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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ ∧∨Chemical Memories Storing a Register per Molecules

␈↓ α∧␈↓␈↓ αTAvogadro's␈αnumber,␈αthe␈αnumber␈αof␈αmolecules␈αin␈αa␈αmole,␈αis␈α6.023␈↓πx␈↓10␈↓∧23␈↓.␈α If␈αwe␈αcould␈αstore␈αa
␈↓ α∧␈↓word␈αor␈αeven␈αa␈α
bit␈αin␈αa␈αmolecule,␈αthe␈α
memory␈αproblem␈αwould␈αbe␈α
solved,␈αso␈αit␈αseems␈αworthwhile␈α
to
␈↓ α∧␈↓ask␈α
whether␈α∞any␈α
fundamental␈α∞laws␈α
of␈α∞physics␈α
or␈α∞chemistry␈α
prevent␈α∞it.␈α
 The␈α∞answer␈α
seems␈α∞to␈α
be
␈↓ α∧␈↓that␈αnothing␈αprevents␈αsuch␈αmemory␈αdensities,␈αso␈αit␈αis␈αjust␈αa␈αquestion␈αof␈αtrying␈αto␈αinvent␈αa␈αsuitable
␈↓ α∧␈↓scheme.  Here is one idea, but there are lots more.

␈↓ α∧␈↓␈↓ αTA␈α
memory␈α
register␈α
is␈α
a␈αchain␈α
molecule.␈α
 These␈α
molecules␈α
are␈αin␈α
solution␈α
or␈α
in␈α
a␈α
solid,␈αbut
␈↓ α∧␈↓they␈αare␈αnot␈α
in␈αany␈αfixed␈αarray,␈α
so␈αthat␈αit␈αis␈α
not␈αnecessary␈αto␈αkeep␈α
track␈αof␈αtheir␈α
locations␈αunlike
␈↓ α∧␈↓the␈αregisters␈αin␈αpresent␈αmemories.␈α They␈α
are␈αaddressed␈αby␈αbroadcasting␈αlight␈αor␈αmicrowave␈α
signals
␈↓ α∧␈↓throughout␈α∃the␈α⊗container.␈α∃ They␈α∃answer␈α⊗by␈α∃emitting␈α∃a␈α⊗photon␈α∃which␈α∃is␈α⊗picked␈α∃up␈α⊗by␈α∃a
␈↓ α∧␈↓photomultiplier.

␈↓ α∧␈↓␈↓ αTEach␈αradical␈αon␈αthe␈αchain␈αrepresents␈αa␈αbit␈αof␈αthe␈αaddress␈αof␈αthe␈αregister.␈α Each␈αhas␈αseveral
␈↓ α∧␈↓bits␈α⊃of␈α⊂state␈α⊃some␈α⊃of␈α⊂may␈α⊃be␈α⊂represented␈α⊃geometrically,␈α⊃i.e.␈α⊂the␈α⊃different␈α⊂states␈α⊃may␈α⊃be␈α⊂stereo
␈↓ α∧␈↓isomers␈α∂of␈α∂each␈α⊂other,␈α∂and␈α∂some␈α∂temporary␈α⊂information␈α∂is␈α∂represented␈α∂by␈α⊂electronic␈α∂excitation.
␈↓ α∧␈↓Transitions␈α∞are␈α∞brought␈α∞about␈α∞by␈α∞signals␈α∞of␈α∞particular␈α∞wave␈α∞lengths␈α∞and␈α∞are␈α∞influenced␈α∞by␈α∞the
␈↓ α∧␈↓state of the radical and by the state of its neighbor to the "left".

␈↓ α∧␈↓␈↓ αTThus␈αeach␈αregister␈αis␈αa␈αkind␈αof␈αcellular␈αautomaton␈αof␈αa␈αnew␈αsort.␈α The␈αnovelty␈αis␈αthat␈αa␈αcell
␈↓ α∧␈↓is␈α
affected␈αby␈α
the␈αstates␈α
of␈α
its␈αneigbors␈α
and␈αalso␈α
by␈α
broadcast␈αglobal␈α
signals.␈α Let␈α
us␈α
discuss␈αfirst
␈↓ α∧␈↓what kind of cellular automaton we want before discussing how it might be realized chemically.

