Navigating our world with a mental GPS | Vijay Balasubramanian | TEDxPenn

tell me what’s really good so hi I’m

tell me what’s really good so hi I’m Vijay Bala Subramanian and I’m a

Vijay Bala Subramanian and I’m a

Vijay Bala Subramanian and I’m a theoretical physicist and I think about

theoretical physicist and I think about

theoretical physicist and I think about this thing up there it’s your brain the

this thing up there it’s your brain the

this thing up there it’s your brain the thing inside your head and I’m

thing inside your head and I’m

thing inside your head and I’m interested in trying to understand the

interested in trying to understand the

interested in trying to understand the rules and principles laws if you will

rules and principles laws if you will

rules and principles laws if you will that govern how the circuits inside your

that govern how the circuits inside your

that govern how the circuits inside your head let you live love learn and

head let you live love learn and

head let you live love learn and understand TED talks

understand TED talks

understand TED talks now um that’s a big topic and to

now um that’s a big topic and to

now um that’s a big topic and to illustrate the kind of approach I take I

illustrate the kind of approach I take I

illustrate the kind of approach I take I think it’s useful to have an example so

think it’s useful to have an example so

think it’s useful to have an example so we’re going to talk about a small

we’re going to talk about a small

we’re going to talk about a small example and the example we’re going to

example and the example we’re going to

example and the example we’re going to discuss is how your brain maintains your

discuss is how your brain maintains your

discuss is how your brain maintains your sense of place how you know where you

sense of place how you know where you

sense of place how you know where you are in an environment now the brain at

are in an environment now the brain at

are in an environment now the brain at its fundamentals is made of neurons and

its fundamentals is made of neurons and

its fundamentals is made of neurons and neurons are cells like any other cell in

neurons are cells like any other cell in

neurons are cells like any other cell in your body but they’re special cells at

your body but they’re special cells at

your body but they’re special cells at the top in this picture behind me you

the top in this picture behind me you

the top in this picture behind me you see these wires coming in the dendrites

see these wires coming in the dendrites

see these wires coming in the dendrites those are the input wires of a neuron

those are the input wires of a neuron

those are the input wires of a neuron that allow it to take in information

that allow it to take in information

that allow it to take in information from other things like the environment

from other things like the environment

from other things like the environment or other neurons will bring it into the

or other neurons will bring it into the

or other neurons will bring it into the neuron the neuron then does something

neuron the neuron then does something

neuron the neuron then does something figures out if it’s interesting and then

figures out if it’s interesting and then

figures out if it’s interesting and then sends messages out through an output

sends messages out through an output

sends messages out through an output wire which is the long wire coming down

wire which is the long wire coming down

wire which is the long wire coming down from the neuron that’s the axon and that

from the neuron that’s the axon and that

from the neuron that’s the axon and that sends messages elsewhere

sends messages elsewhere

sends messages elsewhere now what sorts of messages are these

now what sorts of messages are these

now what sorts of messages are these well neurons are electrical circuit

well neurons are electrical circuit

well neurons are electrical circuit elements just like transistors and

elements just like transistors and

elements just like transistors and diodes and what have you in silicon

diodes and what have you in silicon

diodes and what have you in silicon circuits so neurons their body the cell

circuits so neurons their body the cell

circuits so neurons their body the cell body is normally at a voltage of about

body is normally at a voltage of about

body is normally at a voltage of about let’s say minus 70 millivolts

let’s say minus 70 millivolts

let’s say minus 70 millivolts and then if the neuron find something

and then if the neuron find something

and then if the neuron find something interesting in its input it goes boom

interesting in its input it goes boom

interesting in its input it goes boom and makes a very rapid voltage spike

and makes a very rapid voltage spike

and makes a very rapid voltage spike they’re called action potentials in the

they’re called action potentials in the

they’re called action potentials in the trade and anyway you make this little

trade and anyway you make this little

trade and anyway you make this little voltage spike and go Zook down the axon

voltage spike and go Zook down the axon

voltage spike and go Zook down the axon and sends messages to other places so

and sends messages to other places so

and sends messages to other places so all of your thoughts are really

all of your thoughts are really

all of your thoughts are really electrical signals like there would be

electrical signals like there would be

electrical signals like there would be in the computer but of course a single

in the computer but of course a single

in the computer but of course a single neuron can’t appreciate poetry

neuron can’t appreciate poetry

neuron can’t appreciate poetry can’t love somebody else and so all of

can’t love somebody else and so all of

can’t love somebody else and so all of that must come from more and indeed

that must come from more and indeed

that must come from more and indeed neurons are gathered together in two

neurons are gathered together in two

neurons are gathered together in two circuits and networks of a very big size

circuits and networks of a very big size

circuits and networks of a very big size in the brain so behind me there’s a very

