Ok, so it's a great pleasure to give this talk in honor of Alan Vallette, who as Claire just mentioned is a very brilliant student that I had at some point. And I mean it's quite striking to notice the conjunction between Alan and Yeshua. Because they are both 60 this year. So which means that they must have been born more or less at the same time. In the same room. Yes, and also I mean it's quite striking that Alan has played a very important role in the administrative part of the Council of Yeshua. And it's also quite striking to see that his mathematical inspiration is very very close to few of the great people in Yeshua like Misha and so on. So I mean he has both this taste for geometry and analysis and so on that we all appreciate very much. So I will come back to that at the end. Ok, so today what I want to explain is quite simple. It's a joint paper with the Shamsedin and Sahelokalman. And if you want it's a strange thing because it is the fact that the spectral action which I will explain is in fact surprisingly related to entropy. But through this relation so I can tell you right away what is the point and if you want what is the main result. So the main fact is that through this link between the spectral action and the entropy. Normally when one defines a spectral action one uses an arbitrary test function. So I mean the spectral action is something which is defined for spectral triples. I will explain what it is by some function of the operator D which defines the metric. And a priori the function F is like an arbitrary test function. But in the link with entropy which I will explain the function takes very specific form. And what we were quite amazed by when we wrote this paper was that this function is in fact intimately related to the Riemann Zeta function. So this came out as a total surprise. And so if you want the motivation of all this work which I have been doing with Shamsedin, Mukhanov and Sahelokalman and several people, the motivation came from the idea that it's probably a misconception to think that when we look at space or spacetime it is the continuum at any scale. And the person that actually already said that from the very beginning is Riemann himself. What he said when you look at his inaugural lecture on geometry, what he said is that if you take the notion of a solid body or of a ray of light on which he was basing if you want the Riemann paradigm of ds squared equals g mu dx mu dx nu. So what he is saying is that in general you cannot rely on this notion of solid body or ray of light in the infinitely small. And in fact you have to be careful. And so what he says is that it's therefore quite conceivable that the metric relations in the very small do not conform to what he had set up as the hypothesis of geometry. And then he goes further actually and he explains that in fact if this is a case when you look for the foundation as the forces, the binding forces which if you want hold the physics and they should be involved in the geometry of the basic geometry if you want the geometry of space or spacetime. So in fact it turns out that quantum mechanics gives forces you to take a paradigm for geometry which is more flexible than having continuum and having the g mu dx mu dx nu locally and so on. And this paradigm took some time to reach and its notion of spectral geometry And spectral geometry is given by a triple. So you have three ingredients. Well in fact you have two ingredients which are in the middle which are acting in the same space. This is the Hilbert space, infinite dimensional countable basis. This is an algebra. So it's an algebra but which is acting as operators in this Hilbert space. And this guy, this d is a symbol for the Dirac operator. This is what you have to keep in mind. But it will be if you want the inverse line element very soon. So it turns out that this notion of spectral geometry it has three aspects and it would be a mistake to take one of these aspects as being the main one because each of them plays a role. So the first aspect is the k-homology. And this aspect in k-homology is quite rooted in mathematics. And this means that when you consider if you want the data which is here it has meaning because when you have a manifold it's not just space up to a motopy. It does characteristic classes like the Pontragon classes which are finer than just giving the space up to a motopy. And this wouldn't be seen if you take ordinary homology but it is seen when you take k-homology. And essentially this triple, if you want that part the k-homological part gives you the fundamental class. Now the second aspect is the metric aspect. And it turns out that in metric aspect instead of measuring distances by taking an arc between two points and taking the smallest length of the arc using the square root of the square you do something different. And the fact that you do something different allows you to measure distances in spaces which are for instance totally disconnected which don't have any arc. But the distance gives you the same formula when you are dealing with an ordinary space and the duality between the two formulas is the contour of each type. Duality which is familiar in the transport equation a transport of stuff like a mange and so on. So this is the metric aspect. The metric aspect is quite important. Quite important because it will make sense in a commutative case as well. And finally probably the topic that will be most important for today is the link with physics. So in the link with physics what happens is that physicists in the quantum they have what are called Feynman diagrams and I mean when you consider Feynman diagrams which have to do with fermions then there are things which relate two very close by points together and this is the fermion propagator and it turns out that in a commutative geometry I mean with the spectral triple sorry this is really the line element. So it turns out that it fits it fits with a lot of things and we shall use this link with physics when we find the link with entropy. Okay so I'll go very fast in the first part because this is not my point today I want to explain the link with entropy so I will go very fast just to tell you what is the framework, the general framework just to survey the general framework. So as I said you know the notion of manifold is more delicate than just having poincare duality in ordinary homology and I mean this comes essentially from one result which is very striking which is due to Sullivan and which says that if you take a micro bundle so the micro bundle will exist as soon as you have a space which has poincare duality in ordinary homology if it's simply connected you put it in a usual RN space it has a normal bundle but it's not a bundle it's a micro bundle and if you could make this micro bundle into a bundle, vector bundle then you could use term transversality to make it into a manifold but in general you cannot and what is missing is exactly what is needed for a micro bundle to become a PL bundle let's say which in dimension 4 is the same thing which is what is called the k-orientation so this is the usual stuff now this stuff is purely topological and that stuff which was purely topological becomes now related to in the space because of the work of Attia and Singer on index theory so both Attia and Singer understood that there was an abstract way to formulate index theory which was with abstract elliptic operators which are acting in the in the space and then gradually through the work of many people Brown Douglas Fillmore and finally Kasparov with the Kasparov theory it turned out that this allowed to reformulate the dual theory to k-theory which is k-o-homology in terms of Hilbert space so this accounts if you want for the homological part and so I mean one has a very simple dictionary so in that dictionary in the classical column what you have is the usual Riemannian formulation and what you have in the other column in the quantum column you have the translation in the computer geometry but as I said I mean the main point is that now you have abstracted the idea of manifold and you have also abstracted also now the possibility to use an algebra which is no longer commutative that makes a big big difference that gives you more freedom and now what turns out to be the case is that the square of the line element now we have been able to extract the square root this extraction of square root is the extraction of the square root of the Laplacian which replaces the Laplacian by the Dirac operator so that was fine the extraction of the square root but then if you want when you think about the general framework and you try to apply it to physics and so on you wonder how can you understand if you want the role of the algebra A and it turns out that the way this role was unveiled if you want was by doing exactly the same thing for the position variables for the coordinates if you want as the Dirac operator does for the momentum so the Dirac operator it assembles the momentum into a single thing which is the Dirac operator and in the same way what we did with Shamselian Mukanov was to assemble the position variable exactly in the same way by a Feynman slash so the Feynman slash means that you add you put gamma matrices the idea is very simple for instance instead of thinking of four coordinates you can think of a single quaternion that's very nice because then you can manipulate with four coordinates as a single symbol as a single element so the gamma matrices are exactly playing that role and then it turned out that what we did was to understand a geometry as an irreducible representation and an irreducible representation of what the simplest example of spectral geometry is obtained by the circle of lengths 2 pi how do you get the circle of lengths 2 pi out of an irreducible representation well you consider the following thing you consider a unitary operator you look for the matrix so the matrix is this D you don't know what it is but you write a presentation you write an equation and the equation that you write is you start the commutator U is equal to 1 this is a kind of Eisenberg commutation relation you spell out the irreducible representations it's not difficult an exercise because why is it an exercise because this is telling you that the operator of these two guys this is a self-adjoint operator this is unitary now this self-adjoint operator will have a spectrum but this spectrum has to be if it's irreducible it has to be the integers up to a shift why because D minus U D U star I'm messing it up so it's U star D U minus D is equal to 1 so this U star D U is equal to D plus 1 so this is the spectrum has to be shift invariant by 1 so then you get these irreducible representations and once you have these irreducible representations you can compute the distance the matrix and everything and you get the ordinary circle but with lengths 2 pi now this is very