Entangled Things
Entangled Things
Episode 146: Relational Intelligence and Quantum Entertainment with Bob Coecke
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In Episode 146, Bob Coecke, Founder and CEO of Relational Intelligence returns alongside Alessandro Cheli, Categorical Machine Learning Operations at Relational Intelligence, to introduce two brand new companies. The bulk of the conversation covers Relational Intelligence, built on the idea that intelligence — human, mechanical, or otherwise — is better understood through relationships than through the reductive, static frameworks that dominate western scientific thinking. The team dig into relational modeling, the DisCoPy Python library for working with string diagrams and category theory, and why this approach produces AI that is interpretable and formally verifiable in a way neural networks are not. The conversation also touches on how the architecture is quantum-native from the ground up, meaning it won't need to be retrofitted when scalable quantum hardware arrives. Bob closes with a brief look at Quantum Entertainment Berlin, including a quantum guitar performance at Wacken Open Air and a VR game designed to teach quantum mechanics by being genuinely fun to play.
Hey Cyprian, how are you doing? Hey, Patrick, I'm doing well. I'm looking forward to another great episode of Untangled Things. So we're joined today by somebody who's been on a couple of times but is doing a lot of new things. So Bob, do you mind reintroducing yourself to our audience?
SPEAKER_04Oh hi, I'm Bob. Bob Cooker, to pronounce my surname too. I was for 20 years uh professor at Oxford University, where I build a big quantum group at a time, which at the time was actually the biggest in the world, I think. Then I was five years chief scientist with Quantinium. And now we got two brand new companies which I would like to talk about today.
SPEAKER_03We'd definitely like to hear about them. What's uh what which which one would you want to talk about first?
SPEAKER_04Let's talk about the one which already exists, which we launched uh in uh late February and really started to work in practice in May, uh with with a team in Paris, and it's called Relational Intelligence. And uh, so of course I can explain the name where it comes from at some point. And then the other one uh we would talk about is called Quantum Entertainment Berlin, which will be incorporated next week. Uh not in Berlin, but at Wacken, which is like the most famous, notorious metal festival in the world, where it will be uh and uh so yeah, there let's do it in that order. First relational intelligence.
SPEAKER_03I think that's a good idea.
SPEAKER_04And so Alexandra Alexander Alessandro Kelly, who's actually sitting next to me here, hey everyone is one of the main implementers of all the software and all the things we do at relational intelligence.
SPEAKER_03Excellent. So can you can you tell fill us in on what you're trying to accomplish with that company?
SPEAKER_04So so so the name the name relational intelligence has two parts. One is called one is relational and one is intelligence in the name. Uh, intelligence is clear. I mean, it's it's obviously somewhat connected to AI, but uh a priori don't think intelligence should be limited to artificial intelligence, like this also basically understanding human intelligence in a more direct way, besides making mechanical intelligence, which I think is even a better, is a better way than artificial intelligence to some extent. You've got human intelligence, you've got mechanical intelligence, and then maybe we've got some other forms of virtual intelligence. One couldn't even think about like alien intelligence. That's that's an interesting third category. Because we need to understand these things once we meet them, you know. That's uh quite an interesting part of stuff. Now, the relational that's that's something which goes back as far as the pre-Socratics. So ancient Greek philosophy before Socrates, so Western scientific thinking, uh I mean saying it naively uh to make it simple, sort of was at a bifurcation there about how are we gonna understand the world, how are we gonna produce science, and two important names at a time were uh Heraclitus and Parmenides. So Parmenides is the person who kind of was followed most by Western scientific tradition. Uh Parmenides' idea on the world was that the world was static, it was about being. We're constantly like in a static picture frame. And then of course, it's not always things evolve, but the evolution is just going from one static picture frame to the next static picture frame. And when you're taught a physics course, you exactly get that. You first get thought the kinematics, uh, which is the picture, uh, and then the dynamics, which tells you how to go from one picture to the next one. That's how theories of physics are basically thought and set up, be it like Newtonian mechanics, be it be it relativity theory, be it also the way quantum mechanics is kind of presented, same thing, although that of course become confusing because in the in the kinematic picture, you already have projection postulate, change of chain uh state, which is actually more something that belongs in the evolution part, because it's it's it's something which changes the system, and and in certain uh quantum computational paradigms like measurement-based quantum computing, it's pretty much the only dynamics. You you you basically evolve your system or you do your computation by observing only. So quantum mechanics kind of messed this up, and so quantum mechanics kind of pushes us away from like this uh Parmenides dichotomy