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thank you it's an honor to give I think

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the last talk and thank you for sticking

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around I'll try to be somewhat

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interesting if I can I want to talk

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about talking about why this doesn't

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work all right then all right we got one

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slide that's good well I want to talk

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about where it all starts the

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foundations the the the deeper

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understanding that we would all like

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about what's going on in the world and

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particularly what's going on in the

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universe as a whole how it got this way

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and how any understanding that we might

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have of the universe as a whole could be

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applied locally to our own situations

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and to some of the phenomenon that we're

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Bernie talked about the constants of the

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universe and physical laws of the

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universe and I won't say a whole lot

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more about that but it's worth just

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reflecting on the fact that it seems

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that there are a few numbers a few

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constants a few parameters that

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determine a great deal of what goes on

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in the universe and the phenomenon that

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takes place within it and these

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constants seem at least to be somewhat

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independent and rather arbitrary and yet

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we know that in several cases these

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constants are very finely tuned to

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support the kind of universe that we see

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in the life that we experience here and

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if they were different the universe

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would have been different and we would

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not have evolved to have noticed this so

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there's a question about how it got

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there how those constants got that way

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and by the way how did all that stuff

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get out there in particular

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places how did all this get to be the

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way it is even if we knew what those

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constants those parameters were the

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determined the physical laws and the

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properties of matter and energy we would

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still have this question of the initial

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condition why is it that the cosmic

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background radiation the oldest thing we

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can measure is not uniform as a matter

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of fact it seems to have some pattern to

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it

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get that way and how are these

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parameters derived in the first place

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well let me talk about oh that's

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interesting this is interesting I think

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you have my presentation from last year

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or two years ago that there's a slide

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that wasn't in there well it's alright

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we'll go on yeah there's there's

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something that got scrambled in the file

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it's alright yeah let's just do it this

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yeah I'm sorry but we've got the wrong

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presentation can we look at the stick

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again yeah could the universe be some

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other way the constants could be

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determined a lot of different ways here

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are four of them by some supernatural

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being perhaps they've determined random

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and there are a lot of different sub

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universes that have different values for

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these constants in which case we sort of

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this constants and those laws could have

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been in some way determined by our

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interactions with them our observations

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we created all by observing somewhat

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like similar previous talk or the the

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case that I'm more interested in perhaps

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that these constant really aren't

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independent and arbitrary but rather are

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mathematically derived and related in

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some interesting way so I'll give a

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couple of thoughts about that I'm

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reminded of Clarke's third law and by

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the way he added a fourth law in 99 for

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every expert there's an equal and

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opposite expert if if you've ever been

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involved in patent litigation as I have

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this is very apropos so I think it's any

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sufficiently advanced technology is

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indistinguishable from God we're really

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not imaginative enough to think of what

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advanced technology really advanced

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technology could be like and to say as

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some would say that they can't be here

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because it would violate the speed of

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light and too much energy has involved

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in all that kind of stuff is nonsense

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they have complete control of time and

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space and a lot more things that we

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haven't even thought of yet so if you

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think you have a guardian angel or some

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interaction with God

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I don't see any way to rule out that as

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being interaction with really advanced

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beings and advanced technology but

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beside the point back to physical

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constants here are some of them Bernie

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gave a nice summary of of a particular

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list Michio Kaku thinks maybe there are

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19 numbers numerate says John Baez

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counts 26 numbers

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Martin Reese's book just six numbers

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which is a very nice read derives the

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basis in an entirely different way using

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dimensionless numbers number of spatial

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dimensions and so on another interesting

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way of saying how many degrees of

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freedom are there maybe the real number

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is somewhere between six and twenty six

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I don't I don't know the usual

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assumptions that are made before we

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start thinking about these things I have

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some trouble with not because the

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principles are necessarily invalid for

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any reason but because of the way

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they're usually thought about

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materialism usually means there's stuff

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out there there are things in space

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whether those things are particles and

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fields or whether they are strings or

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some other abstract structure I'm much

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more tending these days toward thinking

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about differences and boundaries and

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transitions rather than the objects to

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me the the difference is to find the

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objects not the other way around

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and there's some precedents for this or

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maybe be able to go into that a little

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bit more later reductionism the idea

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that the whole is equal to sum of the

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parts people always say no now something

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emerges when you get all the parts

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together that wasn't there among the

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parts forgetting that if you know the

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parts and all their interactions you

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really do have the whole nevertheless

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three reductionism is not the only way

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to understand things and I would like to