␈↓ α∧␈↓Reading

␈↓ α∧␈↓␈↓ αTThe␈α
register␈α
is␈α
a␈α
linear␈α
chain␈α
of␈α∞cells,␈α
each␈α
storing␈α
one␈α
bit.␈α
 The␈α
cells␈α
are␈α∞identical␈α
except
␈↓ α∧␈↓that␈α
the␈α
two␈α
end␈α
cells␈α
are␈α
special.␈α
 The␈α
global␈α
signal␈α
has␈α
three␈α
values␈α
-␈α
0,␈α
1,␈α
and␈α
space.␈α
 A␈α
cell␈α
may
␈↓ α∧␈↓␈↓↓contain␈↓ a 0 or a 1, and it may be in any of 3 excitation states, i.e. it has six states.

␈↓ α∧␈↓␈↓ αTCells␈α
are␈α
normally␈α
in␈α
excitation␈α
state␈α
0.␈α A␈α
cell␈α
goes␈α
from␈α
excitation␈α
state␈α
0␈α
to␈αexcitation␈α
state
␈↓ α∧␈↓1␈αif␈αits␈αleft␈αhand␈αneigbor␈αis␈αin␈αexcitation␈αstate␈α2␈αand␈αthe␈αglobal␈αsignal␈αmatches␈αits␈αinformation␈αbit.
␈↓ α∧␈↓It␈α
goes␈α
from␈α
excitation␈α
state␈α
1␈α
to␈α
excitation␈α
state␈α2␈α
if␈α
the␈α
global␈α
signal␈α
is␈α
a␈α
space.␈α
 In␈α
any␈αother␈α
case
␈↓ α∧␈↓it goes to or remains in excitation state 0.

␈↓ α∧␈↓␈↓ αTA␈αcell␈αat␈αthe␈αleft␈αend␈αof␈αa␈αchain␈αgoes␈αto␈αexcitation␈αstate␈α2␈αif␈αan␈αonly␈αif␈αit␈αreceives␈αa␈αspecial
␈↓ α∧␈↓"start" signal.

␈↓ α∧␈↓␈↓ αTNow␈α∩suppose␈α⊃that␈α∩a␈α⊃signal␈α∩consisting␈α⊃of␈α∩"start"␈α⊃followed␈α∩by␈α⊃a␈α∩sequence␈α⊃of␈α∩0's␈α∩and␈α⊃1's
␈↓ α∧␈↓separated␈αby␈αspaces␈αis␈αgiven␈αto␈αa␈αcollection␈αof␈αregisters.␈α As␈αlong␈αas␈αthe␈αinput␈αsequence␈αof␈α0's␈αand
␈↓ α∧␈↓1's␈α∞agrees␈α∞with␈α∞the␈α∞sequence␈α∞of␈α∞bits␈α∞contained␈α∞in␈α∞the␈α∞cells␈α∞of␈α∞the␈α∞register,␈α∞the␈α∂signal␈α∞propagates
␈↓ α∧␈↓along␈α∂the␈α⊂register,␈α∂but␈α⊂as␈α∂soon␈α⊂as␈α∂there␈α∂is␈α⊂a␈α∂discrepancy,␈α⊂the␈α∂signal␈α⊂dies.␈α∂ Thus␈α⊂the␈α∂excitation
␈↓ α∧␈↓reaches␈α
the␈α
data␈α
region␈αof␈α
the␈α
register␈α
only␈αif␈α
the␈α
address␈α
encoded␈αin␈α
the␈α
global␈α
signal␈αmatches␈α
the
␈↓ α∧␈↓address of the register.