to a fundamental process-based view of reality, where you take processes as first-class citizens rather than the static description. And uh the something which most people now will know in quantum computing circle and beyond is uh something I started a long time ago, categorical quantum mechanics, of which a thing called ZX calculus is part, and this is literally a theory based on processes, and the other uh ancient Greek, which I mentioned, Heraclitus, Heraclitus, he said that we're in a constant flux, we're in constant process. It's a being versus becoming. So being was Paramides, becoming was was like Heraclitus. There were other ideas going around around at the time, so this is about like moving from viewing things as static things to viewing things as processes. Now, another pre-Socratic Democritus uh told us that we should understand the world by breaking it down in parts and by understanding the smaller parts where the word atom came from. Uh we'll understand everything. And if you look, for example, at particle physicists, uh that's that's what they do. They try to understand the world by looking for elementary particles smaller and smaller and smaller. When you look at biology, that's what geneticists do, and uh and anatomy was also part of it, is like understanding things by how they are made up. In mathematics, it's set theory, understanding things by the fundamental building blocks, which are elements. So, all of Western science is kind of uh built up with that. Now, there's another view which was already present in uh in this pre-Socratic tradition, but was probably articulated in the strongest form by Leibniz, which is that the alternative is to understand things, not how they are made up, but in their relationship to other things. So, and and and I mean, if you think think about ourselves as humans, we don't understand each other by chopping each other up and see what inside. We understand no, not anymore, not anymore. We understand each other by basically understanding relations between ourselves and others, and also between others among themselves. That's that's really how we understand the world. And if you go to uh developmental psychology, which which is an important part, then there's very clear indications that children, when they were born very early on, they have relational thinking inside of them, they think relationally, they think about the relationship between mother and food and all of these things, rather than breaking things down in what they are made up from, and then gradually, as we are taught more and more science, we start to think more in a reductionist static way, uh, as I explained. So, relational intelligence. Now we understand where the word relation will come from. It was a long story, but this is where it comes from, and so we we do relational modeling. This is not this is not relations in the strict mathematical sense of the word relation, but the word relation in the more broader semantic of what relation means, and so that's where the name comes from. Like thinking of uh intelligence systems in terms of relationships, uh, a layer which we put on top of that, because we've done quite a bit of work before on this, is that this provides you, and that's I think where Cyprian will get very interested, in an interpretable form of if you want artificial intelligence as a as an instance. So we're very much focusing on the interpretability and in resun uh research and which we did before and which we are doing now, we also see that byproducts from that are, for example, scalability, which means you can train small, you need much less data, and then you can do your tests very big. This is something we did before. Uh, work we did at Quantinium in uh 2004 was, I think, selected by Quantum Insider as the second most important result in the quantum computing space, where we showed the scalability that you could literally test on small laptops and then execute on very big quantum well, big quantum computers, which are borderline not similar anymore, something like that. So, so that's the sort of stuff we do, this responsibility. And there's so many application areas which I don't really want to go into too much now. Uh uh, so maybe Alessandro, you can say something high-level about the sort of software we are developing.
SPEAKER_01Uh, so I joined a company um with uh Alexis that invited me, and I had the chance to work with Alexis Tumi, which was Bob's PhD student and was my previous colleague uh in another company, and we were doing artificial intelligence, and we're also doing it with category theory. So um we were composing and talking about processes, and the system that we were developing was um basically using very similar building blocks, which Bob uh has put a lot of effort into developing and writing books about, especially in the field of quantum computing, which are called string diagrams. And um Alexis has um taken over the development of this really nice Python library called Discopy that gives you the building blocks to um construct all of the kinds of string diagrams, which you can see as pictures of processes going on, but they um they they represent proper format calculi, and you can do proofs and derivations inside of them, which uh are how uh Bob basically has developed categorical quantum mechanics and his two books, Picturing Quantum Processes, and another one, uh Quantum in Pictures, uh that he's using with experiments to show that high schoolers correct me if I'm wrong.
SPEAKER_04Oh, I mean we can go in on that later because that that actually proves my philosophical points of before the results which we get at. But yeah, continue.