in the brain so behind me there’s a very

in the brain so behind me there’s a very famous and very beautiful picture of the

famous and very beautiful picture of the

famous and very beautiful picture of the retina which is a piece of your brain

retina which is a piece of your brain

retina which is a piece of your brain stuck at the back of your eye that

stuck at the back of your eye that

stuck at the back of your eye that converts photons into particles of light

converts photons into particles of light

converts photons into particles of light into electrical signals for processing

into electrical signals for processing

into electrical signals for processing in the brain now this picture that

in the brain now this picture that

in the brain now this picture that Ramona cahal the founder of Neuroscience

Ramona cahal the founder of Neuroscience

Ramona cahal the founder of Neuroscience drew about a hundred years ago shows

drew about a hundred years ago shows

drew about a hundred years ago shows many many kinds of neurons connected

many many kinds of neurons connected

many many kinds of neurons connected together in some very complex Network

together in some very complex Network

together in some very complex Network just as if you were to look at a

just as if you were to look at a

just as if you were to look at a microchip you would find many kinds of

microchip you would find many kinds of

microchip you would find many kinds of circuit elements connected together in a

circuit elements connected together in a

circuit elements connected together in a complicated circuit so fine so there are

complicated circuit so fine so there are

complicated circuit so fine so there are circuits of this kind but of course this

circuits of this kind but of course this

circuits of this kind but of course this is a specific circuit it does one thing

is a specific circuit it does one thing

is a specific circuit it does one thing it takes light and makes electrical

it takes light and makes electrical

it takes light and makes electrical signals and if you think about the whole

signals and if you think about the whole

signals and if you think about the whole variety of talks that you have there

variety of talks that you have there

variety of talks that you have there must be more still and indeed there is

must be more still and indeed there is

must be more still and indeed there is so this is the whole brain the whole

so this is the whole brain the whole

so this is the whole brain the whole brain has different kinds of circuits

brain has different kinds of circuits

brain has different kinds of circuits and networks embedded all over it that

and networks embedded all over it that

and networks embedded all over it that do all the different things that we do

do all the different things that we do

do all the different things that we do so for example right here on the back of

so for example right here on the back of

so for example right here on the back of your head there’s the visual cortex that

your head there’s the visual cortex that

your head there’s the visual cortex that has the circuits that allow you to see

has the circuits that allow you to see

has the circuits that allow you to see and process visual images in the front

and process visual images in the front

and process visual images in the front over here and your prefrontal cortex

over here and your prefrontal cortex

over here and your prefrontal cortex there are the circuits that help form

there are the circuits that help form

there are the circuits that help form your personality and help you with

your personality and help you with

your personality and help you with things like planning and decisions and

things like planning and decisions and

things like planning and decisions and things of this nature

things of this nature

things of this nature today we’re interested in your sense of

today we’re interested in your sense of

today we’re interested in your sense of place how you know where you are and the

place how you know where you are and the

place how you know where you are and the circuits that help you know where you

circuits that help you know where you

circuits that help you know where you are are stored in the middle of the

are are stored in the middle of the

are are stored in the middle of the brain so in the middle can’t draw it so

brain so in the middle can’t draw it so

brain so in the middle can’t draw it so easily in the picture there and in two

easily in the picture there and in two

easily in the picture there and in two areas of the brain called the

areas of the brain called the

areas of the brain called the hippocampus and the ento Reinold cortex

hippocampus and the ento Reinold cortex

hippocampus and the ento Reinold cortex we’re mostly going to talk about the

we’re mostly going to talk about the

we’re mostly going to talk about the internal cortex great

internal cortex great

internal cortex great so that’s your introduction to

so that’s your introduction to

so that’s your introduction to neuroscience now I’ve been talking about

neuroscience now I’ve been talking about

neuroscience now I’ve been talking about your sense of place now what we mean by

your sense of place now what we mean by

your sense of place now what we mean by that we should start by discussing what

that we should start by discussing what

that we should start by discussing what you mean by your sense of space of

you mean by your sense of space of

you mean by your sense of space of location so here’s a location a place

location so here’s a location a place

location so here’s a location a place that I’m familiar with this is my living

that I’m familiar with this is my living

that I’m familiar with this is my living room and I know it very well when I’m in

