed money to it. For example, in Linux, we invested $1 billion to the Linux Foundation. We committed, make significant code contributions. For example, the Apache HTTP server, the Eclipse Java IDE framework, and more recently the high-pledged fabric, right? We also dedicated resources to this as well, right? For example, technical resources, engineers, developers to contribute code on a sustained basis as well as lead projects, some of these projects, right? And we also provide legal help for these communities in terms of writing those licenses as well as supporting them in marketing activities, right? Because we've got to create the grantors around open source and some of these projects, right? One interesting we also do is that we also arbitrate differences within the community. A good example would be Node.js, right? There's a point in time where the folks in Node.js in the community had differences of opinion and they were about to fork, right? And they came to IBM and we helped arbitrate so that it came back together, right? So those are some of the things that we've been doing, right? And in the last five years, we've actually ramped up further our investment commitment to open source, right? And this is from enabling enterprise capability in open source all the way from Cloud Foundry to Docker, Cloud Data Computing Foundation, Kubernetes, TensorFlow Node, I mean hundreds of projects, right? But from a monthly perspective, right, we're looking for a month, right? We are contributing to about 400 projects in the open source community at any point in time. So that's a real brief around IBM, right? So I just want to touch a little bit about, you know, how does IBM, you know, why is this important to IBM, right? But before that, let me put it in context, right? What's happening in the industry today is that lots of, and I'm speaking from enterprise perspective because that's where IBM is focused on, okay? And if you look at that right, enterprises today are, most of them are going through some sort of digital transformation, right? And that digital transformation is expected to drive innovation and growth. But the innovation and growth doesn't start with the CXOs or the guys at the top, right? It fundamentally starts with the developers, the coders, data scientists, basically the folks who are here, when you guys, you guys are the ones who are fundamentally driving that innovation and growth. In fact, in recent research, right, the study says that 95% of IT implementation today are influenced by developers like yourself, right? And half of that are actually making buying decisions. So, you know, out of that whole lot of developers, 50% are contributing to open source, whether in their individual capacity or part of a company, right? So now you know, right? Developers contributing to open source driving innovation. So that's kind of intuitive, right? Innovation power drives open source is kind of intuitive. The concept that all of us together are smarter than any one of us, right, makes sense. And you cannot drive that pace of innovation without a collaborative development effort. But what is not intuitive or not obvious is the economic benefits of open source, right? And let me put that, let me illustrate to you guys, right, for example, right, in IBM, and I'm bringing IBM Context here, you've got IBM engineers participating in these open source projects, right? And they take that, we go back to our products and put it into our products, and then we enhance it or incorporate enterprise capabilities, scalability, availability, reliability, all those things that enterprise need, right? Then we take that product and then sell it, right, and we make profit, right? We make profit, sell it to the customers, the customers come back and tell us feedback, give us feedback, or additional requirements. That's where the reinvestment happens. The same engineers go back into the community and now make the project even better and in turn make the product better, right? And that drives even more profit, okay? It creates a whole new market because we create a new product. We've got creating more of a shareholder value, right? And that cycle again, right, continues to expand and accelerate. So that's the power of innovation and in turn the economic benefits of open source. And in IBM, what we're doing is that open source technology is fundamental to everything that we're doing from a strategic perspective, whether it's cloud, data, AI, even quantum computing, right? What does that mean? It means that open source, open data, open standards, and an architecture that is open by design. So if you take a look at our cloud platform, we're incorporating, we're trying to drive commonality of platforms across private and public cloud, whether it's our cloud or anybody else's cloud, leveraging containers and Kubernetes. And you heard my colleague earlier on, Rahul, talk about how we're leveraging open source and AI as well. In blockchain, we're driving the leveraging, the hyperlegia fabric, right? Even in emerging technology like quantum computing, we have opened up the quantum computing toolkits like QuizKit to the public, right? And this is, you know, I think it's critical because even in emerging technology, we strongly believe that the open approach is much better than a proprietary