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From YouTube: Performing basic math with grid and displacement cells
Description
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/rhyolight_
A
Hey
Jasper,
thanks
for
for
joining
I'm
gonna
talk
about
some
forum
questions
here,
and
so
let's
talk
about
this
idea
of
math
a
little
cuz
I
think
this
is
interesting.
Some
someone
was
someone
wanted
to
try
and
like
teach
HTM
to
represent
low,
very
low
level
mathematical
operations.
Like
addition,
subtraction
and
stuff
I'm
a
bit
discouraging
about
this
and
I
and
I,
was
in
the
in
this
post
earlier.
A
You
know
it
is
interesting.
I
think
it's
interesting
to
think
about,
but
I
don't
think
this
is
the
direction
to
go.
If
you
want
to
try
and
do
it
the
way
your
brain
is
doing
it
and
I
mean
this
is
my
opinion.
Okay,
this
is
not
something
that
Numenta
is
investigating
or
anything
weird
we're
still
trying
to
understand.
A
very
high-level
object,
recognition,
type
stuff
and
I
I
feel
like.
So.
A
Let
me
address
this
I
said:
remember
that
mathematics
is
a
cultural
creation,
so
the
thing
that
I
mean
about
that
is
like
numerosity
is
not
cultural,
numerosity
just
exists,
and
it's
certainly
possible-
or
it's
certainly
probably
evident-
that
brains
have
an
ability
to
identify
numerosity
like
three
versus
two
or
something
but
I,
but
the
concepts
of
mathematics
that
I'm
talking
about
like.
If
you
take
a
number
and
you
operate
upon
it
in
this
way,
with
another
number
it
equals
another
result.
That
is
an
idea
that
is
well
beyond
numerosity.
A
It's
well
beyond
just
being
able
to
count
and
your
point
about
bees
being
able
to
use
some.
You
know:
four
brain
cells
are
enough
to
count.
Yeah
counting
is
easy,
I
mean
you
can
read
igger
you
can
count
really
easily
with
computers
or
with
neurons
its
concepts
that
are
hard.
It's
con
its.
But
it's
it's
more
than
just
that.
These
four
brain
cells,
when
you
see
evidence
of
numerosity
and
in
neurons
it's
hard
to
point
exactly
to
what
that
really
means,
what
those
neurons
are
really
responding
to.
A
Each
one
of
them
might
be
responding
to
numerosity
in
a
specific
context
or
pattern
and
like
what
bit
king
is
saying.
It's
the
shape
pattern.
Recognition
is
not
math,
yeah
yeah,
that's
what
it
is.
That's
that's
more
like
what
he's
saying
it's
just
sort
of
grouping.
It's
like
saying.
If
I
look
at
a
handful
of
things,
I
have
a
general
idea.
If
there's
like
about
10
things
there,
you
don't
even
have
to
count
it
there's,
maybe
20
rocks
in
my
hand.
A
You
know
when
you
look
at
a
jar
of
and
guess
how
many
M&Ms
there
are
you're
really
bad
at
that,
because
you
have
to
do
math,
you
have
to
do
math
to
figure
it
out,
but
with
very
small
numbers.
You're
really
good
at
it.
Yeah,
because
humans
are
really
good
at
counting
small
numbers,
perhaps
because
we
have
a
lot
of
small
numbers
in
front
of
us
all.
The
time
that
we
used
to
calculate
with
the
tips
of
our
fingers,
but
very
large
numbers,
or
that
takes
concepts,
concepts
that
takes
movement.
A
Okay
and
I
mean
movement
like
literally
when
you're
talking
about
the
conceptual
space
of
mathematics.
Mathematics
is
a
cultural
creation.
I
say
that,
because
it's
a
it's
mimetic,
it's
mimetic,
it's
it's
someone
had
a
concept
of
Oh
algebra,
and
that
is
a
meme
that
trans
that
transfers
from
brain
to
brain
and
is
taught
it's
a
it's
much
more
than
just
being
able
to
recognize
numbers.
It's
performing
calculations
in
a
in
a
conceptual
space
and
an
abstract
space
of
mathematics.
