8/12/2019 Mackenzie, Adrian - Sets
1/26
1/26
Sets
Adrian Mackenzie, Cesagen, Lancaster University, UK
The 'persnal prductivity' system, !etting Things "ne r !T" stands n the
periphery # ne$ ecnmy and net$rk sciality. !T" represents an attempt t
rganise multiple, ver#l$ing demands # $rk and li#e %y de#ining things in
terms # sets. Like many persnal imprvement r develpment techni&ues,
!T" appeals t rth American crprate managers, and %usiness (urnalists.
)$ever, its ppularity e*tends $ell %eynd crprate U.+.A t research
scial science and humanities academics, #r instance, in the U.K. The ##icial
descriptin runs-
!T"is the ppular shrthand #r /!etting Things "ne/, the
grund%reaking $rk0li#e management system and %k %y "avid Allen that
trans#rms persnal ver$helm and verlad int an integrated system #
stress0#ree prductivity 1"avid Allen 2 C. 34456
The ppularity # "avid Allen's !T" culd %e understd #rm many
perspectives- as a symptm # the chrnic dislcatin # la%ur that 7ar%ara
8hrenreich descri%es in 7ait and +$itch 18hrenreich 34496: # $hat ;gymunt
7auman sees in Li&uid Mdernity as '#ree0#lating capitalism, marked %y the
8/12/2019 Mackenzie, Adrian - Sets
2/26
2/26
disengagement and lsening # ties linking capital and la%ur' 17auman 3444,
8/12/2019 Mackenzie, Adrian - Sets
3/26
3/26
really a practice. ?e casually grup, encunter, cllect r srt things in sets.