room and I know it very well when I’m in

room and I know it very well when I’m in it I know I’m there I can close my eyes

it I know I’m there I can close my eyes

it I know I’m there I can close my eyes and I can walk about and basically not

and I can walk about and basically not

and I can walk about and basically not bump into stuff

bump into stuff

bump into stuff somehow somewhere inside my head here

somehow somewhere inside my head here

somehow somewhere inside my head here that place is stored and we’d like to

that place is stored and we’d like to

that place is stored and we’d like to know how now how is here stored well I

know how now how is here stored well I

know how now how is here stored well I already told you that everything in the

already told you that everything in the

already told you that everything in the brain is made of neurons firing

brain is made of neurons firing

brain is made of neurons firing electrical signals so somehow this place

electrical signals so somehow this place

electrical signals so somehow this place must be an abstract pattern of neural

must be an abstract pattern of neural

must be an abstract pattern of neural firing inside your head and somehow that

firing inside your head and somehow that

firing inside your head and somehow that abstract pattern of neural firing must

abstract pattern of neural firing must

abstract pattern of neural firing must maintain a map of your location in the

maintain a map of your location in the

maintain a map of your location in the trade that map is called the cognitive

trade that map is called the cognitive

trade that map is called the cognitive map and people have been wanting for a

map and people have been wanting for a

map and people have been wanting for a long time to understand this now about

long time to understand this now about

long time to understand this now about 12 years ago a very important clue

12 years ago a very important clue

12 years ago a very important clue developed in our understanding of this

developed in our understanding of this

developed in our understanding of this cognitive map so there was a land in

cognitive map so there was a land in

cognitive map so there was a land in Norway of Edouard Maybrick Moser and

Norway of Edouard Maybrick Moser and

Norway of Edouard Maybrick Moser and they had rats running around some

they had rats running around some

they had rats running around some enclosure and they had implanted

enclosure and they had implanted

enclosure and they had implanted electrodes to record from a piece of the

electrodes to record from a piece of the

electrodes to record from a piece of the brain the n-terminal cortex which has

brain the n-terminal cortex which has

brain the n-terminal cortex which has been misspelled there

been misspelled there

been misspelled there the enter rival cortex and um the arm

the enter rival cortex and um the arm

the enter rival cortex and um the arm and what did they find

and what did they find

and what did they find well they would record from a neuron and

well they would record from a neuron and

well they would record from a neuron and they would find that the neuron would

they would find that the neuron would

they would find that the neuron would fire when the rat was in specific

fire when the rat was in specific

fire when the rat was in specific locations in this room so Gobert stop

locations in this room so Gobert stop

locations in this room so Gobert stop murder stop as the rat walked run so

murder stop as the rat walked run so

murder stop as the rat walked run so they kept that they collated all this

they kept that they collated all this

they kept that they collated all this firing and up top in the topmost picture

firing and up top in the topmost picture

firing and up top in the topmost picture you see a hotspots of where this neuron

you see a hotspots of where this neuron

you see a hotspots of where this neuron fired or where the rat was with his

fired or where the rat was with his

fired or where the rat was with his neuron fired and what do you see you see

neuron fired and what do you see you see

neuron fired and what do you see you see that this particular neuron fired when

that this particular neuron fired when

that this particular neuron fired when the rat was in this enigmatic grid of

the rat was in this enigmatic grid of

the rat was in this enigmatic grid of locations in the air inside the room

locations in the air inside the room

locations in the air inside the room even more surprisingly or interestingly

even more surprisingly or interestingly

even more surprisingly or interestingly as they poked deeper into the internal

as they poked deeper into the internal

as they poked deeper into the internal cortex with their electrode they found

cortex with their electrode they found

cortex with their electrode they found other neurons that fired on bigger grids

other neurons that fired on bigger grids

other neurons that fired on bigger grids and then on bigger grid still so there

and then on bigger grid still so there

and then on bigger grid still so there were these lattices in the world arm

were these lattices in the world arm

were these lattices in the world arm which at which these neurons fire so

which at which these neurons fire so

which at which these neurons fire so here’s the question Oh what’s more even

here’s the question Oh what’s more even

here’s the question Oh what’s more even more interestingly by the way if you

more interestingly by the way if you

more interestingly by the way if you took the rat away right and brought it

took the rat away right and brought it

took the rat away right and brought it back the next day this kind of map if

back the next day this kind of map if

back the next day this kind of map if you like of the world he’s kind of grids

you like of the world he’s kind of grids

you like of the world he’s kind of grids embedded on the world were uploaded were

