What Can Mathematics Teach Us About Mind/Brain?

00:00:00 so I am at an obsession I'm director of the Centers and I'd like to welcome you to this meeting on what mathematics can tell us about the mind and the brain the idea for this roundtable was generated during a dinner conversation with Sylvain Capel who's head of the mathematics Institute at NYU and charles moore who's a psychiatrist and chairman

00:00:30 of the department at nyu so they thought that this would be a very timely subject for us to have a roundtable about at the helix center and i want to thank them for it just briefly we have a number of programs set up already for the fall and I'd like to mention them I think the first one after this is a program on why economists disagree which will be on

00:01:01 October 13th and will have economies from the two sides of the intellectual or scientific areas discussing it the following day on Sunday and is it at 2:30 we will have a program called poetry and jazz where we have a poet and a jazz musician who will play recite and

00:01:35 discuss the relationship between poetry and jazz following that in October over Friday and aside they will have two roundtables one of them is going to be on I wrote the exact title song work life and movement and the other would be on male-male competition globalization war and violence these two roundtables have been organized and proposed by

00:02:06 Maxine sheets Johnson who is an emeritus professor of philosophy of science from Oregon University and who was here during the Philoctetes days and either two or three programs for us so our website is up and one of the ideas that has always propelled us is that these roundtables should not just end here but there should be an ongoing conversation

00:02:37 taking place after that afterwards and we were not set up before for it and I think we are and maybe Rob can say what what you do for that yes thank you first of all go to WWE LX center.org or helix and org and that will access the website and there's a link to sign up after which you can

00:03:10 participate in conversations on the on the website you can either join a topic a question that has already been posed by someone else related to one of the events here or you can propose a new subject for discussion the other thing is that if you want to comment on anything that's going on here you can twitter at the helix center okay

00:03:40 so as I said today's subject is has a very easy title but it is a rather complicated subject and we have people who I think and discuss it leaders in this field I will start with Ned block who's been to us a number of times he is the silver professor of philosophy psychology and neuroscience at NYU he came to NYU from MIT where he

00:04:14 was chair of the philosophy program there he works in philosophy of mind and foundations of neuroscience and cognitive science border Armentrout who is unfortunately unable to be here today but is with us via Skype is distinguished University professor of computational biology and professor of mathematics at the University of Pittsburgh he's written more than 200 papers in mad philosophy physics and

00:04:47 math biology physics and neuroscience and he has a software called XP PA UT for the simulation of an analysis of dynamical systems and has written a number of books and one of them is available here for you if you would like to purchase it ken Miller this professor department of neuroscience department of physiology and center for neurological about new theoretical neurobiology at Columbia

00:05:19 University his co-director of this warts program in theoretical neurobiology and it's center of theoretical neuroscience is also co-director of its neurobiology and behavior graduate program he serves as vice chair of the department of neuroscience he's the founding editor of the journal of computational neuroscience recipient of the Alfred Lisa P Sloan research fellowship soul

00:05:49 scholars award award the biology fellowship National Science Foundation graduate fellowship and author of many articles all of the people have books and you can see them after the meeting George Ricky jr. is associate professor with tenure and head of the laboratory of biological modeling at the Rockefeller University and the senior fellow of the neurosciences Institute he developed the first micro

00:06:19 process processor controlled lab instruments and x-ray camera and his four-year synthesis software was used to solve many protein structures worldwide beginning in the 70s his interest has to turn to problems of pattern recognition perceptual categorization and motor control which he studies primarily through computer simulations of relevant neuronal systems Xiao Jing Wang am i pronouncing it wrong

00:06:51 he's professor of Neurobiology the adjunct professor of physics applied mathematics and psychology director of the Schwartz program in theoretical neuroscience at the University he is a theoretical neuroscientist studying executive and cognitive function whose group has pioneered neural circuit models of the prefrontal cortex discovering a specific neural circuit mechanism for decision-making he's also

00:07:23 studying I believe schizophrenia dr. Wang was a recipient of the Alfred P Sloan fellow National Science Foundation Career Award and John Simon Guggenheim memorial founder John Simon Guggenheim Memorial Foundation fellow is that it okay so that's it and we can get going

00:08:01 it's probably a very naive scientist point of view which I'm sure the philosophers will correct me but essentially the mind comes from the brain and the natural world mathematically develop you know or at least a lot of mathematics was developed in the study of physics of you know moving objects and how collections of objects new properties emerge at a

00:08:31 higher level and in essence studying the mind by studying the brain is no different we're studying a physical system that has many many levels many interacting parts at each level leading to new phenomena at the next level and of the next from the molecules to the cells to the circuits and the circuit behavior to the ultimately to the animals behavior and what we use math for is to understand how these

00:09:02 interacting pieces produce the phenomena that we see and in particular I think one of the biggest things that we do is we're studying things at one level like we have a lot of cells connected with some circuitry and they have some function we sponsor say I study visual cortex and so as a visual image comes in the neurons have certain responses to the individual world which have been well studied and but how do those responses with all of their details and complexity emerge out of the circuit

00:09:34 what are the circuit motifs that you know the interactions between the cells that lead to this behavior emerging and then so these these multi level one behavior at one level emerging from another level from interaction and many things at another level is sort of the essence of what we try to understand as we try to understand the brain and ultimately all the elements of our minds are things that we would like to identify as emergent properties of what neurons do in the same sense and so mathematics is a tool above taking

00:10:09 objects that you might say are blindly interacting they're interacting according to some rules the rules might have some intelligence but you know they're interacting according to some rules and understanding what emerges out of them and that's so to the extent to which you know the mind is a emanation of the natural physical world mathematics is a way to understand what happens there okay could I go on from what you said because it's a perfect introduction I think I'd like to make a

00:10:40 distinction that I would like the audience to go home with between math as a tool for studying the brain which involves both statistics you know physics and chemistry as you've pointed out how we use computers to simulate what goes on with neurons with ions in the brain with you know with blood flow and all of these things and on the other hand the question of whether mathematics should have a role in our theories about cognition and things at a higher level

00:11:11 like the question of consciousness and freewill and all these things where it's not so obvious that there's a connection I think the place where a connection does come in and Annette Bach knows something about this is the theory called functionalism which says that the material that the brain is made out of really doesn't matter it's the what the functions that the various parts carry out and how they interact with each other and if we call that a kind of

00:11:43 mathematics because to work out in detail what it implies does involve some mathematics then I think one has to be very careful not to go too far and what we see today is this metaphor if you will that the brain is a kind of computer you know it started out with the first electronic computers after the war which we're called electronic brains in the papers and magazines of that era you still hear that phrase once in a while and so we have a whole field where

00:12:15 every paper you read now says this piece of cortex computes this and this does that and I think ex post facto you can't deny that as signals come in there are electric signals on neurons they go into some areas some stuff happens and other electrical signals come out and ex post facto that you can describe that as a computation and but what that hides is how did it get to work that way but what part did evolution play and especially ontogeny which by which I mean the development of

00:12:47 the individual interacting with the world and that's why some of us think it's important to work not just with totally abstract mathematical models but things like robots actually moving around in the world and receiving visual input from cameras and you know trying to do something like an animal or human we're doing in the real world so whole set up now I've taken enough time but I just think it's very important to distinguish between those two kinds of areas where we use math as a theory and

00:13:17 as a tool and the the consequences are different the metaphor of the brain is a computer has faded I think it's well it's still every day of neuroscience journals okay but here's the problem the one of the the hallmarks of a computer is that there can be many ways of realizing of making the same computational structure so it's you know

00:13:49 commonly said in introductory books about computation that you know you can do a computation with using an electronic computer you could do the same computation using something with wheels and pulleys and gears you could make hydraulic setup that that uses the same computational principles the same program at some level of abstraction but does it completely differently but the

00:14:20 upshot of a lot of neuroscience it's not so easy to see how you could do the same computation differently multiple realizability seems to be fading away when we see the complexity of the electrochemical processes so neurons influence other neurons by sending out chemicals and those chemicals diffuse and it's not clear that the computational picture is the right way of describing that yeah that's