SPEAKER_01And so um so this package basically can let you represent uh all of the different kinds of uh categories and the different constraints that they put on the relations uh and the connectivity between things and represent actual um other Python objects through functorial uh through functoriality, so structure-preserving maps, and you can do a lot of very cool transformations with uh with that in between uh whatever you can represent with that. And so what we've been putting together in the past two months uh was the proper infrastructure to launch large-scale machine learning experiments that are gonna scale up to quantum two months, two months. In two months, yeah. I'm finishing up the infrastructure right now of orchestrating large-scale um deployments of uh uh yeah, basically massively scaling uh machine learning experiments where we can just like choose massive amounts of memory and GPU processing power. And that is also gonna be the building blocks that you can use to run quantum simulations without a quantum computer. And our goal is to actually develop something where we can speed up uh the process that it takes for a researcher to that knows um about category theory and machine learning to spin up a real world experiment that can then be deployed as well on quantum machines.
SPEAKER_04Yeah, I want to say complementary to that, which is uh what was implicit in uh what uh Alessandro said. So so one of the things we'll soon have is that think just of think of it as an AI, that whatever answer you get, you get a formal proof of why it gives the answer.
SPEAKER_03That's good.
SPEAKER_04So it's totally verifiable, explainable, all these things. So we have the we have the the roadmap to do this fairly soon.
SPEAKER_03I think there are governments that are requiring that.
SPEAKER_02That's that's that's way more than good, Patrick. That is uh literally a game changer.
SPEAKER_03Very, very important.
SPEAKER_04So it's no, I mean, I can't, it's not even a secret, but our sort of pre-seed investor, our main pre-seed investor, and he also helped to set up the company, was also an early investor of Anthropic. Because Anthropic sort of went already a little bit with this ambition, but we're just going all the way.
SPEAKER_03Cool. Uh I've seen a lot of buzz about quantum aiding machine learning. And that and and I don't understand the the confluence of those two things. But is that something that you think is we're gonna see more and more of?
SPEAKER_04Uh we're actually seeing less and less of that.
SPEAKER_03Okay.
SPEAKER_04Uh a lot less. So there used to be this field quantum, well, it still exists, of course, quantum machine learning. But the the way this was approached is you stay you take like a traditional machine learning task, and you see that in any way you can get quantum advantage by but by pretty much still sticking to the original task and doing the original thing. So so what we are doing comes from a completely different direction. And uh so so what I what I just explained would be like quantum for AI.
SPEAKER_03Okay.
SPEAKER_04Quantum helps AI. So then there is another thing which is actually, and that's very much increasing, which is uh AI helps quantum.
SPEAKER_03Right, yeah.
SPEAKER_04It's where you basically use like like big heavy AI methods to do things uh which are difficult and important, like circuit optimization, reducing your circuit, like error correction stuff. Uh people are now doing uh also trying to help make AI help discovering quantum algorithms like so that that's the other direction. I would say that we are not neither of the two, we're at where quantum and AI intersects structurally. And this is an observation which which which uh we first made somewhere in 2007, that the compositional structure of quantum, if you formulate it like in a category of quantum mechanics, uh category theory terms, then the linguistic structure in language totally coincides with the compositional structure in quantum. So to basically, if you want to have a theory, and that's where the interpretability comes from, where uh your mathematical object and your software implementation actually reflects the structure of the phenomenon. Uh in this case, language that's what you really want in science. That's how whole science has been. Whatever you reason about in some way in your theory should reflect the structure of the thing we're reaching, uh you're reasoning about. It's kind of a no-brainer, but that's not true with neural networks. It's not true, and that's why it's a black box and we don't know what what works. And so part of the thing we're pushing is is to actually have this structure reflected. And like I said, this comes with a lot of things, this comes with uh the idea that we can interpret what's going on, the this very interesting scalability, and that's because you actually make explicit the structure of the context, which is a very important thing, which which is not present in uh in neural networks, and enables then also to basically get this formal proofs of what you conclude from from what is given. So it all comes to basically do something which is so basic in all science that what you're working with, what you build, reflects the structure of the phenomenon. So that's what we are doing.
SPEAKER_02I I would be curious to to to learn a little bit more about the what is the equivalent of the the training or the learning process from like the classical neural network-based AI in this paradigm? Like uh as much as you can obviously describe in a in a public way.