embedded on the world were uploaded were

embedded on the world were uploaded were reloaded in to the rat’s brain

reloaded in to the rat’s brain

reloaded in to the rat’s brain instantaneously so it really felt like

instantaneously so it really felt like

instantaneously so it really felt like this is some kind of map of the world

this is some kind of map of the world

this is some kind of map of the world but the question is how right what do

but the question is how right what do

but the question is how right what do these patterns mean but how did they

these patterns mean but how did they

these patterns mean but how did they maintain a map of the world now I’m a

maintain a map of the world now I’m a

maintain a map of the world now I’m a theoretical physicist and my job in life

theoretical physicist and my job in life

theoretical physicist and my job in life is to dream up explanations for

is to dream up explanations for

is to dream up explanations for interesting things that happen in the

interesting things that happen in the

interesting things that happen in the world that’s what I like to do for a

world that’s what I like to do for a

world that’s what I like to do for a living

living

living that’s what I do for a living now that’s

that’s what I do for a living now that’s

that’s what I do for a living now that’s a trade that’s a job that requires two

a trade that’s a job that requires two

a trade that’s a job that requires two important traits one is imagination

important traits one is imagination

important traits one is imagination because you need to dream up new

because you need to dream up new

because you need to dream up new explanations for things and it needs

explanations for things and it needs

explanations for things and it needs courage because you can often be wrong

courage because you can often be wrong

courage because you can often be wrong okay but nevertheless let’s try let’s

okay but nevertheless let’s try let’s

okay but nevertheless let’s try let’s try to imagine an interpretation of

try to imagine an interpretation of

try to imagine an interpretation of these experimental findings okay so I’m

these experimental findings okay so I’m

these experimental findings okay so I’m going to follow the method the

going to follow the method the

going to follow the method the physicists usually follow which is to

physicists usually follow which is to

physicists usually follow which is to first simplify the problem right I’m

first simplify the problem right I’m

first simplify the problem right I’m going to imagine that we live in a

going to imagine that we live in a

going to imagine that we live in a one-dimensional world that’s the line

one-dimensional world that’s the line

one-dimensional world that’s the line you know we live on a line and that the

you know we live on a line and that the

you know we live on a line and that the whole world is eight meters long and

whole world is eight meters long and

whole world is eight meters long and that for whatever reason we need to know

that for whatever reason we need to know

that for whatever reason we need to know where we are with a resolution of

where we are with a resolution of

where we are with a resolution of precision of one meter so I want to

precision of one meter so I want to

precision of one meter so I want to imagine how I would devise a neural

imagine how I would devise a neural

imagine how I would devise a neural system to tell me where I am with that

system to tell me where I am with that

system to tell me where I am with that position

position

position well easy right I’ll break up the world

well easy right I’ll break up the world

well easy right I’ll break up the world into eight blocks like so up there and

into eight blocks like so up there and

into eight blocks like so up there and then I’ll assign one neuron the fire in

then I’ll assign one neuron the fire in

then I’ll assign one neuron the fire in each of those eight blocks so as you

each of those eight blocks so as you

each of those eight blocks so as you move around if your neuron number three

move around if your neuron number three

move around if your neuron number three you fire when they’re Rath isn’t block

you fire when they’re Rath isn’t block

you fire when they’re Rath isn’t block number three that kind of thing well

number three that kind of thing well

number three that kind of thing well clearly that’s a map of the world right

clearly that’s a map of the world right

clearly that’s a map of the world right it’s a kind of representation of where

it’s a kind of representation of where

it’s a kind of representation of where you are and it requires eight neurons so

you are and it requires eight neurons so

you are and it requires eight neurons so here’s another way what you could do is

here’s another way what you could do is

here’s another way what you could do is you could take the whole room and divide

you could take the whole room and divide

you could take the whole room and divide it into two halves I’ve colored that’s

it into two halves I’ve colored that’s

it into two halves I’ve colored that’s the top line over there and I’ve colored

the top line over there and I’ve colored

the top line over there and I’ve colored the left half blue and the right half

the left half blue and the right half

the left half blue and the right half orange and we get the blue neuron to

orange and we get the blue neuron to

orange and we get the blue neuron to fire when you’re on the left half of the

fire when you’re on the left half of the

fire when you’re on the left half of the room and the orange neuron to fire

room and the orange neuron to fire

room and the orange neuron to fire when you’re in the right half of the

when you’re in the right half of the

when you’re in the right half of the room then you divide the room into

room then you divide the room into

room then you divide the room into quarters okay and now I again assigned

quarters okay and now I again assigned

quarters okay and now I again assigned two neurons want to fire along the

two neurons want to fire along the

two neurons want to fire along the second line there want to fire in the

second line there want to fire in the

second line there want to fire in the left half of the left half of the room

left half of the left half of the room

left half of the left half of the room at the left half of the right half of

at the left half of the right half of

at the left half of the right half of the room and the aura and another neuron

the room and the aura and another neuron

the room and the aura and another neuron the orange one to fire in the right half