00:14:50 just a nice way to agree with that to some extent but I the first the guy right before that I don't know who's speaking at any kink but at any given time but you know they give robots and an external world and internal world I mean I don't see how that his shin of the use of mathematics math is all those and to address some recent point you know baby the he has a good point the brain is a

00:15:23 computer in fact if we go back the brain has been many things it was back in Harris tunnels time I think it was pumps and water and things like that and you know more recently I've heard you know that I heard a talk that that it was all done by quantum mechanics and things like that so whatever the newest theory is is what the brain is and it always bugs me because I think the brain is what it is and math is just the way as Ken said of taking lots of abstract

00:15:55 boxes and arrows that experimentalist put together at least to me I'm a hardened reductionist and it's just the way of taking boxes and arrows and using it to you know it's sort of an existence proof that this is the right mechanism so I might I'm too stupid to a school I but I'm I'm a big fan of how has been said you know I guess what

00:16:30 reason that mass is really important in neuroscience is that neurosciences Wow the fields in biology that the most quantitative experiment so the the the neurophysiology the measurements the experiments really quantitative has had a very long tradition of very quantitative you know measurements and analysis and that actually is the important to bear in mind that's why we are capable of using mathematical models and theory in

00:17:02 this field and it's clear already I guess from what we heard that we don't really know how to conceptualize the brain you know we have all kinds of analogies but certainly when you really compare brain with computer they're just so dramatically different right so what computer is really great at like making zillions of computations very quickly

00:17:34 we're not very good at what we are really wonderful at like recognizing objects recognizing a face in a crowd in a fuzzy in a foggy kind of environment computer is incapable of doing today's computer right so this is dramatically different you know dramatic differences between brain and the command and computers as we know today but on the other hand clearly if not consciousness we need to think about the

00:18:04 computation what kind of computations that brain does so that's you know another way of thinking about the connection between the brain and the mathematics I'm not sure the computation is going to turn out to be so important you know copy you as number of people have mentioned there are different levels of description and computation would be important at one level but not at another a standard example of this is the explanation of why a rigid square peg doesn't go

00:18:35 through a hole in a rigid board which can be done on the basis of the rigidity of the materials and the geometry of the hole and the the peg so at that level there really isn't anything that would be called computation of course if you go to the elementary particle level then you haven't you could get an explanation which is computational but which obscures the simple level of description so it's not always so I don't think you could unless you trivialize the notion

00:19:06 of computation by assuming that anything is the computation it's a common place that you could regard a river as computing the rate of erosion of its banks by as an analog model it's a computer that that computes its own rate of erosion so you can trivialize the notion of computation but I don't think we can just assume a priori that the right way to think about the mind is going to be a computational level

00:19:37 computational a at the the most abstract level that's fair I guess you could say so what's the alternative one alternative would be what really matters is behavior and sound maybe mental life and our behavior right can you describe those things without talking about the computation well just that's the guy in the screen said we're always using the latest technology the to describe the mind and he there's

00:20:09 a famous paper by John neuroscientist John Marshall that goes into the history of this and he mentioned a few cases but you know there at the time of the popularity of the cat apparent people's theory of vision was that there's little little catapults on objects that catapult a tiny simulacrum of the object into your eye and then of course the famous telephone exchange model of the brain at the ER in the early days of telephones so you know the computer is a

00:20:41 very notable artifact and if you trivialize the notion of computation we can describe everything as a computer but that doesn't mean that company that we know now that computation is going to be important in describing for example consciousness well I think I mean computer is a loaded word because it means you know the things that we have on there and our death the brain does

00:21:12 but computation I mean I think the reason to use a word like that I mean it maybe it's a matter of semantics and defining what we mean by it but you know the heart its biological function obviously is to make sure that blood and nutrition you know gets to every cell in the body and so it has to be a very good pump and has to react you know pump more and less under different circumstances the brain is a piece of meat sitting

00:21:42 inside whose function is in some way to take in information about the sensory world and God behavior toward the animals you know to hold the animals goals and God behavior toward those goals and to me computation means that you have to process information and that's the job of the brain and that's all the computation means to me but it's very clearly you know it's not what the heart does that's not what the liver does

00:22:13 that's what the brain is for for processing the information coming in from the sensory world and processing you know having a built-in sense of your of the animals goals and working out the behaviors that are going to achieve those goals that's a lot of information processing and that's the reason for me for the word computation it doesn't process the information anything like a computer does is the diffusion of a chemical is that computation it can be

00:22:44 described computationally but is there predation no it's a diffusion of the chemical on the brain so I don't see you know just seems to me to be trivializing the issue to call that the question are you people Stephen Wolfram called a cellular automata computation and you know I think we're getting hung up on semantics here and I do want to say that the metaphor of a computer or computation is

00:23:16 going to be really careful because when we do a computation on our computer if we type anything we get the same response every time and the really cool thing about the brain is the fact that you don't and that turns out to be really important right because if you get the same thing every time then you can't learn you can't change you can't adapt and that's one real difference I think the metaphor of a computer and and a real brain is that it it you know you

00:23:48 don't get the same thing every time you do something what I want to add to what Ken said and it fits right with what you said is I have a slogan the function of the brain is not to process information it is to create information and there's a distinction really trying to draw it between a process in the sense of an L or a pre-planned design where you you know perform operations on numerical quantities and get some result but but it's this renewal this learning this

00:24:19 this initialization if you will of the infant who comes into the world not doing any of these things and somehow figures out not because a programmer comes in and we tweak some neurons around to make it work right but just by having experience in the world and that's what the Industrial well I say the you know the desktop computer doesn't have and as long as we understand that then yeah we're fine to say as Ken does some you know the visual cortex you know computes edges and that sort of

00:24:50 thing sure I think we're very naive about what it computes but it's clearly taking in the visual world and ultimately leading us to open our eyes and see people and chairs and you know mites and to see objects and their relationships and to know a lot about them but exactly what it does computer to do that I don't think we really know that you know the way you ask ourselves or ask people you know in daily lives

00:25:21 you think you know I don't really tall thing in terms of computation or you know what's my goal what I need to do today so in that sense you start with a go you make decisions in order to achieve you go and you seek actively information from the environment you know and sometimes you have to process you know information forced on you but but there is an active process that the you know the main thing is to try to achieve your goals right the behavior goes so in that sense it's not you know it's different from the certainly very

00:25:52 different from information processing from the computer perspective and it's also always trying to predict I mean you you you get partial information and you anticipate nobody you know you don't you you watch me to ball and they're automatically nobody nobody is born with Newton's in there but you you figure out how to do this because you're trying to predict trajectories and you're predicting what somebody's gonna say there's all kinds of cool cycle physics

00:26:24 experiments that can exploit this and that's another thing a computer really doesn't do very well is sort of extrapolate to the future because we have to do that to interact with the real world so one terms of the question of the role of mathematics I'd like to just you know return to the idea of yeah because I think I mean for me you know we're

00:26:56 theory plays and in theory is basically building models which are mathematical and computer models to try to put together the pieces to figure out how they explain phenomena and so it's when I say theory you could substitute math if you like and what the roller theory the baseball and trying to understand the brain has to do with with this idea of properties emerging at one level out

00:27:27 of the complexity at another level I mean physics has pioneered some thinking about that kind of problem in terms of you know understanding how you take a lot of water a lot of molecules and they end up having properties of being liquid and having a certain volume and a pressure and so how the interactions at one level lead to these at a very different level these qualities like being liquid and being viscous that you know in terms of molecule I would have no meaning but it

00:27:58 emerges out of the interaction and many many molecules but the apparatus that physics developed it's pretty specialized in those situations and the brain is just unbelievably more complex of course and but but always what we're you know we're we really we're theory really gives you insight is when you know a lot of things at one level and you know a lot of things at the next level you know you know how these neurons respond to this situation and you know something about what the

00:28:28 neurons are made of and how they're connected to each other but you have no idea how you get from here to there and you try to put them together in terms of what you know you know you have some ideas and you you find suddenly a principal say of how a circuit can be organized so that these properties these these actual responses to the world up here will emerge some of these neurons down here and and but again and again at every level it's that process of new

