►
From YouTube: Numenta Research Meeting - Dec 4, 2019
Description
Marcus Lewis will draw a connection between the "Sparse Manifold Transform" paper and Numenta's general "location" idea.
http://papers.nips.cc/paper/8251-the-sparse-manifold-transform
Discussion at https://discourse.numenta.org/t/numenta-research-meeting-dec-4-2019/6881
A
B
A
Paper
came
out
for
Europe's.
The
first
place
I
saw
presented
was
at
the
Science
Institute
the
same
place
you
presented
in
that
class
I
think
April
yeah,
one
April
now
I'm
I
am
presenting
this
as
if
you
haven't
seen
it
before,
but
I'm,
not
presenting
all
of
it.
I'm
presenting
the
parts
that
are
this
seem
especially
relevant
to
us
and
I'll.
A
I'm
kind
of
leaving
that
out
of
this,
for
the
most
part,
I'm
just
focusing
on
a
single
column,
so
just
to
start
this
off
and
what
was
stop
provoking
to
me
and
what
made
me
want
to
really
understand
this
paper
was
once
I
understood
it
somewhat.
Well.
I
realized
that
this
diagram
that
I've
drawn
here
of
some
Serena
Cooke
coming
in
being
mapped
to
a
sparse
code
and
then,
which
is
then
mapped
to
another
representation.
That
is
a
kind
of
a
point
in
a
metric
space,
a
Euclidean
representation,
a
grid.
C
A
C
A
A
C
A
A
D
D
D
B
C
D
C
B
C
C
A
I
think
it's
useful
before
I
dive
into
there's,
to
talk
to
do
a
quick
review
of
of
will
have
written
metric
spaces
in
the
brain,
from
the
perspective
of
good
cells
and
and
what
types
of
things
we
know
that
grid
cells
seem
to
represent.
There's
the
classic
example:
I'm
gonna
spend
two
seconds
on
this
grid
cells.
This
this,
the
it's
the
seminal
paper
of
rats
moving
around
represents
physical
location.
A
A
C
C
A
There's
this
is
a
bad
drawing
of
a
treadmill
of
an
actual
treadmill,
often
and
often
in
neuroscience
experiments.
They
call
something
a
treadmill
when
an
animal's
running
on
a
wheel
and
spinning
it
like
a
hamster
wheel,
but
this
is
this
is
a
natural
treadmill
where
it's
like
almost
like
a
machine,
that's
running
under
it.
What
the
rat
does
is.
It
runs
around
the
figure.
Eight.
It
gets
here,
there's
a
barrier
here.
There's
they
can't,
they
can't
advance.
A
C
A
Presumably,
some
grid
cell
modules
track
how
much
time
the
rat
has
been
on
the
treadmill
some
track,
how
much
distance
that
has
run
on
the
treadmill
and
others
track.
Some
weird
production
of
the
to
some
weird
combination,
where
the
time
elapsed
causes
the
Babu
to
move
in
a
certain
direction
and
the
distance
elapsed
causes
the
bump
to
move
in
another
direction
as
if.
B
A
Rat
is
representing
some
projection
in
spate
in
this
space
of
all,
the
relevant
variables
were
one
variables
time
elapsed.
One
barrier
variable
is
distance,
elapsed,
and
so
today,
so
the
principle
here
is
that
grid
cells
are
representing
some
projection.
A
path.
Integration
is
screwing.
With
things
there's,
there
are
possible
other
explanations.
This
is
a
little
messy,
but
it's
possibly
suggestive
of
all
that.
A
B
C
C
A
A
A
A
B
C
B
A
Where
is
the
center
of
physical
or
filter?
How
big
is
it
and
and
and
how
is
it
rotated
now
from
the
perspective?
It's
not
now
in
in
this
language
here
I
mean
I,
haven't
really
said
anything
yet
I'm,
just
just
laying
out
like
to
take
this
view
of
the
world.
Take
this
view
of
what
anyone's
doing
in
this
language,
what
the
sparse
filters,
what
Bruno's
kind
of
classic
work
does?