the orange one to fire in the right half

the orange one to fire in the right half of the left half of the room at the

of the left half of the room at the

of the left half of the room at the right half of the right half you get the

right half of the right half you get the

right half of the right half you get the picture

picture

picture you subdivide by twos okay now suppose I

you subdivide by twos okay now suppose I

you subdivide by twos okay now suppose I was going to call these neurons the zero

was going to call these neurons the zero

was going to call these neurons the zero neuron under one neuron based upon left

neuron under one neuron based upon left

neuron under one neuron based upon left versus right then the first two location

versus right then the first two location

versus right then the first two location the one on this side would be labeled

the one on this side would be labeled

the one on this side would be labeled zero one zero and the second location

zero one zero and the second location

zero one zero and the second location marked the second dashed line would be

marked the second dashed line would be

marked the second dashed line would be labeled one zero one clearly this is

labeled one zero one clearly this is

labeled one zero one clearly this is also a way of maintaining a map of the

also a way of maintaining a map of the

also a way of maintaining a map of the world if you were a computer scientist

world if you were a computer scientist

world if you were a computer scientist you’d probably do it this way and this

you’d probably do it this way and this

you’d probably do it this way and this would be what’s called a binary code for

would be what’s called a binary code for

would be what’s called a binary code for the world in a binary because of zeros

the world in a binary because of zeros

the world in a binary because of zeros and ones and using binary codes to

and ones and using binary codes to

and ones and using binary codes to number out all the locations if you

number out all the locations if you

number out all the locations if you wanted you can use divide into tens and

wanted you can use divide into tens and

wanted you can use divide into tens and make a decimal code okay so these are

make a decimal code okay so these are

make a decimal code okay so these are the ways we can imagine writing out your

the ways we can imagine writing out your

the ways we can imagine writing out your location in one dimension so let’s apply

location in one dimension so let’s apply

location in one dimension so let’s apply this experience to thinking about how

this experience to thinking about how

this experience to thinking about how you would map out your location in two

you would map out your location in two

you would map out your location in two dimensions because that’s what we seem

dimensions because that’s what we seem

dimensions because that’s what we seem to do that’s what the rats seem to do as

to do that’s what the rats seem to do as

to do that’s what the rats seem to do as they walk around the world so here we go

