Although Shakespeare and Company is best known as a hub for expatriate literary communities in Paris and the publication of James Joyce’s Ulysses, the Project provides a great deal of data about the day-to-day operations of the lending library, specifically from the logbooks, which provide daily records about when members joined, renewed, purchased supplements, made separate payments, and received reimbursements.6

Figure 1 details the breakdown of these membership activities across categories and visualizes the unevenness of these activities over the lifespan of the lending library. Overall, the data in the logbooks is remarkably consistent; however, not all the logbooks have survived. Project researchers have compiled a list of all logbooks, which we used to uncover gaps in these records. Based on these dates, we have identified seven large gaps ranging from two months to over a year and a half (fig. 2).7 While these gaps do not prevent researchers from using the Project’s data, they represent a challenge for any downstream computational analyses that assume consistent patterns.

To start “reading” this missing data, we turned to forecasting models, and specifically created a time series model to predict missing events not covered by the logbooks. To generate these predictions, we aggregated extant membership activity by week based on the date of each event (subscription purchase date for subscriptions, renewals and supplements; start date for everything else).8 Forecasting is a popular methodology in data science, often used to identify trends that can impact business decisions (Taylor and Letham 1, 2). We believe this approach is well-suited to modeling logbooks, which after all track business transactions. With these models, information from periods covered by the logbooks can be used to extrapolate the likely activity that occurred during the gaps. We implemented our forecasts with the popular Python library, Prophet, described as “a time series forecasting model designed to handle the common features of business time series” (Taylor and Letham 5). We selected this library because the parameters and outputs are specifically designed to support the fine-tuning of the models.9 Whereas a business analyst might design and interpret a forecast based on their knowledge of market size or the impact of new products, we use our knowledge of the membership activity after the logbook gaps.

To create figure 3, we fit a Prophet model based on the number of membership events per week, and then use that model to forecast over the identified gaps. Because of the large gaps and the difference in activity between the 1920s and the 1930s, we fit two separate models for the time periods. When we aggregate the forecast values for the weeks included in these gaps, we arrive at a total of 2,335 missing events, with an upper bound of 3,601 and a lower bound of 1,095.10 Adding our estimate to the existing 11,601 events from the logbooks results in an estimated total of 13,936 events (upper 15,203; lower 12,350) that would be documented if all the logbooks were available. Based on this estimate, eighty-three percent of membership events (upper seventy-six percent; lower ninety-four percent) are represented in the surviving logbooks. When we account for the 1,438 membership events drawn from other sources, we conclude that ninety-four percent (upper eighty-six percent; lower 106 percent) of membership events are present in the published dataset.

Since Prophet produces a fairly complex model, we can compare forecast numbers to estimates made from some basic assumptions about membership activity and back-of-the-envelope math.11 Using the 11,601 membership events from the logbooks, we calculate an average of 1.3 events per day for dates covered by existing logbooks, including weekends and holidays. While events did not actually occur at this rate, we can apply that average to the 1,538 days in our identified gaps to arrive at an estimate of 1,999 missing events for a total of 13,600 events that would be documented in all the logbooks. Accounting for supplemental membership events from address books and lending library cards, we end up with a total of 13,042 membership events, which would lead us to conclude that ninety-five percent of all membership activity is documented in the dataset. Given that our Prophet model, which is more sensitive to the actual historical data, gives us a ninety-three percent estimate, we are relatively confident that the current database is only missing between five–seven percent of membership activity.

Since the percentage of missing membership activity is relatively small, one might assume that all members in the library are listed.12 Yet because membership data is missing for much of 1931 and 1932, and all of 1937, it is likely that there are some lending library members who are not represented in the dataset. That is, members who were only active within those time periods, whose lending library cards were not preserved, and who were not documented in either address book used to supplement the logbook gaps.

In figure 4, we graph the frequency of new members in the library. We consider a member to be “new” based on the date of the earliest event associated with an account. The majority of new member events come from the logbooks, but by aggregating and identifying members who only appeared in the address books (329 members) or lending library cards (124 members), we can see both the full rise and fall of the library’s membership over time, as well as those time periods where the address books supplement significant portions of membership data for missing logbooks.