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promote more constructivism that is

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starting from first principles or no

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principles and building upwards as well

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as reductionism taking things apart and

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trying to figure out how they work so

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the usual interpretation of that bothers

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me a bit randomness and the idea that

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there are truly causeless events at the

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core of physics I've totally bogus that

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one it seems to me that quantum

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measurement is not random at all and

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there's a big mistake that we've been

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making by making that assumption and it

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is an assumption in quantum mechanics it

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just happens to work very well so we

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believe it but I don't think anything is

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truly random in the sense of being

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causeless event even at the core of

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physics cause and effects might might be

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the most pernicious about of these in

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the sense that everyone thinks about

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cause and effect as a unidirectional

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thing and Liat this leads to the idea of

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time as a dimension

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and flowing in one direction and so on

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bad idea it seems to me that physics is

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telling us that everything is

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symmetrical in time and that all

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relationships of the causal nature are

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bi-directional and influence travels in

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both directions if we take these

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assumptions and formalize them in some

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way we usually get what's called a

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system of axioms you could say the

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standard model of physics is a kind of

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set of formal assumptions quantum theory

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in mathematics set theory and predicate

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calculus and so forth so we tend to

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formalize this and one might say that

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the more complex well let's say the less

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complex the set of axioms and beliefs

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are the more likely it is that we're

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close to the bottom that we're close to

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really understanding something or closer

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to bedrock and the more complex things

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are the rivers so here's an example from

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mathematics the Ximena Franco and the

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axiom of choice set theory eight axioms

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two of which at least are infinite axiom

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schema now I ask you does this look like

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we really understand the fundations of

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set theory or maybe sets are not such a

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good idea in the first place which is

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where where it's where I go Henry won't

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want car a said later generations will

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regard set theory as a disease from

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which one has recovered what we haven't

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recovered yet this is really one of the

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most fundamental things that are taught

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in mathematics congruent versus deep

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models a congruent model is really a

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kind of a theory it's an abstract

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something another that we sometimes try

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to tune to be the same shape as whatever

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it is we're modeling and so the more

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tuning is necessary that added

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assumptions and FUD factors show up and

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and this is not necessarily explaining

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things but merely modeling them so we

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can do stuff and try things to the model

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that will then be reflected in the in

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the real world somehow whereas a deeper

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model has something that's simpler and

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it was really more fundamental and more

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like how it really is how the the

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phenomenon or whatever it is is actually

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generated and tells us something more

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about its place in the world

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here are some discrete physical models

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that I think are

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really becoming more and more

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interesting

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string theory hasn't quite paid off but

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still there's something very importantly

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correct about it even if it's not the

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whole story even in the standard model

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group symmetries as an abstract idea can

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model three of the four forces at least

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in some respects some of you may have

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seen causal dynamical triangulations a

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terrible name if I've ever heard one

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it's the cover story in scientific

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Scientific American this month by Renata

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Lowe and some others they claim to have

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derived from first principles the

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dimensionality of our space three plus

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one or four dimensions questionable

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again but again I bring these forward

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just to say here's an interesting

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direction and this kind of thing is what

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we ought to be looking at Garrett Lisi

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in the ee8 Lee algebra showed up as a

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possible candidate for a theory of

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everything last year and Steven

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Wolfram's new kind of science which is

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tries to explain everything in terms of

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cellular automata again a very abstract

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notion at the base of it all here's the

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e8 Theory 248 dimensional lis algebra if

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you decompose this into various parts

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sub algebra Lisi would say that you get

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a very good correspondence to gravity

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the forces particles and so on some

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people who know a lot more group theory

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in mathematical physics and I do have

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said this really doesn't map well and

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it's not the answer but it's a good try

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so let's go to the other end of the

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spectrum the the simplest possible thing

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what's the simplest possible thing we

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could imagine in the abstract where

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what's the starting place for everything

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that we must all share and the answer I

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think is nothing the void and I don't

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mean the vacuum the empty set any of

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that kind of stuff I mean nothing

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suppose we take nothing we take the

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smallest step we can away from nothing

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what would that be something it doesn't

278
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have a name it's not nothing okay that's

279
00:12:27,170 --> 00:12:26,070
the first distinction this is from G

280
00:12:30,500 --> 00:12:27,180
Spencer Browns

281
00:12:32,750 --> 00:12:30,510
laws of form two distinctions can be

282
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made in two different ways cardinality