SPEAKER_04Yeah, so so so the way we are doing it is uh to some extent, but I mean, in a way, you can just train over these structures, which we've done already. That's the work we did uh in 2004 at Quantinium. Uh, I mean you can find the papers online, they're all in the public domain. There's a blog post which Ilias Kell and I wrote about it, so you can just read these online. Uh, and then we you you can train basically over service. Now, in the same way that people usually train vectors of meaning, vectors, so we we train processes and gates, and they sometimes they are higher order processes, so processes that act on the process, so so that's that's what we do, but it's learning. There's actually a theorem, a theorem, which I never even properly written down in a paper, so it's only public domain, but I proved it because I simply didn't have time to write like this theory paper. We have a theorem that if you want to respect the structure of language, the compositional structure of language, like our words, for example, compose, uh, and and then you want to have a mechanism for learn, learning, just in the way that we train over vector-like structures, be it like linear maps or I order the maps, then you're automatically forced in what's called the category of Hilbert spaces, linear maps with the tensor product. So it kind of forces you, if you want to have a theory which has these two properties, reflecting the structure of the of the substance uh which you work with, the phenomenon, and at the same time having the ability to learn over it, you end up with a quantum formalism, whether you implement it on a quantum computer or on a classical computer. So that's that's that that's a theoretical fact. So you can't you can't get around it basically, and then it comes with all these nice byproducts like getting a proof of what you do and the scalability.
SPEAKER_01And for for computer scientists, the approach um um the approach is um is usually like in tradition, the approach is to work with trees, which are symbolic expressions, programs, think about Lisp or N programming methods, yeah, yeah, and and vectors when you talk about numerics and you talk about neural networks. And uh in the same way that Bob has described, uh, that you can describe both natural language and quantum computing with the same structure. Uh so you change the interpretation that you give to the tensor product, and when you see it visually, it's just um composing circuits in parallel. And the semantics of the tensor product then uh changes based on what realm uh you're interpreting, like quantum computing, language, or could be um audio digital signal processing as well that we're gonna take a look at. And uh once you generalize, you get these sort of like circuits that give you like formal um logic properties, which are not because circuits in computer science, when you represent them, um they're graphs and a lot of software that just works on graphs and it doesn't give you formal provable, like theorem prover semantics that give you a real proof. And once you start working with those structures that have this like built-in um formality over the syntax, over the syntactic structure, then uh a lot of things come a lot more naturally. So if you use them as the building blocks that you that you work with neural networks, because intuitively you can see a neural network as a circuit, and you can also feed it into a neural network, then interesting things start happening. Because it's a lot more elegant. Yeah.
SPEAKER_02That's yeah, that's that's that's that's I think it's fascinating. Like it's it's absolutely uh uh fascinating. Um so I'm curious, right, in terms of the underlying representations of what you learn, right? Uh what are you are you using to, because like I I would dare to say classical or uh uh old AI, right? It's using the representation in the form of the weights in the neural networks, right? What is in your case the representation? of what's being learned.
SPEAKER_04So so we work with something that's called I call this I call these tech structures. I introduced them in 2019, 2020, which are tensor networks, just like uh in a way neural networks are tensor networks. But they they they are built on like represent a representation of the logic of reality.
SPEAKER_02And this is this is present in language, this is present in uh cognition this is present in how we think visually how like maybe a movie like the the the script of a movie is set up and uh we also have like just spatial reasoning in the stores it's it's like the way a story is told whatever the story is about whether whether the story is uh the way we reason the story is uh like a book uh well one interesting thing about this because I mean there have been grammatical structures around for of course very long time going to the 50s with Lambeck and Chomsky and and and things like that and then at some point I think in 2007 2008 uh we turned this into not just the structure of language structure combined with meaning of language in a formalism we called disco cat at the time and the all the first quantum natural language process experiments which I think you both are aware of going back to 1920 used that structure the only reason we could actually do something like NLP on a quantum computer is because the structure helped us so much and we didn't need to load lots of data on a quantum computer which you couldn't do anyway which you couldn't do anyway exactly so at that time it basically enabled us to even do something so now we're going way beyond that and now we're using that to actually do things much better also in class so so uh again alessandro was was hinting at that at the moment we're going two paths we're going both classical and quantum so classical because also these structures allow very elegant and efficient translation on on on on big big big uh networks of GPUs so that's something we are doing too and actually a lot of work there has been done so so uh in the company it's myself and I've got two co-founders Alex Tumi was already mentioned but by Alessandro other one is Giovanni de Felice who did a lot of work on like like uh like like semantics of uh combining different processes and stuff like that so that that's all new work which we're using too so that there's a lot of machinery and it all sort of nicely falls together it's all part of the same thing so you don't have to sort of artificially stick different structures together it's all the same core structure whatever you do with it whatever you're gonna stick it on a quantum computer whatever you're gonna stick it on classical computers now the nice thing about these text circuits is they're so naturally fit on a quantum computer and we've already implemented them on a quantum computer we've already done that and uh it it it it works very nicely trains very well so so yeah it's uh that that's sort of the big picture of what we're doing like we like I said we're technically two months in so but we've already done a lot so at the moment if if you count uh depending on how you count if you count like also the sort of uh senior advisors who work part-time uh and all of that then we're about 13 people now we're going into our second funding round and then obviously after that we're gonna grow quite a bit uh so officially it's a UK company and officially it's here where I'm speaking now uh this is an audio this is an audio recording but if you would see where I'm seeing which people probably have seen a lot in my videos like it's the pop music studio where I'm always sitting so that's officially the address but the offices are in Paris because for some reason all the people who work for us which are mainly Italians they all live in Paris I don't know why actually Alessandro lives in Berlin but he's gonna move to Paris yeah and I think this is also great to to to hear that you're let's say technically speaking you're not bound to like wait for the scalable uh error corrected quantum computers right no you can already do like very powerful stuff even by going the route of classical which which I I think it's also remarkable.
