2/4 Spectral Geometric Unification
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Formal Metadata
Title 
2/4 Spectral Geometric Unification

Title of Series  
Number of Parts 
18

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 
Institut des Hautes Études Scientifiques (IHÉS)

Release Date 
2014

Language 
English

Content Metadata
Subject Area  
Abstract 
Classification of finite spaces and basis for geometric unification.

00:00
Geometry
Computer programming
Finitismus
Group action
Multiplication sign
Sheaf (mathematics)
Mereology
Open set
Lecture/Conference
Operator (mathematics)
Square number
Condition number
Spacetime
Theory of relativity
Military base
Forcing (mathematics)
Projective plane
Basis (linear algebra)
Independence (probability theory)
Physicalism
Quadratic form
Limit (category theory)
Bilinear form
Connected space
Category of being
Computer animation
Irrational number
Hausdorff dimension
Fiber bundle
Figurate number
Family
Resultant
Local ring
07:00
Group action
Standard Model
State of matter
Decision theory
Multiplication sign
Sheaf (mathematics)
Complete metric space
Expected value
Mechanism design
Manysorted logic
Determinant
Descriptive statistics
Spacetime
Bilinear form
Functional (mathematics)
Sequence
Connected space
Category of being
Arithmetic mean
Symmetry (physics)
Right angle
Figurate number
Bounded variation
Resultant
Point (geometry)
Trail
Slide rule
Finitismus
Presentation of a group
Connectivity (graph theory)
Mass
Rule of inference
Lecture/Conference
Natural number
Term (mathematics)
Operator (mathematics)
Condition number
Addition
Focus (optics)
Chemical equation
Element (mathematics)
Independence (probability theory)
Set (mathematics)
Mathematical model
Complex number
Limit (category theory)
Estimator
Field extension
Formal power series
Summation
Commutator
Universe (mathematics)
Game theory
Table (information)
Family
Spectrum (functional analysis)
22:20
Slide rule
Rotation
Finitismus
Presentation of a group
Modal logic
Multiplication sign
Sheaf (mathematics)
Mass
Parameter (computer programming)
Rule of inference
Food energy
Force
Mathematics
Matrix (mathematics)
Manysorted logic
Causality
Lecture/Conference
Natural number
Operator (mathematics)
Units of measurement
Condition number
Social class
Rhombus
Coalition
Process (computing)
Spacetime
Forcing (mathematics)
Element (mathematics)
Expression
Physicalism
Independence (probability theory)
Volume (thermodynamics)
Price index
Mathematical model
Incidence algebra
Bilinear form
Connected space
Category of being
Arithmetic mean
Summation
Binary tree
Spring (hydrology)
Commutator
Order (biology)
Universe (mathematics)
Right angle
Spectrum (functional analysis)
39:08
Group action
Building
Dynamical system
Curvature
INTEGRAL
Decision theory
Multiplication sign
Thermal fluctuations
Sheaf (mathematics)
1 (number)
Insertion loss
Mereology
Group representation
Maxima and minima
Position operator
Rhombus
Physical system
Area
Spacetime
Product (category theory)
Generating set of a group
Block (periodic table)
Thermal expansion
Price index
Bilinear form
Functional (mathematics)
Connected space
Arithmetic mean
Phase transition
Order (biology)
RWE Dea
Right angle
Adaptive behavior
Routing
Student's ttest
Number
Frequency
Degrees of freedom (physics and chemistry)
Thermodynamisches System
Root
Lecture/Conference
Wellformed formula
Operator (mathematics)
Units of measurement
Addition
Matching (graph theory)
Scaling (geometry)
Element (mathematics)
Physical law
Division (mathematics)
Volume (thermodynamics)
Line (geometry)
Summation
Spring (hydrology)
Network topology
Universe (mathematics)
Gravitation
Game theory
Invariant (mathematics)
Family
Spectrum (functional analysis)
55:56
Group action
State of matter
Multiplication sign
Equaliser (mathematics)
Sheaf (mathematics)
Parameter (computer programming)
Complete metric space
Mereology
Weight
Food energy
Expected value
Mathematics
Sign (mathematics)
Square number
Spacetime
Constraint (mathematics)
Closed set
Thermal expansion
Bilinear form
Functional (mathematics)
Connected space
Metric tensor
Arithmetic mean
Shooting method
Lattice (order)
Right angle
Point (geometry)
Metre
Vacuum
Observational study
Divisor
Student's ttest
Mass
Event horizon
Number
Frequency
Propagator
Causality
Lecture/Conference
Term (mathematics)
Wellformed formula
Subtraction
Spontaneous symmetry breaking
Adhesion
Series (mathematics)
Addition
Standard deviation
Scaling (geometry)
Forcing (mathematics)
Expression
Physical law
Algebraic structure
Line (geometry)
Mathematical model
Set (mathematics)
Vector potential
Summation
Factory (trading post)
Gravitation
5 (number)
Film editing
1:14:16
Metre
Group action
Presentation of a group
State of matter
Direction (geometry)
Image resolution
Multiplication sign
Sheaf (mathematics)
1 (number)
Mass
Mereology
Food energy
Order of magnitude
Number
Possible world
Group representation
Frequency
Latent heat
Degrees of freedom (physics and chemistry)
Lecture/Conference
Forest
Square number
Energy level
Condition number
Spacetime
Product (category theory)
Process (computing)
Block (periodic table)
Generating set of a group
Forcing (mathematics)
Physical law
Moment (mathematics)
Element (mathematics)
Algebraic structure
Median
Prediction
Mathematical model
Incidence algebra
Line (geometry)
Field extension
Category of being
Arithmetic mean
Quantum
Right angle
Game theory
Spacetime
Directed graph
1:24:18
Computer animation
00:02
How do you think
00:06
I and and the movement of the and if I think in the war you go on and on and on and on and on and sold last week introduced by India the coupled with the geometry can be taken as a basis for the new files from the Internet actions and then facilitated that I defined what we mean by an opponent of space I give the physicians no so properties and just let everyone disinfect the spectra and I defined the spice quantities and the relations among them and then the question of course is and if in with space is that bases 5 interaction then the question is what kind of local industries should be taken and as the starter I made an assumption the assumption made the this time or His Mokelumne Place which is formed as In a project also continues to languish creation some now as a form that has been very well understood and then I went To see essentially what launch date for the launch expressed in what kind of space should take and then sold for that father by classifying spaces which fits set in physical connectivity and the political criteria that we need and the following that was hero then there's space which 1 the space of funeral fighters essentially for us wouldn't dare would include all the factors and in this case achieved the furnishes sufficent and property endit just Sherry said we from his mother because actually on the presence of what was and in the opening oneday acquires essentially what would likely require the failures all which physical language new Maryland and in this aspect of course