On a Con ibu ion o Memb ane Compu ing
o a Cul u al Syn hesis o Compu e Science,
Ma hema ics, and Biological Sciences
Adam Ob uÃlowicz
Ins i u e o Ma hema ics, Polish Academy o Sciences,
´
Sniadeckich 8, P.O.Box 21, 00-956 Wa saw, Poland
e-mail: [email p o ec ed] .pl
Summa y. Some opic con ibu ion o memb ane compu ing o a cul u al syn hesis o
compu e science, ma hema ics and biological sciences is p esen ed.
1 In oduc ion
A e a mo e han decade o he esea ches in he a ea o memb ane compu ing,
c . [19], ini ia ed by Gheo ghe P˘aun i is wo h o p opose a discussion abou
a con ibu ion o hese esea ches o a cul u al syn hesis o compu e science,
ma hema ics, and biological sciences.
An aim o he p esen pape is o ini ia e he discussion ocusing on hese i s as-
pec s which a e amilia o he au ho whose esea ch a ea comp ises ma hema ical
ounda ions o compu e science and ounda ions o ma hema ics i sel .
The heme o he discussion was inspi ed by [11] and [2], whe e he goal o [11]
is o p opose a amewo k ha should allow a heal hy and posi i e ole o specu-
la ions in ma hema ics al hough adi ional ma hema ical no ms discou age spec-
ula ion whe eas i is he ab ic o heo e ical physics. Thus a cul u al syn hesis o
ma hema ics and heo e ical physics is unde s ood in [11] mo e o less explici ly
as a mu ual inspi a ion be ween he discussed a eas.
We poin ou he e ha specula ion in ma hema ics can be ein o ced by com-
pu e expe imen s, c . p o oca i e a icle [10], which could ex end he discussion
in [11] o compu e science wi h a ega d o he ela ions be ween ma hema ical
hinking and algo i hmic hinking, c . [12].
The esponses in [2] con ain a ious opinions abou a ole o specula ion in
ma hema ics om a de ense o an impo ance o p oo s, see S. Mac Lane’s esponse
con inued in [14], o an accep ance o specula ion as possessing equal igh s o
p oo s. The esponse due o R. Thom in [2] sugges s also a cul u al syn hesis o
ma hema ics and biology.
288 A. Ob uÃlowicz
We p opose a looking o wa d app oach o a cul u al syn hesis o he a eas
men ioned in he i le o he p esen pape , whe e a cul u al syn hesis is also
unde s ood as mu ual inspi a ion.
In he nex sec ion we ou line some opic con ibu ion o memb ane compu ing
o his cul u al syn hesis.
2 Topic con ibu ion
We poin ou he ollowing opics as a con ibu ion o memb ane compu ing o he
discussed syn hesis:
A) biologically inspi ed sel -assembly ( andomized, c . [15] and [16]) P sys ems
(wi h memb ane di ision and c ea ion) o sol ing NP comple e p oblems,
c . [17] and [21], which ex end algo i hmic hinking by a new idea o a ( an-
domized) algo i hm o a cons uc ion o a sel -assembly dis ibu ed sys em
ealizing massi ely pa allel compu a ion,
B) spiking neu al P sys ems, c . [18], wi h lea ning p oblem solu ion, c . [9], which
a e a s ep owa ds digi aliza ion1o neu al ne wo ks wi hin ma hema ical neu-
oscience, c . e.g. [3],
C) ac al cons uc s gene a ed by P sys ems, c . [8], wi h P sys ems o ob aining
homology g oups, c . [5], and a possibili y o expe imen wi h hem ( o p edic
some ma hema ical esul s like in [10] o be p o ed wi h ma hema ical p ecision
like in [14]) ia P-lingua p og amming en i onmen designed in Se ille, c . [4]
and [20].
Conce ning A) one can ask o a ela ion o andomized P sys ems in [15] and
andomized Gandy–P˘aun–Rozenbe g machines [16] wi h p obabilis ic compu ing
de ices discussed in [1].
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