they walk around the world so here we go

they walk around the world so here we go imagine again in a simplified way but

imagine again in a simplified way but

imagine again in a simplified way but the world is an eight meter by eight

the world is an eight meter by eight

the world is an eight meter by eight meter box and that I need to know where

meter box and that I need to know where

meter box and that I need to know where I am with a precision a resolution of

I am with a precision a resolution of

I am with a precision a resolution of one meter by one meter that’s what I

one meter by one meter that’s what I

one meter by one meter that’s what I need for my behavior how could I do this

need for my behavior how could I do this

need for my behavior how could I do this but following what we imagined before I

but following what we imagined before I

but following what we imagined before I could break up the whole world into 64

could break up the whole world into 64

could break up the whole world into 64 little boxes that are one meter by one

little boxes that are one meter by one

little boxes that are one meter by one meter

meter

meter assign one neuron the fire in each of

assign one neuron the fire in each of

assign one neuron the fire in each of these little boxes and I would have a

these little boxes and I would have a

these little boxes and I would have a map of the world it would cost you 64

map of the world it would cost you 64

map of the world it would cost you 64 neurons but you could definitely do this

neurons but you could definitely do this

neurons but you could definitely do this so that’s one thing we could imagine

so that’s one thing we could imagine

so that’s one thing we could imagine here’s another thing we could imagine

here’s another thing we could imagine

here’s another thing we could imagine I’ll start but breaking up the world

I’ll start but breaking up the world

I’ll start but breaking up the world into four corners Northwest northeast

into four corners Northwest northeast

into four corners Northwest northeast Southwest southeast all colored

Southwest southeast all colored

Southwest southeast all colored differently here

differently here

differently here then I’ll take let’s say the northwest

then I’ll take let’s say the northwest

then I’ll take let’s say the northwest corner

corner

corner and break it up into quarters then take

and break it up into quarters then take

and break it up into quarters then take each of the species and break it up the

each of the species and break it up the

each of the species and break it up the quarters this is just like what I did

quarters this is just like what I did

quarters this is just like what I did before if it was a one-dimensional world

before if it was a one-dimensional world

before if it was a one-dimensional world right and then if I wanted to tell you

right and then if I wanted to tell you

right and then if I wanted to tell you where the cross is in that picture I

where the cross is in that picture I

where the cross is in that picture I would say it’s in the blue yellow blue

would say it’s in the blue yellow blue

would say it’s in the blue yellow blue right that’s a way of telling you where

right that’s a way of telling you where

right that’s a way of telling you where you are so that is one way of producing

you are so that is one way of producing

you are so that is one way of producing another kind of map of the world and of

another kind of map of the world and of

another kind of map of the world and of course you could subdivide the tens like

course you could subdivide the tens like

course you could subdivide the tens like decimal systems on all these kinds of

decimal systems on all these kinds of

decimal systems on all these kinds of things so this is a way of describing

things so this is a way of describing

things so this is a way of describing where you are so I would now like to

where you are so I would now like to

where you are so I would now like to draw an analogy look at these pictures

draw an analogy look at these pictures

draw an analogy look at these pictures on the left side we have the

on the left side we have the

on the left side we have the experimental data on the right side is

experimental data on the right side is

experimental data on the right side is the thing we just imagined as a way of

the thing we just imagined as a way of

the thing we just imagined as a way of describing position don’t they look

describing position don’t they look

describing position don’t they look similar first at one end you have big

similar first at one end you have big

similar first at one end you have big grids then you have smaller grids then

grids then you have smaller grids then

grids then you have smaller grids then you have smallest grids and in some way

you have smallest grids and in some way

you have smallest grids and in some way you can put this information potentially

you can put this information potentially

you can put this information potentially together so if you believe the analogy

together so if you believe the analogy

together so if you believe the analogy we would say that somehow the brain the

we would say that somehow the brain the

we would say that somehow the brain the internal cortex has developed a sort of

internal cortex has developed a sort of

internal cortex has developed a sort of 2-dimensional fuzzy sort of number

2-dimensional fuzzy sort of number

2-dimensional fuzzy sort of number system for numbering out locations in

system for numbering out locations in

system for numbering out locations in the world that would be the

the world that would be the

the world that would be the interpretation you would place on this

interpretation you would place on this

interpretation you would place on this so that’s a curious talking how can you

so that’s a curious talking how can you

so that’s a curious talking how can you build evidence for this right to build

build evidence for this right to build

build evidence for this right to build evidence for a theory you need to make a

evidence for a theory you need to make a

evidence for a theory you need to make a prediction that you can test so let’s go

prediction that you can test so let’s go

prediction that you can test so let’s go for that so how do you build such a

for that so how do you build such a

for that so how do you build such a prediction well if this is like a number

prediction well if this is like a number

prediction well if this is like a number system I could ask should the brain

system I could ask should the brain

system I could ask should the brain build a binary number system should it

build a binary number system should it

build a binary number system should it build a decimal number system what

build a decimal number system what

build a decimal number system what should it do and in this neural context

should it do and in this neural context

should it do and in this neural context whether it’s binary or decimal really

whether it’s binary or decimal really

whether it’s binary or decimal really what that’s really talking about is you

what that’s really talking about is you

what that’s really talking about is you see how these grids get bigger and

see how these grids get bigger and

see how these grids get bigger and bigger and bigger well you can take the

bigger and bigger well you can take the

bigger and bigger well you can take the ratio of the size of one grid divided by

ratio of the size of one grid divided by

ratio of the size of one grid divided by the size of the next smaller grid

the size of the next smaller grid

the size of the next smaller grid telling you how to scales up and that’s

telling you how to scales up and that’s

telling you how to scales up and that’s really telling you what kind of number

really telling you what kind of number

really telling you what kind of number system you would have so if it scales up

system you would have so if it scales up

system you would have so if it scales up by factors of 2 it’s like binary if it’s