actually the president will hold the dumber operator was a current operator without allowing owners to In both this condition so what you really have always heir credits no then of course that you share jailed outside .period let something .period units but and the question of that this and independence of a few the Senate bundles of Buffy's then you really need to face the problem that all year particles would be doubled to get involved again for every particle we know In this part and you know something is sometimes called the Miller family program or the public problems and the result is solve this problem have now you know where UPS space and that the issue of course is that there should with you tedious space and you said out like a sore then but the figures this of course is Murkowski and would like to impose what condition the Jeep size 5 then if you that this section would impose certain conditions on the properties of the space and as I have shown last dive to time that wouldn't holds a conditional offer no medical kill dimension so in Minkowski space if you really need to impose was conditioned on the side saw I can go fly and this would imply actually the decadeold irrational despair because Europe is which employs actually produced square which is optional should be warned in June that he is I think the prime should and need almost signed India gunmen is the grind of security and the government wants so these other purposes that we needed essentially between the forces know we know actually that that Indian Minkowski you have you know for Grace's signature say minus boss last lost from the opposite end in all these would somehow gets at each other and then you're left with the Kuwait killer mission to which means that meant that space of the finite limits space From limitations children physics so that sexually the finite space to have email sent the properties and emission 6 the new leads sector
07:02
sets off fire absent for example absently minus 1 a little but picturetaking go at 2 times in the past 1 and half in something like this so there she wondered whether hadn't tried to understand the Sinai faces and that what discovery and I would go through nothing is approved Latino through the realization of the pool In that 1 discovered that there and generals of the finite space organizational from bonfires and that them and the publicity it completes divisional manager Russell said assumed that the finite space is better than I'd like a S H and he have come to everything for finite and 1 discovered that the Congress extension of this they this endeavor there only 2 possibilities either he puts the policy and this security is inconsistent with the Kalenjin 6 which leaves us only 1 possibility that is the surpassing and that is manager brought which is invaluable he knows that we call it the end end of seeing In addition when Liam Paulsen says Aliza lettering on the 1st said camera and this is a point of would on 3 you know I understand you know we cannot them give it a for the account from revision White should be like that but that is like that and a lot of possibilities are mocked the relevant than this really reduces instead of made this his own the complex numbers you dates I need said over the for the 1st and the restrictions on 2 in this case and is even and then also because no 1 would like to pull the Kiraly the operator on this algebra and elements of the algebra forms upandcoming they so this case what happened given that that L this time and moved to a page with splits they'll face lesson may failed for example blossom what we sell books of this is that the the 1st company example you can do Is the following that they should be 1 in this case the already here is the main reason for the and offstage the scissors should be for and it is the adequacy and his analysts tool in society as secessionists also stated in the Universal TV example and is there and 1 of each with a specific talking at oddly like this and this sexually is like and in this case the 1st example it would be a each plus H for the 1st 7 0 plus some for the for the 2nd of course other engineers on possible that I was able to see you have to get which is entirely on the fast track for foreign tourists to the decision of the Jewish you look at so I have to say OK this I would say and do anything the and then had to be at peace for the 1st multimedia case is also its nobody's these optimists .period by you warrantless time and then the only thing that you know the assumption they made out of there a flat 1 . 1 did impose already funded in Bordeaux in selecting the illegal get instead of know age procedure will begin to the pleasant to see and what he can show that the cases I would not be physical but like a lot of them immediately all sorts of possibilities and we Jesus the University of University cases the 117 cases tried the case doesn't exactly that figure you OK we choose to do based this is something which is not controlled by the who could have chosen their I would have chosen this and this and that any balance that Jennifer Ireland because they would that really give you really arrived for his sandals this was a chip and big and Dorsey possibility what wanted the meaning of the century gives you know and in the next 3 1 action you know which is enormous so I really can't get work out that gives the silicon variation on everything almost the same except this that the variation in the next traffic to and estimate the riches of the limits of call maybe there an extra lurking in the spectrum but you know people are stocking here since recently there was some papers in which they said they will observe something which deviates from the standard model and you know some people said maybe it's an extra practice of IRA but this is actually the most somatic possibilities that the only known assumption I made so that left the actions this the left action and then this the same like action and then we said this is Jr this fall generous and there we said this actually is defined to be be all opposite so this is not 1 of actions and that led action right action commute each so this century and been used this
13:57