00:29:02 phenomenon emerging out of the interactions of a complex interaction too many things at a different level that's I think the most striking point where math the best example of that is one of the best examples is the first example of that the hodgkin-huxley theory which basically took a hypothesis about channels and gates and use that equations down very simple just for

00:29:33 differential equations and we're able to completely explain the action potential this grid that was the first real example of mathematics doing something very specific and you know I think things have continued on like that idea that's exactly what you know it's what can send you how do you take pieces of stuff and get emergent properties the only way you can do that is with fear and the only way you can do that is and the only way you can do that kind of theory is with mathematics and that's the big difference between neuroscience

00:30:04 and say physics is every physics experiment is driven by theory and neural science experiments almost are ever driven by theory and it's just the kind of an immature science so far I think I disagree that well I disagree that neuroscience isn't driven by theory certainly in the visual system most duckin are at least a great deal of what we know was derived from the psychology

00:30:35 of the visual that was discovered before we knew the neuroscience of it you know the three kinds of cones the opponent process system that was all discovered by visual psychologists well before we understood the neural underpinnings and Gestalt psychologists who contributed a things about what's salient in a visual scene and so forth but pushing experiments and hard case there I don't I agree with you

00:31:05 guys it's just not you know not completely but guess what we can and part articulated is to understand how you explain behavior at some level in terms of the interactions and dynamics at the level below Alden is it so in a way I guess my PhD otherwise it used to say the world is like onion there are many layers and it really you can't satisfaction the scientists by be able

00:31:37 to explain something in terms of what's more fundamental maybe underneath it there's another aspect of it that really address why mathematics is really important for neuroscience that is the nerve system has a lot of feedback loops okay and there's positive feedback loops so this neuron excites the other neuron that excites back this neural orders inhibitory you know negative feedback loops like any you know system with a lot of feedback loops it's very hard to

00:32:08 predict what's gonna happen when you do something right somewhere so I guess why example I like to give is you know you know this stays people talk about the connectivity right and so if you know connectivity the connectome among jeans or my neurons you it's very important information you really know a lot by knowing that not only in the connectivity but the examine the give you illustrates why that's not enough -

00:32:39 okay imagine give you a circle there was just two neurons that we know give it to each other okay neuron one if it's your own - I'm doing what I can to predict what's going to be the behavior again well very long time people think the behavior would be half Santos later so neuron one is up it suppresses in your own - and then for some reason they are this one goes up it goes down okay that's the motive for generating

00:33:11 movements so if you walk left right left right okay so that's the circuit to get this kind of pattern generation but it turns out that when you really analyze the dynamics of this kind of circuit you can have some other way of you could have for example neuro one being up all the time and I was surprising your own - so you have a switch okay you give it a kick for neuron - that's which is you know when you're on - up and suppresses in your own voice so that you know gives

00:33:41 you a mechanism to build a switch does that make sense and it turns out that surprisingly in fact under some conditions even if those two neurons inhibit each other sometimes they are completely in sync so they go up together let's go down together they go up together right and this is a very counterintuitive kind of behavior of perfect synchrony by mutual abyssion turns out to be you know actually happening in real life in the brain and

00:34:13 this is the mechanism now while the mechanisms at least for explaining brain waves that we all see you know into EEG measurements for example this is I think a very very interesting example where only by looking at the dynamics with the help of math we can really figure out what's possible in this kind of system with feedback loops and accidently just built on that because say in that case you know the idea of them working together is essentially they both fire

00:34:44 they both suppress each other and then they both recover together and then they're active they both fire they both suppress each other so it gives you a new intuition you study the math maybe you hadn't thought of that before but you've got down the equations you studied them and you discover this other regime where where things are going together instead of opposite which is all you'd really thought of and then once the math has shown you this new regime now I can explain it to you without any equations it's the math often acts like a scaffolding out of which we could you know that we use to

00:35:17 gain an intuitive understanding that we can then express without the math so that's at least when I really feel like I understand something but the math is that the math is incredibly rich I mean that the full details are in there but as you study it and you start to see it behave in ways you didn't expect and then you start to try to work out why exactly is it doing that you ultimately come up with the story you can tell and when you can tell yourself a story that explains it which is a new intuition that you didn't have before now but you you discovered it by you by you know

00:35:47 working on the math and figuring out why it's doing what it's doing you know that's that's the the scaffolding of math leading to the intuitive understanding so you say it's not that you have an intuition and then the math can explain it but you are saying that the math itself creates the intuition elite what by banging on the math and the behaviors that you don't understand and figuring out why they're doing what they're doing you can't do intuitions yeah well maybe I it's important in this is that the correct math

00:36:19 level may be quite different from the correct amounts at another level and the example of the computer is good case so you know the computer operates by these binary elements but of course at a deeper level they're not binary at all they you know they fluctuate fluctuations of voltage but at the computational love we wanted we have to think of them as binary in order to understand the computation so if I understand correctly I mean math has always had the place in

00:36:51 neurophysiology because when you talked about electric currents and voltages and so on so you always had a kind of high school math or college math in when I went to medical school that was there but what you are saying is that what we are doing is not just understanding what happens let's say when a current goes along a nerve how can we explain it physically and mathematically but that

00:37:22 mathematical ideas allow us to understand things that without them we couldn't even imagine or there absolutely yep yep yeah like you know how if you press your I press your hands please and you'll start to see little flashlights for a while you'll start to see you know geometric patterns like checker boards flashing to things like that so why you know what is what is going on there and you know it's not

00:37:53 obvious that you know this is all probably in the visual cortex but what's the mechanism and math kind of gives you this umbrella and for example the example that I was in gave of two and mutually inhibitory neurons one guy making one guy a switch okay that's a switch and it's completely symmetric one guy can be up one guy the other guy can be up okay that's an example the simplest example of what we'll call spontaneous pattern formation and what

00:38:23 math does is give you this sort of broad brush in which to explain lots and lots of patterns that you see for example can is done lots of work on things called ocular dominance patterns in the visual cortex and it's all based and and I've done stuff on the phosphor I just told you about the the flicker and and pressing your eyeballs and they all work with the same basic principle I guess we call you can Hat there's exhibition we're also we can

00:38:56 call it Reaganomics where you help the guy that help your buddies and then you inhibit everybody else it's called lat inhibition I forgot to say that it's been known from horseshoe crab and all the way up and it pretty much can do you know it's a very straightforward concept but it allows you to explain so many

00:39:26 things and there's it's all under sort of a there's a very broad medical theory that there's all these cases well are you done Barda yeah what what I'm thinkin backswing Ned said way back at the beginning about different multiple solutions to the same problem and just looking at the math alone and never mind the neuroscience we we find that there

00:39:57 are different kinds of math we can use to apply to a neural system or a neural network if I'll use that word and so we find in our field that sometimes people get stuck in one or another of these and maybe a conversation like this can can help what I'm thinking of is I edited a book where some authors with a lot of different subjects but there were authors in there who felt that most of them neural modeling that people are doing today is all wrong because it divides neurons up into little pieces

00:40:27 called compartmental models where you say everything that's going on in this little bit is the same and then it's looked to another little bit by a resistor and that simplifies the computation but that's not really right because the voltage along the membrane changes in a continuous manner and so you really should use differential equations and so what you end up is pages and pages of so-called green's function solutions and things in the most complicated system these guys have been able to work out is two neurons

00:40:59 talking to each other and you get a lot of insight from that and you get a lot of insight from understanding how the diameter of the cable as it changes as you get farther away from the cell body effects you know how the voltage is G and you can go out like that and spend a whole career doing that and meanwhile you haven't gone to the next level up as Ken and many of us are interested in so it behooves all of us who are in this field I think to be aware of these different levels and be willing to move

00:41:29 up and down among them as befits the particular problem of interest maybe what I said is super obvious and to pick up on that one thing that I think the idea is maybe surprising to people not in the field is that it's not the case that you put in every detail into your model yeah if you do you're always lost you don't have any hope at all because