+et0related inscriptins such as la%els, tags r cdings are a part # rutine
kn$ledge0making acrss humanities, scial sciences, engineering and natural
sciences tday, and data is itsel# #ten seen as a kind # set, the dataset. Many
methds %ks in the scial sciences advcate &uasi0#rmal set0making ha%its
in researchers 1usually in the #rm # 'cding'6. +#t$are t assist in the cnduct
# &ualitative and &uantitative analysis # scial and ecnmic data 1the
standard statistics package +++ analysed in 1Uprichard, 7urr$s, and 7yrne
3446, r the standard &ualitative data packages such as viv and Atlas.ti,
etc.6 relies n sets and sets # sets as %asic rdering devices 1cding, gruping,
tagging, cases6. The dispsiti#s # imprtant cntemprary net$rk services
and prducts such as !gle search, Bace7k pages, Amazn, ?ikipedia,
uTu%e, and Blickr, the playlists, li%raries, trees, menus, address%ks,
%kmarks, tags and la%els # all manner # m%ile devices, s#t$are inter#aces
and data%ases, r %dies # scienti#ic kn$ledge such as u%Med, r
!ene7ank- every item in this list can %e entail set0making. Dn such settings,
in#rmal inscriptive practices # cllecting, srting and gruping are
increasingly shad$ed %y much mre #rmal, intensively rganised #rms #
set0making and set analysis. Dn the light # the 'cming crisis # empirical
scilgy' 1+avage and 7urr$s 344E6 ccasined %y rutine cllectin and
analysis # transactinal data, the &uestin # h$ sets are made, and h$
#rms # relatinality materialise #rm set0speci#ic practices %ecmes highly
signi#icant. ractices # set0making partly esta%lished in scial sciences n$
structure the %(ects # analysis. 7y implicatin, scial scientists and
researchers $uld %ene#it #rm an increased a$areness # h$ peple's sense
8/12/2019 Mackenzie, Adrian - Sets
4/26
4/26
# %elnging, grup, and inclusin em%dies acts # set0making.
Techni&ues derived #rm the mathematical e*pressin # set making, 'set
thery,' underpin many # the mst intense and pervasive instantiatins #
net$rk media clla%ratin 1#r instance, ?ikiedia6, grup discussin
1Bace7k6, entertainment 1Amazn %k recmmendatins: et#li* "F"
recmmendatin, last#m.cm6, %lgging, kn$ledge, pr#iling and transactin,
the pr#iling # cnsumers in markets segments, and the predictive analytics
used every$here #rm Tesc's supermarket shel#0stcking plicies t airline
#light scheduling. +ets make p$er#ul calls t rder, and act as $rld0making
#rms # cllectin and gruping. )ere '$rld' means mre than cmmunity, r
scial gruping, %ecause it '%ecause it necessarily includes mre peple than
can %e identi#ied, mre spaces than can %e mapped %eynd a #e$ re#erence
pints, mdes # #eeling that can %e learned rather than e*perienced as a
%irthright' 17erlant and ?arner
8/12/2019 Mackenzie, Adrian - Sets
5/26
5/26
gverned %y sets. !T" ##ers a practice # the sel# that addresses a site #
distress $here e*changes and cmmunicatin %et$een ha%its, values,
practices, transactins and institutins intensi#y-
?e're all$ing in huge amunts # in#rmatin and cmmunicatin #rm the
uter $rld and generating an e&ually large vlume # ideas and agreements
$ith urselves and thers #rm ur inner $rld. And $e haven't %een $ell
e&uipped t deal $ith this huge num%er # internal and e*ternal
cmmitments 1Allen 344
8/12/2019 Mackenzie, Adrian - Sets
6/26
8/12/2019 Mackenzie, Adrian - Sets
7/26
7/26
ther $rds, the distance%et$een any pint *in Uand the edge # Uis
al$ays greater than zer 1?ikipedia 34456.
7y cntrast, a clsed set includes its %undary r limits pints-
IAJ clsed set is a set $hich cntains all # its limit pints. There#re, a clsed
set C is ne #r $hich, $hatever pint * is picked utside # C, * can al$ays
%e islated in sme pen set $hich desn't tuch C. 1?eisstein 3445%6
The di##erence %et$een pen and clsed as used in set thery is that an pen
set al$ays includes sme mre space t mve arund. Dt might nt %e much
rm, %ut there is al$ays space t $riggle in an pen set. An pen set has an
edge that al$ays all$s a %it # mvement that might tuch smething else.
ut di##erently, $e might regard an pen set as al$ays e*panda%le. Mre rm
can al$ays %e #und. A clsed set, %y cntrast, has a %undary and that means
that things can %e islated #rm it. Br a clsed set, inclusin and e*clusin
have strng e##ects.
Figure 2: Open set
http://en.wikipedia.org/wiki/Distancehttp://en.wikipedia.org/wiki/Distance8/12/2019 Mackenzie, Adrian - Sets
8/26
8/26
A set is clsed $hen n mre entries r elements can %e added t it. Dt is pen
t the e*tent that mre can %e added t it. H# curse, in many situatins sets
are su%(ect t cnstant re0rdering, and this all$s lists t respnd t change.
7ut h$ des a set respnd t smething ne$G Dt can d that either %y %eing
pen r clsed, %y either #inding $hat happens in itsel# 1as an element, as a
su%set, as a relatin %et$een e*isting elements, etc6 r %y adding smething
ne$ t the set. ?hat is interesting a%ut the predicament # !T" as a set #
lists is that it tries t %e %th pen and clsed. Hn the ne hand, the #eeling #
cntrl and prductivity cmes #rm the cnvictin that everything trivial r
imprtant has %een captured %y the system and its $rk#l$. Dn set language,
this means that it is clsed. Hn the ther hand, the system must remain
cnstitutively pen i# nly t the %are #act # the presence # thers. Dn that
sense, it must %e an pen set. This dual re&uirement t engender a sense #
penness and clsure intrduces a certain insta%ility that D #ind symptmatic #
cntemprary set0making mre generally. Hne culd say that set0making is
respnse t the pr%lem # h$ t srt things cming #rm the utside and
things generated #rm the inside. +ets are devices #r $rking n the
%undaries and edges # cllectins. Dn the case # !T", the slutin t the
pr%lem # h$ t negtiate inner and uter is %y cntrlling time. Timing and
calendrical rutines ranging #rm time scales # minutes t years ensure i#
they are adhered t that the sets # lists, pr(ects and events $ill %e regularly
updated, resrted and kept current. The cnstant tensin %et$een %eing pen
t ne$ things and keeping cntrl # $hat is already in the system is
8/12/2019 Mackenzie, Adrian - Sets
9/26
9/26
maintained and regulated %y rutinised revie$s and checks n the list. "uring
these revie$s, sets pen. Hutside the revie$ times, $rk is devted t making
sure that the set stays clsed. This clsure is diagrammatically e*pressed in
the !T" $rk#l$ diagram 1see Bigure 36 that prmpts peple n h$ they
shuld prcess events.