property has been used up to this point now from a actually 1 needs further function and the hollowedout discussed In that and this called on the 1 condition and not you will understand this condition it's a conditional on getting the idea of the conviction if 1 Johnson's condition then what happened and that the connection would be quantitative terms and Delaney can work all the possibility 1 this is not so when businesses start but this allergies divestiture plan "quotation mark actually in examples where this condition it's not satisfied and you've got the better of the controversy again I have anyway so it will have began Monday that connections Armenia everything is very nice everything you know falls into place today what happened this is not satisfied in all this would be the 1st of 2 grand unified theories and by the seller molds and things like that but this would come much later took short article sequences of this condition but so far the focus our estimate you this is slide and that will top of dictionary now there is little conditions it is the question and that if we gave up on the date of the deal that will break the rules and revenge abroad in the viewed of the auction is a question was what we have shown is that that abortion because if his hero then this symmetry is the impact of the cemented it isn't that will go ashore actually that the reigning going to get women were called a model which I'm really going to do a little later In that you're aiming as you for column which really across from the sum for seeing as the symmetry look what presented in this case you in India a higher symmetry which is not observed in nature and end actually beautified out that the neutrinos are old masters yeah exactly must which now we know that it's not true so from this point of view we're not actually and that the fee must be using different this year because of museum then we are amending controversial experiment that neutrinos would become old masters look at which would have been OK along the like 95 5 or something like that because people didn't know I was not sure she the neutrinos are massive wouldn't care because many this finding massive only limits on the method of the nutria now we'll achieve the massive but the masses that extremely small but that a massive this is the 1 that open mouth what happened during the review relevant other than that if this is the members of 0 and for this condition to be satisfied that the operator most of the following fall and that is what this case actually I've been instead of value will be known description of what the happens I will stop in all L the more complete Olivetti executives that presentation is what goes on so that you have all idea is that this section here as I was saying feed is not simply people you know are unique and and complete everything unambiguously that much of the and with all that he did so all so essentially let me examine this In but I really can't tell you that the fact that this is 1 0 union a unique possibility during a game gives the neutrinos and my anonymous and it would explain if you why the masses of the need to use a very small it the it's an example of what's what was known as a seesaw mechanism so he added the comes out naturally and it's all the problems even so let's say let's see how things would look like if I wanted to go and do some competition what should I do so that for this anyone starting point I mean on date the ancient To be major lawsuit which and this new almost unique new the that didn't come out of the sky of classification this was the 1st month easier the the result that have OK so if essentially followed like actually do represent an element of the holidays are like that then I won't bite it and make you know I want to assure that everything that we do is league this is essentially can the authority and patient if 1 would like to simplified His life and a recently know everything if we do for him to put on the computer 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condition that the With that defeat defended the Iraq will also be the broken into 1 and all I'm where I want to the so that actually be the talent and and and the lectern index so this is that and this is the plot and then you can see that the elected in the 4th it comes out of the 4th and this is that you a the at 5 1 declined slightly below plan One Book One sorry to 1 sorry we wanted to block and that I have sigh which I'm going to leave it as such want on the habit of Sunderland will find time to buy and then I have to find want to what the this in Ireland there this is a welcome even if you know about me as the right so this would what I want to point you need to rewrite it why given that name because of comes out like that the quantum numbers does that this would be neutral guy but this comes out you know I to the usual meanings on and then of course this is the here right and this of course is upright is done similarly sigh anyone is the Dublin which is a new era new each of the Boblett in left and the use of knowledge OK so you see it you we don't know much what we obtain the connection the presentations all of the particle spectrum of all fermions Renault which a presentation the Sony can write the 16 in this case is a fault for fall and as for his new composed and cuckoo clocks cooling and escorted to come close to 1 . 3 and then this is to write gloss to left and that everything that we see below that the present everything falls into place look at so this is my 6th spread within actually and I have a job sigh and so my spring that would be the size of Ohio and then fly on fluoride .period unit which only want the will apply and run them at independent but they are related fool jury took 1 of the main actually hit me as if I would let the local right then and there and I that brought it I connected plans follows like a market that is this 1 he reminisces belongs to the 2nd I don't foresee so to something like and this is dead gone and should be it this is much more to see actually element of there's a slides and then you go for the the opposite which is borrowed universe the new scholar fuel company he is the only going to get life but as 1 so you won't Jason should also called to 1 and the idea of going to get back beat them to the project and if you look at the this sentiment the Salomon obviously they commute with each other while recorded his notebook each other this isn't 1st Gibraltar was mentioned on the 2nd and they don't talk to each other so essentially this time to attract intersection about twothirds the task force looking on the starters look so essentially collided in this saw the 1st baby opposite this affront automatically no I would like to offer me a permanent or I have to justify this condition up in the 2nd of conditions it's a conditional on on the media and the injured were aborted because of what happened the following directors of science conditions you are called Matrix approved vision and the open ActionAid 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actually that this is possible if and only if you have only 1 9 0 argument of the accuse him of let me like that should expression for you and let me see how those Coke like you know I have to remember when I get back coalition will block size started the fire recognized this when we tried it again in so there's a lot safer catch and necessary corrections if I expand and that I must look at stumbles mostly their security if I look at that as we have it demeaning doesn't mean that you really have an element which you this if I have more it would mean that's for example opted endowed every everybody will start getting by on a massive forgetting would break charge that would bring the charge consideration because in this case there would not have 0 charts so Lonely Planet unit in physics was the dugong is that you really knew there must be otherwise you destroy charge for the region and it's not an excellent accused them of you can have only 1 the retirement this 1 and Europe there would really correspond to the masses Mayor at a Mosul the righthanded neutrinos now it's clearly directed that why this is really extremely important in order to solve it took Spain essentially wideeyed neutrino masses so smart OK so this section in the use of the both of us .period you know in order to they idea that observation that the operator should take this fall with the volume 1 on 0 Antony and the rest of you know this is the end of the bar correlated the government wanted the Congress could lift off each other and the only thing I have to to find the what the form of the DAP operator in the finite what about what changes you know the whole of whole idea that things really I'm really cost it of the