simple so this is what is written here this is very simple but what is much more interesting now well here you see in this example the algebra was commutative now what is quite surprising and beautiful is that you can get much more interesting algebras than the circle I mean much more interesting spaces than the circle but by doing the following so now what you do is you take 2 by 2 matrices so you take M2 of C and to this algebra now I add a punctuation symbol by punctuation symbol I mean a Y which satisfies Y squared equals 1 and Y equals Y star so it's self-adjoint and now you compute so these things don't commute so the Y doesn't commute with M2 of C they don't commute, so you form words individually taken they are nothing 2 by 2 matrices is very discrete space finite dimension also same for Y, it's nothing but when you put them together and you write words and so on what you find is 2 by 2 matrices of functions and no relation among these the only relation is this relation namely that the trace is 0, that's all so when you compute with that you find 2 by 2 matrices of functions versus two-sphere so what I am saying now is that it's simpler to define the algebra of 2 by 2 matrices of functions than the algebra of functions of the two-sphere what do you gain you gain something which is quite amazing what you gain is that the non-commutativity of the algebra now will give you the gauge fields automatically because when you will compute what are the matrix and what are called the inner fluctuations of the matrix, you see the fact that the algebra is non-commutative gives you inner automorphisms these inner automorphisms when you compute what they are in the case of matrices of functions you find that they are exactly maps, smooth maps to the group SUN and when you divide by inner automorphisms you find the ordinary different morphisms and moreover when you do the same thing but for matrix what you find is that the matrix now they have the gm news but they also have new ingredients and these new ingredients are exactly the gauge fields of gauge theory here for SUN so in fact what we asked with my collaborators what we ask is we ask a purely geometric question purely geometric question was the following is it possible to describe now four manifolds not the two sphere by such an equation by such very simple presentation so we started we started and we started from the analog of the relation which I had written of the relation which I had written there for the circle which was a kind of Eisenberg relation you see this is very close to the Eisenberg equation pq and so on and so we wrote an analog of this equation now in dimension n and we began to classify the solutions of this type of equation and at first we were quite disappointed because when we looked at this equation and we classified the solutions what we found is that it's only the sphere or it's disjoint union of spheres of unit volume when we talk about physics this size of the sphere will be the Planckian size so at first we were disappointed and we had found this type of bubbles I mean many little very tiny little spheres but then we realized that we had not here at any dimension n here it's very general but then we thought much more and we found out that we should have involved a key ingredient of the story because it's a nuance between k and ko theory and it's very important for instance in the theorem of Suleyman so then we wrote down if you want the ko refinement of this equation and what we found out then is that for the ko equation there was an infinitely better theorem so there is this higher equation which you don't need to know in detail but what we found out for this ko equation to have solutions is that we needed two cliford algebras and in dimension 4 we need two cliford algebras which corresponded to because it's a sphere so to 5 pluses and also the cliford algebra which corresponded to 5 minuses we needed both so then we looked at the table of cliford algebras and what we found out is that by looking at this table we got exactly the algebras that we had to put by hand to get the standard model coupled to gravity in dimension 4 so the conclusion which I drew out of that is that purely geometric model if you want to present the algebra of functions in the simplest possible manner purely combinatorially by using these symbols and these punctuation symbols it gives you exactly the algebras that we had found from a bottom up if you want story to get the standard model with the x all these mechanisms v minus c and all this stuff ok so this we concluded from that that what ok ok I was a constant center you see what you find now you have to use an action functional to get the standard model this is spectral action that I am going to discuss now ok so what was the action the dream was that the action in physics should only depend on the spectrum of the line element so not on the space but just on the spectrum of the line element ok and this was confirmed because you know normally when you write many gym news all sorts of notations and so on but it turns out that what we had found is that when you expand this function in terms of heat equation expansion and so on and so forth you find several terms and among these terms I mean there is a first cosmological term which is like lambda 4 times the volume then there is a term lambda square times the Einstein Hilbert action ok plus the x square term and then plus when you look at the coefficient of lambda 0 you find the Young Mills terms the x quartic self interaction you find exactly what you need to find ok but we were very bothered for a long time by this term lambda 4 times the volume which is like a cosmological term because it's very huge however what the equation what the Eisenberg equation does is to quantize the volume so in other words exactly as in the case of the circle which I was describing here where the length of the circle was 2 pi it turns out that when you write this Eisenberg equation the theorem is the following the theorem is that in dimension 4 dimension 4 is critical because in order to get a solution you need to cover the sphere in two ways by two maps in such a way that when you pull back the volume form of the sphere and you add the two pull back you get something which never vanishes so for that dimension 4 is critical and the reason why dimension 4 is critical is that in general you can get a ramified cover of the sphere which is ramified in a variety of dimension n minus 2 when you are in dimension n but if you take two of them then they will intersect you know they will intersect when this is n or less or equal to n and this gives you n less than 4 exactly and for n equals 4 it's very tricky actually to be able to do that it's not true for p2 of c but it's true amazingly for n is pin manifold so for n is pin 4 manifold compact what you can do you can cover so you have this picture if you want what you can do is you can cover the sphere by two maps and then because the cover can have multiplicity which is arbitrary large but it has to be at least 5 or something like that then if you want what it means is that you can get a space whose volume now with size if you want will be very large in Planck units if you couldn't get all these integers you couldn't get something out of the sphere you would be stuck with a very small sphere so now I come to the subject of my talk which is really the spectral action so spectral action and I said you know it had a bothering cosmological leading term but now this cosmological leading term is totally unimportant because the volume is quantized so this is an integer so the fact that the volume is quantized tells you that when you take the variational equations with respect to this action you won't have this cosmological term anymore ok it disappears integer means positive integer positive integer positive ok so the volume is positive integer so we were not worried anymore about this and then if you want the idea the general idea which will require a lot of work of course is that one should see the geometry as emerging from the quantum in other words all of the stuff which I have explained it's all operators in Hilbert space and so on I didn't put the geometry by hand from the start you know I'm just looking at operator equations out of the spectrum and so on emerges the geometry so this is the idea ok but now we come to this you know usually when you say that to physicists they say ok fine fine fine but what about the second quantization because what I have told you so far is really at the first quantized level if you want it's a story which is not taking quantum field theory and so on into account ok it's a story of course you know it's very important that you have a good starting point so I think we have a good starting point in order to recover geometry from the quantum but ok we need to understand how if you want how the second quantization will enter ok and so as I said you know the fundamental problem is to understand at this point of the story ok which was several years ago you understand the role of second quantization now this is the reason why I explain this stuff about case theory and chaos theory at the beginning because you see what has happened is that thanks to the index theorem the dual of case theory case theory was known before but the dual of topological case theory did appear to bring with itself you know with the suit cases the quantum because the cycles were defined by representations universe space and so on now it turns out that there is a magnificent generalization of topological case theory which is a Quillen algebraic case theory and which is a theory which is quite quite more elaborate if you want and more difficult to define than case theory than ordinary case theory and so far nobody has developed what is the dual of the Quillen algebraic case theory in fact in my inaugural talk in the college de France in 1985 I mentioned this as a fundamental question ok and so we have with my collaborators exactly you see, k homology is dual to case theory and what I believe is that the second quantization quantum theory will be dual to Quillen case theory ok and I will give you some some confidence for that ok I had at the time well ok I mean we are working overseas you see I mean ok you could worry about non-archimedean places but we shall not do that today ok today we are over the complex numbers ok so so the reason why this is very interesting the following is that you see the one characteristic property of the spectral action of this function is the fact that if you take two spaces which are disjoint you take the disjoint sum of two spaces then this functional will be additive whatever function you take and the reason is that the operator d will be the sum like d1 direct sum d2 so the function will be you know it will be like adding the trace in two different Hilbert spaces so it will be obviously