A
When
you
learn
the
multiplication
tables,
you
learn
some
poor
rules
of
math
and
you've
learned
how
to
transform
numbers
by
multiplying
them
from
one
space
to
another
and
I.
Think
all
of
these
ideas
can
be
tied
to
location
to
location
spaces.
You
know
act
like
we
are
always
talking
about
location
spaces,
hello,
mister,
I,
don't
which
I'd
rather
Center
named
mstr
treat
just
treat
surgery.
A
What
about
our
autistic
people,
who
can
count
hundreds
of
items
sign
instantaneously?
They've
got
something
going
on
in
their
neurons
that
lets
them.
Do
that
I,
don't
know,
I,
don't
know
how
how
it
just
sticks,
work
works,
autism
works,
I,
don't
think
a
lot
of
people
do
I,
don't
think
we
haven't
figured
that
out
yeah.
You
know
what
exactly
autism
is
how
to
treat
it.
What
causes
it.
A
A
A
If
you
grew
up
out
in
the
woods
and
were
raised
by
wolves,
you
would
you'd
have
a
very
rough
idea,
perhaps
of
multiplication.
But
would
you
ever
need
to
do
it
out
in
the
world
unless
you
were
maybe
we're
doing
agriculture,
in
which
case
you
might
want
to
do
some
math?
But
even
then,
if
you're
doing
agriculture,
you
probably
learned
to
do
that
from
someone
and
they've
taught
you
so
I
would
say.
A
Some
languages
don't
have
words
for
each
number:
that's
unfortunate
yeah,
so
let
math
is
a
reference
frame
just
like
a
language
as
a
reference
frame.
I
think
and
there's
different
reference
to
reference
frames
have
other
reference
frames
in
them.
So
I'm
going
to
talk
about
reference
frames
in
our
next
topic,
too.
I
think
when
we
talk
about
again
about
agency,
so
strawberry
Jesus
says
I'm
wondering
what
you're
reading
off
up
offline
you've
talked
to
mark
about.
It
I
checked
the
stream
recording,
but
maybe
you
could
repeat
with
it.
A
This
is
what
I'm
trying
to
read
right
now,
it's
how
we
remember
by
a
hassle,
hassle,
no
but
I
haven't
made
much
progress,
but
that's
what
I'm
trying
to
read
offline
Jeff
suggested
it.
A
great
book
on
the
topic
is
the
language
instinct
by
Steven,
Pinker
I've
read
the
language
instinct.
I
thought
it
was
interesting,
but
I
don't
think
that
there
is
an
instinct
for
language
I,
don't
think
its
genetic
we're
genetically
pre-positioned
for
language,
so
I
totally
disagree
with
him
there.
Although
I
thought
the
book
was
interesting.
A
A
If
you're
gonna
go
with
Hameroff
I'm,
not
gonna,
make
you
take
any
pills,
but
no
hasselmo,
hasselmo,
Michael,
hasselmo
he's
a
famous
neuroscientist
and
we've
read
a
lot
of
his
stuff,
and
this
is
a
great
hate
to
call
it
an
introduction,
because
it's
much
more
than
an
introduction.
It's
way
over
my
head,
but
there's
a
lot
of
great
pictures
and
stuff
in
here.
So
if
you
want
to
learn
what
grid
cells
and
place
cells
and
head
Direction
cells
and
all
that
stuff
yeah
hammer
up
is
the
anesthesiologist
he
studies
consciousness.
A
A
Okay,
sorry
I'm
totally
I'm
getting
off
the
subject.
I
wanted
to
try
and
address
this
algebra
is
a
lot
more
concept:
Khan,
complex
and
abstract.
So
you're
talking
about
simple
arithmetic,
but
even
when
you
do
simple
arithmetic,
when
you
say
you're,
transforming
at
a
certain
count
into
another
account,
that's
also
a
mental
space
you're
doing
that
transformation
in
a
mental
space.
Perhaps
you
can
create
that
space
in
your
own
mind
and
you
don't
need
it
to
be
created
culturally.
Is
it?
If
that's
your
point?
That's
fine
I
agree
with
you.
A
It
doesn't
all
come
culturally,
but
any
of
the
high-level
mathematical
concepts
that
we
deal
with
everyday
as
humans
are
definitely
cultural
or
at
least
they're
taught
to
you
by
someone.