approach, right? So, you know, that's sort of a brief on, you know, why from an IBM perspective, right? I just want to add a couple of more points here, right? So you made me thinking, is this just a vendor play? No, it's not just a vendor play. It's not just a community play also. It is now, I think, it's an enterprise play because enterprises now, large organizations, not just technology providers, are invested in open source because they are realizing the reward and the benefits and reaping the benefits of open source innovation, right? You look at AT&T, Morgan Stanley, all these organizations, even the space program, right? You look at NASA, they've opened up the code for the mass robo program to spur innovation from the 24 million developers that we have across the world, right? So and the enterprises are not just doing for the innovation, right? They're also trying to reduce vendor lock-in. They're trying to reduce vendor lock-in, increase interoperability, portability, as well as, and I think fundamental to this is they have access to this mass pool of developers in the open source environment who are driving innovation for them. So that's a little brief around how, from an enterprise perspective, from a company like IBM perspective, how open source is benefiting us. Okay, thank you very much. It was kind of a good circle from a corporate perspective, but I also remember years, maybe not so much IBM, but other companies that had a different opinion about open source, and Graham is smiling already. And yeah, and like I also know your story, right? I mean, we heard about it like that you have been a contributor for many years to free open source software. So for you personally, this is also a very personal story because today you're working for Microsoft, and it would be very interesting to hear a bit of your story, how things have changed over time, and how you ended up actually working for Microsoft today and being convinced that this is a good thing, right? Because you're really were in the freeze of a community or are a member of the community, and yeah, maybe you could share your personal story. Thank you, thank you, Maria. So I do find myself in a company today that I spent most of my life fighting against. Indeed, to the extent that my children grew up with no Microsoft in the household at all. We were a completely open source family, if you like. And I date my involvement in the open source community back to the 1980s. Back in the Australian National University in those days, Andrew Trigel was there with us, Paul McCarras, Martin Schwenke, Martin Schwenke and I, and Martin is in IBM. Martin Schwenke and I developed one of the first packaging tools for Emacs, and given that we have precedence of a poll, how many Emacs users are in the audience? Oh, so few. How many Vi users? How many Vi users? Hey, wrong conference. How many VS Code users? Wow, that's a good number too. How many VS Code server users? Does anyone know VS Code server? So check VS Code server, just recently browser based. All of them are open source tools. So I started off, I stuck with Emacs, Emacs can do everything that Vi can do and more. But still alive. And still today, use Emacs and purely open source stack, I've been involved in the LaTeX community as well, setting up CTAN, CTAN the precursor of CRAN for R, C-PAN for Pearl and so on. So I've spent 30 or more years very much in the open source community. And I brought open source to the Australian government's data science capabilities 12 years ago. And it's a fairly telling story. Actually, before I tell that story, let me tell a story from the 90s when I was working with our Department of Health, which really underlined for me why open source is so important. We were developing AI based systems. My day job is a machine learning researcher, AI researcher. We built AI machine learning based tools for health in Australia, Department of Health in the 1990s. We used a tremendous, a really advanced tool at that time. It was IBM's intelligent miner. Really nice tool for doing data science, data mining and so on. We implemented a system for the Australian healthcare to identify fraudulent behaviour amongst medical practitioners and amongst patients. We implemented that system, deployed it. Fortunately, and we had really good relationships with IBM, I should say. Unfortunately, as with many products and any vendor, they decided that that product was end of life. Maybe it was before its time. It was end of life and we had spent in the department millions of dollars investing in that product. And we came to a dead end. Now we could use the product, but we couldn't develop further on it. We couldn't get into the source and maintain it and so on.  And that was a very costly experience for us. And that really reinforced for me the importance of open source. And another thing I kind of probably want to get out of my system is why do we have F at the beginning of FOSS and the question was raised earlier on today. I think a lot of you in the audience were probably sharing with me that actually F is not free as in free beer. It's F as in freedom. And that's the most important thing for me about why open source is so important. It's the freedom that it gives me and my teams and developers to innovate and to use that software in ways that we want to use it. Now of course, and so I was going to tell the story. 