additive at the conceptual level is the key property now there is another way to find an additive function of spectral triple which begins to look like second gradization and what is it so it's you take a spectral triple ok you take a spectral geometry ahd ok and what do you do well you think of the Hilbert space now as a real Hilbert space so you take the underlying real Hilbert space to the Hilbert space H so that's what I denote by H sub r ok so this is a Euclidean space if you want and to that space you can assign a Clifford Algebra which if you want now is much more congenial for Neumann Algebras and so on but I look at it as a c star infinite of course so how you you know you see you take the well you take topology you take the norm which is uniquely defined by taking all unitary representations of the Clifford relations ok so you see you have vectors you have gamma of psi for every vector here and you have the relations of the gamma of psi square is equal to psi square you take representations of that ok and then if you take linear combination of these guys or product and so on you get a norm because it's a c star algebra ok so c star algebra which is well known this c star algebra is in fact a co-limit of finite dimensional c star algebra because you can take finite dimensional subspaces to be the co-limit of these and then it turns out if you want that the right way to think about it is the following is that now we have the spectral triple the spectral triple was spectral geometry but now we think of it with replace the Hilbert space by the Clifford algebra ok so we replace the Hilbert space by the Clifford algebra in the middle we replace the operator d now by a one parameter group of automorphisms of the Clifford algebra how is it done well you see I mean the one parameter group sigma t is a group which is corresponding by factoriality of the construction to exponential i t d exponential i t d these are orthogonal transformations sigma t is coming from h r automorphism of h r these are automorphisms of h r sigma t is automorphisms of Cliff ok so sigma t are automorphisms of this Clifford algebra which come from which come from the guy by factoriality ok so what I am saying is that this defines a group of orthogonal transformation which is underlying Hilbert space so I can view it as automorphisms of the Clifford algebra it came from the d in the spectral triple ok ok it comes from the d ok now you can say where is the algebra playing a role well the algebra does play a role sorry the algebra does play a role I mean the algebra plays a role because you can the way the algebra was playing a role in the previous case is called the inner fluctuations of the operator d so it's deformations of the operator d which come from the gauge potentials so this will deform this one parameter group in the same way so we have a way to second quantize our data our original data now we are going to use it and we are going to use it because of the entropy which is the fundamental entropy and the fundamental entropy which I will introduce very shortly as a property that if you take a tensor product of two situations type one the entropy is additive so the entropy of a tensor product is now the sum of the entropy so this will recuperate the additivity of the spectral action and it will tell us that when you compute the entropy of the corresponding second quantized stuff it will give us a spectral action ok so now I am coming so entropy of what so ok so we use this thing ok we have this one parameter group of automorphisms of automorphisms of the clifford algebra and so we have if you want the clifford algebra and the one parameter group that's what we have ok we have this stuff how do we get a state out of this well by the KMS condition so the KMS condition is a condition which relates one parameter group of automorphisms of the clifford algebra with a state and this for every value of beta where beta is an inverse temperature this state might exist might not exist might be unique, might be many they form a convex set I mean and so on and so forth ok there is a whole story about it in this situation where we are so this is the KMS condition if you don't know it, forget it I mean it's a condition if you want which relates normally the state which is given by trace of e to the minus beta h with the Eisenberg evolution which is given by ith dot minus ith so it's a condition that relates the time evolution with the state but of course this is a very simple case in general as I said on the C star algebra endowed with a group of automorphisms it might or might not exist so here it turns out that in our situation it's quite nice it exists and it's unique so if we take a complexive space a self-adjoint operator with compact resolvent we take the clifford algebra the complexified clifford algebra of the real number space and we take the corresponding automorphisms then for any beta positive there exists a unique KMS beta state this is not difficult to show, why because as I said the clifford algebra is a co-limit of finite dimensional stuff now the operator has this spectrum so you can take the co-limit according to the subspaces on which the operator is diagonal now you look in each of these spaces it's a matrix algebra and ok and you have a uniqueness of the KMS state so this is not difficult this is not difficult at all ok ok so you could have type 2 1 factor you could have factors of various types however in our situation where the operator has a property where the Dirac operator is finite dimensional so it has a property that if you want the resolvent or 1 plus d2 to the power minus n over 2 will be a trace class so this will be finite for a finite n so because of that because of that what happens in our case is that this operator turns out to be trace class and then it turns out that the states that you obtain on the Clifford algebra is type 1 ok I mean there are situations where it would be type 2 but here it's type 1 so the fact that it's type 1 allows us to use the fundamental entropy so what is the fundamental entropy if you take a type 1 state you can always write the state in terms of a density matrix ok so this is the fundamental sorry what is the fundamental entropy so fundamental entropy is the following you take your state you write it from a density matrix so you write your state psi of an observable a is given by trace of rho times a where rho is called the density matrix and normalized and what not and it turns out then the fundamental entropy is given by the fundamental entropy of the state so it's an information theoretic entropy so the fundamental entropy is given by minus trace of rho log ok so this is definition fine so this is where we stand now and so I mean so this is just the construction by what is called the Dirac C of the corresponding state this is standard stuff and now here is the entropy so here is the definition of the fundamental entropy ok and now we apply this to our situation we have a unique KMS state it turns out to be type 1 so we can define its entropy and we know because of the fact that the entropy for a tensor product is the sum of the entropy that it has to be a spectral action but for which function this is the issue which function so we compute and what do we find we find that because of this additivity ok it turns out that the function that we shall get I mean you know first of all let me use this notation epsilon of x this epsilon of x is the entropy of the partition for which the ratio of the sizes of the two intervals is equal to x so it's the entropy of the easy thing where you have only two two subsets ok and you assume that the ratio between the two lengths is x so I'll give you this stupid function ok and now what you do is there is the following theorem so the following theorem is that now if you do the fundamental entropy you find that it's equal to the spectral action of beta d so we have the spectral action and this is the spectral function it's h of x equals the previous function evaluated on e to the minus x ok now this is very simple it looks very very simple and what was our surprise was to find the link between this and the Riemann zeta function ok so this is really the mathematical content of the paper ok and so what did we do to do that well this is the function first of all it's a very good function you know because in the spectral action you want the function to be positive you want the function to decay very fast at infinity and you want it to be a kind of cutoff function but it shouldn't be a sharp cutoff because this would be bad you want it to be smooth yes this is the epsilon of e to the minus x first of all why is it an even function well because if I change x to minus x e to the minus x change to the inverse but I told you that this was the entropy when the ratio of the two intervals so of course you know if you have two intervals and they have a ratio of 10 if I exchange them they will have a ratio of 1 over 10 so the function is even ok so that function is even there is no problem when you look at it a little more closely this function what do you find you find that its derivative is actually without a log and its derivative is given by this formula is given by minus x over 4 the hyperbolic cosine square of x over 2 and this is where things begin to be interesting because that function you know the function being function h being even has to be a function of x square so you have to be able to rewrite things in terms of x square so this is what you begin to do you write this formula now its calculus so what you do is you write this formula this is not a big deal you check this formula with the sum over z begins to look like one dimensional kind of Heisenstein series and then what you find out is that you see you would like to write your function as Laplace transform because then you can use the heat expansion to expand the various terms so you begin to do that but not for the function itself piece of the function which was given by the square root and what do you find you find that this function g of t because of this equality is of this form so it looks like a theta function in fact it is a theta function very closely in fact so this function g of t turns out to be given by this formula and this is extremely useful because you can use the you know you can use the modularity and to prove properties so you use properties and what do you get at the end of the day you get that you can write the original function the test function which is forced on you by the entropy you can write it as an integral from 0 to infinity of e to the minus t x square very important to have x square because then we will put this square and we shall use the heat expansion of a certain test I mean of certain integration function g tilde and this function g tilde is trivially obtained from the previous is g of t over 2t ok so this allows you to go now why