Figure 3: GTD wrk!lw ("su 200#)
Outside open and closed: R
"es the ppsitin, unsta%le as it is in !T", %et$een pen vs clsed sets
represent the primary #eature # set thinking and set practiceG At this pint, D
think it use#ul t turn a much larger scale set0making practices- thse
em%died in the predminating data%ase architecture # the last t$ decades,
8/12/2019 Mackenzie, Adrian - Sets
10/26
8/12/2019 Mackenzie, Adrian - Sets
11/26
11/26
lng0lived search synta* called +L 1+tructured uery Language6, still #rm the
'engine' # many data%ase0driven activities ranging acrss cmmercial,
gvernment and academic settings. The technlgy # relatinal data%ase has
%een e*panded t gigantic and shrunk t miniature scales. Hn the ne hand,
vast enterprise architectures in data0centres r increasingly in 'the Clud'
1Naeger 34456 stre trillins # item # data that survey ppulatins, markets,
envirnments and institutins. Hn the ther hand, a variety # mre r less
em%edded persnal data%ases rganise and sets pre#erences, cntacts,
addresses and re#erences 1#r instance, in the #rm # re#erence and
%i%ligraphical management s#t$are $idely used %y academics6.
Cntemprary %ip$er, in all its guises and #acets ranging #rm clinical drug
trials thrugh t patient health recrds r child prtectin data%ases, depends
n relatinal data%ases r O"7M+ 1Oelatinal "ata%ase Management +ystems6
such as Hracle's
8/12/2019 Mackenzie, Adrian - Sets
12/26
12/26
EE6.
This desire t 'prtect' users #rm kn$ledge still prevails tday. The &ueries,
searches, and srts that rganise and animate %usiness prcesses, certain
aspects # scienti#ic $rk, and the layut # $e%sites %ear the traces # the
relatinal data%ase as a prphylactic against kn$ledge # #rm. Dn this setting,
$hat sets prvide is a $ay # %ringing data int relatin $ithut #i*ing that
relatin r making thse relatins #ully visi%le. +et0making retains #rms #
#le*i%ility that ther #igures and devices 1net$rk, list, in#erence, deductin,
etc.6 #ind it harder t match. This #le*i%ility, the #le*i%ility that D am suggesting
generates the stresses and verheating that !T" tries t &uench, pivts n the
relatin O. ?hat is a relatin hereG 8.B. Cdd $rites-
The term relatin is used here in its accepted mathematical sense. !iven
sets +
8/12/2019 Mackenzie, Adrian - Sets
13/26
13/26
multiples that O gives rise t in cntemprary data0driven cllectives.6
A $hle series # rami#icatins #ll$ #rm this. They include techni&ues #
data%ase management. Br e*ample, a key techni&ue in relatinal data%ase
design is the prcess # 'nrmalizatin' r 'eliminatin # nn0simple dmains'
1Cdd
8/12/2019 Mackenzie, Adrian - Sets
14/26
14/26
practices and prmises respnd t sets.