00:42:03 I get a couple of reasons some one is that there's there's many many many details you know exactly what kinds of channels do you have in the membrane and what what what are the physical properties of each of these channels and how do they respond in which way what's their density and on and on and on how many how exactly your dendrites spread out in space most of those details we don't really know we know that there are such things and that they have some structure and we

00:42:33 have maybe some range in which they all live but so the more of these details you put in the more unconstrained by data unconstrained by data freedom you put into your model the more unconstrained by data complexity you put into your model and and if your model then goes and does something how are you going to figure out why it does it when there's so many unconstrained details and so part of the the real art of modeling is the art of simplification the art of knowing what are the key

00:43:06 relationships that I want to model and then I want to understand what emerges and I'm gonna throw all the rest away to simplify to just understand what do these dynamics of these simple entities that I'm going to model lead to and can I identify that and I then understand what's going on in their brain with this simplification and then in some way that's it's testable this says oh well it's this simple structure leads to all this stuff then it also should lead to this other stuff people haven't looked

00:43:36 at so let's go and measure that somebody I think it's what Eden Segev is another theoretical neuroscientist and I think maybe he was quoting forecast oh I've kind of lost track of it quotes but it talked about modeling as the lie that reveals the truth because you start out with a lie you start out with a simple and there's actually a big to do in the field right now there there's something called the Blue Brain Project and amarka in Switzerland where is claim and belief

00:44:10 is that he's going to put every detail into the computer and out is going to merge the brain and then we're going to and the brain and I have to say every theoretical neuroscientist I know thinks that is nuts thank you because something will happen God knows why god knows what it depends on God does which detail was important and which wasn't maybe you can maneuver it to do things like the brain maybe you can't I mean at the moment they they have some very basic behavior things

00:44:40 exciting here but other things I mean nothing very specific and they say see we replicated the print but when you throw in every detail I mean the essence of understanding that that you know when we build this scaffold and then eventually I can tell you a story that story can't have a billion moving parts in it because our brains can't handle it and so we don't understand it now if if we knew what those billion moving parts were down to the physical details then like physicists where they do know those

00:45:12 billion moving parts you know in real detail they can just put it in the computer and see what it does because they really have control over all of that complexity from the data but we don't and so we have to simplify and we have to come to stories of how some interaction at one level leads to an interaction to another level so that I you know I do models where very often sometimes I use more complicated models but very often I use models where I take a neuron which is you know spatially extended object with dendrites that are

00:45:43 you know extending over hundreds of microns that are communicating with each other in complicated ways receiving all kinds of inputs at different places and integrating that input in complicated ways and I describe it as a point neuron that just takes a lot of input some sums them does a certain non-linearity to them but then I study how these interactions who's connected to who the circuitry among these point neurons what behavior that leads to and lo and behold you discover things that tell you a lot it give you a new insight into how the

00:46:15 brain works now we thrown away a lot of detail of integration and that worries me maybe those details of integration when we put them in are going to radically change things but the fact that you come up with an insight that unifies an awful lot behavior in a simple way and it's testable and the test bear out that gives me a lot of confidence although not a certainty that that all those details are not going to overturn what I've learned by studying things at this level well so you learn both by what you can explain them and what you can't so

00:46:47 you can't explain nothing it shows that the detail was important well no because you don't know reg you dismissed it right you know you know you don't know why you're capped you know negative result when you can then you've really got the hands on something it's hard to get nonexistent proof in these things yeah the other thing I think this is building what Ken said is it you know you start with something simple and you see what it does important or on or whatever and then you use that to build up your come on oh I think I I want to point the other side of the coin we've

00:47:18 been talking a lot about what mathematics can do for neuroscience but but the other thing is what can neuroscience do for mathematics and you know there's one of these big questions or what a question that beam us are very interested in is if you've got many many detailed models neurons hooked together is there a principled way you make a a simplified model out of that and people call this trying to derive a mean feel to from some sort of spiking neurons now

00:47:49 Jing has done a lot of this I've done some of this I don't know about the other guys Ken might have but I get that this request new mathematics as well and difficult mathematics because there's noise and stochasticity and things love so I think you know there's this great I did a feedback but no signs of math a lot of nice mathematics has come out of trying to answer some even some of the

00:48:20 simplest neuroscience questions we only heard about every other word cutting out a lot yeah it seems to be bad right what's the matter is it my connection no okay if I keep trying I mean I'm hearing I'm hearing enough that I can make sense if ever maybe it's because I know I know

00:48:52 some of the words are being left out just maybe just really calculate me what Bart was saying basically saying that you know I guess rephrasing it you could say you know in the past or even today physics is really a major source of mathematics right a lot of physics problems you know particle physics especially for example has led to many new branches in math and maybe today

00:49:23 biological sciences especially in neuroscience in fact it's going to provide a new source for you know problems and maybe ideas that will inspire new math so one of the specific example part mentioned is the so called mean field theory how do you go from small spy illogically based action potential kind of neural models and neural network models to population description okay where you say you know

00:49:56 for each little group of neurons you know they all within this group all the neurons are more less doing the same thing what I really care about is the dynamics of the activity the overall population activity of this neuron group so can I find a systematic way mathematical way to derive you know mobile physical base the spiking neural model to a population description that's why

00:50:27 essentially I guess I just add it's really true people actually feel like today there there's gonna be really a lot of interesting questions in part from neuroscience that's inspired new masters so for example not just neuroscience because I guess I would just mention why example is you know the the kind of dynamics that really deep in very very high dimensional space ok so if you think about you know really the nerve system describe it in certain ways you basically need the zillions of

00:50:59 variables zillions of activity variables for neurons or neural populations so you have to describe the dynamics in a very high dimensional space and you know the math of dynamics in very high dimensional space is - in neuroscience and may be true in some other scientific branches given the data we now have today so and I think that's one of the examples where you know this science including neuroscience Drive smash yeah I can give another example that I just

00:51:29 ran into on a thesis committee of a physics student at Rockefeller named bowtie a fooi who was interested but he comes down to the random walk problem but it expressed in terms of a neuron you have a neuron some noise sources the membrane potential is fluctuating around and a question you'd like to ask is how long do you expect it will be before one of those fluctuations goes over the threshold and the neuron fires and so if you look at the fluctuations as what was called a random walk in other areas of

00:52:01 biology or chemistry you know this is a problem where a lot of work has been done but he was able by looking at it from the point of view of a neuroscience problem to produce some new mathematics that that adds to that whole body of work so there's another just an example I think a very beautiful example of making some new Mathis some work done by Fred Lawson and his group in Germany

00:52:32 that was recently published in science without they're trying to understand certain patterns that form on the in the arrangement of the neurons in the visual cortex of what neurons neurons envision the primary visual cortex are responsive to light dark edges of a certain orientation and they care very much about the orientation responding and the what orientation they prefer is laid out

00:53:02 in a way that sort of rotates periodically as you move across the cortex so that all the orientations are represented but it's laid out in a in a particular kind of pattern and Fred so in physics there's quite a lot of literature on pattern formation on how you know interactions among chemicals may lead to some kind of stripy behavior and so forth to some pattern emerging and there's a very established

00:53:33 literature of how you can go about analyzing those processes those have always dealt with with real valued variables those you all know about real numbers and complex numbers complex numbers important part of mathematics but in the pattern formation literature just because these are physical variables these have all been real valued variables that are organizing into patterns it turns out that the proper description of these patterns you need to use complex valued variables and

00:54:04 that required thread to really revise or extend the existing methodology on pattern formation into that case and then and he also had to bring another extension to it which is in physics all of the interactions are local things just talk to their neighbors they're not able to talk to somebody way over here directly because there's no long-range connections between molecules say but in among there are long range connections and so we had to bring in the role of long-range connections as well into how

00:54:36 this influences pattern formation and the the upshot is it I mean he spent 10 or 15 years developing this theory layer by layer by layer by layer and the great triumph was he was able to predict that the structure of the maps it should have a certain signature which is the the density of points where all orientations meet which are called pinwheels or singularities and that that density and