283
00:12:36,650 --> 00:12:34,290
and bosons flow from the first

284
00:12:38,180 --> 00:12:36,660
ordinality and Fermo fermions from the

285
00:12:40,660 --> 00:12:38,190
second so I think we're really onto

286
00:12:43,690 --> 00:12:40,670
something here

287
00:12:46,310 --> 00:12:43,700
some friends in Great Britain took this

288
00:12:48,680 --> 00:12:46,320
idea which they developed separately by

289
00:12:52,640 --> 00:12:48,690
the way not from Spencer Brown and tried

290
00:12:54,200 --> 00:12:52,650
to make a hierarchy of groups by

291
00:12:55,610 --> 00:12:54,210
instantiating the number of different

292
00:12:59,990 --> 00:12:55,620
things you could distinguish at each

293
00:13:07,520 --> 00:13:00,000
level 2 3 7 and 127 the total number of

294
00:13:10,850 --> 00:13:07,530
symbols then is 2 3 10 137 and really

295
00:13:12,740 --> 00:13:10,860
big now this caught their attention

296
00:13:14,270 --> 00:13:12,750
because 137 is very close to the

297
00:13:17,630 --> 00:13:14,280
reciprocal of the fine-structure

298
00:13:20,570 --> 00:13:17,640
constant and 3 10 137 and really big are

299
00:13:22,910 --> 00:13:20,580
something like the ratios of the

300
00:13:24,320 --> 00:13:22,920
strengths of the four forces so this

301
00:13:25,790 --> 00:13:24,330
group has been looking to this quite a

302
00:13:27,440 --> 00:13:25,800
bit further than I can tell you about he

303
00:13:28,760 --> 00:13:27,450
ran out and again I don't know whether

304
00:13:31,220 --> 00:13:28,770
this is going anywhere or not but it

305
00:13:33,170 --> 00:13:31,230
certainly is interesting

306
00:13:35,150 --> 00:13:33,180
stepping to relativity everybody knows

307
00:13:38,210 --> 00:13:35,160
that Lorentz transformation of the

308
00:13:40,280 --> 00:13:38,220
Lorentz factor is very critical and

309
00:13:41,840 --> 00:13:40,290
connected to lots of things in physics

310
00:13:45,380 --> 00:13:41,850
as you can see from this diagram in

311
00:13:47,510 --> 00:13:45,390
Lucas and Hodgson's book and they go in

312
00:13:51,110 --> 00:13:47,520
the in the into this book and derive

313
00:13:52,490 --> 00:13:51,120
Lorentz factors from a wide variety of

314
00:13:54,670 --> 00:13:52,500
different viewpoints there's something

315
00:13:57,410 --> 00:13:54,680
very important about the Lorentz factor

316
00:13:59,870 --> 00:13:57,420
but I'd like to see it described and

317
00:14:02,840 --> 00:13:59,880
derived discretely so here I have an

318
00:14:07,220 --> 00:14:02,850
object and a very very simple notion of

319
00:14:09,230 --> 00:14:07,230
motion that is to say if it moves 1 if

320
00:14:12,320 --> 00:14:09,240
it moves to the right I count +1 if it

321
00:14:15,650 --> 00:14:12,330
moves to the left I count minus 1 that's

322
00:14:19,910 --> 00:14:15,660
the simplest possible definition of

323
00:14:22,310 --> 00:14:19,920
motion I can think of there's no rulers

324
00:14:24,140 --> 00:14:22,320
here there's no clocks when it moves I

325
00:14:26,660 --> 00:14:24,150
kick my clock if it moves in either

326
00:14:30,230 --> 00:14:26,670
direction I take my clock and I keep

327
00:14:32,960 --> 00:14:30,240
track of by counting these dimensionless

328
00:14:34,640 --> 00:14:32,970
things how far it's moved here's the

329
00:14:36,260 --> 00:14:34,650
number that it moves plus minus the

330
00:14:39,829 --> 00:14:36,270
number it moved - that's kind of a

331
00:14:41,480 --> 00:14:39,839
distance the number it moved plus plus

332
00:14:43,850 --> 00:14:41,490
the number of times it moved in the

333
00:14:45,800 --> 00:14:43,860
other direction and that's sort of a

334
00:14:47,540 --> 00:14:45,810
time but we have no independent clocks

335
00:14:50,119 --> 00:14:47,550
whatsoever so we turn that into a

336
00:14:54,710 --> 00:14:50,129
probability using a the sum of these

337
00:14:56,720 --> 00:14:54,720
accounts and for simplicity in the

338