␈↓ α∧␈↓␈↓ αTThe␈α
data␈α
part␈αof␈α
a␈α
register␈αis␈α
similar␈α
except␈αthat␈α
a␈α
cell␈αcan␈α
be␈α
excited␈αto␈α
fluoresce,␈α
i.e.␈αemit␈α
a
␈↓ α∧␈↓photon,␈αprovided␈α
its␈αleft␈α
neighbor␈αis␈α
in␈αstate␈α2,␈α
and␈αthe␈α
fluorescence␈αexciter␈α
leaves␈αthe␈αneighbor␈α
in
␈↓ α∧␈↓state␈α
2.␈α
 The␈α
wave␈α
length␈αof␈α
the␈α
fluorescence␈α
depends␈α
on␈αthe␈α
information␈α
bit␈α
of␈α
the␈α
cell.␈α There
␈↓ α∧␈↓are␈α
two␈αfilters␈α
covering␈αphoton␈α
detectors␈α-␈α
one␈α
that␈αadmits␈α
only␈αphotons␈α
corresponding␈αto␈α
a␈α0␈α
data
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓bit␈α∂and␈α∂one␈α∂that␈α∂only␈α∂admits␈α∂photons␈α∂corresponding␈α∂to␈α∂a␈α∂1␈α∂data␈α∂bit.␈α∂ Since␈α∂the␈α∂probability␈α∂of
␈↓ α∧␈↓detecting␈α∂the␈α∂photon␈α∂is␈α∂not␈α∂one,␈α∂the␈α∂fluorescence␈α∂is␈α∂excited␈α∂repeatedly␈α∂until␈α∂one␈α∂of␈α⊂the␈α∂photon
␈↓ α∧␈↓detectors registers a hit.

␈↓ α∧␈↓␈↓ αTNow␈αconsider␈αthe␈αchemistry␈αof␈αpossible␈αrealizations␈αof␈αthis␈αscheme.␈α We␈αtentatively␈αsuppose
␈↓ α∧␈↓that␈α
whether␈α
a␈α
cell␈α
␈↓↓contains␈↓␈α
0␈α
or␈α
1␈α
is␈α
represented␈α
by␈α
an␈α
isomeric␈α
state␈α
of␈α
the␈α
cell.␈α
 The␈α
1␈α∞and␈α
2
␈↓ α∧␈↓excitation␈αstates␈αare␈αhigher␈αquantum␈αstates␈αof␈αparts␈αof␈αthe␈αcell.␈α The␈αoutput␈αsignal␈αis␈αthe␈αemission
␈↓ α∧␈↓of␈α↔a␈α↔photon␈α⊗of␈α↔an␈α↔energy␈α↔depending␈α⊗on␈α↔the␈α↔bit␈α↔stored.␈α⊗ The␈α↔photons␈α↔are␈α↔detected␈α⊗by
␈↓ α∧␈↓photomultipliers.␈α Since␈αthe␈αdetection␈αis␈αnot␈α
perfectly␈αefficient,␈αwe␈αmust␈αeither␈αexcite␈αthe␈α
end␈αcells
␈↓ α∧␈↓repeatedly or have many registers with the same information.  The former seems preferable.

␈↓ α∧␈↓␈↓ αTThe␈α∞big␈α∂chemical␈α∞problem␈α∞is␈α∂designing␈α∞the␈α∞cells␈α∂so␈α∞that␈α∞their␈α∂excitability␈α∞by␈α∂the␈α∞photons
␈↓ α∧␈↓representing␈α
0␈α
and␈α
1␈α
depends␈α
appropriately␈α
on␈α
their␈α
contents␈α
and␈α
on␈α
the␈α
excitation␈α
of␈α
their␈α
left
␈↓ α∧␈↓neighbors.  It should not depend on their right neighbors.