Is
it
takes
this
four.
A
That
might
be
this
one
here
and
I've
drawn
this
sort
of
schematically
I've
drawn
it
two
dimensional,
because
you
can't
draw
a
four
dimensional
shape
and
under
this
view,
under
this
view,
these
these
these
units,
the
units
are,
are
uniformly
distributed
through
this
manifold,
keep
in
mind,
I
haven't
presented
anything
new
yet
and
I'm.
Putting
a
narrative.
B
A
And
any
stimulus
is
then
represented
as
like
a
sparse
code
of
these
and
okay.
This.
This
is
a
point
of
view
on
sparse
coding,
the
next
step
they
take
the.
Finally,
the
new
thing
is:
they
want
to
represent
this
metric
space
explicitly
they
want
a
population
that
is
actually
rather
than
being
just
like
a
bunch
of
coordinates
like
how
close
is
the
stimulus
to
this
cell?
How
close
is
it
to
this
cell?
They.
C
A
D
C
A
C
A
A
B
A
E
A
E
A
B
A
A
C
I
mean
this
is
the
same
thing.
The
way
I
would
think
about
it
is
that
the
different,
if
we're
talking
about
do
you
want-
and
these
are
three
different
columns
that
are
representing
the
three
different
edges
each
one
of
those
continent-
many
columns
a
bit
bigger
columns
each
one
of
those
concept,
its
own
location,
in
a
space
of
the
larger
object,
but
they're
not
sharing
the.
C
C
A
A
C
E
D
A
D
A
A
Is
they
use
a
population
code
that
you
a
set
of
neurons
yeah?
They
use
a
population
code
where
each
one,
okay,
what's
the
right
way
to
say
this,
I'll
put
this
in
like
48
terms
where
I,
if
you
want
to
it's
almost
like
they
treat
this
as
an
image
that
they
that
they
want
to
put
describe
using
some
basis
where
the
basis
vectors
are
these.
These
individual,
these
individual,
that
this
is
a
basis
for
describing
sets
of
sets
of
points.
If
you
treat.
B
A
A
Responds
to
certain
locations
in
this
Euclidean
space,
so
you
location
some
in
this
metric
space
and
and
one
of
them
will
respond
in
kind
of
the
center
ones.
Another
one
will
respond
kind
of
like
yes
over
here,
no
over
no
down
here,
the
other
one
will
be
kind
of
they
become
more
honestly
grid
like
that.
They
become
something
like
this
and
what
I
find
interesting
when
I
look
at
this
is,
if
you
were
to
report
cells,
that
look
a
lot
like
this
as
the
represented
location
moves
around
2d
space.
B
C
A
And
an
interesting
possibility
from
all
this
is
okay.
Okay,
conceptually
all
of
us
have
kind
of
been
right.
It
is
representing
a
location
in
some
metric
space,
but
maybe
another
thing
that
comes
along
if
you,
the
reason
why
they
needed
all
of
these
various
basis
functions
is
because
they
wanted
to
be
able
to
represent
multiple
points
simultaneously.
A
C
C
In
the
sensor,
you
could
be
recalculate
how
far
you
have
to
go
to
some
bomb
that
in
that
this
is
the
question
then
you're
saying
if
I
take
them.
If
I
take
the
sum
of
all
these
or
the
protection
or
balloons,
or
something
like
that,
I
end
up
with
other
this
mishmash
of
cells
we
actually
see
which
are
actually
encoding,
multiple
points
at
the
same
time
and
that
representation
up
there
on
its
own
really
isn't
metric
I
can't
give
a
motor
command
to
it
and
have
an
updated
properly
right.
C
Collection,
the
the
circle
with
the
three
dots
I
think
I
need
guys
in
the
bottom
here.
The
basis
function
to
have
a
single
point:
I
can
give
her
a
motor
command
and
they
up
there,
but
now
I'm,
combining
them
somehow
to
create
what
these
other
cells
in
the
circle,
with
the
three
dots
there
that,
on
its
own
I,
can't
just
being
a
motor
command
to
I
have
to
feed
it
into
the
basis
functions.