we can go we can go because precisely in the heat expansion we can expand the trace of exponential minus t delta delta will be the square of d as a sum and it is exactly in this coefficients that are appearing the quantized volume the Einstein Hilbert action with the x quadratic term the Yang-Mills terms and so on so we know that these terms are here we know that these terms are around but now we want to know the coefficients so we want to know if you want these integrals here we want to know these integrals and playing a little bit with these integrals what do you find you find that you write the usual formula for a power in terms of the gamma function ok and then you find out that actually you can rewrite the coefficients in the following form ok so this is just triviality ok but then we have to compute it for our specific function and when you compute it for our specific function you get the following surprise you get that the coefficient which will appear for instance in front of the Einstein Hilbert action is zeta of 3 involves zeta of 3 and the coefficient which will appear in front of the volume is this one with zeta of 5 and more generally when you compute moments ok you begin to find this strange expression where this is the Riemann zeta function ok ok so then you begin to worry because you see it should be true that this integral should define in fact an entire function of alpha so you begin to worry you begin to worry about poles about this about that ok and so I mean in the heat expansion actually this is the closed formula that you have ok and so begin to worry about these terms sorry heat equation takes place because ok in terms of the operator d you see as I said the operator d right sure it's from the spectral geometry and the operator d has in it not only the metric gminus but all the gauge potentials and so on it will spit out exactly what you want which was very very surprising at the very beginning ok so but now we look at the coefficients ok we look at the coefficients and this is the type of coefficients that we get and we begin to worry about these coefficients you know because as I said it should be an entire function so begin to worry about the poles and what not ok and you find out that there is no problem it's really an entire function so you work with it for some time you are worried you know I spent afternoon worrying you don't know whether something might be wrong in the whole thing ok and for instance you have to have rationality when you look at the expansion because the function h has only rational coefficients when you write down the expansion into the Taylor expansion except for the first term and what you find is that actually this is ok because in zeta the values of zeta at odd integers at odd negative integers are ok for that so that's what you get you get reassured but finally what you find is that the xy function of a Riemann multiplier appears so the normalization when you work in the coefficient of the heat expansion a alpha t alpha will be the following after many calculations what we find is that it's given by this elementary coefficient totally elementary times the xy function of Riemann at 2 alpha so typically if you are in dimension 4 you will have a term like a-2 t-2 as the first term then you will have a term a-1 t-1 and so on and so forth ok but with some coefficients which are these gammas and when you look at the table when you look at the table which gives these gammas this is what you find so this is for dimension 4 this would be in dimension 3 this is the term corresponding to the Einstein term in dimension 4 and then you have the other term now the very beautiful thing is the following I will finish there the very beautiful thing is that the functional equation of the xy function gives you a duality between the even dimensions and the even dimensions at large energy and the odd dimensions at low energy and conversely that's what it gives so this would be the conclusion ok so I mean so we were extremely surprised if you want we were extremely surprised because somehow before what was going on with this whole setup was that there was a freedom and there was no sort of how to say complete conceptual understanding of why we should take the spectral action while now just by touching by touching from in a very mild manner with a second quantized theory you find that there is a beautiful interpretation of the spectral action but for a very specific function and of course now the name of the game will be to see precisely with respect to the constants of the standard model how this will fit but there is if you want a freedom in this story the freedom in this story is a spectral triple that you get for the finite space so if you want the general idea what should be said as follows that what this theory uncovers it uncovers that it's probably wrong and Riemann was right to believe that when you go in the infinitely small the the structure is constantly the continuum no I mean the structure is more subtle it has some fine structure and the beauty is that this whole fine structure is encoded by the line element exactly as Riemann was saying because he was saying that the geometry should be specified by the forces which actually hold the space together that's exactly what is going on in this story then I'm not really a physicist so the issue is whether this understanding can be continued can be continued really at the second quantized level and what we are doing at the moment with Shamsedin and Sylocum we have realized that the Y which was the Feynman slash of the coordinates is actually a sigma model with values in a sphere and these are rather well understood in physics so this will give the quantization of this other side also which is not present at the moment which is totally the type of second quantization I was discussing is very simple ok so I think I will finish here ah let me now finish with the most important ok yes and you will see I am in it, it's a great time for the sixties you will see the generalized Heisenberg does it specify to the ordinary Heisenberg input no no no the pq is very very simple the pq would not allow you an arbitrary geometry I mean the beauty if you want of the equation which I wrote down is that the irreducibles are related to geometries and if you want one difficulty with this quantum gravity whatever is that the geometry has to appear from some irreducible representation here it appears from irreducible representation of this relation it's very strange it's very strange what do you mean by the second quantization the second quantization I mean the following ok mathematically speaking I mean the following we replace the spectral triples or the spectral geometry the inverse space is replaced by the Clifford algebra the real one the operator Dirac operator is replaced by one parameter group of automorphisms and the algebra itself is manifest by the inner fluctuations ok now what would be great is if a mathematician or physicist and so on would have the idea to develop this as not kaomology but you know algebraic I don't know the name that would be dual to algebraic k theory and I know this is worthwhile because I knew for a long time you know that what are called the Schringer terms in physics are dual to algebraic k2 so there is already some little int but it's another story to develop the whole thing I mean this would mean you know that physics is teaching us what is really the geometry it's much more subtle than we think of course we are just starting so physics from the quantum is sort of trying to teach us what is the geometry and it's very involved because so far if you want the picture which I told you and so on it's a one particle picture it's not the full story which is much more involved for sure no question


the French text but as soon as you start reading the second word it's it's over and you just start laughing so at any rate where we welcome to the talk hacker ethics many things are hacked from for reasons of activism fun or just pure curiosity and you keep having to ask yourself how far can I go what's okay what isn't yes that person is crap but can I publish the info of everyone who has ever used their services but someone in the audience has an opinion on that already there are many cases where it isn't clear how to proceed it's not like Hollywood where we have white hats and black hat hackers the good and the bad we are very often in a gray area and we have to consider what we do and there's that's where hacker ethics come in that's been a topic for a long time and today we get an introduction by Frank he has been a speaker at the CCC for years and he has been active in the CCC for years and I am very glad to have him here today and even for myself to just get a reintroduction to hacker ethics so let's welcome him with a heartfelt round of applause yeah well thanks so hacker ethics hacker ethics as used by the CCC is not the youngest anymore it was originally formulated or sketched out by an American journalist Steven Beal he wrote a book on hacker culture in the 80s and that was put out in 1984 fittingly and many of those rules and points that we using the CCC hacker ethics come from there really all of them some of these values that we that we hold high we've adapted or Val Holland did back then from there and that's what I want to talk about today why why do we need something called hacker ethics what's the point can't you just do what you want you know just fun with devices no more thinking required well our impulse here is that power creates responsibility as we look around who moves in hacker circles it's people who no more can do more than average who have more energy even though it doesn't always look that way have this impulse to research things this this curiosity this endless patience for finding out how things work and making things that look like magic from the outside techno magicians and resulting from that we have the possibility to do things that aren't that great who are better bad and where we can do wrong to people and abuse them and make them have worse lives and we try to stop that and prevent that and this idea that power creates responsibility is not as popular as it used to be in current society we have this tendency to move away from the values of the enlightenment and towards division and separation and towards this this idea of at least I myself can live my life and I don't care what these others do us here at this contrast especially believe that this is the wrong path and that we should value the values of enlightenment and fact-based communication and that we shouldn't go towards wishful thinking but based on what is and one of the first rules of hacker ethics is that the access to computers and everything that can show you how this world works should be unlimited and complete we had this value from enlightenment that the accessibility of knowledge this the