►
Description
Last month, Marcus Lewis proposed an alternate view of grid cells which enables the creation of maps of novel environments and objects in a predictive basis. In this meeting, he extends his grid cell proposal to a machine learning model. The agent in this model uses spatial displacements and its grid cells (for self-location) to create a grid cell representation of the attended location. The agent then goes through a series of attention shifts to activate the proper grid cell representations in order to reconstruct object vector cells. Marcus then describes how this model can contribute to explanations that can be tested using some empirical grid cell results.
Dec 21, 2020 Research Meeting (Using Grid Cells as a Predictive-Enabling Basis): https://youtu.be/7tF-ofr7VUo
Dec 23, 2020 Research Meeting (Informal Follow-up): https://youtu.be/uZ4qC2SltXA
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A
A
A
This
is
gonna
revolve
around
this
email
that
I
sent
all
the
people
here,
so
so
I'll
walk
through
the
email,
so
yeah
that
that's
that's.
How
I'll
organize
this
so
yeah
summary.
A
few
weeks
ago,
I
presented
a
way
of
thinking
about
grid
cells
rather
than
grid
cells
being
primarily
concerned
with
learning
maps
of
specific
environments.
Grid
cells
learn
a
sensory
basis
for
representing
arbitrary
environments,
but
it's
a
special
kind
of
basis
that
enables
prediction
and
I'll
bring
up
a
slide
from
there.
A
Another
way
of
saying
this
that
that
jeff,
I
know
found
instructive
was
that
if
you
enter
a
room
from
two
different
places,
a
novel
environment,
then
you
walk
from
one
place
to
the
other,
either
way
you're
gonna,
you
know
end
up
with
the
same
representation.
It's
there's!
No
random
selection,
the
the
selection,
the
grid
cell
representation,
is
based
on
what
you
send,
but
it
has
this
property
of
path.
Integration.
B
B
Is
this
consistent
with
the
idea
that
you
might
be
describing
more
what's
going
on
in
the
grids
in
the
place
cell
world,
because
that's
all
sensory
driven
and
that
and
that
place
cells
are
really
sort
of
defining
the
environments
which
are
sensory
inputs
to
finding
the
environment
and
then
the
grid
cells
there
are
to
to
assist?
I
mean
this
idea
that
that
you
just
described
you
enter
the
room
in
two
different
directions.
B
A
B
But
why
why
why
would
you
think
grid
cells
have
a
problem?
Wouldn't
you
couldn't
you
just
say
that,
couldn't
you
just
say
it
so
to
extend
the
grid
cell
network
to
include
place
cells
and
say:
oh,
this
network
has
that
property
I
mean.
Why
does
it
have
to
all
be
just
in
the
grid
cells
themselves,
because
clearly,
grid
cells
themselves
are-
or
you
know,
as
they're
classically
defined
or
just
really
driven
by
motor
behavior
and
nothing
about
sensory
input
and
so.
B
Know
I
know
so
I'm
just
trying
to
make
I'm
trying
to
I'm
trying
to
see
if
I
could
say
that
what
you
come
up
with
is
is
a
better
way
of
thinking
about
grid
cells.
That's
really
sensory
driven,
but
that's
consistent
with.
What's
what's
going
on
with
place
cells,
interacting
with
good
cells,
I
mean
my
question
is:
could
you
could
what
you
be
describing
is
what
actually
is
going
on
in
the
throttle?
Cortex,
if
I
include
place
cells,
that's
another
way
of
putting.
A
B
B
You
randomly
anchor
your
your
grid,
cells
and
you're,
saying
no,
you
don't
randomly
accurate
grid
cells,
you're
you
even
when
you're
in
a
novel
environment,
you
anchor
your
grid
cells
based
on
sensory
input,
and
so
I
could,
I
could
just
say
it's
the
same
thing
everyone's
been
talking
about
between
great
sense
and
place
up
with
this
new
twist
that
you
don't
randomly
anchor
grid
cells
in
a
new
environment.
You're
going
to
pick
them
judiciously.
B
A
A
The
reason
I
used
time
and
wanting
the
grid
cells
to
update
linearly
over
time,
why
my
motivation
for
that
was
that
it
could
explain
good
cell
distortions,
but
now
now
I
have
a
different
explanation
for
that.
So
so
my
next
slide
said,
like
the
obvious
alternate
version
of
this,
is
one
that
uses
movement
to
update
good
cells
and
that
the
same
movement
applied
multiple
times
is
going
to
cause
the
same
update
to
the
grid
cells.