A
D
F
B
F
Features
project
two
in
this
example,
a
common
location
and
and
there's
multiple
sets
of
these
things.
It's
replicated
over
multiple
locations
in
this
metric
space
is
that
what
you're
saying
there's
a
grid
of
the
of
these
and
each
one
of
them
has
an
array
of
these.
These
features
that
they
can
fire.
A
Down
here,
yeah,
so
the
so
that
this
is
the
second
population
and
in
the
model,
basically
so
I'll,
step
back
and
say,
and
this
sparse
manifold
transform
paper
they're
proposing
a
second
population
of
cells.
So
they
start
with
the
sparse
code
that
comes
from
the
traditional,
sparse
coding
and
then
now
they
want
to
take
it
and
represent
it
in
kind
of
a
more
metric
way.
C
E
B
C
A
Don't
understand,
I
should
say
another
another
way
describe
it
as
this
is
a
the
sparse
coded
representation
is
a
high
dimensional,
sparse
code.
This
is
a
low
dimensional
non
sparse
code.
If
I
dimensional,
where
its
goal
is
now
to
be
of
the
keep
saying
metric,
it
is
an
embedding
and
it's
Euclidean.
So.
E
A
E
B
C
A
A
C
A
Okay,
now
the
principle
they
want
how
how
this
metric
space
gets
learned
and
what
properties
that
has
so,
as
your
input
changes
over
time,
the
that
the
the
green
dots
are.
The
black
dots
also
changes
over
time.
They'll
they
shift
around
as
the
as
the
galore
filter
moves
around
rotates.
It
gets
larger
dose
down
around
as
well
the
learning
objective
that
have,
as
as
they
want
those
paths
over
short
timescales
to
tend
to
be
straight
and
smooth.
A
A
C
A
C
A
You're
watching
a
person
visiting
well
okay,
I,
get
like
ten,
but
I
feel
like
I
might
run
into
this
song.
So
if
you're
watching,
if
you're
watching
like
a
cartoon,
stapler
just
opening
and
closing
that
should
cause
that's
one
example.
This
is
kind
of
a
crazy
example.
I
should
have
maybe
started
with
something
easier
like
as
something
moves
across
your
visual
field.
This
should
tend
to
cause
this
should
or.
B
B
B
C
You
know
if
you've
used
an
example
of
a
map
of
the
town
like
a
grid
cell
here
I
know
my
location
in
the
town.
Well,
a
metric
space
says:
oh,
give
me
two
points.
I
can
tell
you
how
far
apart
they
are.
Give
me
two
points.
I
can
tell
you
how
to
get
from
one
point
to
the
other
point,
even
if
I've
never
gone
that
way
before
right.
C
So
I
may
walk
from
here
to
the
library
and
I'm
where
I
am
so
loud
right
now,
where
the
ends
of
Starbucks
but
I'm,
not
the
library
I
can
figure
out
how
to
get
to
those
stuff.
I
think
I've
never
done
that
before.
That's
because
there's
this
regular
structure
to
the
to
the
space
and
then
movements
have
the
same
effect
everywhere.
I
can
stuff
so.
C
E
E
C
E
E
C
You
still
represent
in
the
sensory
on,
but
you're,
not
really
representing
its
location
anywhere
you're.
Just
if
I
understand
what
you
said,
it's
just
I'm
just
representing
this
input
in
a
way
that
has
certain
properties,
but
it's
not
at
all.
Like
the
concept
we
have
a
location
of
a
in
the
world.
It's.
D
C
A
A
B
C
Object,
I
need
to
be
able
to
say
I.
Don't
there
has
me
this
existing
metric
space
that
has
all
the
properties
I
want
once
I
just
talked
about
before
I've
been
populated
before
I
said
it
what's
in
it
right,
because
I
may
find
there's
something
in
some
location
or
may
not
as
though
I
have
I
start
with
the
map
of
the
town
and
I
haven't
explored
that
part
of
the
town
yet,
but
the
locations.