The relatively austere #rmalism # the 'relatin' as a set # rdered sets
underlying the dminant cntemprary data%ase architectures des represent
the apgee # the set as device. +metime in Nuly 344E, the !gle search
engine s$itched t a di##erent inde* # the $e% 1Chen and +chlsser 344:
Catanzar, +undaram, and Keutzer 344: 8kanayake, allickara, and B* 344:
"ean 344P6. A slight reductin in the time taken #r search &ueries might have
%een the nly sign # this change. Dn the thusands # servers seried in
!gle's scarcely visi%le data center, $rk n the s$itch had %een ging n #r
several mnths. A shi#t in data%ase architecture a$ay #rm the relatinal
data%ase mdel t an even mre radically simpli#ied set theretical cnstruct,
Map0Oeduce, tk place. This change, part # the %rader migratin # data
#rm single data%ases t #ederatins # data%ases the Clud als suggests
the need t re0think a%ut the e*periential dimensins # set0making, t %egin
t #rmulate accunts # h$ the in#rmal prcesses # gruping and cllecting
characteristic # s many cultural settings ent$ine $ith the nging
trans#rmatins in the technical, ecnmic, scienti#ic and plitical prductin #
sets.
An animated and mtivated engagement $ith sets can %e #und in recent
8urpean philsphical thught. )ere a key pint # re#erence $uld the $rk
# the Brench philspher Alain 7aidu. )e uses set thery as a 'guide #r an
ntlgical thught # the pure multiple' 17adiu 3444, =E6. The intricacies #
7adiu's thught are t cmplicated t #ll$ in any detail here, %ut his %asic
8/12/2019 Mackenzie, Adrian - Sets
15/26
15/26
ntin # 'pure multiple' is 'everything is nt ne.' Dt may d t #cus n h$ his
re0rendering # the %asic ppsitin %et$een pen and clsed sets might re0
cn#igure the predicament em%died in !T" and in !gle's mve #rm a
relatinal data%ase structure t MapOeduce.6
?hy des 7adiu say that a set is thinka%le nly i# $e d $ithut the
ppsitin %et$een pen and clsed setsG D# sets und the %asic ppsitin
%et$een pen and clsed, then it $uld %e imprtant t track $hat this means
in practice, in the practices # kn$ledge0making and cntemprary $rld0
making. ?hile it $uld %e pssi%le t simply e*amine the prli#erating pen
and clsed sets # the present, the prmise # the set as 'neutral0multiple' lies
else$here, in the ptential t understand h$ ne$ patterns and cn#iguratins
# pen and clsed sets materialise tday. D# this su%tractin %tains in practice,
1 The significance of this contrast between open and closed sets can be traced in terms of the theoretical polemic that
adio! cond!cted with "ele!#e aro!nd sets o$er se$eral %ears in the 1970s& "ele!#e' following ergson' resists set(
based thin)ing as a wa% to thin) the m!ltiple& The notion of set' for "ele!#e' thwarts thin)ing m!ltiplicit% beca!se a
set is an e*ternal or anal%tical m!ltiplicit% comprising parts or elements& +othing happens in sets or lists beca!se the
parts are e*ternal to each other& , $ital m!ltiplicit% for him -and for man% others who ma)e deri$e their notion of
m!ltiplicit% from ergson. has no parts or elements& t onl% has intensi$e differences act!alising as e*tended things'
with bo!ndaries' with orderings& hile a set might displa% bo!ndaries' partitions' forms of incl!sion and e*cl!sion'
or e$en hierarchical sites s!ch as the top and bottom we find in lists' the set itself onl% act!alises something
intensi$e&
8/12/2019 Mackenzie, Adrian - Sets
16/26
16/26
a very di##erent perspective n cntemprary practices # set0making might
pen up.