But
my
criticism
of
this
was
always
that
it
wouldn't
explain.
A
Grid
cell
distortions
in
parentheses
and
a
lot
of
people
are
really
un
they're
really
uncomfortable
with
calling
grid
cells
metric
because
of
the
grid
cell
distortions.
It
makes
people
nervous,
like
maybe
we're
getting
something
wrong
about
it.
So
what
I'm
presenting
today
is
is
my
realization
that
I've
had
since
the
last
presentation
that,
in
fact,
this
model
can
explain
good
cell
distortions.
In
fact,
you
would
expect
it
when
you
use
this
sensory
basis,
viewpoint
of
good
cells,
that
you
will
expect
something
like
this
and
and
today.
A
So
there
were
a
set
of
exciting
realizations
happened
here,
so
so
in
those
realizations.
I'm
going
to
give
is
like
a
set
of
bullet
points
in
this
email,
but
first
I'm
going
to
present
the
model.
So
this
this
first
bullet
point
was
just
where
I'm
embracing
the
metric
view
or
the
path
integration
view.
Rather
than
that
time
view,
but
but
just
to
say,
I
might
bring
the
time
view
back
to
talk
about
representing
other
variables
and
make
grid
cells
do
other
things,
but
putting
that
aside
completely
for
now.
A
So
I
won't
even
read
the
rest
of
this
paragraph.
I'm
going
to
come
back
to
these
bullet
points
where
I
talk
about
all
the
various
parts
of
grid
cells
that
just
kind
of
fall
into
place.
When
you
adopt
this
view,
I'm
going
to
go
ahead
and
give
you
the
model,
then
come
back
up
and
talk
about
these,
and
so
I'm
going
to
describe
this
in
terms
of
a
figure.
A
A
This
input
was
these
object,
vector
cells,
which
kind
of
denote
like
where
you
know
objects
or
boundaries,
are
relative
to
the
animal,
but
in
an
external
reference
frame
and
and
what
the
network
wanted
to
do
was
represent
the
input
and
do
a
good
job
of
representing
the
input,
for
example
via
reconstruction
error.
But
there
are
other
ways,
but
I'm
changing
the
second
part
of
this
objective,
where
it's
no
longer
using
time.
A
So
but
but
of
course
it's
in
the
reference
frame
of
the
room,
it's
rotated
with
the
room.
What
I'm
changing
now
is
I'm
making
it
more
of
an
attentional
system
rather
than
using
the
surroundings
of
the
animal.
The
the
agent
is
going
to
attend
to
different
locations
in
the
room
and
it's
going
to
reuse
those
same
object,
vector
cells,
except
it's
going
to
use
them
relative
to
the
attended
location.
A
A
Yes,
I
have
a
the
next
figure
shows
this
I'll
read
after
I
show
this
figure
I'll
scroll
up
and
just
read
through
the
text
a
little
bit,
but
yes,
I'm
going
to
use
the
displacement
from
the
space
around
the
agent
to
the
attended
area
of
space
and
that
that
is
going
to
play
into
that.
This
is
an
important
part,
so
I'll
go
ahead
and
read
these
two
short
paragraphs
because
they're
short
and
just
making
sure
I
cover
everything.
A
So
an
agent
uses
attention
to
observe
a
set
of
points
in
the
environment
and
at
each
point
the
agent
gets
an
input
image.
So
this
image
can
be
object,
vector
cells,
boundary
vector
cells,
but
but
but
they're
relative
to
the
attended
location,
they're,
not
relative
to
the
agent.
You
don't
have
to
have
object,
vector
cells
extending
out
into
infinity.
You
can
reuse
the
same
set
relative
to
the
attended
location.
A
A
B
Can
I
just
should
we
set
that
sentence
again,
yeah
you're,
saying
the
representation
of
my
location,
which
I'd
normally
think
of,
is
that,
oh,
how
am
I
anchoring
my
grid
cells?
I'm
not
sure
if
that's
still
what
it
is
here,
but
that
representation
actually
tells
you
what
those
things
are
at
those
locations
out
there.
B
This
seems
to
become
a
numerical
problem
with
that
the
the
number
of
well-
maybe
not-
I
don't,
know
the
number
of
possible
combinations
of
things
that
I
might
see
when
I
attend
to
them
is
quite
large
right.