by factors of 2 it’s like binary if it’s

by factors of 2 it’s like binary if it’s like fales up plus scales up with

like fales up plus scales up with

like fales up plus scales up with factors of 10 then it’s like decimal so

factors of 10 then it’s like decimal so

factors of 10 then it’s like decimal so we could try to predict this but if you

we could try to predict this but if you

we could try to predict this but if you really believe our theory of the brain

really believe our theory of the brain

really believe our theory of the brain that we’re building here we should be

that we’re building here we should be

that we’re building here we should be able to predict

able to predict

able to predict what sort of number system the brain

what sort of number system the brain

what sort of number system the brain should use to represent location in a

should use to represent location in a

should use to represent location in a 2-dimensional world for that Li the

2-dimensional world for that Li the

2-dimensional world for that Li the principle what principle can you use

principle what principle can you use

principle what principle can you use well so here’s the idea so I’m saying

well so here’s the idea so I’m saying

well so here’s the idea so I’m saying the brain should have a certain kind of

the brain should have a certain kind of

the brain should have a certain kind of two-dimensional number system to

two-dimensional number system to

two-dimensional number system to describe the world well here’s a

describe the world well here’s a

describe the world well here’s a principle that neural circuits should be

principle that neural circuits should be

principle that neural circuits should be organized to consume resources

organized to consume resources

organized to consume resources efficiently while I saying this well the

efficiently while I saying this well the

efficiently while I saying this well the brain you know on the one hand is

brain you know on the one hand is

brain you know on the one hand is extremely efficient it consumes about

extremely efficient it consumes about

extremely efficient it consumes about twelve to twenty watts of power whereas

twelve to twenty watts of power whereas

twelve to twenty watts of power whereas your laptop consumes about 80 watts of

your laptop consumes about 80 watts of

your laptop consumes about 80 watts of power and you know your laptop doesn’t

power and you know your laptop doesn’t

power and you know your laptop doesn’t write poetry

write poetry

write poetry right so it’s somehow extremely

right so it’s somehow extremely

right so it’s somehow extremely efficient on the other hand your brain

efficient on the other hand your brain

efficient on the other hand your brain is also extremely expensive it’s 2% of

is also extremely expensive it’s 2% of

is also extremely expensive it’s 2% of your body weight but fully 20% of a

your body weight but fully 20% of a

your body weight but fully 20% of a metabolic load your brain costs you more

metabolic load your brain costs you more

metabolic load your brain costs you more than muscle when you’re working out so

than muscle when you’re working out so

than muscle when you’re working out so this is lead neuroscientists to suppose

this is lead neuroscientists to suppose

this is lead neuroscientists to suppose the neural circuits should be efficient

the neural circuits should be efficient

the neural circuits should be efficient in their consumption of resources

in their consumption of resources

in their consumption of resources because they’re already so expensive

because they’re already so expensive

because they’re already so expensive that there should be something in their

that there should be something in their

that there should be something in their organization that makes them efficient

organization that makes them efficient

organization that makes them efficient in using up you know power and space and

in using up you know power and space and

in using up you know power and space and so on in the head so we can hypothesize

so on in the head so we can hypothesize

so on in the head so we can hypothesize that the grid system that I told you

that the grid system that I told you

that the grid system that I told you about in the head is in number system

about in the head is in number system

about in the head is in number system and that it should be organized to

and that it should be organized to

and that it should be organized to minimize the cost of representing where

minimize the cost of representing where

minimize the cost of representing where you are in the world okay so physicists

you are in the world okay so physicists

you are in the world okay so physicists purists like me what do we do when we

purists like me what do we do when we

purists like me what do we do when we see a thing like this

see a thing like this

see a thing like this we mathematize it you know make it more

we mathematize it you know make it more

we mathematize it you know make it more abstract so here’s an abstract

abstract so here’s an abstract

abstract so here’s an abstract description of the grid we put down some

description of the grid we put down some

description of the grid we put down some variables into parameters and we build a

variables into parameters and we build a

variables into parameters and we build a theory we say okay the resolution the

theory we say okay the resolution the

theory we say okay the resolution the precision of this abstract description

precision of this abstract description

precision of this abstract description of the world should be set by the

of the world should be set by the

of the world should be set by the behavior of the animal we say that the

behavior of the animal we say that the

behavior of the animal we say that the cost of the grid of the system should

cost of the grid of the system should

cost of the grid of the system should grow with the number of neurons because

grow with the number of neurons because

grow with the number of neurons because surely the more the neurons you need the

surely the more the neurons you need the

surely the more the neurons you need the more expensive the whole thing is going

more expensive the whole thing is going

more expensive the whole thing is going to be and that will agree that what we

to be and that will agree that what we

to be and that will agree that what we want to predict is how this thing scales

want to predict is how this thing scales

want to predict is how this thing scales up the ratio of the sizes between these

up the ratio of the sizes between these

up the ratio of the sizes between these scales okay and then a good theorist can

scales okay and then a good theorist can

scales okay and then a good theorist can write down a mathematical theory of this