00:55:08 in the right unit should be the number pi and they went and they measured it and some people had measured and to do that they had to develop new quantitative methods of measuring the density of pinwheels because there's always a lot of noise and it depends on how you filter things and they had to find ways of filtering out the noise that didn't filter out the signal which people people hadn't had good ways of measuring pinwheel density before so they developed new mathematics for that and people that studied maybe a few maps

00:55:38 at a time but they studied a hundred maps with 10,000 singularities in order to get good enough statistics and they found that the density was PI to within plus minus 2% meaning that's and what what that meant for us in terms of the physics of it or in terms of what happened how did these patterns emerge is basically this number PI this organization that's characterized by this number of Pi emerges very naturally out of self-organization meaning it's not every cell isn't told by genetics

00:56:10 what orientation to develop rather they develop by interacting with one another maybe they excite their neighbors and they may have some long-range suppression and so they're developing through interaction and this self-organization among all these moving parts leads to this pattern and the fact that he was able to show that you get this very robust prediction of PI under that scenario and then he went and measured it and that's right what was there and it was there across three different species that are separated by hundreds of millions of years an evolution and in fact separated so

00:56:40 far that the common ancestor had such a tiny visual cortex that it probably didn't have these patterns at all meaning that it had the evolved that this pie pattern had to evolve twice independently well that would happen naturally if it's just this if it happens by the self-organization process if you think it's genetically specified that would be very hard to explain so I think this was a huge triumph it was advanced in the math and advanced in our understanding of the biology an argument that the pinwheel structure isn't genetically

00:57:11 determined least not the way as McGann cursors ferrets where he was able to set up something where that they use their auditory cortex to perceive visually able to rewire the Ference at a very early age they also show that that that auditory cortex shows that pinwheel is true actually it does it does so pinwheels but I don't think it's that that that characteristic structure that the thread is identified so I think so different than wheels yeah yeah I think it's a lot it's you know I think it's

00:57:42 different I'm not awfully certain to that but I think it's different well we seem to be at a dead moment so I'll just change the subject slightly and say there's still plenty of room for new progress in this whole field and the diffusion of molecules isn't mentioned a couple of times I just wanted to say I suggested in a book chapter sometime ago this in studying the brain we needed to

00:58:14 combine not just what neurons are doing that what molecules are doing it and proposed using a kind of finite element modeling which is what engineers do who build skyscrapers and bridges you know looking at the physics of how little blocks of matter interact under pressure and and this was rejected by referees as being ridiculous although I thought it might have something to do for example with studying tumors in the brain and how a tumor might press on another part of the brain and caused something not to

00:58:45 function because pressure might be changing the activity of panels are saying but I just saw in a recent document that I'm reading which is well it's a PhD thesis that this is now being applied this kind of idea in the eye where people are working on retinal prophecies you know and the idea there is 20 by incursion who's lost the visual receptors it's known that the so-called retinal ganglion cells the cells that

00:59:17 pretend the output of the retina back to the brain those are often still functional even when the receptors are not so the person is blind but that part of the eye is good so the proposal in it and it's been tried now and you know in real life by a different groups you know as to stick some sort of array of electrodes into the back of the eye and stimulate these retinal ganglion cells to provide some sort of prosthetic vision and so this thesis that I'm reading has done just he of course never saw my proposal it must have come out of

00:59:47 his own ideas but the idea of making a finite element model of the fluid in the eye began and then using the laws of you know the law the laws of electricity and magnetism to figure out how when you put a little current into an electrode how does that spread through that fluid and which ganglion cells does it affect yeah so you can figure out what's the best way to compute what now in a computer you know what stimulus to put into that

01:00:18 electrode array to get the most natural vision so there's a very new kind of extension of what we've all been doing looking at just one neuron talking to another and taking into account this ionic environment and I think you know this is a very positive thing to be happening right now you may know more about this than I do I think you know you bring up okay so his cease we've sort of switched a little bit the pathology yeah I guess because this is a bad retina can you guys hear me every

01:00:52 other word or do I speak to or okay okay okay all right so you know let me give you an example of where math can be very helpful in pathologies is one of the classic mechanisms for Parkinson's disease is something called deep brain stimulation and the problem of deep brain stimulation is is really really stupid it just does the same thing over and over again and it doesn't depend on

01:01:23 any feedback or anything else but there's a number of groups there's groups in Germany and there's groups in the US that have developed much smarter much smarter versions of deep brain stimulation based on you writing down some balls for what happens in the basal ganglia whether you treat them as oscillators or as excitatory inhibitory networks and by using that they've been able to come up with techniques or deep

01:01:53 brain stimulation and this is this could not be have done could not have been done without the math predicting this method would work but much more efficient ways of doing deep brain stimulation that that won't come on until there's sense that something's wrong and when it comes on it does it much more efficiently instead of jolting it with you know hundreds of millivolts of stuff they can do things in much lower levels and therefore improve things like battery life and also reduce damage a great deal

01:02:26 to the brain you know some of that work is going on at Rockefeller - in the lab of Donald five I want to mention because it's not the board of this sponsoring us today he has a student doing deep brain stimulation in a mouse model of traumatic brain injury and they're they're not unimportant perhaps were unfortunately not doing what you say in terms of the math of what the network is doing but what they have done is to try out different modes of stimulation you

01:02:58 know whether it's a random or a chaotic or a poor of sequa you know a pure asila regular oscillation and do these different modes of stimulation produce better results in that mouse model so again this is something kind of new that's going on in just a few places and very positive I think also was mentioning something related so actually I'm on my way to to kind of short summer school so-called

01:03:32 a computational psychiatry there are several places including Yale and Germany and Yosi are in London where people feel like if we have some we are starting to have some understanding about circuit and mechanisms of brain structures especially the prefrontal cortex that are implicated in mental disorders so if we know something about the secretary in this part of the brain so it's not all the brands are really

01:04:03 the same okay so we know that whereas early sensory areas that are you know optimized for information processing and then there are some you know kind of more cognitive areas that are more implicated in decision-making and control of our behaviors or prefrontal cortex is one you know the best example perhaps of cognitive type circuitry that's implicated in many mental illness disorder types so there's a sense that

01:04:34 the you know and again the systems are very complex to just try to understand by intuition along and the circuit modeling has helped together with experimentation to kind of tease out you know what really might go go go on any normal subjects as well as seen patients excuse Finnick patients or autism for example I mean we know a bit about schizophrenia may be much less varied it

01:05:05 all still but something about since Affinia but even there's some autism I think but still the idea is that if if mathematics the really you know biologically based model of prefrontal cortex even such a thing can be done would provide a very useful platform to really explore what make around if this goes down if that goes up you know if you know at the secretary level and and if that's the

01:05:35 case it really provides a tool for us to also try to understand what really underlines cognitive deficits in in mental disorders hypothesis and speculation but there are so the cerebral cortex is you know the domain the stuff that makes us smart it's the it's what too peculiar to mammals the part of the brain that evolved

01:06:06 specifically in mammals it's all the folded up stuff you see on the surface and it's what you see with and hear with and think with and pretty much I think it's fair to say that your whole conscious life that's computed there I don't want to say where cut what consciousness is but let's say whatever does enter continence is computed there and it has what has always fascinated anyone who tries to study cortex is that it looks so much the same no matter what it's doing whether it's doing you know here's a piece that's that's analyzing

01:06:37 the visual scene here's a piece that's analyzing touch here's a piece that's analyzing audition here's a piece that's involved in motor planning and and thinking and you know speaking and there are differences there definitely are differences but the first thing that strikes you is how much they look alike how much they seem to be the same architecture the same processing unit and so it makes all of us dream at least that there is a fundamental processing unit that was invented in mammalian

01:07:07 evolution that's very good at doing something which when we really understand it we'll be able to fill in what that something is but something like being able to take a during world find invariant structure in it represent that invariant structure associatively and then do that again and again and again so there's also hypothesis that some diseases like schizophrenia or autism might be not specifically cognitive deficit to the cortex specifically deficits in you know

01:07:38 particular cognitive regions but they might be deficits in that processing unit that therefore would manifest not only in higher order cognitive processing but you would also see it in low-level visual processing and indeed in schizophrenia for example there's something in caught in much of sensory cortex called surround suppression it's a lateral inhibition that bard was talking about before which is that if I'm if I have a neuron that responds to some visual stimulus here