It's
really
really
big
and,
and
so
my
possible
encoding
of
my
locations
have
has
to
accommodate
that.
A
B
B
All
right
it
somehow
it
just
seems
too
magical.
I
still
don't
understand
how
it
works,
but
it
seems
magical
that
you
could
do
this
and
that,
even
if
you
did
it
from
different
directions,
you
know
the
two
entries
to
the
room
would
still
work.
So
it's
it's
pretty
amazing.
If
it
worked,
I
still
don't
understand
it.
But,
okay,
I'm
sorry
to
keep
interrupting.
A
So
so,
just
just
to
re
well
just
to
fill
in
the
blanks
of
the
just
the
missing
piece
I
haven't
said
yet
the
agent
uses
the
the
I'm
sorry,
I
must
have
not
read
a
sentence.
The
agent
combines
its
grid
cells
representing
itself
location
with
the
with
the
displacement.
It's
just
a
standard
grid
cell
displacement
to
obtain
the
grid
cell
representation
for
the
attended
location,
so
the
same
set
of
cells
that
it
used
for
object,
vector
cells
relative
to
itself.
A
B
A
And
so
soon
I'll
talk
about
this
network
diagram
I'll
even
bring
it
in
view.
As
I
read,
the
agent
then
uses
the
attended
locations
grid
cell
representation
to
reconstruct
the
input,
and
then
they
they
do
error
correction.
They
they
adjust
the
representation
as
needed
to
better
reconstruct
the
actual
input
image.
A
This
diagram-
I
you
could
have
you-
could
have
written
down
this
diagram
from
the
description
above,
but
this
just
makes
it
all
explicit
this
self-location.
This
is
standard
good
cells.
This
is
the
location
of
the
animal
in
an
external
reference
frame,
as
the
animal
attends
to
locations
what's
happening.
Is
the
attention
system
is
setting
that
this
displacement?
It's
setting
the
displacement
of
the
attended
location
from
the
self
location
that
is
being
combined
with
the
self
location
to
get
the
grid
cell
representation
of
the
attended
location.
A
These
very
well
might
be
one
population
or
they
could
be
two
separate
populations
this.
This
is
a
common
theme.
Whenever
we
talk
about
adding
displacements
to
grid
cells,
it
could
always
be
two
populations
or
it
could
be
one
one,
that's
oscillating
or
something
yeah,
and
then
then
this
is
being
used
to
reconstruct
the
object,
vector
cells
and,
of
course,
when
I
say
object,
vector
cells.
Here,
it's
standing
in
for
a
whole
suite
of
cell
types,
it
could
be
landmark
vector,
it
could
be
boundary
vector.
A
It
could
be
something
other
things
that
have
not
yet
been
defined
that
are
sort
of
a
high
level
description
of
the
input
image.
It
could
be
a
lot
of
things,
so
the
attentional
system
is
actually
playing
a
role
in
both
both
parts
of
these.
As
you
might
notice,
the
the
displacement
is
being
set
by
the
attention
system,
or
vice
versa.
You
could
say
the
displacement
is
setting
the
attention
system,
but
then
it's
also
influencing
what
image
comes
in
to
the
system.
A
This
is
this
circuit
is,
quite
you,
know
simple
if
you
just
like
stare
at
it
for
a
little
while,
with
this
in
mind,
I
mean
this
is
a
system
that
you
you,
you
move
your
your
area
of
attention
around
the
room
and
you
do
that
repeatedly
moving
to
a
certain
set
of
locations,
probably
using
heuristics
based
on.
What's
you
know
the
most
distinctive,
what
stands
out?
What's
what's
useful
to
pay
attention
to
and
using
that
you
build
up
your
grid
cell
representation
that
enables
you
to
reconstruct
all
of
those
you.
B
B
B
A
B
You
know
sometimes,
when
I
think
about
a
firing
rate.
You
usually
think
about
okay,
there's
some
graded
response
to
something
like
there's
a
lot
of
this
or
a
little
this
or
something
like
that.
I
I
I'm
trying
to
understand
what
would
that
mean
here
like
okay?
Well,
this
good
cell's
firing
half
the
rate
of
this
dress
so
well.
What
does
that
mean?
B
A
Well,
in
the
in
what
I
presented
before,
using
the
simplicity
using
a
very
simplistic
basis
for
reconstruction,
it
was,
it
was
act.