12, 15 years ago I joined the Australian government from research organisation Australia and they wanted me to build their analytics team. They had 150 data analysts. I was purely open source. They had already gone through the procurement process. They acquired SAS. SAS, what's called minor, something minor, enterprise minor. And they asked us to come in. I set up a team, mostly open source people from researchers. And they sat us in front of this commercial software and asked us to stop using the open source software that could already do more than what this closed source software could do and just use this commercial product. And it took me three years to build infrastructure. The first open source stack of using Debian across Australia. We set up a network of servers running Debian and an open source stack to do data science and took me three years. And a lot of that three years were spent fighting the IT department, if you like. And the fight with IT was around, hey, we've got a standard operating environment. It's Microsoft. Microsoft is telling us open source software is really, really dangerous. This was the Halloween times. This was the Microsoft CEO telling open source people how bad we are. We're communists. We are against American society. That's probably exaggerating it a bit or maybe not. But it was a really challenging time to convince our IT departments that actually open source software is so much better and more secure. We can look at it. We can innovate with it. We can change it. We have the freedom to do what we want to do with this software. And that's been my mantra forever, really, that I want the freedom to do with the software what I want to do to innovate. So three years ago, I was finishing up my time with the Australian government. And Microsoft came knocking on the door. And hey, this is ludicrous. Publicly, I'm very anti-Microsoft. But they were knocking on the door and spent some time convincing me that Microsoft today is a very different company. And I'm still there after three years, which still tells me that, okay, I'm convinced that there's a massive cultural change happening. And to me, I think open source will win always in the end. Microsoft is a very big open source company today. Now, of course, I'm from Microsoft, I'm paid by Microsoft, I'm going to say that. But I stay with Microsoft because I truly see that transformation happening. Microsoft wouldn't buy, wouldn't purchase GitHub if it wasn't in that transformation. Microsoft has always been a developer focused company. It kind of wants to be the platform for developers. And previously, it wanted to be the platform for developers and make the developers only use whatever they produce. It was a closed platform, it was their platform. It was Microsoft and nothing but Microsoft. Under our new executives, that culture has changed dramatically. It still wants to be the platform of choice for developers. And everything we're doing now is to support developers. How do we support any developers, whatever platform they're developing on? The other side of it, of course, is purely commercial. You look at the cloud. What's a major percentage of the operating system running on the cloud is open source, is Linux. A major percentage of that is Ubuntu. Debian has a strong presence, of course, Red Hat and Fedora also have strong presence in the cloud. People are saying, we want to use Linux on the cloud as well as Windows. And hence, from a commercial point of view, from an Azure and a cloud point of view, we make money out of Linux on the cloud as well as Windows on the cloud. And that's kind of the platform future for Microsoft. I have a team of data scientists, machine learning, AI people, part of a team worldwide, there's 60 data scientists in our group. All of our work, all of my work is open source. We work with customers. We use R and Python, deep learning algorithms, my favorite and research areas around ensembles and decision trees. All using open source and only open source software working for the enterprise customers. Everything that we learn, most importantly for me, we feed back into the community. So all of the work that we do with our customers, not the intellectual property that relates to the competitive advantage of the company, but the intellectual property that relates to the technology that we're using to develop that intellectual property for the company. So that algorithmic development we publish in GitHub in open source. We have recommendation toolkits that we publish, computer vision toolkits, a large collection of open source software to support the data scientists. But more than that, we're also trying to see how do we empower everyone to do AI and machine learning. Everyone's talking about AI machine learning at the moment. I've been in the community for 40 years. This is the fourth surge of interest in AI machine learning. But how do we get that technology into lots of people's hands? We do that by packaging and sharing things. And as I mentioned, one of my first ever open source projects was how to package packages for Emacs. I've been involved with CTAN, Comprehensive Tech Archive, packaging packages for LaTeX, packaging packages for R, packaging packages for Debian and so on. I wrote