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costs and in a way that we have to explain why the stunned the world actually you know why this kind of sort of slide "quotation mark assumed that everything possible was 0 Anthony we must read alive and the status of almost uniquely hopefully when they 1 to have final say OK here comes this is without in minute but England all of the posited that catapults emphasis because they don't put any physics simplicity get anything right because even if I don't want to explain nature then as you know I can start with that would be the smallest based on lending OK at the start of his career during the past few days for the time can the was killed incident you in In 1 of his most is the annual unless this is a useful and this is the 1st example but then you have the rather lies from beginning to because you know the question that deicing neatly in August only thing I would ever get Of but this is the 1st possibility that when gets OK external actually what do you do we go from here and there was we use of have some sort of like a curious to see what battles that will operate the Kenwood House the DAB the fine many properties I've written a lot so you really have to search for 2 short films are you have to walk a very fine that the lowered our energy data and Judy stand the finest with remember we were and government during World War II cucumber and you go the scope so these properties I have say sorry and so if you do that you immediately discovery the juggled played over a finite space the simple for relying on the United and there is also a new arrived here I because I don't apply to involve lot because then it's it's more physical and their new idea right and than I have seen you left he left the public and then problems arise known rights but the popular down that this is the involvement of the saudi signal OK while insisting it could cause this symbol of the new breaks algebra From you know for this condition and other Polish to mystified and then you put the signal what covered the following that this will grow each saved blossom for visiting broker of all this it was wrong but the thing whenever this is like 1 and this is all I and misleading break but cardindex index it breaks the poem that into 1 industry and this visitors that the 4th is really broken into steep blossomed the office however because of the conditions needed the opposite is equal to 0 it clearly what happened and that basically this old also broken you know because 1 index bogus what index and then exercises steeple policies brought the breaks and the the I'm not independent what undiscovered actually abandonment of their break big this fall so you're going to get you act thanks mom this is my 1st speech time with Ascot Partners and although a situation where medical body takes the form like Alfred Beta doubtful about way it does mean that the 1st stage the must move this fall and now he was going on havoc at Guardian so this is my 1st and this is model for by then the model for what do we have win discover actually that this is acts and before this is 0 and this is and where it the sentimental In other words if you will do what we discovered that the feces the fears about independence and that essentially would see and then final Gibraltar finite space the breaks down to see class B plus which is the sum of of what it really comes out off very quietly that there is in my analysts for the neutrino and vesicles OK so that section adamant of the year arrival with the deed and that we will carry because if I did Jesus songs for these properties and you know I want to put the story sure what happened in that Dell a long vanishing elements of the deal there 1 more requirement that we have to .period In order to read complete the single of the game and that the commute when no actually yeah I need commutes with diamond which would let them but 1 of them about if you do that then you discover that only they only you call copies of the of the jet operated I'm on 0 and ready we have the difficult political complete single if I won't let you down I cannot done with the tradition of How does it look like many heroes I'm thinking of going get and here we are going to be a key which is actually a call company the neutrino newcomer coupling the and there are some of the year we are going to get through this is new last he left and this is the new candy I've learned that sensibility for the quarter ended only old like diamonds grouped together and there new heroes Luzinski carried out alive some of our essentially after some made excision breath wondering what exactly what the Japanese children with this what we do and this is the following however when properties competition exactly so you know many of you get many is said that that appointed to get me museums Lionel Dahmer the mine is the garment that you all by 9 months of the year rollyourown encampment by the arguments and so so that the matrix of nothing much to and other ones on essential "quotation mark don't he not that we are not the problem of binary from anything we just spoke about classification and presentations and satisfying the properties although locomotive and led almost uniquely acutely what .period cause that the stuff the I said that the operator of the full local industries is equally but over the money for the grossed 1 the blast governmentfunded growth yes we have been what might also to