D
C
There
I'm
there
going
to
be
the
same
location
so
when
I
get
there
doesn't
matter,
it's
gonna
be
the
same
location.
I
might
find
a
library,
my
five
o'clock
shop,
but
that
location
doesn't
change
based
on
what
I
find
them.
It's
it's
still
the
same
location
on
the
map.
It
seems
like
there's
something
on
that
product.
A
A
C
C
C
B
B
A
Bigger
packs
the
exposition
of
my
finger
and
know
what
the,
why
of,
to
what
yeah
sure,
Pat,
fine
and
and
I'm
saying
that
as
I
move
around
a
visual
depiction,
I
already
know,
I
already
know
like
that,
when
I
move
my
finger
down
and
to
the
right
like
I,
will
say,
coffee
cup
handle
as
I
move.
My
finger
to
here,
I
already
know
how
to
update
this
code.
I
already
know
that
I'm
going
to
like
do
this
yeah
and
so.
A
C
C
C
See
if
it's
driven
from
these
inputs
these,
if
you
have
anything
to
do
with
the
position,
scale
and
orientation,
then
it's
not
independent
of
of
what
was
sense,
because
I
could
send
something
please
jumping
at
the
same
location
and
I'm
missing
something
basic
here.
It
seems
like
you,
you
have
two
completely
separate
out
what
sensed
from
your
location.
They
have
two
orthogonal
things
which
then
are
associated
in
normal,
but
yeah.
C
C
A
D
B
C
A
A
C
E
C
Those
associates
like
the
burden,
things
that
that
was
learned.
That's
the
assumption
there
at
least
my
assumption.
That
was
learned.
It
wasn't
the
a
priori
mapping
there
out
of
birds
that
if
the
birds
changed
differently,
then
you
would
have
different
mapping.
So
I
guess
I'm
just
trying
to
get
the
fundamental
concept
here
and
I'm
lost
now.
D
C
A
E
B
E
F
B
A
A
Objects
just
from
the
pixel
info,
because
the
manifolds
are
hopelessly
entangled
and
the
principle
they
want
to
to
make
use
of
is
at
each
successive
level
of
the
visual
ventral
stream
there
they're
making
it
where
a
given
object,
given
objects,
the
manifold
of
thing
of
representations
that
it
covers
becomes
less
and
less
tangled.
It
becomes
more
and
more
flat,
it
becomes
more
and
more
separated,
and
so.
F
A
C
A
C
B
A
B
A
A
C
C
A
A
A
B
A
A
D
D
C
Salsa
problems,
our
basic
theory
there,
maybe
is
a
solution.
You
the
basic
theories.
You
have
some
sort
of
input
to
a
column
and
you
want
to
represent
it.
Somehow,
that's
a
you
can
think
of
that.
It's
like
play
cells,
it's
a
it's
an
encoding.
It
represents
the
employed,
that's
unique
to
some
places
in
the
world.
You
have
another
thing
which
is
so.
This
can
be
sensory.
D
C
C
And
this
is
gonna,
be
updated
by
mood
and-
and
then
we
do
this-
this
associated
learning
between
this
metric
space,
which
is
totally
independent
of
what
the
input
is,
of
course,
the
input
could
then
invoke
a
space,
but
the
movement
command
does
not
care
what
you're
sensing
movement
comes
in.
You
move
here
to
your
location,
and
this
is
drive
this
and
it
doesn't
tell
you
where
you
are
only
you
can
tell
you.
Where
are
my
associate
learning
to
this?
That's
our
basic
idea.
We
there's.
D
C
Of
stuff,
we
don't
know
about
this,
we
do
not
know.
We've
assumed
that
this
is
some
sort
of
grid
cell
representation
out
here,
but
we
don't
really
know
it
understanding
how
its
represented
the
current
thinking
is.
You
takes
multiple
of
these
bits
on
modules
and
we
somehow
combine
them
together,
but
this
is
but
there's
the
evidence
of
that.