␈↓ α∧␈↓Writing

␈↓ α∧␈↓␈↓ αTWith␈α⊂so␈α∂much␈α⊂memory,␈α∂it␈α⊂seems␈α∂as␈α⊂though␈α∂we␈α⊂should␈α∂settle␈α⊂for␈α∂a␈α⊂"write␈α⊂once"␈α∂memory.
␈↓ α∧␈↓Both␈α
the␈α
address␈αand␈α
the␈α
contents␈α
are␈αwritten.␈α
 Again␈α
the␈α
writing␈αshould␈α
require␈α
the␈αleft␈α
neighbor
␈↓ α∧␈↓to␈αbe␈α
in␈αan␈αexcited␈α
state,␈αso␈αthat␈α
the␈αwriting␈αwill␈α
propagate␈αalong␈αthe␈α
register.␈α Again␈αthere␈α
should
␈↓ α∧␈↓be␈α
a␈α∞"start␈α
writing"␈α∞signal,␈α
but␈α
it␈α∞should␈α
be␈α∞weak␈α
enough␈α∞so␈α
that␈α
it␈α∞excites␈α
the␈α∞left␈α
cells␈α∞of␈α
only
␈↓ α∧␈↓about␈α⊂the␈α⊂desired␈α⊂number␈α⊂of␈α⊂unwritten␈α⊂registers.␈α⊂ A␈α⊂register␈α⊂that␈α⊂has␈α⊂previously␈α⊂been␈α⊂written
␈↓ α∧␈↓should␈αhave␈αits␈αstart␈αcell␈αin␈αa␈αstate␈αthat␈αis␈αimmune␈αto␈αfurther␈α"start␈αwriting"␈αsignals.␈α It␈αwould␈αbe
␈↓ α∧␈↓best␈α∩if␈α∩the␈α∩writing␈α∩could␈α∩be␈α∩done␈α∩in␈α⊃a␈α∩memory␈α∩box␈α∩that␈α∩contained␈α∩written␈α∩registers,␈α∩but␈α⊃if
␈↓ α∧␈↓necessary,␈α
we␈α∞could␈α
imagine␈α
that␈α∞registers␈α
are␈α
written␈α∞separately␈α
and␈α
then␈α∞added␈α
to␈α∞the␈α
memory
␈↓ α∧␈↓box.  Since it would involve physical motion, it should be avoided if possible.

␈↓ α∧␈↓␈↓ αTWe␈α∪want␈α∪the␈α∪0's␈α∀and␈α∪1's␈α∪in␈α∪the␈α∀memory␈α∪to␈α∪be␈α∪very␈α∀stable␈α∪so␈α∪that␈α∪they␈α∀don't␈α∪make
␈↓ α∧␈↓spontaneous␈α
transitions,␈α
and␈α
this␈α
suggests␈α
stereo␈α
isomers.␈α
 The␈α
unwritten␈α
state␈α
should␈α
be␈α∞a␈α
third
␈↓ α∧␈↓state␈α
of␈α
the␈α
cell␈α
that␈α
can␈α
make␈α
a␈α
transition␈α
to␈α
a␈α
0␈α
or␈α
1␈α
state,␈α
but␈α
requires␈α
for␈α
this␈α
transition␈α
that␈α
the
␈↓ α∧␈↓left neighbor be already written.

␈↓ α∧␈↓␈↓ αTExcept␈α
for␈αthe␈α
final␈αfluorescence␈α
which␈α
takes␈αa␈α
few␈αnanoseconds,␈α
each␈α
of␈αthe␈α
other␈αsteps␈α
can
␈↓ α∧␈↓apparently be accomplished in a few picoseconds if it is desired to read and write that fast.

␈↓ α∧␈↓␈↓ αTI␈αdon't␈αunderstand␈α
the␈αchemical␈αproblems␈αof␈α
realizing␈αthis␈αkind␈αof␈α
memory␈αcell,␈αbut␈α
if␈αthis
␈↓ α∧␈↓doesn't work, other schemes can be devised.