SPEAKER_04That's the whole idea indeed like not to just wait. Yeah just play and just because all these properties which we mentioned they're super relevant classically now that the the thing is at some point you're gonna because it takes a bit it costs a little bit to it costs of course a little bit to use the structure I mean it it also costs less in the sense that it makes things more efficient and you need less data but still the the compositional structure it's still a tensor structure so it's quite expensive in its own right and we have results of of which which clearly indicate that there may be some exponential advantage of a quantum computer there is not many problems where you can say this for that you're gonna get exponential advantage of a quantum computer but here it seems like so which is really cool.
SPEAKER_02But to test this of course we need we need the bigger quantum computers to just even prove that point the the the problem with uh anything which involves learning and uh data which is which which is not exact which is like real world data it's really hard to to have watertight exact mathematical theorems there needs to be some empirical verification to really say yes and yeah I mean you mentioned before what what I said before about quantum machine learning that was the big problem there was no theorems uh justifying that whatever you got from a groover algorithm wouldn't be undone by the training and and what also I I think is a very important aspect of of what you're building and correct me if I'm wrong is that what you build works right in on classical computing but when the time comes to have the scalable quantum computers you will not need to retrofit like it's the case with with classical machine learning attempting to retrofit it for quantum it basically will be native for quantum it's because the classical stuff is quantum inspired yeah yeah the quantum stuff is native yeah that's I think that's a huge that's a huge differentiator I I absolutely love it so I I hate to change the subjects but we're right we're we're coming up on 30 minutes and we want to talk about the other company too oh so before we go is there anything else we need to know about I'm gonna say two very brief things then okay so first because it was alluded to like uh about this this this uh that through quantum in pictures we have been teaching at high school children quantum I mean you can find the the articles out there there's a garden article about it that you actually these structures we're talking about children understand them better than quantum mechanical formalism and you can teach quantum theory as a whole to teenagers I mean we we did this as an experiment a while back then another experiment was done in Pakistan with children as young as 13 years to basically teach them quantum mechanics and then give them an Oxford University grade exam in these pictures now even this week I was there in Hertfordshire in uh here in the UK uh an in-person large scale project is going on and I was there and it's it's amazing I just want to say that this and this also this also proved my point one of the nice results we had is the younger the children are the better they do which has which goes back to my uh development which makes a lot of sense we haven't beaten it out of them yet that they they they have less to unlearn exactly yeah yeah now then as a as a last brief thing so we're also starting another company uh we're gonna incorporate next week in Berlin and that's Quantum Entertainment Berlin uh there's gonna be a few aspects to that myself I've built a quantum guitar uh it's literally sitting here in the room where where where I'm speaking now and next week I'm playing at like a very big metal festival uh Wacken Open Air It's uh most sort of known metal festival in the world uh so so for those of us that don't understand it I I assume a quantum guitar is not so tiny that I can't see it it's something else what is a quantum guitar i'm I'm dying to learn as well how does a quantum guitar work so so it's basically built on top of a regular guitar so and then you think of the fretboard of the regular guitar as a space time where things happen.