It's
kind
of
fuzzy
and-
and
if
you
we
do
those
all
within
the
column,
which
is
very
small,
so
there's
this
question
of
how
does
this
metric
space
come
about?
C
I
know
the
properties
that
it
needs
to
have
I
mentioned
them
earlier,
but
how
is
it
derived?
We
don't
know
that
simple.
We
don't
really
know
all
these
about
how
these
inputs
and
coded
we
raise
your
pool
today,
which
is
pretty
simple,
but
just
yesterday,
I
was
talking
about
Alex
or
a
Monday
of
summer
house
doesn't
really
map
into
what
we
see
in
the
cortex
completely.
C
They're
not
always,
linear,
though,
is
that
movement
it
get
distorted
and
so
on.
We
need
something,
that's
not
distorted
so,
and
we
also
know,
as
you
point
out,
that
many
different
types
of
cells
enhance
we're
outer
cortex
that
are
into
playing
and
working
together
and
orientation
and
different,
so
I
think
what
I
got
out
of
today,
maybe
I'm
not
what
you
presented.
C
Maybe
it
is,
but
what
I
got
today
is
that
potentially
the
way
to
understand
this
is
that
there's
a
there
is
a
set
of
simpler
basic
functions,
we're
not
going
to
call
those
things
over
there,
and
these
guys
are
like
mini
grid
cells
that
are
like
zero
and
it
being
a
little
mini
grid.
These
are
like
so,
but
different
worry
different
population
in
grid
cells,
and
they
combine
to
form
our
location
right
before
we
were
thinking
about
as
the
grid
cells
themselves
are
the
basis,
and
we
need
to
do
multiple
bits
on
modules.
This.
B
D
C
I
need
multiple
those
modules
which
are
trying
to
be
like,
but
not
a
little
grid
like
right.
There,
there
it's
sort
of
one-dimensional,
if
I,
think
about
they're,
like
one
dimensional
grid
cells
of
certain
repeating
properties
or
something
is
that
so
there's
some
basis
function
here,
and
in
that
case
the
movement
command
goes
into
these
guys
and
what
we
see
as
grid
cells
is
not
really
being
driven
by
movement
because
of
being
driven
by
movement,
and
they
come
on
in
a
way
that
looks
bit
like
we're.
C
A
A
C
A
C
C
They
and
they
just
state
this
parcel
out
space.
Somehow,
and
if
you
have
a
bunch
of
one
dimensional
grid
cell
models,
they
could
figure
out
any
in
dimensional
space
and-
and
so
there
is
the
classic.
2D
plastic
itself
is
originally
seen
by
the
monsters.
Is
this
two-dimensional
bump
that
moves
around
in
two-dimensional
space
and
we
were
trying
to
make
that
working
to
create
an
n-dimensional
space,
but
it's
much
more
healthy.
If
I
have
a
bunch
of
one-dimensional
thanks.
C
Is
we
don't
understand
how
this
Cody
comes
about?
We
we
don't
really
understand
it
deeply,
there's
a
lot
of
mysteries
about
that.
We
also
have
mysteries
about
this,
but
the
basic
principle,
I
think
is
right
for
me.
I
hope,
I'm
sticking
with
it
for
now.
So
maybe
this
paper
gives
us
some
new
insights
about
how
it
is
that
actually
this
encoding
comes
about,
and
how
does
the
different
quarry
comes
about,
but
my
arguments
during
your
during
the
presentation
here
is
that
these
really
are
two
separate
worlds
say
they.
C
This
has
to
exist
independent
of
this
kind
of
that,
and
only
by
associative
learning.
Do
we
then
start
to
learn
the
web
structure?
Is
an
object?
Is
instructor
another?
That's
how
I
was
approaching
you're
talking
with
a
dread
wrong.
That's
how
I
was
approaching
it
and
I
see
like
what
you
were
focusing
a
lot
here
talking
about
these
things
and
you're
figuring
out
an
encoding
up
here
that
made
sense.