I
I
did
something
that
was
quite
fourier-like,
where
it
was
actually
looking
for
frequencies
to
reconstruct
a
picture
of
the
object,
vector
cells,
and
so
it
was
actually
the
presence
of
a
certain
frequency
it
was.
It
was
whether
the
object
vector
cells
happen
to
be
aligned
in
a
way
that
almost
like,
almost
whether
they
land
in
a
certain
gabor
filter,
almost
as
if
the
there
are
boundaries
in
the
room.
B
B
A
A
A
What
I'm
claiming
to
you
now
is
that
what
I
just
presented
is
absolutely
gonna
have
good
cell
distortions,
so
this
first
sentence
is
a
little
confusing
because
I'm
trying
to
introduce
it
as
we
go
so
here
I'll
jump
to
here.
The
grid
cells
are
going
to
prioritize,
reconstructing
nearby
object,
vector
cells
and
boundary,
vector
cells
and
it
and
because
they're
it's
going
to
prioritize
nearby
objects
and
boundaries.
There
will
naturally
be
distortions
to
make
sense
of
this.
I
should
read
the
next
sentence.
A
So
so
what
I'm
saying
here
is
like,
if,
as
you
look
around
the
room
as
you
as
you,
as
you
put
your
attention
at
different
locations
in
the
room,
further
away
locations
are
going
to
have
more
uncertainty
in
the
displacement
vector
and
and
how?
How
far
away
the
thing
is
that
you're
attending
to,
and
it's
also
going
to
have
more
uncertainty
and
the
actual
visual
input
itself.
A
And
so,
if
you
have
reconstruction
error
there,
if
your
grid
cell
representation
is
kind
of
mediocre
at
reconstructing,
what's
out
there,
you
might
not
even
know
it
because
there's
so
much
uncertainty
there
that
it's
just
not
going
to
be
prioritized
by
your
by
the
representation.
The
representation
wants
to
represent
what's
nearby,
because
that's
where
it
has
the
most
accurate
data
so
the
so.
B
B
B
A
Right-
and
so
this
is,
I
went
with
the
the
explanation
that
assumes
the
least
I
base
this.
I
based
this
on
uncertainty.
Uncertainty
alone
is
going
to
explain,
is
going
to
explain
distortions
if
you
use
this
basis,
point
of
view,
but
but
it's
it's
quite
reasonable
to
go
further
and
say
at
different
locations.
The
animal
is
going
to
attend
to
different
landmarks
or
objects,
or
or
at
least
give
more
emphasis
to
certain
ones.
A
Yeah.
It
will
attend
the
nearby
ones
more
anyway
or
anyway,
the
distribute,
the
distribution
of
which
landmarks
are.
You
know
weighted
which
one's
received
the
most
important
is
going
to
change
anyway,
so
so
that
you'll
ex
you'll
especially
expect
this
to
happen.
But
I
don't
depend
on
this,
though
it
seems
quite
likely
that
you
would
attend
to
different
objects
at
different
locations
in
the
room
this
offers.
I
basically
fit
it
into
there.
This.
A
The
another
thing
I
was
excited
about,
so
this
is
a
thing
I
intentionally
didn't
bring
up
before
in
my
life
and
the
other
big
presentation,
because
I
knew
it
was
the
weakness
and
and
what
I
was
presenting
a
classic
thing
about
grid
cells
that
makes
people
think
about
them
as
learning
a
map
is
that
if
you
put
an
animal
in
a
familiar
environment,
let
them
become
very
acquainted
with
it.
Take
them
out
compress
the
environment,
make
put
push
the
walls
closer
together
along
one
axis,
put
the
animal
back
in
it
compresses
the
grid.
A
A
Grid
cells,
don't
learn
environments,
just
as
the
spatial
pooler
doesn't
learn
objects,
so,
instead,
as
an
animal
spends
a
lot
of
time
in
a
single
environment,
the
basis
is
being
modified
to
better
able
to
better
represent
the
environment
and
environment
similar
to
it.
This
is
a
little
bit
like
I'm
going
to
keep
using
our
models.
A
B
And
we're
going
to
run
out
of
time,
I'm
probably
great,
but
one
of
the
things
that
seems
to
be
missing
from
this
is
that
you
know
our
current
thinking
about
when
you
learn
a
room,
there's
a
lot
of
things
to
learn
your
room.
You
might
learn,
and
so
the
idea
is
that
you
would
assign
these
things
at
different
displacements
or
locations
in
the
room.