Figure $: %&en-clsed' &arts-elements
?hat happens t the pen vs. clsed distinctin $hen 7adiu thinks the set as
pure multipleG There is n #undamental di##erence %et$een pen and clsed at
the level # the set as multiple. That means, #r 7adiu, that any attempt t
valrise penness as the lcus # vitality, creativity, event r di##erence is
pr%lematic. "espite the many appeals made t penness, the pen has n
special privilege, and there is nthing intrinsically unethical r negative a%ut
%eing in a clsed set. 1D# 7adiu is right, then much cntemprary scial,
8/12/2019 Mackenzie, Adrian - Sets
17/26
17/26
plitical, cultural and rganisatinal thught, in its attempt t lcate vitality in
penness $ill run int pr%lems.6 7adius alternative is try t think h$
IeJvery multiple is indeed actually haunted %y an e*cess # p$er that nthing
can give shape t, e*cept #r an al$ays aleatry decisin $hich is nly given
thrugh its e##ects 17adiu 344=, E56. +, $hile the pen vs. clsed distinctin
cannt grund any (udgment a%ut sets, e*cess can. ?hat is e*cess in setsG
'The immanent e*cess that animates a set, and $hich makes it such that the
multiple is internally marked %y the undecida%le, results directly #rm the #act
that it pssesses nt nly elements, %ut als parts' 1E6. This '#act' sends us
%ack t a di##erent distinctin, that %et$een %elnging and inclusin. +me
things elements %elng t sets, sme things parts are included. Br
instance, a !T"er's lists cmprise hundreds # entries r elements 1many
phtgraphic e*amples # this can %e #und n the $e%, particularly at pht
sites such as #lickr.cm6. The ntin # the element is recursive 0 elements r
entries can themselves %e sets. The !T"ers nte%k cntains lists # lists 1#r
instance, the !T" central list # pr(ects has elements that themselves must
sner r later, gradually r suddenly, %e made int sets # 'ne*t actins'6.
)$ever, a part can include many elements. ?hat then is a 'part'G Dn set
thery, a part is a su%set. A set A is a su%set # a set 7 i# A is 'cntained' r
'included' in 7. A part may cmprise ne r many elements, %ut it des nt
%elng in the same $ay t a set. ?hen 7adiu $rites 'there is an ntlgical
e*cess # representatin ver presentatin' 1E6, he re#ers t a set e*cess that
des nt cme #rm the utside, r #rm li#e r chas, %ut #rm the internal
nn0chesin # the set $ith itsel#, #rm the relatin %et$een elements that
%elng and parts that are included r cntained. ?hat he calls the 'actual' r
8/12/2019 Mackenzie, Adrian - Sets
18/26
18/26
'immanent' e*cess # p$er # the multiple cmes the irreduci%ly insta%le
relatins %et$een elements and parts, %et$een 'the t$ types # immanence'
1E6.
D# it seems that cntemprary data%ases teem $ith cnstant revisins,
mdi#icatins, additins and almalgamatins, it might %e %ecause # this
ntlgical e*cess. D# it seems that s many cntemprary scial0technical
prcesses entail cllecting, la%elling, tagging, srting r searching, they might
%e e*periential attempts t determine this e*cess, t present it, t manage it,
t und it r t pliticise it. ?hile di##erences %et$een pen and clsed matter
greatly in the inha%itatin in the tplgically cnnected spaces # data%ases,
they d nt e*haust the ver#l$s that animate sets.
Other settings
T $hat pr%lems in interdisciplinary research des attentin t sets respndG D
$uld argue that set0making is already a strng, al%eit sme$hat latent,
impulse in many scial science and humanities methds attempts t prduce
kn$ledge thrugh narrative, and thrugh e*planatin. ?herever datasets,
practices # cding, gruping r clustering ccur, set0making $ith all its
relatinality 1pen, clsed, elements, parts, e*cess6 is nt #ar %ehind. The $rk
# set0making, $hse dynamics D have e*plred in the cnte*t # data%ase
architectures and in persnal prductivity systems 1a dmain nt s #ar
remved #rm the practical e*igencies # any academic tday6, necessarily
#igures in any # the prcesses # cllecting, srting, citing and rdering that
underpin all research. At the present mment, there is smething mre speci#ic
8/12/2019 Mackenzie, Adrian - Sets
19/26
19/26
at stake in sets. Baced $ith much cmpetitin #rm market research and
%usiness analytics that access vast data%ases # transactins, actins,
cmmunicatin and cnsumptin, scilgists have called #r rene$ed
attentin t the $rk # descriptin. Mst prminently, Mike +avage argues #r
a shi#t a$ay #rm attempts t prvide general r speci#ic causal e*planatins
#r particular phenmena t an engagement $ith the $idescale deplyment #
inscriptin devices such as $e%sites and lyalty cards 1+avage 3445,
8/12/2019 Mackenzie, Adrian - Sets
20/26
20/26
nt (ust #eminist epistemlgies # scienti#ic kn$ledge. +ets and set0making
ntlgies are ne $ay # #iguring this splitting #r researchers $h are al$ays
in the cntradictry psitin # a##irming radical histrical cntingency and
imagining histrical change #r the %etter.
