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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ βnChemical Memories Storing a Bit in One or a few 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∧␈↓bit␈α
in␈α∞a␈α
molecule,␈α∞the␈α
memory␈α∞problem␈α
would␈α
be␈α∞solved,␈α
so␈α∞it␈α
seems␈α∞worthwhile␈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␈α
nothing
␈↓ α∧␈↓prevents␈α∂such␈α∂memory␈α∂densities,␈α∂so␈α∂it␈α∂is␈α⊂just␈α∂a␈α∂question␈α∂of␈α∂trying␈α∂to␈α∂invent␈α∂a␈α⊂suitable␈α∂scheme.
␈↓ α∧␈↓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␈αof␈αstate␈αsome␈αof␈α
which␈αare␈αrepresented␈αgeometrically,␈αi.e.␈α
the␈αdifferent␈αstates␈αare␈αstereo␈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␈α∞of␈α
the
␈↓ α∧␈↓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∂affect␈α∂by␈α∞both␈α∂its␈α∂neigbors␈α∞and␈α∂by␈α∂global␈α∂signals.␈α∞ Let␈α∂us␈α∂discuss␈α∞first␈α∂what␈α∂kind␈α∂of␈α∞cellular
␈↓ α∧␈↓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␈↓␈αa␈α0␈αor␈αa␈α1,␈αit␈αmay␈αbe␈αexcited␈αor␈αnot,␈αand␈αit␈αmay␈αbe␈αready␈αor␈αnot,␈αi.e.␈αit␈αhas␈αeight␈αstates.␈α A
␈↓ α∧␈↓space␈α⊂signal␈α⊂makes␈α∂a␈α⊂cell␈α⊂ready␈α∂and␈α⊂any␈α⊂other␈α⊂signal␈α∂makes␈α⊂it␈α⊂unready.␈α∂ If␈α⊂a␈α⊂cell␈α⊂is␈α∂unready,
␈↓ α∧␈↓neither␈αa␈α
0␈αnor␈αa␈α
1␈αhas␈α
any␈αeffect.␈α If␈α
a␈αcell␈αis␈α
ready␈αand␈α
unexcited␈αand␈αits␈α
left␈αneighbor␈αis␈α
excited
␈↓ α∧␈↓and␈α
if␈α
the␈α
signal␈α
received␈α
(0␈α
or␈α
1)␈α
agrees␈α
with␈α
its␈α
contents␈α
(0␈α
or␈α
1),␈α
then␈α
it␈α
becomes␈α
excited␈α
and
␈↓ α∧␈↓unready.  Otherwise, it becomes unexcited and unready.

␈↓ α∧␈↓␈↓ αTA␈α
cell␈α∞at␈α
the␈α
left␈α∞end␈α
of␈α
a␈α∞chain␈α
becomes␈α∞excited␈α
if␈α
an␈α∞only␈α
if␈α
it␈α∞receives␈α
a␈α∞special␈α
"start"
␈↓ α∧␈↓signal.␈α⊂ It␈α⊂is␈α⊂then␈α⊂unready.␈α⊂ A␈α⊂cell␈α⊂at␈α⊂the␈α∂right␈α⊂end␈α⊂of␈α⊂a␈α⊂chain␈α⊂becomes␈α⊂excited␈α⊂when␈α⊂its␈α∂left
␈↓ α∧␈↓neighbor is excited and emits an output signal that depends on whether it "contains" 0 or 1.

␈↓ 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␈αthe␈αregister,␈αbut␈αas␈αsoon␈αas␈αthere␈αis␈αa␈αdiscrepancy,␈αthe␈αsignal␈αdies.␈α If␈αit␈αreaches␈αthe␈αend,␈αthe
␈↓ α∧␈↓output signal corresponding to the contents of the register is emitted.

␈↓ α∧␈↓␈↓ αTIt␈αis␈αpossible␈αto␈αstore␈αmany␈αbits␈αin␈αa␈αregister␈αby␈αproviding␈αan␈αoutput␈αsequence␈αof␈αcells␈αalong
␈↓ α∧␈↓which␈α
the␈α
signal␈αcan␈α
further␈α
propagate␈α
and␈αeach␈α
of␈α
which␈α
emits␈αa␈α
signal␈α
that␈α
depends␈αon␈α
whether
␈↓ α∧␈↓it␈αcontains␈αa␈α0␈αor␈α1.␈α The␈αsignals␈αthat␈αcause␈αpropagation␈αcan␈αbe␈αof␈αone␈αkind␈αonly,␈αe.g.␈αall␈α0's,␈αbut
␈↓ α∧␈↓they must again be punctuated by spaces.
␈↓ α∧␈↓␈↓ u2


␈↓ 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
 Readiness␈αand
␈↓ α∧␈↓excitedness␈αare␈αhigher␈αquantum␈αstates␈αof␈αparts␈αof␈αthe␈αcell.␈α The␈αoutput␈αsignal␈αis␈αthe␈αemission␈αof␈αa
␈↓ α∧␈↓photon␈αof␈αan␈αenergy␈αdepending␈αon␈αthe␈αbit␈αstored.␈α The␈αphotons␈αare␈αdetected␈αby␈αphotomultipliers.
␈↓ α∧␈↓Since␈αthe␈αdetection␈αis␈αnot␈αperfectly␈αefficient,␈αwe␈αmust␈αeither␈αexcite␈αthe␈αend␈αcells␈αrepeatedly␈αor␈αhave
␈↓ α∧␈↓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∃readiness,␈α∀their␈α∀contents␈α∀and␈α∃on␈α∀the
␈↓ α∧␈↓excitation of their left 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∧␈↓␈↓ εtJohn McCarthy

␈↓ α∧␈↓This draft of CHEMEM[W79,JMC] pubbed at 11:39 on March 20, 1979.