availability of scientific results and including documenting your source code yes I know that this is a core of our being the availability of information was a problem for a long time let's remember 1984 I can remember during the mid 80s when I wanted information on how to use computers and how it worked I have to pirate handbooks from the East German Republic as a person from the West it was very difficult to get information in the mid 80s remember information was was was not easy to get at that time and accessibility and availability was not as free as today if you wanted to have information on a microprocessor from the East German Republic you'd have to look for a long time today you just take a smartphone out of your pocket and then you just look it up online in a search machine of your choice and you'd have the information but still the question of getting the information is still a question of political activism today because we now have the problem that information is being paid for by giving away information for example when you look on search on Google or when you look at publishers that sell information related to scientific publishing that is also not free so access to information is still a very important question and topic radical way on formulating this is to say that all information must be free for some time I don't know if you remember it on the ad decays communication congress we showed network statistics and we had a nice graph on that showed that we uploaded more data then we downloaded there was those were good congresses there's also the flip of the coin all information well pretty much all information dealing with all information we have to have the following rule we need to protect private data and public data must be useful that's a good rule so that nobody is forced to allow access to his personal information it's not normal that other people have access to your personal information it's not normal that when you use a messenger all your contacts gets uploaded to another server from people that haven't to who didn't understand that their private data might have a value which might affect their personal possibilities and the choices that they can make and what they can do this yes remember we're talking about 1984 here here saying public data public data that benefits us all knowing how traffic flows for example when is it possible to take the train like simple data like like schedules for trains there are talks at the congress about these topics this is never growing old the state and the big companies sit on this these huge public data which can improve our future and allow us to have a better time but our private data where we were with whom what we like what we did what we pay for what we what we buy what we wish for these highly private data those those are being privatized and sold to the highest bidder especially Facebook and Google and some other companies have gathered in huge amounts private data and sold it and and that shows that this field is still current and still relevant and as we are being creative and critical with technology we quite often run into these conflict areas just today somebody sent me a mail having found a database with data of thousands of people highly private data and he asked me what do I do now what do I do should I make it public should I try talking to the service provider should I ignore it should I send a mail to all of them and tell them hey look your data is freely available on the internet that's an easy choice you've got a great power there you can do a lot of crap there and it's going to affect a lot of people's lives very negatively and handling this responsibility is not always easy at past congresses on my phone number we had the hacker ethics hotline we where we said if you coincidentally stumbled across things where you think that might be dangerous call us and almost always the calls we got were about data that was badly protected and we were always in this kind of bind there our advice was always do the least amount of harm that still ensures that this bad situation is fixed and typically that men talking to the provider of these systems if you are in such a situation come to us will help you how to do that it's usually a lot easier if your call is hi I'm Frank Riegel from the chaos community computer club I'd like to talk to your technical manager typically I get through immediately versus if you try hello I'm John Doe I have your data that usually doesn't work out so well hi's a security does something similar there so we're not the only ones but I mean we try to help promote others who and help others who can handle these cases in a qualified manner and the next question is of course do these companies really have a sense of wrong and right do they even care do they just ignore it and so what we encounter here is often this embracing strategy oh how wonderful that you call it's great that you want to help us but we're gonna take half a year to do that and yeah if that's a real issue and they play it for time and they they waste time and during that time the data is typically still unprotected in the internet which is not acceptable at all so fixing these these bad situation has to be highest priority the question how we can make the public data also public which is the the lesser version of all of information must be public we have that example of of the publication of all the law file of all the laws in Germany that are made public and you usually think that we have this is this is common but actually we see now well it isn't big because so that was really quick and then the Justice Minister announced that all laws will be available for free in the future so you see it works and this and this prospect that your own activism can change something that you're doing can actually do something the knowledge that you can change something that's what it's about in hacker ethics it's not true that nothing will change out there if you don't do the right thing at the rain time a very important point to make since the beginning of the chaos computer club is that we do not want to judge hackers and female hackers or just hackers in general on how they look or where they come from or how old they are the only important thing is what they know what they can do and what is their goal and you always have to remember that that's a very radical kind of way to think we're meritocracy we don't want to judge people on any based on any other criterion than what they can do and what they do and that's something that for example conservatives are against they say well a high status has to account for something or people they're not that different after all and you always have to remember 1984 there was a time where nerds in classrooms they were being stuck into trash cans or toilets for example where if you were good at math you were not the popular kid in school and if you were a person that was interested in computer science and computers you're not usually not the the popular person in your class and the cast computer club has always been a home for such people most of us got there because that was the first time where we met people who had the same interest as us and the prevailing feeling when you arrive at the congress is you're at home finally finally you're with people who also value what I value and who are also interested in the things that I do and I'm interested in the things that other people do here at congress and this dogma that everyone is equal is something that we will not change next essential thing is distrust authorities and make decentralization stronger because one of because some circuits of course are more active than others in the chaos computer club but there is no headquarters or something like that and if you look at how the congress is organized there's a huge number of teams of people who do it in their free time and we're looking simply for a task or a goal and say all we want to make this this part or this goal the best and and we put all our energy into that and this is how the chaos computer club works on the whole so you won't define any big structure laid out or the big association that's organized like a pyramid but it's rather think for yourself what you what you can do and and do it and and get to people that are also doing it and don't wait for anyone to to say to tell you all that's the direction to go so if you're looking for for this thinking of of leadership and leadership deciding in which direction things go then that's not the place we have members and they are they are they are running around and doing things and and from that stuff emerges of course this does have this disadvantages like a strategy that's long time planned and you run into the situation where something simply doesn't happen which can have two two reasons like either there's no consents or no one is interested in it the opportunities that we get from that they complement each other well with other and NGOs who are more long-term focused but yeah we don't have that we don't have that send that headquarters deciding now we do that we have people who think oh we have to do that now and who have who like doing this we have fun that and and then do it and just think of it the the whole thing is 17000 people and they're all doing that in their free time in general authority leads to structures settling and we want to not do that if possible next part Karina had that earlier with blackhead described that earlier with whitehead and blackhead is the following there's a there's a call in right now which translators can't hear but the speaker is now apologizing and now you can see the benefits of mistrust authority and decentralized because the authority in this room is now correcting your own talk okay let's move on the question is now what do you do when you've hacked the system and now you have access to a database or for example you have the power to do things that you were not allowed to do or you couldn't do before that's a question that's as old as this club what do you do after you've hacked the system first I want to define the word hacking hacking is a more creative and also a more critical way of dealing with technological systems and the question is now what do you do and that question is not easy to answer in general when we deal with such questions we don't have a fixed set of answers instead we try to ask our own questions and the most important question is and where do now what's how do you want to continue surprisingly most people don't ask themselves this question you only think about and then I will publish this data and I'll make a press announcement and that's all it's gonna be great but in general that's not going to work out well live people move on live goes on and then nothing of change will have happened we have this responsibility that comes with the skill to intrude into other people systems or to