␈↓ α∧␈↓␈↓ αTIf␈α
it␈αis␈α
difficult␈αto␈α
design␈α
cells␈αwith␈α
six␈αstates,␈α
we␈αcan␈α
get␈α
by␈αwith␈α
cells␈αhaving␈α
only␈αtwo␈α
states
␈↓ α∧␈↓as␈αfollows.␈α There␈αare␈αthree␈αkinds␈αof␈αcells:␈αdata␈αcells␈αand␈αleft␈αand␈αright␈αexcitation␈αcells.␈α If␈αa␈αdata
␈↓ α∧␈↓cell's␈αleft␈αneighbor␈α(a␈αleft␈αexcitation␈αcell)␈αis␈αexcited␈αand␈αthe␈αglobal␈αsignal␈αmatches␈αits␈αdata␈αbit,␈αthen
␈↓ α∧␈↓the␈αcell␈αon␈αits␈αright␈α(a␈αright␈αexcitation␈αcell)␈αis␈αexcited.␈α A␈αspace␈αpasses␈αthe␈αexcitation␈αfrom␈αa␈αright
␈↓ α∧␈↓excitation␈αcell␈αto␈αthe␈αleft␈αexcitation␈αcell␈αto␈αthe␈αright␈αof␈αit.␈α It␈αmay␈αbe␈αfeasible␈αto␈αuse␈αthe␈αsame␈αkind
␈↓ α∧␈↓of cell for left and right excitation cells.

␈↓ α∧␈↓␈↓ αTIf␈αthe␈αpulse␈αlength␈αof␈αthe␈αglobal␈αsignal␈αis␈αshort␈αenough␈α(a␈αvery␈αfew␈αpicoseconds),␈αit␈αmay␈αbe
␈↓ α∧␈↓possible␈α∞to␈α∞dispense␈α∞with␈α∞the␈α∞space␈α∞signal.␈α∞ Its␈α∞purpose␈α∞is␈α∞to␈α∞prevent␈α∞an␈α∞addressing␈α∞signal␈α∞from
␈↓ α∧␈↓propagating␈αdown␈α
several␈αaddress␈α
bits␈αthat␈αare␈α
the␈αsame,␈α
as␈αmight␈αhappen␈α
if␈αa␈α
data␈αcell␈αexcites␈α
its
␈↓ α∧␈↓neighbor directly.
␈↓ α∧␈↓␈↓ u3