It's
not
something.
You're
gonna
go
find
out
on
your
own.
Unless
you
read
a
book
that
somebody
wrote
you
know,
I
mean
Einstein
would
not
have
been
Einstein
unless
he
had
all
of
the
resources
standing
on
the
shoulders
of
giants
is
the
term
that
you
always
hear
in
science
and
it's
totally
true
there's.
A
A
So
simply
the
lack
of
sensory
features
a
sense,
so
there's
talking
about
empty
space
again,
you
do
not
need
to
contemplate
empty
space
to
perceive
that
there's
nothing
in
a
space
I'm
not
following
this
argument
very
well.
Unless
the
brain
can
sense
it
and
represent
it
explicitly,
you
don't
have
to
contemplate
empty
space.
You
don't
have
to
represent
empty
space.
If
you're
talking
about
the
concept
of
zero,
that's
an
idea
that
has
its
own
reference
fragment
in
the
mathematics.
Reference
frame
that
is
different
than
empty
space.
Zero
is
different
than
not
sensing.
A
Something
I'm
think
we're
talking
about
two
different
things
here,
so
what
I'm
proposing
he
says
is
to
associate
an
empty
space
explicitly
to
objects
that
have
been
recognized.
For
example,
let's
say
we
have
trained
an
HTM
doing
visual
inference
and
showed
it
the
momenta
cup
floating
inside
an
empty
room.
If
the
cup
wasn't
there,
nothing
would.
A
If
the
cup
wasn't
there,
nothing
would
be
stored
because
there'd
be
no
sensory,
input,
activated
representation
and
will
later
that
will
later
be
stored.
When
the
cup
is
visible,
this
HTM
should
be
able
to
recognize
every
object,
as
both
the
object
and
an
empty
room
be
able
to
recognize
every
object.
I.
A
Don't
understand
what
you
mean
here
by
empty
room.
Empty
room
is
a
concept.
It's
not.
The
empty
room
is
an
idea.
Its
emptiness
is
an
idea
in
the
same
way
that
zero
is
an
idea
if
you're
talking,
I,
don't
understand
where
we're
getting.
This
doesn't
have
anything
to
do
with
the
lack
of
like
this
sensing
of
nothing,
the
lack
of
sensation.
When
nothing
exists.
To
sense,
that's
I,
don't
know
I'm
having
a
hard
time
following
it.
You
can
only
store
the
empty
room
associated
with
something
else,
not
by
itself.
A
Yeah,
that's
a
good
point.
Falco
the
empty
room
is
not
just
a
void.
It's
it's
a
concept.
It's.
It
has
walls
on
the
floor
or
ceiling.
It's
a
room,
you,
you
know.
If
you
just
said
in
empty
space,
yeah
try
to
try
that
thought.
Experiment
out
instead
of
empty
room,
just
say
emptiness,
it
doesn't
work
right,
I,
don't
think
it
works.
Jerry
says
it
seems
like
the
concept
of
deep
space
and
nothingness
are
being
confused.
That's
what
I
believe
is
happening
here
too.
A
Marx
says:
there's
a
class
of
brain
writing
where
the
where
the
write
has
a
list
of
functions.
He
puts
them
in
boxes
and
this
tries
to
arrange
them
in
some
pattern.
That
makes
sense
to
me
Oh
a
class
wait,
the
class
of
brain
writing
or
the
write
has
a
list
of
functions,
puts
them
in
boxes
as
far
as
the
range
into
some
pattern
that
makes
sense
to
them.
What
I've
seen
is
that
very
few
of
these
match
up
biological
hardware?
Oh
right!
Yes!
Yes,
yes,
yes,
okay,
you're!
A
Talking
about
like
people
writing
about
the
brain,
yeah
yeah
yeah!
That's
that's
true!
That
Pinker
does
that!
Definitely
you
just
you
just
come
up
with
a
list
of
functions.
I,
don't
know
the
brain
has
to
do
this.
This
is
this
and
this
and
then
try
and
arrange
them
in
a
way
that
makes
sense
and
turn
it
into
a
story.