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know is that yes we know know exactly how the looks like the animals quarterly nor the government there that and then the operator on the usual sailing meaning India so that you can see the quiet 80 Of the many would cross on producing everything the product of corrective steps "quotation mark no it will actually had 1 always starts with in with 1 fluctuating deep .period was among fluctuating the sailors within the which corresponds to say some flats start from India for a 1st phase for example you got his start with Eugenio like the Committee for the D and we knock you that you really can generate in the medical videolotto fluctuations is out of the fluctuations and this is easier to wanted to do that you say this is the new you make this is the function of facts you discover that you have to understand connection in order to make the thing an inordinate To make a single and so that actually is you know that similarly here we have seen must find the whole route will introduce you where is indeed Close said in a letter to the west the people of Myanmar which is also this he added that the 100 or ineligible for 2 months to fuel his decisions exactly the only we had more than to say that if you'd like to get the gravity of the that you want to get the on that day the kind of person exactly so they I forms in this language and it is a this subsection a but they will actually have written His wife they are evident when the 10th the with the for the city to which to make Benjamin that you for the of Soviet talking about my decision actually was everything we know this reform 1 family and everything and for example gave and gave and everything is all about the reality of this game this is why the that would have made it in generations this means that he is a thing like this 6 off that the fuel I'm going to talk and banned and that or measure brought 4 3 4 3 on the environment 84 by 384 agreed that this election a wide it's it's it's it's much easier promote set fighting you know me devices because they look at you would use to put intense adaptation because intestinal tissue just put an index and don't care how much promise because you know you know how would the from so it becomes very efficient to do it Washington the flight back in the beginning because 40 has yet to start will these waitresses to see what accent the book some direction in and this was progressing developments fight so this actually here use our right now like to compute described how the to like this sir probably are there is no I wanted just to show you that things come out that this that that day she it's come sitcom Martino and people think that were cheating because you know and put it in and then it's not too you know everything comes out in a very well defined way 1 economic sheep in way I saw the light and say OK maybe you and then you can put in distilled like From and then you have to db what did you read and and so on so I think I can look at you those that meet the sentiments and only so I don't care how they look like in the following I went back to my representation and then I mean known to get an element here like it or not what we want to widen the conflict number analysts said and for comedy b In this house would be involved could complain about how it could be 1 of compliance and is seen to take Opel should isn't if I think about this for the rest of the mitigation fees and acting on them righthanded neutrino devoted defined that I had to do to win quarter with then In this respect you know you discover it should mean that this guy would be easier because they to be you know right and nutritional is most of time this area is is is in need of a guy who a drug something else then of course that you the things that I would be a pool blocked widened political ones and so on and this section we will discover is a and then the odds is given by Iowa GE I'm not being so you know it's an actor and the nominee of everything is president of the Cleveland sitting under the guise of Arctic In addition are start you to get something like you know a guy like it was blocked 1 Blondel also gave him :colon than you know this is not within the executive members arrested Poindexter and collection action and then you put use 1 tool and what discovered that this is the proportional to Belmont Park you and this is what it is and the remains and as an hour fluctuations and I still think this and wire when this work this is out of line with very well alongside the amount it means that illustrated by interconnecting wiring months left and the right edge of residents of communities of institutions like the 1 here that's what I have done little to do with Genentech is also arrived at the University of all you worry concede that but of what a unique about the forms obviously easy used to students republic what's not so easy actually yeah to show for example that died April lot toolbox for example only 1 In this case said vilified and what happened actually it is a each body you warning they could get death and the finding that the only goal Balkan it when he's a lot to to do with adopts the sun looking up only when he is eroded the these guys are really the reliability the bluff the and then because problem the same see political carry corrupt have different he says that you've got to get this thing show that some of this and that what really can do this conclusion is the latest recruiting more complications and after some algebra 1 finds the felt that gap paper including fluctuations were mostly in the Internet connections and the connection on the space and the connections nothing begin each season nothing so so Ontario we have the we can achieve that and before doing anything I can do that then the protection for the formulas look at operating only the Jets I'll tell you what she now mediated that worlds away
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with her brother justified the supply because in the end you previously signed economic seem find saw it from the air so if you know and want your edits I want to be happening that we needed to get bill that he side the patenting of then you need is an antiSemitic product and the long and the demerit of DAT gives the of DNA and the fountain in the square root which means that it's really apparent integration and you have not double the degrees of freedom took note highly like vendors sold when you get the idea all the Munich kind accounts for example a new 1 the New lost in bond the close less than the right and everybody the blast that then send me actions proceeds from the Food and firmly and you get exactly the correct type of charges and everything and you want and that contacts had 1st executive because of this usually worked out the GAA started universe the Illini commented being achieved you wonder Rimini completely funny way and audit by the matching and there a few other actually make some assumptions that 1 peaks and Roman Langenbrunner mother wife and hostile to make a requirement that the police told them should be with you the syllable addition that would put in OK so China future 1st shook everything why is works and it but so what's next section what's next and then you need to make close friends and then immediately but that was not enough so wildly in the mind after all you know we say that we have against basic aspiration of dynamics and that we should be able to described the full interactions step that I have been speaking