␈↓ α∧␈↓␈↓ αTHere␈α∞is␈α∞a␈α
variant␈α∞that␈α∞may␈α
be␈α∞easier␈α∞to␈α∞realize.␈α
 There␈α∞are␈α∞three␈α
kinds␈α∞of␈α∞radicals␈α∞in␈α
the
␈↓ α∧␈↓chain␈α~called␈α→A,␈α~B␈α~and␈α→C,␈α~and␈α→they␈α~alternate␈α~cyclically,␈α→i.e.␈α~the␈α→chain␈α~has␈α~the␈α→form
␈↓ α∧␈↓ABCABCABC....␈α
 Radicals␈α
of␈α
type␈α
A␈α
have␈α
two␈α
excitation␈α
states␈α
0␈α
and␈α
1.␈α
 Radicals␈α
of␈α
type␈αB␈α
have
␈↓ α∧␈↓two␈αdata␈α
states␈α0␈αand␈α
1,␈αand␈αradicals␈α
of␈αtype␈α
C␈αhave␈αtwo␈α
excitation␈αstates.␈α Most␈α
of␈αthe␈α
time␈αthe
␈↓ α∧␈↓radicals␈αof␈α
types␈αA␈α
and␈αC␈α
are␈αin␈α
their␈α0␈αstates,␈α
and␈αwhen␈α
this␈αis␈α
the␈αcase,␈α
they␈αare␈αunresponsive␈α
to
␈↓ α∧␈↓stimulation.␈α However,␈αwhen␈αan␈αA␈αis␈αin␈αstate␈α1,␈αit␈αis␈αsensitive␈αto␈αbroadcast␈αinput␈αsignals␈α0␈αand␈α1,
␈↓ α∧␈↓becoming␈α⊃instantaneously␈α⊃excited␈α∩and␈α⊃emitting␈α⊃signals␈α∩of␈α⊃types␈α⊃0␈α⊃and␈α∩1␈α⊃to␈α⊃its␈α∩neighbors.␈α⊃ A
␈↓ α∧␈↓neighbor␈αof␈αtype␈αC␈αis␈αinsensitive␈αto␈αthis␈αstimulation,␈αbut␈αa␈αneighbor␈αof␈αtype␈αB␈αwill␈αrelay␈αa␈αsignal
␈↓ α∧␈↓provided␈α∞the␈α∞signal␈α∞it␈α∞receives␈α∞from␈α∞A␈α∞(which␈α∞corresponds␈α∞to␈α∞the␈α∞broadcast␈α∞bit)␈α∞agrees␈α∞with␈α
its
␈↓ α∧␈↓state.␈α This␈αrelayed␈αsignal␈α
will␈αexcite␈αthe␈αadjacent␈α
radical␈αof␈αtype␈αC␈α
into␈αits␈αstate␈α1.␈α
 A␈αbroadcast
␈↓ α∧␈↓signal␈α⊃"space"␈α⊃propagates␈α⊃the␈α⊃excitation␈α⊃from␈α⊃the␈α⊂radical␈α⊃of␈α⊃type␈α⊃C␈α⊃to␈α⊃the␈α⊃adjacent␈α⊃A.␈α⊂ The
␈↓ α∧␈↓purpose␈α
of␈α
having␈α
type␈α
C␈α
is␈α
analogous␈α
to␈α
the␈α
use␈α
of␈α
a␈α
three␈α
phase␈α
clock␈α
in␈α
circuits␈α
made␈α
of␈α
diodes,
␈↓ α∧␈↓i.e. to make sure the signals propagate only in the desired direction.

␈↓ α∧␈↓␈↓ αTThe␈α∂following␈α∂scheme␈α∞may␈α∂be␈α∂easier␈α∞to␈α∂implement.␈α∂ Instead␈α∞of␈α∂8␈α∂states,␈α∞a␈α∂cell␈α∂has␈α∂just␈α∞4
␈↓ α∧␈↓states.␈α One␈α
bit␈αis␈α
its␈αinformation␈α
bit␈αand␈αthe␈α
other␈αis␈α
an␈αexcitation␈α
bit.␈α However,␈αthe␈α
information
␈↓ α∧␈↓cells␈α∞are␈α∂interspersed␈α∞with␈α∂punctuation␈α∞cells.␈α∂ Punctuation␈α∞cells␈α∂have␈α∞only␈α∂excitation␈α∞bits,␈α∂and␈α∞a
␈↓ α∧␈↓punctuation␈α⊃cell␈α⊃is␈α⊃excited␈α⊂when␈α⊃its␈α⊃left␈α⊃neighbor␈α⊃is␈α⊂excited␈α⊃and␈α⊃it␈α⊃receives␈α⊃the␈α⊂punctuation-
␈↓ α∧␈↓excitation␈α
frequency.␈α
 An␈α
information␈α
cell␈α
is␈α
excited␈αwhen␈α
the␈α
punctuation␈α
cell␈α
on␈α
its␈α
left␈αis␈α
excited
␈↓ α∧␈↓and␈α∞the␈α∞broadcast␈α∞information-excitation␈α∞signal␈α∞matches␈α∞its␈α∞information␈α∞bit.␈α∞ The␈α∞advantage␈α
of
␈↓ α∧␈↓this scheme is that the individual cells can be less complicated.

␈↓ α∧␈↓␈↓ εtJohn McCarthy

␈↓ α∧␈↓This draft of CHEMEM[W79,JMC] pubbed at 13:36 on September 22, 1980.