That
was
work
that
was
more
metric
like
in
these
dimensions.
So
maybe
there's!
Oh,
maybe
there's
a
point.
C
Taking
this
input,
which
is
a
complex,
we
don't
become
input.
That
is,
we
don't
really
know
what
the
dimensionality
of
it
is,
so
it
gets
learned
and
then
again
and
we
don't
know
how
to
represent
instead
of
some
sort
of
dinner
penetration,
pooling
type
of
thing,
it
gets
learning,
but
maybe
it's
it's
learning
in
the
finished
very
specific
way
that
that
is.
C
So
today
we
have
a
very
simple
idea:
here:
we
have
the
space
of
Pooler
and
down
here.
We
have
basically
sort
of
a
sum
of
multiple
bits
on
modules
again
and
we
don't
even
understand
orientation
and
this
either.
So
so
maybe
there's
some
details
in
here
which
help
us
get
a
better
understanding
of
this.
C
C
Well,
sorry,
for
those
we
don't
know
if,
if
like,
if
the
court
chest
can
actually
end
up
record
one
off
that
it
really
is
not
restricted
to
the
number
in
the
end,
we'll
learn
the
correct
number
of
inventions
in
the
space,
or
is
it
always
kind
of
drive?
Is
that
it
sounds
say
no.
This
is
evolutionary
algorithm
designed
around
three
dimensional
world
or
three
dimensions
plus
time,
and
everything
has
to
fit
into
that
and.
C
A
I
think,
maybe
what
makes
there
this
most
confusing
is
that
they
don't
have
any
notion
of
motor.
They
don't
have
any
notion
of
the
given
motor
action
is
always
going
to
move.
This
is
a
fixed
amount
repeating
that
motor
action
is
going
to
move
in
a
fixed
amount.
They
don't
have
anything
like
that.
They
have
just
a
generic
metric
space.
That's
ready
to
have
inputs,
mapped
into
it.
Hope
you
can.
You
can
learn
and
puts
map
it
into
it
in
any
way.
You
want
I
think
part
of
what's
made
that
confuse.
C
C
B
C
What's
appealing
about
this
is
that
somehow
you've
taken
some
input?
Space,
which
is
sensory,
have
birthdays
and
you
divide
it
up
into
two
pieces
which
should
move
linearly
with
movement.
They
should
have
been
in
front
of
them
and
and
then
we
have
these
mini
columns
going
across
here
all
the
time
and
though
each
mini
comic
represents
like
a
more
filter
plus,
they
also
sell
some
certain
directional
sensitivity
to
them
and
so
on.
So
this
this
is
somehow
a
promise
or
a
certificate.
C
The
possibility
that
defining
your
input
in
a
space
like
this,
which
itself
is
not
metric
in
the
sense
of
location,
on
an
object.
It's
just
metric
in
terms
of
these.
These
individual
components
of
the
input
somehow
could
lead
to
the
correct,
dimensionality
and
mapping
down
here,
like
somehow
fighting
by
like
extracting
out
these
four
components
of
the
input
and
saying
those
four
components
behave
linearly
through
movements,
but
they
don't
tell
me
where
I
am
they
just
behave?
C
Literacy
movements
that
somehow
that
could
define
the
dimensionality
down
here
remember
there
was
this
like
D
I
always
had
that
each
mini
column
could
be
a
1
B,
1
D
dimensional
space
it
was
like
I
was
really
intrigued
when
you're
working
on
the
paper
with
Merkel
about
maybe
each
mini
column
would
be
a
1d
basis.
Function
and
I
gave
up
on
that
because
I
just
couldn't
get
it
to
work
or
something
wrong.
I
can't
remember:
I.
C
To
solve
the
whole
problem,
I
think
they've
been
on
that,
so
it
back
fat
with
that.
With
that
then
I
really
liked
it.
Then
the
mini
column
itself
becomes
the
the
basis
function
for
movement
and
for
the
you
know,
somehow
they
they
work
together.
It's
just
the
mini-com
span
this
these
do
things
so
I.