a utility to support the administration of packages in Debian and Ubuntu as well. So I've always been about how do we package up things to get that out there as easily as possible to anybody. And to that extent, I need to wind up. But to that extent, I might just advertise. Saturday I'm talking about something called mlhub.ai. Feel free to visit it. It's a concept of how do we package up and share all that we learn as data scientists back into the community and in five minutes demonstrate lots of different technology. So I invite you to come to that talk and talk to me more outside of that. But let me just finish to say, open source, I think, has one visual studio code is an open source project widely used by the developer community. And the most interesting thing I see is Emacs and Viya users going to VS Code and telling them I'm still Emacs. But they go to VS Code and say, this is the best IDE that is out there. It's open source. And it's got commercial development behind it. A little bit of a plug there. Thank you. Well, thank you very much. There were a lot of projects that are open source. It's really exciting. I got the question before when Microsoft will release GitHub as open source. Do you know about it? I mean, yes or no, it's sufficient. I have no internal knowledge. I've asked the question myself, too. It's a really interesting plus many other products within Microsoft. There is a pipeline of discussion and products that are coming out open source. OK. Thank you very much. One word I have heard a lot from you was change. And I think I would like to have a talk about this because you are working with companies. And companies are not just like that they release code as open source, but it also changes the way companies work. I know that inner source is a big topic here. So what do you observe? What is changing inside companies when they use open source products and collaborate with the open source community? How is that going? And maybe there are also some challenges. What's your view on that? Before I answer that question, I sometimes use Visual Studio code. I'm not a user. So the reason I mentioned is because I think that the value of force for me is more about collaboration. And it really unites us together. No matter what background or status you are, which level now we are independent from community, from cooperation, from enterprise. It was a life-changing experience for me. I wasn't trained as an engineer.  When you are inside the open source community, people are really collaborative. And the patients show you what to do. So last week, I also wrote a script about how to remove WK and different functions in Expressions. So I feel that I also can be a developer. I'm interested in technology. And we don't look at the people based on their status anymore. So you are here, we're all here together. When you want to, I'm sure that if you want to approach Senka or William, maybe you don't meet them in a daily basis. But because of force, everyone here is equal. We are together. We can do things together. And Mario mentioned that, OK, I'm a female. I should be introduced first. I don't care so much. I just want to be the same as anyone else here. We try to be inclusive, method of community inclusive. And so back to the question, what I see in companies a few years back, we focus a lot on the community. So when you go into the forced Asia event, you see a lot of developers. But the situation is also changing. So companies now, so in some community, they have the feeling that, OK, I only want to be close to our developer and company. They always do the bad thing. But it's actually not the case right now. As Dr. Rahams already mentioned, IBM, Microsoft, they contribute a lot to open source. 50% of the audience learn about open source at IBM. How about the other 50%? The reason why? They did not talk about it so much openly in the past year. But more and more companies started to focus to do more outreach. They want to be connected with the community. And there is a term Mario mentioned, inner source. So what is inner source? Inner source is applied the concept of open source, how people develop in the open inside company. Because they believe that when people in different departments and divisions in the company work together, they can become more efficient. And I work with Salando now in Germany. This is a big e-commerce platform in Europe, similar to Amazon, if you know of, but focused on fashion. And the company actually released a lot of open source. What I learned from them is that sometimes cooperation or enterprise, even though they cared about open source, they want to contribute to community. There's a lot of legal compliance issue that you need to go through, so that delays the entire process. So the trend that I'm seeing right now is that companies work together with the developer community to work on solutions to make things easier for the corporate to contribute to open source. There are also a lot of automatic toolings that allow you that guiding, do all the compliance check, so that have your internal developers or department easily release some software to open source. And also, like Dr. Ramon only mentioned a lot, there's so many ways, so many software that these big companies release online. And they really open not only to push out