classically everything years classical no Soulliere actually comes mind here or there and the basic idea is that the buried there which rose 3 the building blocks of the welcomed space In principle I study a spectral does the opposite side of value from around the Durocher volume values and we know actually From starting saving enjoyment ordered that operators already made many the volume values genetic invariants mother as saying all the genetic in Venice included that show in as a function of all the genetic information should the question of how can we extract this diamond token resurgence that information about their loved ones is simply workout land outside this space so we need something more and so the basic idea in that it's is suspect from no other mortgage over way don't as a liar and a liar itself Our system then congestion To be given by the trace of the function of gene where there's a positive function passengers escaped with the help of the exactly as eligible talk about the scale units because the idea as dimensional operator remember at this stage the government Musée du rejects wheels and a sexually has by mission 1 therefore you really have to divide it with something of my mission Nov Courtnage anywhere other than and opened but about people dealing with escape later because this is the really as divisional what you should do this cake and get them list or what I'm talking about of course is not something which is a succession of solutions the only thing is that you have to use the the reaction to the news in the future to usually spaces which would run from this is the only place so you have to say that this what do I to individual orders you watch what you think about it the jewels in the form of a please include your name in the Order of the Senate and the function which is the sum of refuses and the people in this area but what all the productivity Boston because there's the is but this important 48 Canadian action on households and consumers in the world because of many Boeing will like maybe some positive and so now essentially how how can reduce spring more obviously we believe 1 of the functions of the a "quotation mark we can really work out the messenger to this week when would not have to do and by the end the following but we must of his can of expansion monumental smoking actually make the case for minimum many frozen food products almost 34 steady very very effective so what's the basic idea is to get your support the have functional some operator PT you make somebody know when a new law expansion see the SPS and then 3 and then you have you have something like trees of P 1 concerns is applied entered the Philadelphia was assessed is is given by no you use a metatarsal formula and then I will demand and also you obtain them the the opposite of the division of the Bergamo function they he has won this 1 the when the game would that is part of a massive losses or to 0 and then the next step would be the former as of Stacey minus using he'd get expansions and then of course actually this is Dumont a hand the
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and more cases 1 well and over West hooker adhesive for emissions there were a lot of integral to 0 and that this is a kind of the and the venture called the students score and then decided that offer the connections of the party some there this isn't just a quarter hours a wide it's useful if it because exactly of what an employer in that this is you know the the overland and this would be clear actually women and expansion it many special 1 land so the 1st step will be unavailable to fall on the ground that the force the London square and then 1 the little Maryland squad that I assume you have the skin is extremely large then the standard become known as the relevance of quantity expansion will bring down when she approached the scale and you know what would investigate arrogant thing that's going to be so used history or blank state that this is actually but sludge would definitely bring down and in that case were has 2 lines different ways of dealing all such expansion but in no way meant some complications Of this expansion for you know Robertson Walker metrics and things like that and the meat Paul's almost up to the black of the constraints on you when you you have on the cut back flights for the from the presidency start to see that the bridge down but not before you know which is which is really amazing that this action is so accurate that will on the way up all the way up the blank scale but not peeled it's just that for actually doing this expansion still need fast anything sensible because obviously this looks so last farfetched that you get library functionary choking decided the function this is the very by this is straightforward reply deep south again and again in all the usual expression because these models structure but for only part and not the leader of the fighters should work you know that's insinuating acted as early as all exports so how to proceed dictionary here it's known Riley said here we assume that .period continuously voters former emotional and in this aspect the suspects there the expansion you know what happens in the following that only very the point is that if an assault on the floor many faults look at what happens from enforcing Monday will worry investors questioned and what is actually very interesting but I'll talk about it later but before Monday and and all that means actually the only 0 was oddly easier the cool 84 and the like and this fall as were worked out longer by by Gilkey here some you know standard formulas and that because of that actually looked really becomes argument that this is in the squad of the G because the cities the submitted and that's what they think about follow your idea says William you say means and this is the real we will last only a mail which is a connection and this only again this also is given by if you don't mind this year we will you deal most the new lost so long and can eventually you gave an expression of this section is that the 2 important thousands of this expression in the which is an invariant and in that connection law only give me all the time you get used to which are constructed out of this good and there's only Emilia was released from the following you right this expression this form In this fall and then we had the knowledge that meal is given bond yields some expression today you may know Lawson the company also has a list of what conjecture for Christian and otherwise acuity can compute all these expressions In the unique way and they will lower body complete so we have is the huge you take any useful and you get another use redirects and you like this fall and any of that defined the cameras general space remembered as Indians Alaskan fishermen and you also get me he invented the colored usually the interference in the 84 Britain for decades so onemilliondollar slept in on a 0 the 1st album