manipulate systems and at this point in at a factor of scale that we considered impossible in previous times last Congress somebody came to me and they built a botnet well just by accident really yeah for real yeah they found an bug in the popular IoT device and they well they built a bot that sort of spreads and they thought well you know that'd be kind of fun if we could check other devices for the same bug in the same network and I mean the bot didn't do anything it just spread and looked around and spread and phoned home and said here I am and well then they kind of sat there with the little six-figure number of infected devices IoT devices and thought hmm well now now what what do we do and usually you get complications there in a perfect world Hollywood scenario you say well then you use that to fix that bug and delete itself and once you're done with that then you tell the supplier turns out you can't do that without doing damage in some of the cases with certain firmware hardware versions it would have happened that these devices would be broken afterwards well it's not great but on the other hand you can say well I mean somebody else might find it and then just use it to build a DDoS network so would that be better well as it turns out it resolved fairly easily because the manufacturer noticed and and on their own initiative patched it out and fixed it and I mean there's still a couple thousand vulnerable devices but that's not the same dimensions anymore so it will be interesting to just think through this scenario because we have this scenario where we really have a vulnerability and it's not a question of opening one server with the devices and the bandwidth we have we can find all the servers with a certain vulnerability and there's plenty of machines and if you build your patterns that are used to look for vulnerable devices well enough you can find you can almost find all the devices there and then suddenly you have tens of thousands hundreds of thousands millions of devices and it's not impossible it's not unlikely that you could find that many devices and there are cases where you prefer not to look I I found a vulnerability and I'm not going to check for it in any of these in this lookup patterns because I don't even want to know it's kind of irresponsible because you're not going to fix the issue that way but it's understandable so so far we've been talking about opening up systems and finding things and but a lot of us are busy building systems however so making sure that we that our computers work that databases work and aside from the obvious responsibility that our systems are at least somewhat safe as far as things can be there is a responsibility to towards what these systems do as well and we have this problem of scale on the other side as well building a system today let's say a dating portal then in this dating portal we will get a lot of data a lot of very private data do we want this data do we want to store this data in this way can we risk that these will fall victim to some vulnerability that they are used in some criminal way or do we want to build systems that improve lives in the sense that they encrypt that data that they don't even gather that data that the people who use the systems are not left in the dark about what happens to their data and as I look around every year there is this map of companies that work in the ad space thousands of companies companies that do nothing but when you go to a call to your website the data from the cookies or whatever other identifying identifiers you have are distributed as fast as possible and that people are able to bid upon what ads they want to show you and I keep thinking there must be people who program this shit there must be people who sit down and do nothing else their day that the these pictures of dramatically lit tubes of toothpaste arrive in my browser more quickly and they know that peppermint is better than strawberry for me is that really a life goal do you feel good while doing it does anybody here work no hands do you know somebody who works there do they feel good and I think hacker ethics also means thinking about what you do with your time alive what you use your time for what are the things you leave behind what are the things you set in motion the trends you create and I think we should all think about that a bit more I mean I don't judge anyone who works in this field because everybody has to pay their rent but maybe we should try and work on things that create a positive change a lot of us do but some of us and then it's okay to to say I work in a more shady field of IT but in return I get more free time and in my free time I do good things but it's worth thinking about it's worth thinking about the systems we build the things we do and whether they align with our interests and improve the world and it's occasionally a good idea to sit down and think about these topics it doesn't matter whether you build systems or whether you hack systems a good question or a good thing to say is that the goal doesn't make the way you do things good what would for example happen when someone does the same thing that you do except you were the target of course you can make this hypothesis more beautiful but one question or one question is for example what do you do when you have a political enemy what do you do would you feel the same way if instead of hacking a political enemy it would be happen to your friend you could for example say well maybe I should have thought about this a little bit more one variant of this is do we shoot birds with cannons for example look I've opened this online shop the system was a little bit older and I've hacked the system so I found two and a half thousand two thousand six hundred people who buy chocolate cakes is that relevant does your is this very exciting to you well then you have to say well then you'll just have to talk to the owner of this online shop you'll have to update his PHP and then it will be fixed but is that a big deal that's a question we don't have to really make a press announcement yeah for example chocolate cakes online dot-com that's a fictional address is that doesn't really matter if something like that happens important when you deal with very sensitive data maybe data that was stored in a very very amateur way in such cases it could happen that we make a press announcement one of the most beautiful parts of hacker ethics is that you can create art and beautiful things with a computer to most of us this is very obvious because most art you experience comes from a computer for example animations and movies when you go down to the assembly area and you look at what people do with their computers how beautiful it is how much aesthetic aesthetics are in there the charm it's obvious and the interesting thing is back in the day it wasn't that way computers were technical machines and if you really really really abuse the systems you could have maybe a graph for example a fractal Mandelbrot graph or something like that you could print it out maybe and put it on a wall remember the year 1984 still one of the things that impacts me which I feel good about is when computers make art the last point and hacker ethics is one of the most controversial especially if you're coming from the field of IT security for example when you wake up on Monday morning and you read news and then you think and you read the news IT security news when you think maybe I should have not gone into this field of work maybe I should have raised pigs or sheep IT security is a field in which you always have the feeling of nothing it's always getting worse nothing is getting better but don't be so cynical we shouldn't be so cynical it is a truth that in general computers make lives of people better I sometimes go around at Congress and ask people how have computers changed their life for the better their people with disabilities who are older who can't orient themselves and they have computers that help them in dealing with their daily life most of us wouldn't even know how to live their life without any kind of computer or smartphone we wouldn't really know how to get information without a computing device well let's have a look yeah who was in a library in the last four weeks so you see a few people have raised their hands we're not lost after the zombie apocalypse anyway the realities are that not only information retrieval but also communication all the things where you have to orient yourself navigation for example for example Wikipedia in your pocket things where you can download or access so that you can go on holiday without the need for books these are things that computers do that we have built and these are also things that we can extend and make better all the negative aspects we've talked about they're also very interesting think about the hate and so at social media the division in society because facts don't matter anymore these are true but they shouldn't they shouldn't disparage us nobody will die when Facebook is shut down tomorrow for example but we shouldn't make the mistakes of saying oh all these computers are all bad so if someone is working with wood or if they're soldering which is great but this sentence still retains its viability so in this sense thank you for this listening and have fun with your divide


Hello and welcome to the session. In this session we will discuss the following question and the question says, find the difference between the place value and face value of 6 in 65720314. Before we start solving the question, let us first recall what is the place value and face value of a digit in a number? The place value of a digit in a numeral depends upon the place it occupies in the place value chart and the face value of a digit in a numeral remains as it is your clever place it may be occupying in the place value chart. So this is the key idea for this question and using this key idea we will solve the question. Let's start the solution now. We are given this number. So the given number is 65720314. As you can see the number is large number so we insert comma after each period. So in Indian system generation the number is 65720314. Now we have to find the difference between the place value and face value of 6 in this given number. First we will find the place value. So the place value of 6 in 65720314 depends upon the place it occupies in the place value chart. Now under Indian system of numeration 6 occupies the closed place in the place value chart. Now the face value of a digit remains as it is whatever place it may be occupying. So the face value of 6 in 65720314 is equal to 6 itself. So the required difference that is the difference between the place value of 6 and face value of 6 in the given number is equal to 6 cross minus this is equal to 5999994. So the final answer is 5999994 with this we end our session hope you enjoyed the session.