there for you to use, try to offer the solution, but they really want feedback from the community, help them to improve the solution and work together. So not only you offer something to us, the community, but we will also work on tooling and solution that help you to make things easier for the community. So that's what I see. The biggest value is enforcing to bring people together without borders, not only physically, but in terms of background, in terms of position or level. And then I also want to mention here that I have like two people here in the panel that I know for a long time, and I really admire Kastan and Benny. So I read about their work online, so they all have their own Wikipedia page, which is really amazing. But so I just feel that a lot to share, and we can always be in the same page. So I don't see the distance in the people who are doing amazing things. And the normal person like me, so I really appreciate what force can bring us together and give us an opportunity to be connected. I think that Benny and Kastan has more to share. Okay, my turn. Since everyone here gets to ask questions. So, okay, I work at ARM these days. One of the reasons I work here is, or there, so actually here, is that I have spent 10 seconds. I've spent a lot of my life by now doing open source. It was accidental. I never joined it because I wanted to. I barely knew what it was. I wrote a window manager for me. I really didn't care if anyone used it. I thought it was cool. Then someone saw the screenshots and said, we want it. I went, okay, all right, here's a tar ball. I went, oh, but it's a binary. I don't want that. Give me source code and compile it for my Spark or some other system. Okay, here's some source code. And I accidentally stumbled into it. Lo and behold, today, my work on that software that's gone on is now running in hundreds of millions of devices around the world. And most of those devices now use CPUs. So ARM, the company I work at, we design intellectual property. Reality is that almost everyone in the room here is not our customer directly. You don't buy stuff from us. The people who buy stuff from us are worth billions and billions of dollars, and they make chips. So who here is using an ARM CPU in their daily life? Who here thinks they're not? Okay, all right, reality is everyone uses it whether you like it or not. And our customers really demand open source. That is what almost all the things we make run these days in most volume. We build everything from, we design everything from server level chips. So reality is that one of the top 500 supercomputers in the world is in fact ARM based. All the way to everything in your pocket. And it all runs at least on a base of open source. ARM has over the years changed. Very early, it didn't know about open source and didn't care and wasn't interested. Today it has changed to the point where it was about a month or so ago, we announced some new features in one of our new ARM64 architectures. I think it was 8.38255. I keep getting confused which it is because I hear about them all day long. But it was the new P-auth extensions. Literally within days we drop patches for the kernel. And it's at the point where that feature in the CPU isn't even going to hit silicon for another two years and there's already patches in the kernel to support it. So, and then that's not even the product getting into your hands. So reality is it's probably another six months after that. At companies like ARM, open source is so fundamental that we do work so far in advance of you even getting it because that's what our customers demand and that's what the right thing is to do. And that's how deeply embedded open source is in many companies. I will put an asterisk next to that. There's certain parts of ARM that don't believe in this. I don't particularly want to talk about them today. But my division, which is the central engineering open source division is one of the largest in ARM and it's been growing steadily over the years and it's really important because it's important to customers, it's important to the OEMs who build devices and it's an important right thing to do and I don't think there's any stopping it. Open source is an unmovable unchanging force that is going to eventually take over everything. The only question is when do you go and join the party and how effectively do you join the party when you do? Thank you very much and Bunny, you didn't have the chance to say anything yet but I think your perspective is very different because you're not working in a big company. I think you have more like ideas and you just like start them like a customer years ago, I think, but you continue this. So what's your, what's your impression of that? Like where do you see opportunities for openness and what's the take for you on it? Why are you so excited to work in the open? Sure, interesting. So I'm glad you asked us that not all ARM is on the open train because at some point in time, I was gonna say like at some point in time I was feeling we were gonna have a big sort of war and court with ARM and their patents in the open hardware space and architectural stuff because it's been impossible to make an ARM open hardware implementation with all the patents and everyone's accumulating patents and patents and patents and now it's like