Really,
that's
really
intriguing
idea.
C
Monday
those
aren't
that
many
columns,
seen
with
our
in
this
perfect
position
to
define
another
form
of
communications.
It's
it's
not!
It's
not
a
synaptic
communications,
it's
a
physical
communications
across
layers,
and
it's
also
very
intriguing
that
you
know
we
see
these
mini
columns.
Center,
sometimes
parse
up
the
space
in
some
way
in
uniform
way,
and
we
see
those
representations
going
back
down
here.
C
That
moves
laterally
down
here,
I
had
it's
all
very
fuzzy.
I,
don't
understand
that
I'm
just
pointing
out
that
it
would
be
great
if
we
had
a
bunch
of
1d
basis
functions,
but
one
team,
good
cells,
and
that
somehow
the
input
space
itself
decides
how
to
combine
these
into
some
in
dimensional
space.
Here
that
almost
seems
like
it
has
to
be
right,
even
though
I
can't
even
express
it.
It
seems
like
that
almost
has
to
be
right
somehow,
so
this
is
very
intriguing.
F
C
C
F
That
right,
that's
that's
correct,
but
in
the
sense
that
if
there
was
a
distortion
to
your
space,
you
could
you
know
the
cajon
that
could
be
trained
to
undisturbed
it
if
I'm
not
mistaken
or
it
can
represent
it
into
a
parameter
space
that
has
certain
properties
either
geometric
or
topological
I
mean
the
main
thing
is
that
it
is
more
or
less
it's
a
continuous
space.
It's
a
parameter.
Mapping
space,
no
I
mean
you
have
this
fact
that
you've
got
this
two-dimensional
sheet
of
cortical
columns.
You.
F
C
C
C
A
3d
map
of
the
world
and
being
able
to
say
I,
know
how
I
know
where
location
on
me.
If
I
move
in
this
direction
or
I
know,
I
can
calculate
how
to
get
to
this
direction
from
this
direction.
This
point
to
this
point:
I
need
that
and
that's
that's
a
key
part
of
the
whole
cortex
and
that's
people
written.
D
C
F
C
But
I
can't
see
how
you
can
learn
the
metric
measurement
assistant,
if
you
want
to
call
it
that
it
has
to
be
the
building
about
grid
cells
is
in
the
way
it's
also
described
today.
It's
an
inherent
property
of
the
bit
cells.
That's
what
you
want.
You
want
the
space
to
be
in
and
have
an
inherent
ability
so
that
I
can
create
a
whole
new
map
of
a
new
object
and
I.
Don't
learn
anything
I
face
is
work.
C
F
That
and
then
you
have
a
transformation
for
that
to
where
you
have
undistorted
it
wear
whatever
the
driving
function
is
to
say.
Okay,
these
things
are
topologically
near,
but
I
have
some
other
reason
to
believe
that
you
know
I
need
to
displace
them
a
little
bit
further
apart,
because
the
stay
like
a
bop
bop
and
even
though
they're
adjacent
you
know
they
should
be
represented
down
here
as
something
that
you
know
is
what.
C
F
B
F
F
C
C
But
that's
the
whole
premise
of
the
whole
premise
of
them.
Is
that
that's
the
way
they
work
they
built
that
way,
so
there's
multiple
theories
about
how
they
do
that
and
no
one
knows
for
certain.
But
there
are
several
theories
about
how
they
do
that.
We've
discussed
those
there
at
length,
but
the
idea.
B
C
That
is
not
a
learned
thing.
That's
the
whole
point
of
having
the
separate
metric
space.
Is
that
it's
it's
the
it's
like
it's
like
you
have
this
big
blank
sheet
of
paper
which
is
divided
into
squares.
It's
all
there
you,
someone
with
didn't,
get
it,
but
you
can
navigate,
even
though
you
don't
know
what
time
that's
kind
of
what
crystals
do
I
think.
The
idea
here
is
that
I
still
like
this
idea
that
you
can
have
a
whole
bunch
of
one
dimensional.