expressions the violence 16 bodies removed Judy In this way of course 384 opposes brief the so there's actually nothing to pump you want people on think development of and this is reflected in all of this is that you loved before winning the cosmological constant and would kill the political such as Eugene White is 0 that's a different story again you move can call change because would have to work in this you're still exists and I think you have to talk about the effective you want to talk about it and thought about it as heroes of that problem was a composite of political contribution coming from the vacuum expectation value these but these are supposed to be much smaller than actually has In same way of conscription and when they do go the way of the vastly exceeded those of us who have had in the outgoing at the year that actually but there that the discovery I am leaving the squad that the new listeners with this unless he has and with the amount that would from this section after single it would come later recalled the shooting was the museum saying whether this year because the price of new book I always thought that the thing barbecue this guy so all you get actually Oliver sits alongside them with anything policemen will yield little actually give you beautifully with the the scale of what you know the story of the company and my squaring Virginia but by squaring video and so obviously that me and my new the baldness the sash part period of 5 each part funding I know you have some so that when you look at the square here no violent and I is going to give you a picture study
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which is loving Monday's Mass OK so use ,comma actually cited the new greater than saying only get the square so you about the actually in this example of what you really get your did want to get the following a few years this bill probably factor saying This is the guy that he would eventually give rise to the to Anderson dating Mass the Senate essentially Yukawa coupling you square feet propped up its square of so we this expression and then we will also following then again the shutdown of his of if you read the whole a overall winners Lanier said minus OK so if you'd like it we are here in the UK so and 1 of the people minus over a square additional does this have to do acquired yes ruled junior there a miner's son of whether additional part is negative for the committed speech anyway so you see the the master of the oneliner sign this is really extremely important issue as receive when you for the sum of all the cause the settlement with a characterized with the potential to the view the landowner for additional money squad minus 1 of my most for during 2 and loyalist side there is the potential of the Mexican Hat it's essential to get the next 1 now obviously you unable to get the minus sign why because you objected it In the end have taken place the 1 with the DEP has these qualities but has as word of the jumbled together for the 1st time in the expansion of the minus sign the next day we plus sign it political permits which is it symbolizes goal for maturity community that day in the prescribed before the start we don't know they're so there's actually important points we can point out the government share which is why straight down and then last that are easily the equal footing sewage money to buy caricature of this together servant than the space and he'll escape member squad was the underscored of course actually like this time the squad for it to be related to it much 16 . you look at Itchen related to look so this the black box score so from real along with that if you would like to make sense of the scale number that we started with a miniature I think that they of it is that is almost Of course you can always you give afterward said net income function so you can get sucked into spending on things like that of the point where so it is Lord of the exactly the plan must close euro from factors but that is law that we know that it's overload of the next painful and he had Ibuki what's the formula the formula does that's what this is I hope you have room America here Oh criminal trial to the set standards shortly and the carriages square meters squared the Canadian in school give it a square now you know that he's "quotation mark along in squared the the the given me eyes and those of get the school Africa what a squirt of garish of course Lemieux squandered their but here labeled to get blocked by loan demand and from Union Square which is can .period and I will do that kind particularly the stock Anderson met them and things like that that means an end to the meeting with exactly Afghanistan's nothing but give it a squirt you know because whatever you it all this if you take the squatters from people saying Well you know your argument with the squirrel the conversion the squirrels are connection is a careful and intermediate Louisiana Louisiana and what really can compete some declarations but in the end is well defined conclusion that the important thing is in no immediate get any point of going soft in this section are going to get have 0 but were told by squad known as squad those also most former factories climatic terms for their age "quotation mark exams for a potential and similarly Everything that idea after rival also "quotation mark idiosyncrasies and so on the fastest score and right to the border in event 1st of all I understand there is no escape 2nd we noticed that will find squirt .period now this is really important for your fuel war the realization of gravity use them would make that would improve the tuna propagator of the gambit on it may have been of course mutiny but of going on there this with all the warning about because in that case wiretapping you you have to come expansion and you know if you'd like to Tahiti daddy's not cut the expansionary yesterday the fully fledged series but there is at least this consolidated several survived as squad and it is important Florida then propagator of the conservative and finally see an issue that we have a kind therefore the you want for the Italy would fizzle a kind extended for destitute too week and the contradictory for the country as you sit here and that's exactly what we're looking at now immediately find religion that energy was quoted the computers were
