Memory, Spaced Repetition and Life

I have made the case that with the ad­vent of the in­ter­net went the need to mem­o­rize any­thing. Why worry about mem­o­riz­ing when I’ll never be tested for a grade and can ac­cess knowl­edge nearly in­stan­ta­neously? As well, I rea­soned, I have prob­a­bly already mem­o­rized ev­ery­thing I need to. I fo­cused my time in­stead on learn­ing think­ing tech­niques, such as Bayesian calcu­la­tions, ex­pected value calcu­la­tions and var­i­ous things for im­prov­ing emo­tional con­trol.

But af­ter read­ing this a cou­ple months back I de­cided to ex­per­i­ment with Anki, a digi­tal flash­card pro­gram which ex­ploits a cog­ni­tive phe­nomenon called the Spac­ing Effect by im­ple­ment­ing a mem­o­riza­tion tech­nique called Spaced Rep­e­ti­tion. The Spac­ing Effect is the widely ob­served ten­dency for peo­ple to re­call in­for­ma­tion bet­ter when stud­ied a few times over a long pe­riod than when stud­ied many times over a short pe­riod. Balota et al (2007):

Spac­ing effects oc­cur across do­mains (e.g., learn­ing per­cep­tual mo­tor tasks vs. learn­ing lists of words), across species (e.g., rats, pi­geons, and hu­mans), across age groups and in­di­vi­d­u­als with differ­ent mem­ory im­pair­ments, and across re­ten­tion in­ter­vals of sec­onds to months.

Gw­ern analo­gizes the spac­ing effect with ra­dioac­tive de­cay:

You can think of the ‘for­get­ting curve’ as be­ing like a chart of ra­dioac­tive half-lives: each re­view bumps your mem­ory up in strength 50% of the chart, say, but re­view doesn’t do very much in the early days be­cause the mem­ory sim­ply hasn’t de­cayed very much! (Chart)

One con­se­quence of the spac­ing effect is that cram­ming is use­ful for re­call­ing things shortly af­ter mem­o­riz­ing them; how­ever, if those crammed mem­o­ries are not even­tu­ally re­freshed then they are likely to de­cay to noth­ing. From this ob­ser­va­tion came Spaced Rep­e­ti­tion: a mem­o­riza­tion tech­nique us­ing flash­cards (usu­ally) shown at in­creas­ing in­ter­vals of time to op­ti­mize the re­la­tion­ship be­tween num­ber of re­views and strength of mem­ory. The PC ex­plo­sion was a boon to Spaced Rep­e­ti­tion since stor­ing and show­ing flash­cards as well as phys­i­cally calcu­lat­ing their fre­quen­cies were del­e­gated to the com­puter. The pro­gram Anki, for in­stance, per­mits the user to gen­er­ate flash­card decks, spec­ify study ses­sion length and fre­quency, spec­ify how many new cards are in­tro­duced per ses­sion and spec­ify the fre­quency of the cards based on the user’s in­put. Hard ma­te­rial is shown more of­ten than easy ma­te­rial, with the ease or difficulty be­ing de­ter­mined di­rectly by the user se­lect­ing but­tons marked “again,” “easy,” “good,” and “hard.”

That sounds nifty, but how well does it work? As for my­self, us­ing the Anki de­fault set­tings, I was able to thor­oughly mem­o­rize a deck of 80 cog­ni­tive bi­ases and re­lated terms (160 cards to­tal, name to defi­ni­tion and vice avers) in about three weeks us­ing Anki ~15 min­utes/​day. Since the cards are pushed back fur­ther and fur­ther for re­view as I pro­gressed, I have only five cards to re­view to­day. The first one, En­dow­ment Effect, came in­stantly to me so I se­lected the “easy” but­ton. Now, as a re­sult of the Anki al­gorithm, I won’t see that card for 1.3 months. My low ex­pec­ta­tions for the Anki ex­per­i­ment were ex­ceeded.

Piotr Woz­niak, who de­signed the first Su­perMemo al­gorithm in the early 80′s (of which later ver­sions are still in use in Su­perMemo as well as Anki), and de­voted enor­mous en­er­gies to study­ing mod­ern com­puter aided self-in­struc­tion sys­tems pro­motes spaced rep­e­ti­tion. He and two oth­ers de­vel­oped a two-vari­able frame­work for mem­o­riza­tion which they built upon to ex­am­ine a way of op­ti­miz­ing in­ter­val spac­ing in Spaced Rep­e­ti­tion. The first vari­able, mem­ory re­trieval (R), is the prob­a­bil­ity of re­call­ing some­thing and is ap­prox­i­mated by an ex­po­nen­tial de­cay func­tion, while the sec­ond vari­able, mem­ory sta­bil­ity (S), mea­sures how long a mem­ory lasts be­fore it is for­got­ten en­tirely. Woz­niak et al, ex­pressed S as the in­ter-rep­e­ti­tion in­ter­val time that pro­duces R = 90% (the like­li­hood of re­call be­ing a 9 out of 10 chance) and con­cluded the fol­low­ing:

We ex­press the changes in re­triev­abil­ity as:

(3.1) R=e-d*t


  • t—time

  • R—prob­a­bil­ity of re­call at time t (re­triev­abil­ity)

  • d—de­cay con­stant de­pen­dent on the stability

We can re­place the con­stant d de­pen­dent on sta­bil­ity, with a con­stant k that is in­de­pen­dent of sta­bil­ity:

(3.2) R=e-k*t/​S


  • t—time

  • R—prob­a­bil­ity of re­call at time t

  • S—sta­bil­ity ex­pressed by the in­ter-rep­e­ti­tion in­ter­val that re­sults in re­triev­abil­ity of 90% (i.e. R=0.9)

  • k—con­stant in­de­pen­dent of stability

Draw­ing on anal­y­sis of large data sets cul­ti­vated from Su­perMemo, Woz­niak et al provide em­piri­cal ev­i­dence that mem­ory de­cay matches their ex­po­nen­tial de­cay ap­prox­i­ma­tion. The goal of Woz­niak’s Su­perMemo al­gorithm is to op­ti­mize in­ter-rep­e­ti­tion spac­ing by (the­o­ret­i­cally) re­fresh­ing a mem­ory the mo­ment be­fore it de­cays to­tally, thus spik­ing that mem­ory un­til it de­cays near to­tally again and gets spiked again. (Although, de­pend­ing on the im­por­tance of be­ing able to re­call of a piece of in­for­ma­tion, it can be used, the­o­ret­i­cally, to spike a mem­ory ev­ery time it de­cays to like­li­hood of re­call of 90%, 80%, 70%, etc.) In­ter­est­ingly, in a meta-anal­y­sis by Balota et al (2007) , the au­thors con­clude that while spaced rep­e­ti­tion is cer­tainly bet­ter than massed prac­tice (study­ing all at once and then not re­view­ing again), spaced rep­e­ti­tion shows no ad­van­tage over static spaced rep­e­ti­tion (hold­ing in­ter­vals con­stant)! Since most stud­ies cited in the meta-anal­y­sis used a small num­ber (usu­ally three) re­trieval at­tempts, the au­thors sug­gest that fu­ture re­search should ex­pand this num­ber to bet­ter re­flect the way peo­ple can prac­ti­cally use spaced rep­e­ti­tion. In my es­ti­ma­tion, when it comes to mem­o­riza­tion, given the ease of use of these digi­tal flash­cards pro­grams, the spe­cific al­gorithm de­sign is a sec­ondary con­cern to be­ing per­son­ally dis­ci­plined to con­sis­tently re­view ma­te­rial un­til you think you’ve in­ter­nal­ized it fully.

Another con­sid­er­a­tion be­yond al­gorithm de­sign is for­mu­lat­ing a us­able flash­card deck: sim­plify­ing the in­for­ma­tion and im­ple­ment­ing tech­niques to en­hance re­call. Woz­niak et al found ev­i­dence that it was harder to re­call in­for­ma­tion the more com­plex it was. Hence, Woz­niak recom­mends 20 rules for for­mat­ting knowl­edge to make flash­cards more di­gestible dur­ing re­views. The first three rules are stan­dard: un­der­stand be­fore you learn, learn be­fore you mem­o­rize and build on the ba­sics. The re­main­ing rules are spe­cific to de­vel­op­ing and main­tain­ing flash­card decks, such as sim­plify­ing ques­tions, us­ing clozed dele­tion (a sen­tence miss­ing a part re­placed by three dots), in­clud­ing images, avoid­ing sets, etc. If you are plan­ning on cre­at­ing your own deck then fa­mil­iarize your­self with these rules.

Ad­di­tion­ally, I recom­mend in­clud­ing hy­per­links, if available, in your cards to sources with thor­ough ex­pla­na­tions of the top­ics, and to be care­ful do­ing Wikipe­dia-based decks. Hav­ing small pre­vi­ous knowl­edge of cog­ni­tive bi­ases when I started, it was es­sen­tial to read ex­panded ex­pla­na­tions on many of the terms to un­der­stand them com­pletely, so I ac­tu­ally up­dated the deck, which some­one else cre­ated, with hy­per­links on ev­ery card. I think it greatly en­hanced the us­abil­ity and effec­tive­ness of the deck. In­ci­den­tally, when I went to Wikipe­dia to bet­ter grasp many of the terms, I found sev­eral en­tries there lack­ing in cred­i­bil­ity. On at least two oc­ca­sions, af­ter be­ing skep­ti­cal of an en­try on a term, I Googled the term and found ev­ery other men­tion of it on the in­ter­net was ei­ther sourced to Wikipe­dia or di­rectly copied from there.