01:08:09 then what's around it the context can suppress the responses somewhat and it turns out that the people with a friend have much weaker surround suppression in primary visual cortex and you can imagine that it's some kind of you know that that could be some kind of global deficit in integrating you know local information here are local information they're putting it together that perhaps in some way that I couldn't explain to you might add up to the cognitive

01:08:40 deficits that we see in schizophrenia when that deficit is happening in the right brain region so we don't know but it but it's possible that these are diseases of the cortical processing unit and not a very specific cognitive functions thing you need also be able to explain why sometimes a deteriorating condition it should stay the same way just yes I know it's a good question you

01:09:13 know I can't say that I've thought out all the implications really deep into schizophrenia I've been struck by the fact that there are these very low-level deficiencies in schizophrenia and and certainly in autism it's been shown that at low level sensory areas there's much more variability in the processing the the mean response to a given stimulus is the same but there's much more very building in the response so that it gives me the hint that there are maybe more general processing problems in the cortex but I don't know enough to at

01:09:45 that level of detail very specific deficits in especially in the prefrontal cortex in the inhibitory circuitry the some of the some of the receptors become slow or they become weaker just maybe compensation because there's also emphasis and the excitatory stuff so I think it's what basically what Ken was saying is that it's it's basic circuitry there's seven layer or six or seven

01:10:17 layer structure and and there's something that goes wrong with and as Ken pointed out you know if you weaken some of these and things like shell Jing if the if you weaken these inhibitory things for example which him into inhibitory guys or what keep everything controlled I mean the cortex is only recurrent highly excited to recurrent and because of that any kind of perturbation of this controlling inhibition can lead to all kinds of

01:10:47 dramatic pathologies activity where you don't want it not being able to hold activity spread of activity where it shouldn't go that's not you know for example epilepsy and spontaneous activity when it's not there for example hallucinations that are some of the the negative things that happen which they're positive things that happen with so so yeah I think you know and math can really help us tear apart how this these these deficits in in

01:11:20 Mission or deficit in the circuitry can lead to some sort of macroscopic measure for example one thing that they found associated with cognitive deficits in schizophrenia people have greatly reduced certain kinds of things in the brain that they shall Jiang and looted to these ones that are related to mutual inhibition and generating these forty to sixty Hertz rhythms in the brain and and those those rhythms are shown to be

01:11:50 diminished in schizophrenic also so you know math can kind of connect these these deficits in circuitry with the macroscopic rhythms and and and hopefully some of the cognitive deficits so you know to relate to what Barton King just said I guess one way to you know to view this yeah there's a canonical general layout there's a general in an organization of you say several codecs and that's

01:12:24 universal that's it okay it's it's true in early sensory areas like primary visual cortex as well as prefrontal cortex but what's interesting is that there could be some quantitative differences right and so to use the same analogy as used before you have the same matter same material which can be in the nucleus state or solid state depending on the temperature right you could say just by changing something temperature you know query the fashion sometimes by

01:12:56 a small amount if you are near the you know the location the critical point just really the small change of certain things will give you a very different kind of behavior right and that's how I see it like you know comparing sensory area versus the prefrontal cortex okay so and that really is very important and very interesting to realize and then Danica asked even by the same amount of change

01:13:26 of certain scenes due to genetic defect or due to environmental you know insult what's the impact you know sensory system versus more contacts type of system so by understanding that the operational mode the behavior of each system we can you know indeed address you know look at exam how you know abnormalities can occur in each of the areas let me ask an a question because you emphasize the the

01:13:59 unity of structure across the cortex but of course as you well know although there's differences a you know more than a hundred years ago Broadman described all at these numbered areas and they have slight differences in the population of different cell types or the lengths of the dendrites or variants I'm sure you didn't mean to denigrate that but but just do you feel that those anatomical differences that are easily visible can be related in fact the

01:14:30 functional differences that shouting is talking about or you know should we be looking at but whether we can understand why those differences are there or is it just sort of peripheral and unimportant accidental I mean to say I recall XJ I used to call him I guess the J's point that you know this

01:15:01 there may be there may be some commonality but it may be operating in a different regime and in particular one one difference that's very well-known is that in in primary sensory cortex the excitatory neurons make much fewer synapses on to each other so an individual neuron in primary the primary visual cortex might receive 700 excitatory synapses but in prefrontal cortex that might receive 20,000 excitatory synapses and that has an

01:15:32 obvious theoretically what you expect from that is is that there were the place with 20,000 excitatory synapses is much more likely to be able to generate it to own activity in the absence of a stimulus which in fact is one of the big differences between frontal cortex and primary sensory cortex where without a stimulus there's some background activity going on but it doesn't generate the kind of activities but frontal cortex has to generate its own activity it's got to make motor plans and make the make the animal go so that's one example of a you know a

01:16:02 numerical change that leads to a very qualitative change in your operating regime it may have a lot of the same structure underneath I'm sure that that's probably you know if we got down to every one of Rodman's areas every one of them would have some specialization that gives us some little I mean every every specialization and structure has got to be there for some specialization and function and we don't know what it is further it did so it must be something I prefer right now to try to focus on you know what is the basic operation of this unit rather than not before we tackle all of its variation since we're not but I do think between

01:16:32 sensory and motor those are really two fundamentally different things that we need to eat to understand well I wanna have something if I can is it's you know there's also who you're talking to and who talks to you that really matters so the prefrontal cortex gets information from lots of other different things than the visual cortex so even though the the hardware is the same connectivity and I guess we come back to the old connect story is Co different and I think that can also be a

01:17:04 big reason why there's a difference in functionality I mean it's just simply you're getting dipped yoga the CPUs are the same it's just the the memory and who you're talking who is completely different I think the point you were making before about we don't know what the units are yet look I I take the unit story very

01:17:34 seriously it's one thing it seems evolutionarily plausible we know that this reason to think that the you know increase in cortex that we have from earlier stages is just duplication you know we have all these areas that seem to be basically descended from retinas that you know the more coarse actually make another retina so there does seem to be some reason to think that from an

01:18:07 evolutionary point of view it's a matter of just you know duplication but it seems amazing that we don't know what these do nuts are how many new runs in such a unit what's the size of the unit so what we think of it yeah I mean the unit of the totally totally hypothetical speculative object right but what what's commonly thought going back to the work of people in Diesel's 40 50 years ago is that about a square millimeter of cortex is sort of

01:18:39 processing a local a local bit of information and that's contains about a hundred thousand neurons and then when you consider though that these different units are talking to each other because you don't only process local information your modern modulated by your context you know so how big should there should we take the processing unit to be but that that gives you a I've asked again in question two other neuroscientists and sometimes I get the answer ten thousand neurons I mean um it just shows how hypothetical it is if we don't even if we're if we don't have methods of

01:19:12 estimating that well I mean we know how many neurons there are in a given area but that's how big an area should we call it unit yeah yes there was a great interview so I'd like to move it towards question time with postural oh sure any questions there's one back there you have to go to the microphone

01:19:42 we can't have it recorded so it's all you can just walk through here so much of what goes on in the brain depends on pattern recognition all the time every every perception that we make every thought that we have and the whole

01:20:14 world of metaphor depends on a more sophisticated pattern recognition now my simple question is is it conceivable that there is some mathematical expression of whatever matches one pattern to another because we can't work without it so just to say something about what we know about pattern recognition don't know so it was shown

01:20:48 long time ago that pigeons can recognize patterns that we have not been able to make a machine that can recognize so for example it was shown though I think thirty years ago that you so this was done by famous maybe infamous Harvard psychologist named Karen Stein he got a bunch of pictures from the National Geographic that some of which had people or parts of people in them sometimes they were like you know a tree trunk

01:21:19 with some figures on one side and others that had no people in them are no parts of people and he got pigeons too he trained pigeons so that they could recognize the difference between a picture that had a person or a part of a person and they did very well better than some of the students in his lab because that show their flying things I could do better in aerial aerial photographic and they could do better in the aerial analysis we can't wait are the any kind of artificial pattern recognizer that can do that we don't