B
But
when
you,
when
you,
when
you're
pairing
sensory
observations
with
grid
cell
locations,
you
have
a
very,
very
large
abilities
to
make
a
detailed
model
of
the
room
if
I'm
just
if
I'm
trying
to
encode
the
entire
room
just
in
the
grid
cell
activation,
it
seems
like
it's
very
limiting
in
that
regard.
It's
like
I.
I
won't
be
able
to
get
the
details
that
I
might
know
about
a
particular
room.
There's
just
too
many
details
right.
It's
always
going
to
be
based
on
sort
of
you
know.
B
You
know
if
I
think
about
my
dining
room.
I
know
all
these
details
about
all
these
little
things
all
over
the
place.
It's
hard
to
imagine
that's
just
encoded
in
the
grid
cell
encoding
itself,
as
opposed
to
pairing
grid
cells
with
a
spatial
related
data,
which
is,
it
seems,
like
you're,
abandoning
the
separate
representation
of
spatial
related
data
here,
you're
you're
folding
it
into
the
grid
cells
themselves.
A
B
It
seems
like
it
seems,
like
you,
you're,
arguing
that
you're
learning
an
environment
by
by
modifying
the
grid
cells
as
opposed
to
pairing
sensory
observation
with
grid
cell
locations-
and
I
don't
think
you
need
to
abandon
the
latter
part
to
have
the
former
part.
So
I'm
just
pointing
out,
I
don't
think
you
could
encode
everything
in
a
room
purely
in
the
grid-selling
coatings.
I
think
you
could
use
the
basic
features
of
the
room,
which
I
think
is
your
main
hypothesis
here.
B
The
basic
features
of
them,
some
subset
of
basic
structure,
to
figure
out
how
you
can
represent
that
both
in
the
anchoring
and
the
activity
of
grid
cells.
But
then
I
still
might
need
a
pair
of
specific
locations
with
detailed
knowledge
about.
Oh,
where
are
the
specific
things
located
and
lots
of
dozens
and
dozens
of
things
that
might
be
in
this
reference
frame.
Yeah?
B
B
B
All
right,
so
we
don't
have
to
throw
away
the
basic
idea
of
an
environment.
Is
the
size
is
defined
by
a
set
of
displacements
of
sub-objects
relative
to
them
each
other
or
to
the
environment,
but
you
can
you're
getting
partially
the
way
there
with
the
grid
cells.
You're,
saying,
grid
cells
on
their
own
can
essentially
make
they
encode
basic
structure
of
this
environment,
not
all
the
details
but
basic
structure
based
on
some
large-scale
observations,
which
I
think
is
very
cool.
But
that's
I'm
saying
this
just
makes
for
you
to
say
no
jeff.
B
A
B
A
No
you're
you're
good.
What
I
want
to
get
across
here
is
a
set
of
grid
cell
properties.
A
set
of
empirical
results
that
have
confused
me
and
made
me
feel
weird
about
my
understanding
of
grid
cells.
Just
all
fell
into
place
once
once
this
once
this
all
came
together.
So
another
thing
that
really
follows
from
the
previous
points,
from
learned
environments
and
from
distortions
and
everything
was
the
was
merged
environments.
A
A
B
Of
the
distortion
argument
right,
this
is
like
if,
if
I'm
far
I'm
not
far
into
the
room,
I
have
one
set
of
anchorings
and
if,
on
the
other
end
of
them,
I
have
different
anchorings
and
somewhere
in
the
middle,
they
have
to
get
distorted
to
represent
each
other
or
meet
each
other.
Is
that
is
that
correct?
Yes,.
A
A
It's
confused
and
discreetly
hops,
and
so
the
I
think,
the
map
the
basis
viewpoint.
Actually
this
all
works
quite
nicely
with
because
it
can
represent
either
side
of
the
room.
Quite
well,
however,
is
going
to
prioritize
the
nearby
nearby
part,
not
the
far
away
part,
and
so
so
it
all
just
kind
of
will
fall
and.
B
So
it's
like
you
know
it's
it's
not
necessarily
remapping.
It's
just
like
there's
a
very
small
there's,
an
area
where
there's
a
lot
of
commonality
to
be
viewed,
and
so
they
might
get
remapped
quickly
and
some
you
know
or
distorted
quickly,
distorted
quickly.
It's
a
different
view
of
like
oh
new
space,
remap
randomly
no,
it's
like
no
you're
gonna
you're
gonna
going
to
base
your
mapping
on
the
sensory
data,
but
one
once
you
pass
through
the
threshold.