00:14:59,230 --> 00:14:56,730
algebra and we can note right away

339
00:15:02,449 --> 00:14:59,240
there's a maximum velocity which is one

340
00:15:04,759 --> 00:15:02,459
one step per tick if all the movement is

341
00:15:07,970 --> 00:15:04,769
in one direction that's plus C if it's

342
00:15:10,939 --> 00:15:07,980
all it to the left it's minus C now

343
00:15:13,040 --> 00:15:10,949
let's take two such things and try to

344
00:15:15,949 --> 00:15:13,050
add the two velocities together this is

345
00:15:18,769 --> 00:15:15,959
like firing a gun from the front of a

346
00:15:21,199 --> 00:15:18,779
rocket ship let's say so we're going to

347
00:15:22,850 --> 00:15:21,209
watch just the second object which is

348
00:15:24,590 --> 00:15:22,860
moving in a similar way but relative to

349
00:15:27,499 --> 00:15:24,600
the first object so that these things

350
00:15:29,379 --> 00:15:27,509
add up so I add them up here's the first

351
00:15:32,119 --> 00:15:29,389
velocity here's the second velocity and

352
00:15:34,699 --> 00:15:32,129
look look at these two terms right here

353
00:15:36,379 --> 00:15:34,709
when number one goes in to the left and

354
00:15:37,730 --> 00:15:36,389
number two goes to the right we don't

355
00:15:40,879 --> 00:15:37,740
see anything because they cancelled each

356
00:15:42,470 --> 00:15:40,889
other out when number two goes to the

357
00:15:44,749 --> 00:15:42,480
right and number one goes to the left

358
00:15:48,079 --> 00:15:44,759
there's we're cancelling and we don't

359
00:15:51,230 --> 00:15:48,089
take our clock either no no time passes

360
00:15:53,929 --> 00:15:51,240
so we do the mathematics on that just a

361
00:15:58,069 --> 00:15:53,939
little simple algebra gives you this

362
00:16:02,840 --> 00:15:58,079
answer and sure enough one plus V 1 V 1

363
00:16:04,730 --> 00:16:02,850
V 2 is in the denominator so all steps

364
00:16:06,079 --> 00:16:04,740
are still size 1 C is equal to 1 and

365
00:16:08,119 --> 00:16:06,089
when you add the velocities together you

366
00:16:10,369 --> 00:16:08,129
get exactly the factor that special

367
00:16:12,350 --> 00:16:10,379
relativity would tell you can we derive

368
00:16:14,480 --> 00:16:12,360
all of special relativity from this idea

369
00:16:18,049 --> 00:16:14,490
I don't know I haven't done it yet stay

370
00:16:20,090 --> 00:16:18,059
tuned but the idea is that we started it

371
00:16:21,949 --> 00:16:20,100
with something extremely simple before

372
00:16:25,869 --> 00:16:21,959
the usual notions of space and time and

373
00:16:29,860 --> 00:16:25,879
we got to something very quickly that

374
00:16:33,910 --> 00:16:29,870
gives us special relativity relativistic

375
00:16:35,860 --> 00:16:33,920
additive velocities summary summarizing

376
00:16:38,569 --> 00:16:35,870
the constants

377
00:16:40,100 --> 00:16:38,579
seem arbitrary but they might be purely

378
00:16:43,040 --> 00:16:40,110
mathematical and there might be a lot to

379
00:16:45,860 --> 00:16:43,050
be learned about them from studying them

380
00:16:48,740 --> 00:16:45,870
as abstract mathematical objects and

381
00:16:50,809 --> 00:16:48,750
deductions I'm advocating construction

382
00:16:53,449 --> 00:16:50,819
rather than or in addition to the usual

383
00:16:56,230 --> 00:16:53,459
reductionist approach combinatorics and

384
00:16:58,639 --> 00:16:56,240
fourth seem to be very important

385
00:17:00,650 --> 00:16:58,649
suggesting the idea of dick distinction

386
00:17:04,189 --> 00:17:00,660
or difference as prior to object and

387
00:17:06,649 --> 00:17:04,199
maybe the ultimate origins and the idea

388
00:17:08,720 --> 00:17:06,659
of discrete motion from pre space and

389
00:17:11,269 --> 00:17:08,730
time and relativistic velocity addition

390
00:17:13,549 --> 00:17:11,279
may ask you a question how many I've

391
00:17:17,529 --> 00:17:13,559
ever heard of this discrete derivation

392