01:21:50 know how it's done so but I did I do believe that we when we understand it we will understand it mathematically that until you can describe mathematically however you take the image and what you do with it in order to recognize the pattern then we want to understand that and I think you will understand it and we're going to my own feeling is that we're not going to figure it out by trying to invent algorithms we're gonna figure it out by studying how nature did it which is how our brains do it because I don't think we're smart enough to

01:22:21 reinvent that ourselves discover it's an important point that I agree with what you just said but it reveals a real tectonic shift in this field where there was a time when people fought they could discover it they could discover these just by thinking about just by thinking about it you know the analogy I'd like to make is that you know quantum mechanics is the weirdest theory I mean it you know you get used to it and make sense to you but never in a billion

01:22:52 years would anybody have figured it out just by thinking about it physicists had to knock their heads on atoms and the weird way that atoms behave and knock their heads again and again and again for decades until they finally somehow knock their heads enough that they managed to get to the point of quantum mechanics and then it started explaining things and I think understanding how the brain does put you know instantly recognizes things and understand I think it's in the same category I know there's a line over here but I really want to throw in two things first famously in that here in Stein

01:23:24 experiment people complain just what you said that the birds fly around so they would know about trees so he got the pigeons also to recognize scenes that had fish or not fish which the pigeons in everything but no night was going to be yeah we don't know how this works but I firmly believe that part of the story is going to be what I've said earlier this this afternoon the interaction of the young individual with the world that the way we're going to recognize patterns that connect with each other is because they occur together in time or

01:23:56 space on and off during development and parts of the brain are I believe wired in such a way as to respond to those connections and that's what you cannot get by describing the patterns geometrically or you know with words it's it's all part of us and we know that we recall things in connection with stimuli that were part of that scene when we first saw that pattern that may be totally unrelated

01:24:27 you know I recognize a certain Beethoven symphony because when I played the record years and years ago there was a scratch at one point and that scratch is in my brain at that point in the music and and that's how I know that with that so the whole surround not just one thing that makes patterns okay I shut up the

01:24:58 first symposium at the American Psychiatric on game theory in psychiatry and it was roundly ridiculed I just thought you know it and I were roundly ridiculed for this notion that game theory could be applicable to applicable to psychiatry so I've been thinking about these ideas for a long time and I want to thank this panel for bringing this year I think it's absolutely fantastic and cutting edge kind of kind of kind of discussion I just like to say that if the hypothesis for today is whether or not the mind can be described by mathematics I would consider the negation of that I mean if the mind

01:25:29 cannot be discovered explained by mathematics how could you possibly explain it what other language are you going to propose to do it in first your irreducibly a dualist if you propose another life if you propose another that your irreducibly Abdullah's don't listen of all your rejecting evolution because evolution is about maximization under competition which you're mathematically solve only a mathematically solvable problem and third of all you you would have to propose that there's some brain dependent language that do a better job than mathematics which i think is as

01:25:59 close as we get to a brain independent language don't think we need any comments on that I don't think anybody disagree with that here well I don't know maybe the flaw like pressure emerge from the interaction of molecules is the prediction of the panel then that a complete physiological and structural description of some neural system is going to then this lead to the

01:26:31 deduction that we have in front of us a cognitive system in other words once the physical language of a system of neurons is described completely do you think or is it the opinion of the group that we will then come to the conclusion that we Venus in essence describe the mechanism of cognition without being able to fully describe what cognition is perhaps this touches on the notion of consciousness versus not but just let's say even from an information theoretic perspective what are the thoughts of the panel well I said something that's relevant to this earlier the example of the square peg in

01:27:04 the round hole okay so you could get an explanation of that quote explanation in terms of the element the elementary particle clouds but it would just obscure the explanation that you can see in terms of geometry and rigidity you could add to it by explaining why those things that are rigid are rigid or what when they would fail to be rigid but some explanations have an appropriate level that isn't illuminated from from below and sometimes the what's below is so complicated that you have no hope of

01:27:35 deducing the Bolar behavior from from what's below so i think we have to find the right level for any given phenomenon that we're interested in is this in essence become a sort of short that doesn't answer his chin which is will i mean will dist emerge and will consciousness or cognition emerge from this this low level and I you know I think it's reductionist or at least most of us has reductionist the answer has to be yes I don't know how that almost

01:28:07 we'll have to ignore and what course grading we have to do but I don't see how we can't answer that question is yes look if we're there's a distinction between being a physicalist which I am I don't think I don't believe in any soul that somehow interferes with the elementary particles there's a difference between being a physicalist and being a reductionist so you're a physicalist you think okay it's all just matter it's something I've got to be you know consciousness and cognition have to come out of matter but that's different

01:28:37 from thinking you're going to be able to take any explanation you get at the cognitive level and reduce it to an explanation in terms of the smallest items that is a very adventurous controversial claim even for physicalists that's why I keep saying it's the right you have to find the right level understand they alternate well yes it's probably fair to say that

01:29:09 for very good reasons that neuroscience has been for very long time focused on you know early sensory information processing and the motor behavior but it's becoming more and more free you know coming now that people feel like it you can study the neuron logical mechanism of cognitive processes such as decision making a rigorous way so and that's a sea change in my mind so many things that people thought were in the

01:29:40 realm of psychologists and now really being studied in a very cross-disciplinary fashion with with cognitive psychologists and you know physiologists and computational you know theorists really the mechanism of vision cognition and the answer to your comment seems that one of the aspirations then is to be able to come up with the descriptive mechanism to talk about very high dimensionality systems in a sense it's very for any of us it's very hard to do

01:30:11 that in any discipline it seems and so for such an perhaps the most exceptional high dimensionality system it seems very hard to talk about any micro and macro phenomenon other than the physicality from a Casillas person's point of view it's hard to talk about we can come up with dumb little models seems that logic itself has some problems with it but I'm just very curious as to what practicing neuroscientists think of this understood you know in in neural terms and will be

01:30:42 understood in neural terms except maybe conscience itself you know given all of this is going on why do you got a sensation I don't know that that ever can be answered but but but at least you know the the every every mental structure has a neural substrate hopefully in that you know that's an article of faith I think is grounded in that's on one side the other side can be

01:31:13 understood in terms of that neural structure so there's a level of understanding you can't always get more understanding by going to the smaller and smaller horse upwards you work upwards you get the little I'd explained the next guy and but and so forth and then you were you know I don't I don't see why this is such a contradiction I work downwards too and sometimes the downwards is better than the upwards yes

01:31:43 oh I agree I agree you know but you know you have to meet the two ends at some point you know the point is that you're not going to describe the brain in terms of elementary particles but it is often the made of them you've got it you've got to work at some intermediate level of structure to understand the next level structure but you know that we're gonna understand structure we've made out of neurons they correspond to the structures of our mind maybe it's time to throw penrose in here just briefly right there are people who try very hard

01:32:20 to bring in stuff that that we can claim as physical but we don't it's so complicated you know quantum mechanical fluctuations in microtubules in yeah and and so I think all of us believe that's probably wrong and I think we can understand how it might be wrong because because of all the complexity of these levels that we've already talked about are enough to explain it but that's an intuition it's not a proof so you know

01:32:51 that remains to be seen but it'll still be physical I think that there's no argument and I I want to see this I love what you said today land sorry and talk about the language that I'm the kind of people who would like to formalize life and whatever even my speech if we wanted this is what why I was late tonight because I my husband

01:33:22 speak in such less a linear way well while I like I speak or thing 20 mention really I mean I start and I open parenthesis and close and I remember exactly where whatever I opened it and then I and so on after he says he's both but I know that people depend which people for example yesterday I know

01:34:04 today I was bored about some online agendas because I couldn't put inside what I was thinking about I mean also because my email address was hack twice so I prefer to do something simple and I put I start putting some sticky notes from the on a mirror okay let's say the pink one for projects the blue one for contacts and meetings like this the

01:34:37 yellow one so cool the other stuff will be intimately as to do right now tones of this the green one something all but to be the PCs which means okay you get to get up and then I start to to divide into columns and rows because I work databases 15 years so I you know I put a