All
your
sensory
data
is
different.
Therefore,
it's
I
think
that's
I
don't
know.
A
Yeah
base
almost
the
last
thing.
So,
by
the
way,
when
I
talked
about
attention
updating
grid
cells,
I
wasn't
just
making
that
up.
That's
that's
the
thing
that
is
seen
in
primates,
both
humans
and
non-human
primates,
and
so
so
grid
cells
following
your
attention,
is
a
thing
that
we've
sort
of
maybe
had
explanations
for
in
the
past,
but
this
this
this
really
incorporates
it
as
being
just
part
of
the
system,
and
this
would
suggest
that
maybe
even
rats
do
this
to
some
extent
it's
just
I
mean
how
would
you.
A
B
A
Yeah
and
and
other
disclaimer
in
humans
it
was
fmri
but
and
and
and
monkeys.
It
was
a
single
unit.
Recording
and,
and
I've
talked
to
people
who
work
on
this
and
they
they
suspect
that,
as
the
as
you
look
around
a
room,
it's
going
to
occur
as
well,
not
just
looking
at
a
screen,
but
that's
that
remains
to
be
seen.
It's
really
hard
experiment
to
run,
especially
with
fmri.
A
It's
much
usually
easier
to
run
the
fmri
one
on
a
screen,
that's
in
front
of
you,
so,
but
but
but
that
is
a
real
phenomenon
and
I'm
taking
advantage
of
it
and
suggesting
that
maybe
even
raps
have
it
too.
But
how
would
you
test
for
that?
It's
hard
to
test
for
that
and
something
that
doesn't
have
so
much
of
a
you
know,
head
fix
so
much
of
a
visual
system.
A
I
I
I'll
just
say
that
this
gives
you
a
point
of
view
on
like
when
you're
out,
hiking
walking
through
the
wilderness.
You
see
landmarks.
What
what
the
heck
are
your
good
cells
doing
this
point.
This
really
gives
you
a
clear
point
of
view
on
what
might
be
happening
as
you
do
that
it's
it's
more
of
just
like
a
it's
more
of
like
a
continuous,
gradual,
re-anchoring
or
remapping
of
grid
cells,
based
on
the
the
set
of
landmarks
that
you
tend
to
attend
to
when
you're
at
that
location.
B
If
I
want
to
get
from
point
a
to
point
b,
I
can
just
compute
the
distances
in
each
grid
cell
module
and
especially
under
the
certain
conditions
of
my
kids
right
now,
but
that's
one
of
the
main
things
it
allows
you
to
do
now
if
grid
cells
are
no
longer
metric
in
sense
like
linear
metric,
how
do
I
do
that?
I
mean
I'm
in
the
wilderness.
B
A
Right
locally
and
and
also
for
reconstructing,
what's
far
away,
but
no
you're
totally
right.
If
you
have
two
remember,
if
you
have
a,
if
you
know
your
current
location
and
you
have
a
remembered
location,
that's
somewhere
else,
and
you
want
to
know
how
to
get
back
to
that
remembered
location
if
grid
cells
are
distorted
and
more
specifically,
if
the
individual
modules
distort
independent
of
each
other.
B
B
I
know,
but
I
you
know
I'm
I'm
seems
to
be
an
important
thing
to
be
able
to
do
and
that's
why
we
one
of
the
reasons
we
like
linear
metric
grid
cells
right
because
because
it's
an
explanation
but
how
we
might
go
about
that,
it's
also
an
explanation
how
I
might
build
a
model
of
a
model
of
something
that
you
know
a
detailed
model,
something
that's.
I
don't
know
that
I
can.
I
can
visualize
in
any
direction
and
know
how
far
things
away.
B
B
Well,
I
actually
don't
think
it's.
I
I've
moved
to
the
point
where
the
only
grid
cells
are.
That
matter
are
the
ones
that
were
I'm
not
repeating
within
the
environment
that
I'm
modeling.
So
if
I,
if
I
restrict
my
grid
cell
modules
to
the
ones
that
are
large
enough,
the
phases
are
separated
enough.
Then
I
can
and
then
I'm
not
dealing
with
the
repetitive
good
self
point
and
I
don't
have
to
have
a
lookup
table.
I
can
literally
just
say
for
each
let's
say
I
had
a
bunch
of
1d
grid
cell
modules.