Hi everybody! It's the Holiday Panda, welcoming you to ACMI's Holiday Show! Yay! Tonight we're going to have crafts and the ever-popular cookie decorating competition. So stay tuned! Hi everybody! Happy holidays! I'm going to make a wreath today out of candy canes. And first we're going to start with a circle, a piece of cardboard, a piece of paper. This is going to be where I glue on the candy canes. So I'm going to put it right there. I'm going to use the hot glue. First of all, let's see. I have my blue gloves to match my tablecloth today. And what you're going to do is you're going to try to make a heart shape at the top of your cane. I'm just placing them now and then I'm going to glue them. You can do this any way you want. It's a very flexible craft. I think we're going to do two more and then we're going to glue them. Okay, everybody ready? Here we go. Hot glue. It takes a little bit of patience, but I'm going to do it as quickly as I can. Make sure you have lots of glue in your glue gun, which this one doesn't seem to. But anyway, glue it on and then you can put a little decoration in the middle. And you can decorate it any way you want. And when you're finished, whoop, I missed one, right here. Okay, and when you're finished, you can put a string up on the top and hang it from your ceiling or wherever you want to hang it from, on your door. Happy holidays, everybody. Cookie decorating time. Ready in five, four, three, two, one. So I've never decorated cookie before, so I hope I can do this. I'm colorblind, but I'm going to go with this one. I think it's red. And let's make this star beautiful. I'm going to put an eye on him. Another eye. And then I think an orange nose and then a big blue smile. Look at that nice smile. Perfect. And now I want a green hat. And now we're, let's see, maybe some Christmas sprinkles. And all right, I'm done. Can't wait to eat this. All right, I'm going to decorate this cookie. Here we go. Oh, it's not coming out the way I imagined. Oh, no. Oh, this did not, this did not work. All right, no problem. Any situation can be salvaged. Yep, just like that.  And that's okay to have different plans. All right, 10 seconds left. Done. This is definitely not the AC on my logo that I thought it was going to be. But the colors are there. All right, now I'm going to show you how to make a paper snowflake.  You are going to start. Let me just flip to the opposite side so the silver shows up. You're going to start by folding in half diagonally, corner to corner. It's good to like poke, like pinch down on one end and then go across. Make sure your creases are nice and even. And you're going to fold it again, like this. Okay, so now you have a small triangle, equilateral. You are now going to fold this in thirds. So take one corner, fold it part way across, crease. That's like this. Then you'll do the same with the other. Take a corner, fold it part way across and crease. And now you should have a little kind of a semi-rectangular shape in the middle. Next, you are going to take the right corner. Let me see if I can do this correctly. Actually, you'll take left corner, fold it across. And then, sorry, you're going to take right corner, fold it across. Then left corner, fold it across. Now you have a kind of a base of a, the thing that holds a flower pot, not a flower pot, a kind of bouquet of flowers. You have a bouquet of flowers. Now you're going to take a scissor, cut off the top part. And now you're free to cut little pieces and decorate this however you want.  Let me try to do a circle. There we go. It's vaguely circly.  Let me try to do one down here. There we go. Now you have a cut out shape. You're going to carefully unfold it all the way. And now you have a snowflake. Thank you for watching. Twinkle, twinkle, sky, twinkle. This is harder than it looks. Time for some sprinkles and that's it. Happy holidays. Today we are going to make an origami box so you can put your gifts in it. You'll need a square piece of paper. You can use some foil origami. And let's begin. The first step is to make a fold across, open it up. Do the same thing on the opposite side. I just like to push down on my creases to make sure everything's nice and even. And now we're going to take our triangles and bring them into the middle. And fold and just go around the whole shape bringing them in. If you've made one of those fortune cookie shapes when you're a kid or still do for fun, these start off the same exact way. Not bad. The next step is to open up the sides here. And from the top we're going to fold this side right back down into the middle. Let's do the same thing here. Take the side and fold it right down. Line it up into this in the middle. So we have this kind of diamond shape. It opens up like this. Next is a very important step. And almost towards the end, you're going to take your corner and give it a little pinch. And this is how we're going to make the side of the box. Bring the corner in. There we go. Move that pinch. Do the same thing. Pinch the corner in to the side here. Pinch the sides, pinch the sides here. We're kind of making up a box shape. And fold the flap down. Very good. It doesn't need to be perfect. The thought that counts. And we'll do the same thing on the other side. And, you know, don't be frustrated if it doesn't work out the first couple of times. The more you do it, the better it will get. Let's fold this side in. Kind of go around and give it a good clean up. Pinch the edges. Okay. There we go. We have a pretty little box. And you can get another piece of paper and make a lid. There you go. You have a nice gift to give to your friends. Oh, wow. Oh my goodness. Wow. These are beautiful. They're really beautiful. It's going to be hard to make a decision about these. They're gorgeous. So many choices. So many choices. Well, I mean, I guess we can rule that one out.  Oh, it's a little plain. Yeah, although it looks like it tastes good. So it would be the one that I would probably eat under any circumstances. Because it's like, well, it's kind of neutral. See, I like the bright pink. Yeah. Not a fan of the green. Yeah. On any of the ones with the green. Yeah. Well, that kind of looks like it has mustard on it. It's kind of like mustard and wasabi. Yeah, wasabi. That's what it looks like. I love the contrast of the blue and the pink over here. But I don't know. I just feel like the little sprinkled things kind of make it a little messy. A little messy. I got it. A little messy. You know, this is what I like, the points on the end. Yeah. Like the attention to detail. Yeah. I like the color. Yeah. And this one is cute in its own way. You know. It's kind of like. It's kind of ugly cute. Yeah. Kind of like the Christmas tree in Charlie Brown. Yeah. Yeah. Yeah. And this. I don't think there's a lot of, there's a lot going on. There's a lot going on. A lot going on. But you know, it's got a level of coherence to it. And it's potential. Yeah, potential. So let's, I guess we'll do this by process elimination. Okay, okay. So we'll take this one. So. You know. Mustard out. Mustard out, yeah. Mustard out. This one. Yeah, yeah. Out of that one. Yeah. This one. There's something about it. There's something about it. I just can't. Like. Maybe it's his smile. I don't know. It's his smile. It's like, I can't quite get rid of it. So it's between these three, right? Yeah, yeah. Hmm. I'd say this, this one out next. Yeah. It looks like it was trying to do the same thing this one is, but then it got a little bit. Okay, flat one out. That's all right. So now these two. This is tough. Oh no. Well, between these two for me it's easy. That, I take that one. Smiley guy. Yeah. Smiley guy. Smiley guy. Smiley guy. There we go. The winner. Smiley guy. Smiley guy. Consensus. Good work with you. So, I never expected to win this and I've never decorated cookie before. This means a lot to me. I just like, I like when people smile. So I tried to capture that. And thank you so much. This is one of the best moments of my life. Merry Christmas. I didn't want to suck. This year I'm going to expand upon an origami project we've done in the past. So, if you remember a few years back now, I made a star using this pretty origami paper. Fold it in half on the diagonal. Fold it in half on the other diagonal. Open it up. Fold it in half along the rectangle edge and then the other edge so that we have this sort of pattern. Now we're going to fold this point in to here and then back fold. Fold this point in and then back fold that so that we now have this shape. Now we're going to take this and put it to the center fold and then this side and the center fold. Flip it over. Do the same thing on the other side and we need to, so we now have a kite shaped. We now need to just sort of give it a little crease fold like that. Then we're going to open this up. Pull this point up and fold it in on itself. Bring that down. Flip it over and do the same thing on the other side. Crease that down. So we now have another kite shape and we're going to open it up like this. Carefully. This paper is not happy when it's not done right. Oops, I have torn it. But basically we made a star like this. Okay, this looks really bad and I'm sorry. But this year what we're going to do is we're going to take this shape and we're going to continue on to make a poinsettia. So we're going to invert this point down, which essentially means opening it up and folding this point down. And to save an awful lot of time, I've pre-folded it. So we now have sort of the kite with the center bit in. And now what we're going to do is we're going to open up and fold that kite in again. Flip it over, do it on the other side. Okay, so we sort of have this triangle shape. Now, in the center is that little point. So what we're going to do is we are going to fold this up so that the bottom edge is flush with that point. So it kind of looks like that. And then we're going to take this side here and fold it into the center. Do it on the other side. Flip it over. Fold it up to that point. So these two top points should now line up with each other. And again, the sides go to the center. We then turn it this way. Fold it like that. Then we take this point and bring it up to where the other two points are. Fold in the sides. Bring the other point up. Fold in the sides. So we all look like that. Now we're going to kind of open. Carefully open it. Carefully opening it. So that we have this. And we're going to flip it over. And we're going to fold down the backs. And if you tear it down the center, it's not that big a deal. Because you just want to get it out of it. You just want to fold them out of the way so that they sort of fold on top of the points that are on the other side of them. And then you flip it over. You can sort of foof these a bit. Foof these, foof these, whatever. Give them a little three-dimensionality. And there's the green bract. And then we put a red one. And we have a poinsettia. This year I hope you had as much fun as I did. Thank you for joining us at the ACMI Holiday Show. Happy Holidays!