01:35:10 kind of bullet points so I mean sometimes I realized my mind is like a database and that's why I I mean that's why I love math physics for example I remember when when I see the first physics atoms after while I I still what I had all around because everything happens he comes from a dynamic load so even a pain falling down oh I stared the

01:35:41 pain because that parent was connected with this and this and this so what is full of math physics and whatever and thank you for let me understand better

01:36:12 computers behavior there was the same we keep starting from an input you can add already the same output well this is about you can say we can talk we can call them deterministic algorithms but in logic there are also non deterministic algorithm which are like this something something that can happen in different way and different even the starting they say the starting point same and it's hard to develop in a

01:36:43 computer see thank you thank you so I was really interested the idea sorry how you know whatever type of unit we're talking about there there may be similar ones across the cortex I just was doing research in like cross modal stuff and so I'm really interested in that and and

01:37:14 I guess my question is just you know do you think that even though we're talking about reproduction of units in a biological way it may be just sort of the most efficient way of you know growing the brain through time but there could also be this by-product which you know contributes to our sort of unified experience of the world in the sense that these units are similar and therefore it can maybe communicate

01:37:44 through you know communicate to each other more easily and I just wonder if any of you have anything to say about that I mean it's confusing well just the the idea that like whatever unit you're talking about they are reproduced across the cortex and does that I mean do you know if that has any does that have any effect on how easily they communicate to each other and how something happening

01:38:15 in the visual cortex can can be referred to something in the auditory cortex or is it just really you know basically that anyways oh no stuff but they I thought it was interesting yeah I mean I should just say I mean there's there's there's unity at a lot of levels there's unity you know when you look at this one millimeter chunk that it you know it looks deferred there's a lot of similarity no matter where you are in cortex but there's also immunity and you know a lot of sort of higher level

01:38:46 things how different how the different chunks talk to each other across millimeters how one area talks to another area across back how they get their input from the thalamus and how they set and loop through the basal ganglia there's a lot of themes that are conserved across that you know many levels of the hierarchy so it's dense but but we're still it's very early days for really figuring out what the hell that's all about it might be useful to

01:39:16 mention that just the basic mechanisms of communication are pretty much the same I mean there's a large number of neurotransmitters that have been identified but there's a couple of major ones you know glutamate and those are used all over the bridge communicate with another one the other minor transmitters modulate that activity and they may act differently in different places to help produce the different types of you know functionality that

01:39:47 exists in those different places but but the overall scheme is very very much thing you know calcium transmission through ion channels is the same everywhere yeah I'm sorry I mean there's nobody ten kinds of calcium channels bizzle you know what I mean it's them it's the ion that that sends signals so that facilitates what you're asking about right I guess just to crystallize my question is you know if you have one unit over here and another unit over

01:40:20 here and they're similarly structured you know the brains whole the whole function is to communicate things to two different areas and so does that I mean since you guys know so much about this stuff does that similarity in structure in different areas because it often facilitate the communication or is that under the thing is it just I want to hear the frequency and I can sort of I can sort

01:40:50 of say I mean there is there are some theories that if one area doing something for example a famous theory is this one area is oscillating in a particular rhythm that it's much better better chance of communicating with another area that has a similar type of oscillation so I can say you know I don't know if the paraphrasing what you said there correctly or not but there you know that's a that's so-called binding theory and there's there's other

01:41:23 things like that so yeah I mean you guys that are similarly firing or more likely to to hook up together and and communicate and there's a one other thought I have it just I mean somebody what would be the big commonality that you see is this six layer structure of the cells and although we don't know exactly what it means it's clear that that sort of different kinds of input enter in different layers with different functions so called feed-forward input comes in two layer for top-down input

01:41:53 tends to come into layer wander so we don't you know we don't understand what that's about but there is a commonality there which probably means that you know anybody who sends an input into layer one of somebody else that has a certain meaning as opposed to sending it into layer four or somebody else so that's maybe the mic the metaphor is another way that different parts of the brain

01:42:23 communicate using this sensory language like sharp cheese lamb shirt you know so you're getting it into play my comment is about using mathematics to physiology and vice versa and the question is when the architecture of the brain starts to tweak a little bit like in multiple sclerosis you lose some Island in autism you have shorter connections as opposed to the long connections in the brain you have more white matter as opposed to gray

01:42:54 matter in dyslexia you have sort of a neurological junk drawer of cells that aren't aligned can you use this in your model to infer what must be going on you know in other words this is not working and that helps your model to decide what does work I think ultimately yes you know you have to you have to sort of know enough you have to have enough of a model of that particular phenomena that you you then can begin to say well if I change this variable here how is that

01:43:25 going to change things so you know if you're just completely in the dark but obviously you're not going to get there yet but I think in the long run yes well that's not necessarily true small changes don't always small small changes don't always give you small changes of behavior I mean the cortex is very parts of it are very tightly balanced than just small perturbations are enough to kick you in to wildly

01:43:56 different area and that's why it's so hard to control it so but but yeah I think I agree with Ken and I think ultimately we're gonna be able to use you know theory and things to say like if what we do we say you know this happens then why does this lead to this sort of broader phenomena if we we wreck this neuron why do we get this kind of behavior and that's where theory is very helpful

01:44:31 directors initially Ned of course anyone else subsequent to that it's the current my question is focused on the importance of the known differences between the predictive respect to the predictive and conformational values of a mathematical description of an observed system case in point would be Ptolemaic cosmology it was predictive in terms of the observed motions of stars and planets but had nothing to do with the

01:45:02 physical reality of what was being observed you know fixed shelves with planetoids and so on embedded as points of light more to the context at hand would be the Blue Brain Project where these the columnar stack has been modeled mathematically so that there is some allegiance to the input-output signaling but it says nothing about the physical structure inherently about the physical structure of the columnar stack so I wanted to ask that and others is that important to a physical list such

01:45:33 as myself it is but how important to the value of a robust mathematical theory of the neocortex well kind of which is you know this is a text the Ptolemaic of struggling system is a textbook case of how prediction by curve fitting isn't much use prediction is impressive if you do it with a general theory so you know the Copernican theory

01:46:07 had a much better qualitative explanation even though without adding and all that same extra stuff it didn't do as well in prediction so yeah prediction is really important it makes gives you reason to believe that the theory that did the prediction is true but it's no good if the way you got that whole system was just by sticking in all the the data in to begin with Thanks so then so then where are we at with regards to a mathematical description of

01:46:38 neurophysiology in the same capacity is it necessary for and this has been touched on earlier and other questions and so on but how critical is it that at some point for example with string theory we don't know because we don't have the level the technology to investigate that level of scale just yet maybe a fourteen giggle I think everybody would agree that we're at a very early days in neuroscience and we don't have a lot of the theoretical structure that will allow us to do the kind of explanation we want we we don't even really know what the units are we

01:47:09 don't have explanations of things like pattern recognition but you know we can do we can do a lot we can we can add certain levels we can we have a lot of predictive power but I think we're nowhere near having a satisfactory account yeah I think there's there's always sort of a tension between you know the details of your predictions and and sort of the the extent to which you're getting the structure of things right I mean ultimately what you're looking for is you want to really

01:47:39 generalize know you want to predict something that wasn't what you put in to begin with the the you want to be capturing a structure that gives you a new insight and the stuff that you that wasn't what led you to start thinking about it and you know you're never in neurobiology right now you're never going to get things quantitatively very precise because there's just too much stuff going on that you're not incorporating while you're trying to capture sort of some basic relationships but but but and yes you can make a lot of qualitative and to some extent quantitative

01:48:10 predictions that you can you know that you can you can test and verify but you know what you really want is the insight that gives you you know the gets the structure right into it so that you can get our last two new domains with it's a more humanistic aspect of of people can be explained with the models that have been discussed and explained for example

01:48:42 the ocean why somebody will react to a particular event with joy somebody else with sorrow another person with anger can any of this be explained or predicted on the basis either was mystical mathematical model or a physical istic model not today

01:49:33 yeah