SPEAKER_04So there is a model of quantum fields uh due to David Deutsch which says you build a quantum field by associating a quantum system to every point in space-time so that's what I'm doing there is a software which was initially developed by a company called Mott Quantum uh which which also is uh a quantum entertainment company based in London I mean I was actually a founding shareholder there but they're now mainly focusing on uh quant uh on quantum enhancement of games so finding algorithms to make games better or faster uh they just released one something like that uh so they have a software which they developed that it was a quantum synth so I'm actually using this quantum synth to connect to a quantum computer and but instead of like using the synth or or like a key I actually have a whole setup at my feet which by which I control the quantum system I can sort of rotate it I can measure them I can do everything I want and then the sound of what you what you play on your guitar then gets so to say entangled with the qubits and whatever I do to the qubits to basically realize this quantum field and all its states. Wow so it's quite literally it's it's quite literally like quantization going from a quantum system to a quantum field and then the extra degrees of freedom I do with my feet. It's uh like a drummer also uses his feet you know like so so so that so that's it and then I've got a bunch of ideas on quantum guitar pedals which we're gonna implement and then uh the another founder is actually a person who's a specialist in games and VR and there we actually want to sort of uh initially show like make people uh experience quantum so you you are in some environment the each of you are a qubit you can be measured you can be entangled and then you interact with each other in a fun way i've I've played concerts like that at some point that myself and another musician we were so to say quantum systems and then we were entangled and then what we played well when when one got measured the other one also collapsed because of the entanglement and we've played a few concerts like that I'm doing this together with like a world renowned classical musician and he either does this on a grand piano and we also have a symphony together called Quantum Universe which uh is for quantum guitar and orchestral uh cathedral organ. Wow you can you can find the videos online they were released by Oxford University Philosophy department of a concert during the quantum center centenary here in Oxford where there was the premiere of this quantum universe so anyway so we we're gonna incorporate next week and so so that that those are so what what what is the product or the products are going to be for that company oh I mean I mean uh so so on the one hand there will be just this quantum hardware instruments and quantum software instruments and uh they they they they can be for music and they can they be for other sort of art forms so so that's a very obvious thing to do. But the reason we are in Berlin is Berlin is incredibly supportive for something like that. It's it's it's the kind of city which embraces anything like that. And then there will be these quantum VR setups which can be used on occasion and maybe in other things uh I mean like I said we we technically incorporate next week but we already have research grant together where especially like a quantum VR game is being developed.
SPEAKER_00It's supposed to be a a like a game which should be fun in its own right independent I mean the guy I work with is like a very good game developer and he has a nice team around him it should be a game that's that's fun in its own right but at the same time teaches you quantum cool and makes you familiar with quantum so the game itself would be a product nice you're always into something you're always into things that are off the beaten path and very very interesting yeah can I add something yeah please before joining relational intelligence uh I was independently um playing around with um uh a bunch of compilers and languages that were developed in France and uh they're open source and uh basically it's string diagrams so it's category theory so you use the same building blocks that we use a relational intelligence you can make audio stuff with them which is so yeah he's making sort of audio software plugins and things like that based on quantum which you could connect to quantum yeah classic related computers you can you can simulate quantum processes actually pretty pretty easily with category theory so yeah just they're everything's all interrelated what really blows my mind is the concept of using entanglement in a concept like wow hey honestly I had this idea in the 90s I was giving talks about it in the 90s but then then then career changes as well it's we're all on a Mobius strip we'll eventually come around at the same point well it's always interesting to talk to you and it's it's great that you're you're doing new things but uh you know we're hoping to talk keep talking to you on a regular basis because you you never cease to to surprise and amaze thank you thank you always good to speak to you guys and hopefully we see each other in person it should have happened this year but I mean I literally because of this company stuff had to oh yeah we understand do a lot of stuff that particular week maybe we'll all meet in Berlin for a concert yes wouldn't that be great thanks again for joining us and and uh and we'll see everybody soon thank you it's been a real pleasure as always bye everybody hello cybercrime is one of the biggest threats to businesses of all sizes and industries with almost half a million open cyber positions the problem is compounded by the lack of available talent in the marketplace at Pulsar Security our elite team of highly credentialed experts collaborate with you to assess your current defenses and develop solutions tailored to your specific needs. With services ranging from cybersecurity education to advanced penetration testing and red teaming you can start reducing your risks today. Visit pulsarsecurity dot com and let's secure your digital future together