00:17:22,100 --> 00:17:17,539
of velocity addition before nobody okay

393
00:17:24,860 --> 00:17:22,110
thanks it was due to urban Stein and Tom

394
00:17:28,010 --> 00:17:24,870
Meador as I may have said and we're

395
00:17:30,139 --> 00:17:28,020
exploring that a lot further we're

396
00:17:31,399 --> 00:17:30,149
always seeking funding to continue this

397
00:17:46,940 --> 00:17:31,409
research so if anybody's interested

398
00:17:49,909 --> 00:17:46,950
please let me know thank you minutes for

399
00:17:57,260 --> 00:17:49,919
questions and it looks like Dave Leiter

400
00:18:00,760 --> 00:17:57,270
got his hand up first Richard this is

401
00:18:03,549 --> 00:18:00,770
more a an observation than a question

402
00:18:06,860 --> 00:18:03,559
one of the first books that I read

403
00:18:08,539 --> 00:18:06,870
entering into this whole realm and I

404
00:18:11,690 --> 00:18:08,549
think I remember it correctly he was

405
00:18:15,620 --> 00:18:11,700
called cosmic consciousness by Maurice

406
00:18:19,760 --> 00:18:15,630
Burke and what he predicted was that

407
00:18:23,330 --> 00:18:19,770
humanity was gradually becoming more and

408
00:18:27,019 --> 00:18:23,340
more and more intelligent and I'm almost

409
00:18:29,960 --> 00:18:27,029
seeing that happen between the speakers

410
00:18:32,299 --> 00:18:29,970
and and the audience we're kind of

411
00:18:37,669 --> 00:18:32,309
gathered for that that purpose and

412
00:18:51,850 --> 00:18:37,679
because of that growing ability it's a

413
00:18:55,510 --> 00:18:54,130
okay I sort of thought the speaker might

414
00:19:03,040 --> 00:18:55,520
have something to say in response any

415
00:19:05,440 --> 00:19:03,050
other questions I did I'd like to know

416
00:19:08,500 --> 00:19:05,450
what the implications are of the so

417
00:19:11,020 --> 00:19:08,510
called cosmic axis of evil on your model

418
00:19:14,920 --> 00:19:11,030
this idea that the universe has a kites

419
00:19:15,970 --> 00:19:14,930
not distributed evenly you mentioned it

420
00:19:17,050 --> 00:19:15,980
briefly at the beginning of your talk

421
00:19:20,170 --> 00:19:17,060
the background radiation

422
00:19:23,920 --> 00:19:20,180
have some kind of a pattern in it and

423
00:19:26,740 --> 00:19:23,930
there's an area where there's where it's

424
00:19:30,430 --> 00:19:26,750
kind of sparse I have no idea it seems

425
00:19:32,800 --> 00:19:30,440
to me no more interesting than why are

426
00:19:36,820 --> 00:19:32,810
why is that galaxy over here rather than

427
00:19:39,280 --> 00:19:36,830
over there but there's got to be a ton

428
00:19:41,620 --> 00:19:39,290
of information provided some from

429
00:19:43,090 --> 00:19:41,630
someplace so where did that come from is

430
00:19:47,500 --> 00:19:43,100
a very good question but on the other

431
00:19:50,950 --> 00:19:47,510
hand if I gave you a huge number let's

432
00:19:53,110 --> 00:19:50,960
see a huge integer that was oh I don't

433
00:19:56,950 --> 00:19:53,120
know ten to the hundredth digits long or

434
00:19:58,900 --> 00:19:56,960
something like that could I ask you to

435
00:20:00,910 --> 00:19:58,910
tell me how much information is in that

436
00:20:03,370 --> 00:20:00,920
integer in other words how much would it

437
00:20:05,170 --> 00:20:03,380
take in information terms to distinguish

438
00:20:07,870 --> 00:20:05,180
that integer from all other integers of

439
00:20:09,430 --> 00:20:07,880
the same size well it might take a while

440
00:20:12,010 --> 00:20:09,440
to figure out whether or not that it's a

441
00:20:15,520 --> 00:20:12,020
highly composite number I gave you or a

442
00:20:17,260 --> 00:20:15,530
prime or or what and the amount of

443
00:20:19,450 --> 00:20:17,270
information contained in a very complex

444
00:20:22,630 --> 00:20:19,460
thing is not always clear that's my

445
00:20:24,760 --> 00:20:22,640
point so if you think in terms of really

446