This all still sounds nifty, but, I’ll re­peat, why worry about mem­o­riz­ing when I’ll never be tested for a grade and can ac­cess knowl­edge nearly in­stan­ta­neously? As for stan­dard trivia type in­for­ma­tion (state cap­i­tals, etc), mem­o­riza­tion is vir­tu­ally a to­tal waste of time (thank you, tech­nol­ogy!). In­stant re­call of facts, ex­cept on Jeop­ardy or when us­ing a for­eign lan­guage, is gen­er­ally not of value. Think of a time when your in­abil­ity to in­stantly re­call a fact re­sulted in a fi­nan­cial loss for you—I can’t. On the other hand, ev­ery damn day I am con­fronted with dy­namic situ­a­tions where I am forced to make quick de­ci­sions that vary in effec­tive­ness based on how well I an­a­lyze what is hap­pen­ing and con­struct counter-strate­gies that max­i­mize my util­ity. In these mo­ments, when the nec­es­sary facts are right in front of us, what we usu­ally don’t have is a com­pre­hen­sive database of method­olo­gies, heuris­tics and other de­ci­sion the­o­retic knowl­edge to surf through and use for calcu­lat­ing use­ful out­puts. You might be fa­mil­iar with Bayesi­anism, Non­vi­o­lent Com­mu­ni­ca­tion (NVC), PUA, log­i­cal fal­la­cies and the like, but it is un­likely you have in­ter­nal­ized the con­cepts to the point where even in the face of chaos or emo­tional tur­moil (when it likely mat­ters most) you can im­ple­ment them to the best of your men­tal abil­ity. Thus, I recom­mend us­ing digi­tal flash­cards em­ploy­ing Spaced Rep­e­ti­tion to mem­o­rize a rel­a­tively small set of widely ap­pli­ca­ble meth­ods (and re­lated knowl­edge) for use in dy­namic situ­a­tions that re­quire in­stant or near-in­stant ac­tion.

NVC is the poster-child be­cause it is an easy to re­mem­ber step-by-step pro­cess which does not re­quire com­pli­cated in­puts for any of the steps; vir­tu­ally any­one can ob­serve a situ­a­tion, dis­sect rele­vant in­for­ma­tion from it and then run it through the NVC pro­cess. While sim­ple, NVC might be most valuable in chaotic or emo­tion­ally-charged so­cial situ­a­tion when minds are thrust into pri­mate mode, mak­ing it that more im­por­tant to in­grain thor­oughly. Divia, who cre­ated an NVC deck and sev­eral other use­ful Anki decks, re­counts suc­cess­fully us­ing NVC on a train when a drunk sports fan near her was act­ing bel­liger­ent (imag­ine that!). In my ex­pe­rience, hav­ing in­ter­nal­ized a bunch of cog­ni­tive bi­ases, I’m feel like I am vigilant about rec­og­niz­ing them in my thoughts and be­hav­iors and in those of oth­ers, with­out de­vot­ing much con­scious effort to do­ing so. I ex­pect that databas­ing of log­i­cal fal­la­cies and hu­man be­hav­ioral cues will have the same effect. Please list other meth­ods or knowl­edge that you think would be worth de­vot­ing time to mem­o­rize.

In sum, spaced rep­e­ti­tion for mem­o­riza­tion is su­pe­rior to massed con­sump­tion with­out fur­ther re­view, al­though it is un­de­ter­mined what in­ter-rep­e­ti­tion al­gorithm is best. It seems that hav­ing dis­ci­pline and con­sis­tency in re­view is more im­por­tant than the in­ter-rep­e­ti­tion spac­ing, as even static spac­ing works well. Also im­por­tant is the de­sign and main­te­nance of the flash card decks used for spaced rep­e­ti­tion ex­er­cise, with an em­pha­sis on sim­plify­ing the in­for­ma­tion pre­sented. Lastly, be thought­ful about what things use spend time mem­o­riz­ing. Al­most all in­for­ma­tion is just as use­ful to us wher­ever it cur­rently is, es­pe­cially if it is on the in­ter­net, than it would be if we had it mem­o­rized. Thus, I sug­gest us­ing Anki or other spaced rep­e­ti­tion soft­ware to mem­o­rize meth­ods, con­cepts and knowl­edge can be de­ployed in dy­namic situ­a­tions where we are forced to make im­por­tant de­ci­sions in an in­stant or near-in­stant.


Balota, D.A., Duchek, J.M., & Lo­gan, J.M. (2007). Is ex­panded re­trieval prac­tice a su­pe­rior form of spaced re­trieval? A crit­i­cal re­view of the ex­tant liter­a­ture. In J. Nairne (Ed.), The Foun­da­tions of Re­mem­ber­ing: Es­says in Honor of Henry L. Roedi­ger III, (pp. 83-106), Psy­chol­ogy Press, New York.