write down a mathematical theory of this

write down a mathematical theory of this and ask which grid which way of

and ask which grid which way of

and ask which grid which way of representing space of location of the

representing space of location of the

representing space of location of the world is the most efficient

world is the most efficient

world is the most efficient so you can do that and what we found is

so you can do that and what we found is

so you can do that and what we found is that a prediction the prediction is that

that a prediction the prediction is that

that a prediction the prediction is that the way in which these grids will scale

the way in which these grids will scale

the way in which these grids will scale up as you poke into the internal cortex

up as you poke into the internal cortex

up as you poke into the internal cortex is by ratios of the square root of a

is by ratios of the square root of a

is by ratios of the square root of a famous mathematical number called e this

famous mathematical number called e this

famous mathematical number called e this e is Euler’s number a number that Euler

e is Euler’s number a number that Euler

e is Euler’s number a number that Euler the famous mathematician devised for

the famous mathematician devised for

the famous mathematician devised for other purposes and what do you know

other purposes and what do you know

other purposes and what do you know experiments confirm this theory

experiments confirm this theory

experiments confirm this theory precisely so what do we learn from this

precisely so what do we learn from this

precisely so what do we learn from this well I think at the simplest level we

well I think at the simplest level we

well I think at the simplest level we learn that nature seems tough long

learn that nature seems tough long

learn that nature seems tough long before humans did devise these kinds of

before humans did devise these kinds of

before humans did devise these kinds of complicated number systems as and in a

complicated number systems as and in a

complicated number systems as and in a two dimensional fuzzy neural kind of way

two dimensional fuzzy neural kind of way

two dimensional fuzzy neural kind of way and then proceeded to optimize it for

and then proceeded to optimize it for

and then proceeded to optimize it for the neural hardware I think that’s the

the neural hardware I think that’s the

the neural hardware I think that’s the first lesson we learn somewhat more

first lesson we learn somewhat more

first lesson we learn somewhat more broadly these results suggest the brain

broadly these results suggest the brain

broadly these results suggest the brain is a sort of elegant and efficient

is a sort of elegant and efficient

is a sort of elegant and efficient mathematical machine and that we can use

mathematical machine and that we can use

mathematical machine and that we can use this idea of elegance and efficiency of

this idea of elegance and efficiency of

this idea of elegance and efficiency of this engine in our head to build a

this engine in our head to build a

this engine in our head to build a theory of organization of the brain even

theory of organization of the brain even

theory of organization of the brain even more broadly I think what I just told

more broadly I think what I just told

more broadly I think what I just told you has a bearing on a famous dictum of

you has a bearing on a famous dictum of

you has a bearing on a famous dictum of Galileo so hundreds of years ago Galileo

Galileo so hundreds of years ago Galileo

Galileo so hundreds of years ago Galileo wrote that the book of nature is written

wrote that the book of nature is written

wrote that the book of nature is written in the language of mathematics and you

in the language of mathematics and you

in the language of mathematics and you know physicists people like me have

know physicists people like me have

know physicists people like me have especially taken that seriously so over

especially taken that seriously so over

especially taken that seriously so over the decades over centuries there’s a

the decades over centuries there’s a

the decades over centuries there’s a fully mathematical description of the

fully mathematical description of the

fully mathematical description of the world and physicists believe you have

world and physicists believe you have

world and physicists believe you have explained a phenomenon if you have a

explained a phenomenon if you have a

explained a phenomenon if you have a precise mathematical description of it

precise mathematical description of it

precise mathematical description of it and that makes predictions for the next

and that makes predictions for the next

and that makes predictions for the next experiment I believe that this is the

experiment I believe that this is the

experiment I believe that this is the century where the living world will

century where the living world will

century where the living world will receive finally the same kind of

receive finally the same kind of

receive finally the same kind of treatment for you know again for

treatment for you know again for

treatment for you know again for centuries we’ve described life and

centuries we’ve described life and

centuries we’ve described life and living things mostly descriptively but I

living things mostly descriptively but I

living things mostly descriptively but I believe that in this century the study

believe that in this century the study

believe that in this century the study of life will become as mathematical and

of life will become as mathematical and

of life will become as mathematical and beautiful as a study of atoms crystals

beautiful as a study of atoms crystals

beautiful as a study of atoms crystals and the forces of nature thank