References
Alldredge, 7ill. 3449. )ere's ne #r "avid Allen...+eptem%er . Blickr.
http-$$$.#lickr.cmphts%illypalza9==E959.
Allen, "avid. 344
8/12/2019 Mackenzie, Adrian - Sets
21/26
21/26
University ress.
http-$$$.lc.gvcatdirdescriptincam43
8/12/2019 Mackenzie, Adrian - Sets
22/26
22/26
ed. Mari 7iagili,
8/12/2019 Mackenzie, Adrian - Sets
23/26
23/26
?eisstein, 8ric ?. 3445a. Hpen +et 00 #rm ?l#ram Math?rld. Te*t.
http-math$rld.$l#ram.cmHpen+et.html.
. 3445%. Clsed +et 00 #rm ?l#ram Math?rld. Te*t.
http-math$rld.$l#ram.cmClsed+et.html.
?ikipedia. 3445. Hpen set 0 ?ikipedia, the #ree encyclpedia. Nuly 9.
http-en.$ikipedia.rg$ikiHpenVset.
Permissions
Figure 1
u are #ree-
X t cpy, distri%ute, display, and per#rm the $rk
XUnder the #ll$ing cnditins-
X Attri%utin u must give the riginal authr credit.
Attri%ute this $rk-
Dn#rmatin
?hat des /Attri%ute this $rk/ meanG
http://en.wikipedia.org/wiki/Open_sethttp://en.wikipedia.org/wiki/Open_set8/12/2019 Mackenzie, Adrian - Sets
24/26
24/26
The page yu came #rm cntained em%edded licensing metadata,
including h$ the creatr $ishes t %e attri%uted #r re0use. u can use the
)TML here t cite the $rk. "ing s $ill als include metadata n yur page
s that thers can #ind the riginal $rk as $ell.
Xn0Cmmercial u may nt use this $rk #r cmmercial purpses.
X "erivative ?rks u may nt alter, trans#rm, r %uild upn this
$rk.
?ith the understanding that-
X ?aiver Any # the a%ve cnditins can %e $aived i# yu get permissin
#rm the cpyright hlder.
X Hther Oights Dn n $ay are any # the #ll$ing rights a##ected %y the
license-
ur #air dealing r #air use rights:
The authr's mral rights:
Oights ther persns may have either in the $rk itsel# r in h$ the
$rk is used, such as pu%licity r privacy rights.
X tice Br any reuse r distri%utin, yu must make clear t thers the
8/12/2019 Mackenzie, Adrian - Sets
25/26
25/26
licence terms # this $rk.
Figure 2
Authr's $n $rk
Figure 3
t c&* distri+ute* dis&la* and &er!rm t,e wrk
X t make derivative $rks
Under the #ll$ing cnditins-
Attri%utin u must give the riginal authr credit.
Attri%ute this $rk-
Dn#rmatin
?hat des /Attri%ute this $rk/ meanG
The page yu came #rm cntained em%edded licensing metadata,
including h$ the creatr $ishes t %e attri%uted #r re0use. u can use the
)TML here t cite the $rk. "ing s $ill als include metadata n yur page
s that thers can #ind the riginal $rk as $ell.
8/12/2019 Mackenzie, Adrian - Sets
26/26
26/26
X n0Cmmercial u may nt use this $rk #r cmmercial purpses.
?ith the understanding that-
X ?aiver Any # the a%ve cnditins can %e $aived i# yu get permissin
#rm the cpyright hlder.
X Hther Oights Dn n $ay are any # the #ll$ing rights a##ected %y the
license-
ur #air dealing r #air use rights:
The authr's mral rights:
Oights ther persns may have either in the $rk itsel# r in h$ the
$rk is used, such as pu%licity r privacy rights.
X tice Br any reuse r distri%utin, yu must make clear t thers the
licence terms # this $rk.
Figure $
Authrs $n $rk