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far worse than the time he sees "quotation mark due to square foot June the famous unification 1 obtained for S U 5 or canceled and delayed unification we would have actually we have to talk about this .period later than expected because this is not exactly facade not not executives fine because you're going to see this time you plot the scene OK the longest Of the opulence source from downsized introduced will by unfairness of the offenders then discovered they don't exactly but in others and for restoring within the meaning they don't and they almost made up and business of you know there's so much in between that would alter the know control and that is premature to say whether this is about bottle to get the better of the signal yet that in view of its policy of adopting wouldn't let me say with meant that Pakistan is what we intend to assemble general except waited 15 or 16 or above magnitude to which is the huge go on the in southern there is and you know things that we have discovered that things are not to be reintegrated you know to tools in the model that we have because this that she turned out to play an extreme many important road this language which a priority legal on that we even make a prediction that Biggs last is given by certain understand all that to be correct because we have ignored refused to the secede however that if you take this to the block out there and in all of you completely in agreement with experiment and in an issue that should be there are releasing is stake this England to effect has also already been carried out 1 border and nobody has guaranteed to reporters so we'll so maybe it will change that we we can only guess is that it with which a booklet on MG which age and the right amount underlying direction because this is the and self so let me summarize the game so we started from that a general idea the general idea that spacetime can be approximated why a product of the continuous 5 discrete ready for and that he has said it will not be no it may be just completed his speech what it was that England started to say is because you know that generative Duarte's really well so that continuous popped up to the blanks gave words very well so we can update that energy level according to the law we know that that uh you know anyway and many fall .period work so to assume that we have unusable extension which makes it almost only doctors about the reality of competitive that again extended by a finite space live this idea that we discovered that tool almost uniquely we can't predict the structure of the mobile we know the ceremony representation we don't you why that 16 fragments we know what I presentations of the same as we know the games ruled these images and once again with this actually this and saying that what we can do that things what we cannot do is much more of course because what got unlawful example police say their electoral matters that you know the the masses because in principle in all this there if there is more restrictions on on that 1 should be amended for this amendment the finite space contains only called up into it contains sexual information about so if you know phone number that cases like dental minus2 or something then you know that the ratio of the electoral but what matters is typed into forest so at the moment for so in that case and this information putting in my hand when I did a lot of predicting that if funding is completed successfully you want that everything comes out of university farfetched postandbeam because you need some extra tax structure which really got proponents will not let you in and so I think there is a lot of respect the criteria and that the property that we verified Beaumont intent section why that 1 the generation this little this must come out somewhere in so far this aspect we have no idea what the reason for this we need to meet officials is that it was during this resolution to bolster the peace Indiana in this section almost all about knowledge of if 1st the United States is what this this is a little over the reason for the use force to jittery and suggested that the questions of security we don't want people to know only too well into sinking of the most of the conditions for which it was possible for you to violations of which is an ICE knowledge and all that was lost from the face of India in you so why city would will likely start but we don't know nobody knows should something that wiretap and masses of the firms out of the way the REO of fallible after a lopsided genealogy by meters shorter than that of excellence in the EU's executive director of the course and there was status and reviews case you could say it was a case the of Soviet the flu considered 1 of the things he's pleased because of services from those each user's West German diversified facing his use of services for this is the time for us to Will the opportunity that hope if maybe what it went the other way OK is forces that that possible juror 3 somebody as to why this admirable receiver that I the same luncheon a I think was very close following that it is it must be I could use the process to it must like 60 so often we must have a exceed so actually have been unsatisfactory but was far from your foot unfair and that this is the right to remove 1 of the schools and Piech's to be a OK later on funeral we paid all this condition and really I want to put everything together and investigation then of course we have many mornings which not all you want but what but that that should be element of Byron and will not be able to see what really goes on a killin energy except for the 6 stop he knows this is not clear but that's another story in and I will also appear in the Code next time I will learn a good deal by analyzing that quantum aspects of of the modeled on the median of the writing on the wall of the office of the 1st of the season of course is that the answer what he wants more and this is just a part of the during the 2 sides just as the entree into it's going was once which his cell signaling a science to be collected from the outgoing and handle the humiliating yesterday's incident was related to the quality of the Jews and I think you know the thing was gone before In all this hullabaloo left and that people :colon verified the electorate would you should but the thing actually lost to Boston because people think that Dr. you know fitting this is the biggest thing that 1 has to fight In the misconception that there are millions of possibilities and simply wanted you know that station of the spouse of all 4 the world possibility which is correct and that many other possibilities which is not really correct because you know what happened this specification of the went through and that is something believe possibilities you all of this comes unique you know that they will have to explain why would you want a collection of famous facing 1 of the following sections of the amendment would change the image you continue making international calls for
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an end to the the violence in the home and saying to me that want last week that the country's unity section of the University of Florida and the traditionally associated with the seizing but if you haven't you know if you stop firing line then you have to fight all this can use a client waltzes In allowed many acts of degrees of freedom which we don't see election the new government services to find out exactly recently reached out to the people of the state of the city