risk five is somewhere like oh please don't bomb me out of existence and so we'll see how that goes. So in terms of like open, I guess there's maybe the two points I'll try and make it quick. One is that from the standpoint of hardware there's a saying that someone has that any technology that's sufficiently advanced is indistinguishable from magic or something like that, right? And the problem is that when technology becomes magic it becomes religion, right? So you already have these sort of ritualistic things like genius bars that you go to where you bring like your sacrificial device which has your whole life in it and it's not working, you pray to the god or the genius bar and maybe he gives you a thing back to you that you can then get but the thing is it's actually, these are all made by humans at some point in time. It's not like some divine being named Steve Jobs had just like popped into existence and it was incomprehensible to mere mortals, right? But there's an advantage to these companies are trying to convince you that's the case because they make a lot more money selling these things to you instead of letting you repair it yourself, upgrade the battery, fix the battery, let you use your phone for another five years or something like that, right? So to me, a lot about openness is just like you don't have to be a hardware person. Necessarily, I don't insist that everyone has to do that but you have to not feel trapped by your hardware. So if you ever want to hit find the exit to the room you feel like you had too much of the cool you gotta leave the religion. Like here's the trail of breadcrumbs you can pick up take yourself to a freer place if you ever need to get there, right? That's kind of open lease at this point in the harder space is just getting there to that point. We don't have the ability in open heart yet to fully build and replace an open source phone for example but at least we have the trail of breadcrumbs to maybe get you there at some point in time. The other thing that I guess I would bring up from the like the open side that is really helpful is that it's a really, because when you can have conversations about the technology we're building you can actually do very quick validation with the community that something's gonna be there. So like I really like Mitch's story about like in the TV be gone is the thing I built for myself and it turns out like 15 years later I'm like building in people's to one. You could put a room full of Harvard MBAs together and have them think for like a month and a half and they would never come up with this idea because it's just something that you would come up with and then validate with the community it's not obvious to these people, right? And so there's many classic examples in the world like you know for example, Betamax versus VHS. How many people here on the top, how many people remember Betamax and VHS, okay? Yeah, it sort of dates you at a certain age. So there's back in the day we used to have these tapes that we used to record videos on and we actually had to go to stores to rent videos and you didn't download them online and there are two formats one was called Betamax and one was called VHS. Betamax was by Sony and VHS was by JVC. And Betamax, Sony had put a lot of money in and developed it and they made a very close format and they wanted to sell it and they had a lot of really smart people put it in and they were very proud of the fact they had high quality and it was a compact format, right? And then JVC actually almost wanted to kill the project inside a couple of engineers on the inside like just in the dark of the night like pushed the product out and JVC says, well you know, we don't know but let's license it to some other people and see what happens, right?  So we're gonna do a mod on the standard to do a four hour run time. It turns out people didn't care about the quality of it. They wanted to record the whole Super Bowl, right? Without having to swap tapes. That was like the really important thing at the end of the day was to be able to record full broadcast and have run time. And so then RCA made the improvement and went back into the license pool and then that got licensed to like dozens and dozens of other manufacturers and beta was just like killed by that, right? So at the end of the day you can be a really big corporation with a lot of like insight and a lot of marketing and a lot of push to get maybe to your B2B initiatives because you know one customer you can know them really well. But knowing the consumer market, knowing that TV be gone is going to be a thing that people are actually gonna want is not something that's obvious. So having this open conversation and being able to get that validation early on, build the community and have the community make improvements, check them back in the base and then build them out further is like a really important part of that process. So I think we are at the end of the panel. So initially the idea was that we share about the future but I think we already shared about the future. We see in what direction we are heading on all sides. But we have still three minutes and I would like to open the floor to a question here from the audience if there are questions. Yes, Mishari, okay. Is this open source? Okay, so thank you. It's