Now before we start today's video I've got one quick question and that is quite simply do you pull the ball left or do you in fact slice that ball off to the right? Either way what we're going to look at today is a potential issue that is causing both of those problems and I'm hoping that we've got a little bit of a drill that can help eradicate both of those problems. So today's test and the tips video comes from Kered Great Golf. Now that's a new one to me and someone that's obviously the link will be in the description below of Kered's full explanation and maybe a more detailed explanation than the one I'm going to give you today. This is of course my interpretation of Kered Great's instruction but what he's basically saying is there's two things that can call one thing at a time that can cause both of the problems. He concentrates on the fact that it could cause you to pull the ball left but he also touches on the fact that you could in fact also cause you to slice the ball to the right and for me on a personal level the latter is something that I do and it all comes from the movements I make from the top of my backswing that first movement and my first movement tends to be out rather than down and that can be the cause of both of these issues we're going to look at in today's video. Right now let's hope we can get this one in between the showers here at Betty Kered Golf Club which is just an idyllic backdrop I really love it down here but we've got a little bit of rain that is hovering so I'll make this one short and sweet. I've got the camera placed sort of down the line it's really interesting because most of what you're going to see is the movement that takes place like I said from the top of the swing. What Kered explains as being a major issue for a lot of golfers is the fact that when we get to the top of our backswing we make a movement and that movement can often be out and that is something that I do I've got a real issue with it anybody who's watched the main channel for a number of years will see that something and it's commonly known as sort of casting so you get to the top of the swing and the movement starts to come over and then what that does is start to deliver the club head sort of across the ball now that cross the ball with a closed face or what that can mean is that we sort of pull the ball off to the left and that's what Kered sees as the main issue I on the other hand I've got a tendency of getting to the top of that swing moving out and then when I come down I've got a slightly open club face to that path which is mean I hit the fade and that's where I said for me it's a dual problem that this potentially causes and to be honest with you over the years if you said to me if I went for a lesson and people asked me well which is my miss well my miss is often both I've got a left in me and I've got that fade and that's all down to whether or not I've got that club faced closed or open through the impact position but the one thing remains constant is it all stems from that movement at the top so the question is and Kered goes into a lot of description as to what all the issues are I'm going to skip all that bit because I know what they are I think you know what they are and quite simply if you do either of those two things then what you want to know is what is the solution well the solution is when we get to the top of this swing we've got to find a different movement to stop us from casting out the movement should be when we get to the top we should start to drop down a little bit so our immediate movement rather than out should be down and start to see the hands and the club shallowing out as we start to make our move forward and then it's that rotation to release the club head forward so to the top instead of coming out we start to come down drop our hands down and then start to rotate now all we need to do is just look at a couple of shots I played earlier on this morning just testing this out it's a hybrid first shot this morning and I can't believe first of all I'd say how straight it was but it was also had a slight curvature and that curvature being a bit of a draw shape which was really nice to see we then stepped on and I played a mini driver off the tee and exactly the same really solid and if we slow the whole thing down and that movement that I've just made you'll see that the big difference is like I said that move and you can see I start to drop down so as the rain now starts to come down I'll get straight to the point and what is it we need to start doing the drill that we're looking to take away from this and what Kerrard explains is what you need to take to the course or the practice area sorry get to the top of that swing and make that movement down in almost a slow motion and then look to release the club head so we're going to swing to the top we're then going to feel ourselves down then we're going to release the club head so it's almost I find this bit almost more difficult to do but I understand that you've got to get those feels and that's something to talk about in a lot of videos it's very difficult to translate sort of a movement in full speed because first of all doing it in or breaking it down and getting those sort of feels that's a very different feel for me that I would not really be used to like I said the movement is very different and then as you get to that you can then start to obviously build that up into a full swing but what I'm going to do first of all is just try and hit a ball down with what would be you know whether that's a half swing whatever you want to call it but just get to that sort of that location and then see if we can sort of rotate and turn through the shot so we're going to get to the top we're going to come down and then we're going to hit through and like I said let's see if I can do that in a slower motion if you like so out down I actually found that I caught that ball just perhaps a tad heavy but it still worked in the sense that it was a neutral ball flight and hopefully we got into that position but I've got to say whilst I like sort of practicing the drill swinging to the sort of half position and then trying to generate some power I almost felt it kind of it stopped me from getting any sort of fluid motion within my swing so for me again personally the whole idea of testing the tips is me to give my feedback on what I thought from carriage instruction first of all I think it's a real big problem and I think he's right to highlight it but for me like I said I would do practice swings where I'm feeling where I'm at dropping down and turning and rotating love all that but for me I'm going to hit a ball from this position as well the two shots you see me hit earlier was just being full swing but concentrating with one thing in mind and that's when I got to the top of the swing having a conscious mind that what I was trying to do was drop down and drill through the ball and not make that movement out and that made the significant difference so we're going to try one more ball down see if we can hit a full shot while this rain is really now starting to come down with a sort of full swing and see if we can gather a little bit of momentum and pace and it's a real good ball to finish this video well first of all what a real good clip that is I'm not sure if you are you don't know far we are away but that is exactly where I'd want it to be in terms of the line neutral in terms of its ball fight which is really key but also a really good clip I'm working on another video or another tip that we took from Alex Elliott video in terms of the takeaway which is working really well right now as well as you can see that rain is coming down I'm more than happy with the shots that I've hit and it's only been a few but the results have been so so good I love every bit of these tips I genuinely feel like it is helping my game so if you've got that cast motion just checking your swing right now when you next go the driving range or on the course just have a little think do you move out a little bit maybe record yourself would be my tip as well because it's not something I quite realised I did until I watched it back on camera and then you think Jesus yeah that is something that's a movement I make so if you've got a mate that can just switch the phone on just get a little bit of a look at your back swing film it from behind see if you make that cast in motion it's really dangerous like I said it can have a negative impact both left and right and that is the drill from Kenneth Gray to hopefully straighten things out a little right I'm going to get soaking wet we're going to call it a day thank you for watching thank you for supporting the channel testing the tips is flying right now clearly appreciating what is going on I'm clearly appreciating the support that is coming back as well so comments likes notifications subscriptions all and things greatly appreciated see you all soon I'm going to get dry


Hey guys Matt back from free salon education comm here with a review of our Lanza healing oil products that we were sent I'm really excited to talk about these products We get a lot of products in sometimes they don't make it to a review because we just don't love them that much But this is a product that we've really been enjoying. I've had it for about a month now So we've got to use it on every guest. We've actually used up the shampoo and conditioner We're almost out of the oil So that goes to show you that there's some products we have sitting in our basement that we haven't even really touched after the first use So these are definitely products that work really well. So I want to break down what we like about them What we use them for what Lanza has to say about them and kind of go from there So the great thing about this product line is that it has a blend. It's a phytophore complex is what they call it It's basically a blend of four botanical oils So it's really just gonna help keep the hair nice soft shiny bouncy Keeps the volume in the hair, which I love it's sulfate free gluten free sodium free So you don't have to worry about any of your guests with allergies or anything like that So I really love these products for that reason. It's also ideal for all hair types And I've really found that to be true any guests. I put this on it works really well It's got a really nice scent to it. It's it's a strong scent So, you know a lot of clients like a scented shampoo. They like to smell of it So, you know, it's it's beneficial in that way, too I know a lot of our guests when they pick up a shampoo, they don't care about Necessarily what's in the shampoo. They just smell it first and if they like the smell they take it home So this not only has a great scent to it, but it has a lot of great benefits as well There's an oil in the product line as I showed you guys This is something that we're using on almost every guest that walks out the door And we love it because first off, it's not heavy a lot of the oils that are out on the market right now Are really heavy. So this is a light oil. You can have a volume type blowout with it You could smooth the hair with it just works really really well There's also a combing cream the thing I like about this a lot of people talk about cutting lotions and all that stuff You could put in Lotion type products and use them for cutting but a lot of them have alcohol base to them So you don't get that slip through the hair and the hair starts to dry quickly So I love this because it detangles the hair. It's great as a cutting lotion It just works really well and that's you know in our day-to-day job We just look for products that are going to work for us It also they finish it off with a nice firm hairspray. The great thing about this. It's UV protecting It also is humidity resistant and heat protectant So you can use it to do your curling iron sets anything you want and it's going to help protect the hair So this line altogether the keratin healing line from a healing oil line from Lanza is just such a great product I definitely recommend you pick it up for your salon. Check it out. You can check the link below Click on that. It'll take you to Lanza's website You can give somebody a call and they'll hook you up with it But really check it out again You got a shampoo conditioner healing oil combing cream and the finishing spray and you're pretty much set for every guest in The salon so hope you guys like this review leave the comments below We love to answer any questions you have about the product make sure you check us out right here Free salon education comm subscribe to us on YouTube and we'll see you guys on our website. Thanks guys. We'll see you soon