00:20:27,130 --> 00:20:24,770
really really huge numbers it might be

447
00:20:29,260 --> 00:20:27,140
that there's less complexity required to

448
00:20:31,750 --> 00:20:29,270
specify this universe then we would

449
00:20:33,070 --> 00:20:31,760
first think I don't know maybe there's a

450
00:20:35,560 --> 00:20:33,080
lot more patterns that we have not

451
00:20:39,190 --> 00:20:35,570
discerned yet both mathematically and

452
00:20:44,230 --> 00:20:39,200
physically I'm going to get in trouble

453
00:20:45,850 --> 00:20:44,240
for glossing the cosmologists but the

454
00:20:48,250 --> 00:20:45,860
question about the fluctuation in the

455
00:20:50,380 --> 00:20:48,260
background radiation is the current

456
00:20:52,150 --> 00:20:50,390
explanation for why that galaxies over

457
00:20:54,210 --> 00:20:52,160
there yes yes right and this one's over

458
00:20:57,970 --> 00:20:54,220
here and there was a literal conversion

459
00:20:59,100 --> 00:20:57,980
experience in 1990 when the Cobain data

460
00:21:00,990 --> 00:20:59,110
was presented at that

461
00:21:11,190 --> 00:21:01,000
in Florida and they all of a sudden

462
00:21:20,230 --> 00:21:16,090
as you stated randomness is an

463
00:21:24,670 --> 00:21:20,240
assumption that most scientists just

464
00:21:27,100 --> 00:21:24,680
take for granted and get you and a few

465
00:21:30,100 --> 00:21:27,110
others including myself seriously

466
00:21:32,500 --> 00:21:30,110
question that assumption how is it that

467
00:21:34,450 --> 00:21:32,510
you have come to that conclusion if you

468
00:21:36,910 --> 00:21:34,460
can tell us briefly and what

469
00:21:39,100 --> 00:21:36,920
significance does that have for the

470
00:21:41,230 --> 00:21:39,110
evolution of the framework that you're

471
00:21:44,490 --> 00:21:41,240
taking how did I get to the dark side

472
00:21:47,650 --> 00:21:44,500
[Laughter]

473
00:21:51,010 --> 00:21:47,660
well first of all quantum randomness has

474
00:21:55,390 --> 00:21:51,020
been the most controversial kind of

475
00:21:56,770 --> 00:21:55,400
thing contained in in the quantum

476
00:21:58,240 --> 00:21:56,780
measurement problem since the beginning

477
00:21:58,660 --> 00:21:58,250
even the founders didn't like it very

478
00:22:02,140 --> 00:21:58,670
much

479
00:22:05,530 --> 00:22:02,150
and yet it works so very well but I was

480
00:22:10,120 --> 00:22:05,540
I guess first started thinking about

481
00:22:11,620 --> 00:22:10,130
this by some physicists the one that

482
00:22:13,720 --> 00:22:11,630
comes to mind it might not have been the

483
00:22:15,970 --> 00:22:13,730
first that I read but anyway surf and

484
00:22:20,190 --> 00:22:15,980
Adame nicholas urfe and chris Adame at

485
00:22:24,340 --> 00:22:20,200
at Caltech wrote a paper about this

486
00:22:26,380 --> 00:22:24,350
that's been widely ignored and there are

487
00:22:30,100 --> 00:22:26,390
some other justifications for it in

488
00:22:32,170 --> 00:22:30,110
purely quantum theory terms so that got

489
00:22:32,620 --> 00:22:32,180
me started then I started to think about

490
00:22:36,160 --> 00:22:32,630
it

491
00:22:38,320 --> 00:22:36,170
more and look at the evidence from sy4

492
00:22:40,300 --> 00:22:38,330
backwards causation and for backwards

493
00:22:42,730 --> 00:22:40,310
causation this suddenly solves the

494
00:22:44,620 --> 00:22:42,740
problem so it clicked together for me

495
00:22:46,360 --> 00:22:44,630
and the more I look the more I see

496
00:22:49,450 --> 00:22:46,370
evidence that things are symmetrical in

497
00:22:51,430 --> 00:22:49,460
time preparation measurement exactly

498
00:22:55,750 --> 00:22:51,440
symmetrical if you think about that for

499
00:22:58,480 --> 00:22:55,760
a while and I think you have a lot of

500
00:23:00,700 --> 00:22:58,490
things clear up ok unfortunately we're

501
00:23:02,840 --> 00:23:00,710
out of time for questions or discussion