been a very interesting panel. Now what I've been seeing as a trend is that yes, some things are getting more and more open. We have open source Linux getting embraced by big companies, IBM, Microsoft, et cetera, et cetera. But at the same time, I feel that it's, I don't know if it's just me but I feel like it's getting almost schizophrenic. Because on one hand we have like this, then it getting embraced and the open source being embraced. And on the other side we have cloud providers which are creating closed ecosystems and patents and even companies like Facebook which are completely closed but actively involved in open. So I'm wondering is the net result, are we getting more open or is it actually a red herring where the openness is hiding the fact that we are all getting driven to a closed ecosystem that we will be very difficult to come out of? Any takers? I think there is an interesting sort of, you bring up a good point and there's an interesting question that's gonna come up in terms of the algorithms versus the data, particularly machine learning. The actual code that runs the models and inference engine is not as valuable as the data sets themselves, right? And so you can have open license code and we can all fork it all sort of stuff but we can't get access to the massive data sets to train these engines, it's gonna be worthless, right? And so there is a bit of a danger that we are walking into and also you can have plenty of open source infrastructure but then the user accounts and the data that's inside the cloud inside Google Drive whatever is really where it's at. And these are the real things. And so as a kind of a community you do bring up a very big concern that I have is that maybe we are just playing into some larger corporate strategy to just leverage our ability to help build up their word chest and they just accumulate data, users and they just put a different license on some things that's not functional through a sort of a quirk of the system and then we end up essentially weaponizing an ecosystem that we're hoping to demilitarize at the end of the day. Can I make a comment too? Very good point and I think I am optimistic that as I said open source will win out in the end and we are moving in very, very strongly at the moment in the right direction. For my future forward looking bit I was going to say that open is really, really important but privacy is also very, very important and at the moment we're going through a phase where we've got companies collecting massive amounts of data centrally. We're building massive machine learning models. We're spending weeks and weeks of multiple GPUs to build these models and that's where the power kind of lies at the moment. I think we're slowly starting to see the pendulum swinging with regard to privacy back into the right direction to regain our privacy and it's great to see Tim Berners-Lee's project around regaining privacy and regaining the internet but the models that we spend hours building we are also now starting to try and share that as well. So our computer vision models we saw the IBM AI, what was it called? An area to publish AI models. We're developing similar stuff for publishing pre-built AI models and to try and share that openly. So building the outcomes as well as the open source that drives those outcomes. Yeah, so just a quick one, I represent a corporation. From an IBM perspective, I think what from an IBM perspective is that open source, like you said, it is the future. And companies like IBM look at our open source as a future for ourselves as well. So if you look at all the platforms that I mentioned, there's cloud, AI, a blockchain, a quantum, right? Everything is based on open source or open technology. And this is a core part of our strategy. It is fundamental to IBM's innovation, right? And I think that alone tells you that when you look at open source, most organizations, when you look at the core platform, the plumbing is where I think open source will be a critical difference. Where IBM comes in and where we try to add value is on the place of the peripherals where we had the last mile incorporated, the last mile capabilities around what an enterprise needs, right? From a scalability, from an availability, a reliable perspective, right? That's where we add the value, right? But at the core of it, right, it is going to be open source in the future. I believe that. Okay, this is the future. It's, we hope it will go in this direction. It all looks like it. But like, we'll find out, right? The future is arriving. So I would like to, I think there are many more people who would like to talk to you. So would you be staying here for a little bit more time so people have questions? They can also come to you. I hope you're here anyways, I guess, right? Graham, you have a talk also in the AI track, yeah? So you'll be available for further discussions and casting. You will also be here and giving a talk in the hardware track on Saturday, as well as Bunny. We'll see you again in the hardware track. So more opportunities to catch up and get together. I think we couldn't answer all the questions. There's much more, as always, right? But it was very, very interesting here. It was a very nice panel. So thank you very much to all the panelists. And thank you very much for joining us.