When new members joined the lending library, the first step was to pay for a subscription, usually with a deposit that was kept as security and reimbursed when the account was closed (Kotin and Koeser, “Data Sets” 4). And indeed, when we look at the first events for members, the overwhelming majority start with subscriptions. Because the extant logbook data is so consistent, and because the logbooks are the primary source of subscription information, we can use a similar forecasting approach to estimate the number of new member subscriptions lost due to the missing logbooks. We start by identifying all members who had a subscription or renewal recorded in the logbooks as their first event (4,320 members).13 We then aggregate the number of new member subscriptions to create a time series similar to the one discussed in the previous section and then fit a model to forecast estimates for new subscriptions during the gaps.

Figures 5 and 6 represent two different Prophet models for forecasting the same missing new subscriptions, based on linear and logistic growth models respectively. The default linear model predicted fewer missing subscriptions (458) than the total number of members supplemented from non-logbook sources (819); meaning that the datasets have more members than would have been included if all logbooks were available. Yet a visual inspection of the graph for this forecast model indicates that it is picking up a downward trend from the data before our larger gaps, which results in a forecast that does not match the data after the gap. To further validate and finetune this model, we reran the forecast using a logistic growth model, and set a cap of nineteen based on the maximum number of new subscriptions from all weeks in our data (the peak is the week of November 8, 1925). When the estimates from the growth forecasts are aggregated, we arrive at an estimate of 1,027 missing new member subscriptions (upper 1,725; lower 368). When tallied with the existing 4,320 records from the logbooks we arrive at an estimated total of 5,346 new member subscriptions (upper 6,045; lower 4,688). When compared to the 5,139 total number of members across all sources, this estimate indicates that we are missing 207 members (upper 906; lower 0) and that the dataset covers ninety-six percent (upper eighty-five percent; lower 110 percent) of the full membership.

To check the results from our Prophet models, we can again estimate using some simple calculations to see how they compare. On average, there are about 0.4 unique members per membership event in the logbooks; that is, roughly every third event adds a new member. If we assume that this ratio is consistent for the lifetime of the library, then based on our previous estimation for all logbook membership events we arrive at a total of 5,538 (upper 6,040; lower 4,904) members included in the logbooks if there were no gaps (399 missing members; upper 901). Based on the 5,139 accounts in the dataset, this estimate indicates the dataset includes ninety-three percent (upper eighty-five percent; lower 105 percent) of the members who would be included in the full set of logbooks. However, since this estimate is based on our previous estimate for missing membership, the uncertainty is compounded.

There’s additional complexity to estimating missing members, since the total number of accounts in the dataset is slightly inflated; there are members with the same name who are represented as separate accounts, due to Project merge guidelines.14 For example, there are nine different accounts for members named Kohlberg with dates ranging from 1933 to 1942; at least some of these accounts are likely the same person, but perhaps not all, and certainly not all for other members with more common names. As a counter to the inflated member estimates, to provide a minimum estimate for members we ran the same calculations but aggregated events by unique member names instead of unique member ids (effectively merging all unmerged accounts for people with the same name, which results in a total of 4,720 accounts). Rerunning Prophet on new subscriptions for these accounts results in an estimate of 897 missing new subscriptions (upper 1,463; lower 283). When tallied with the existing 3,975 records from the logbooks, this gives an estimated total of 4,872 new subscriptions (upper 5,539, lower 4,258), and 152 members missing from the complete dataset (upper 818), resulting in ninety-seven percent (upper eighty-five percent, lower 111 percent) coverage of the full membership. When we recalculate the simpler estimate using the same aggregation, the rate of unique members per membership event goes from 0.4 to 0.36 and produces a tally of 332 missing members, but the actual percentages are unchanged: ninety-three percent (upper eighty-six percent, lower 105 percent) coverage. This result aligns with our intuition that over the lifetime of the library there would be fewer new members over time, as previous or existing members returned or renewed their subscriptions. This matches the forecasted trend for estimated percentage of members missing going down over time, indicating that we are missing fewer member accounts than one might expect.

Our estimates offer some bounds for the total membership: 5,350 based on Project identifiers (which is a slight overestimate) or 4,872 based on unique names (which is an underestimate). However, in either case the data includes over ninety percent, or almost all the members.

We hope that the prior estimates will be of use to scholars studying lending library members, but we expect that many scholars will be most interested in the borrowing activities of members. Borrowing activity—that is, the specific books and periodicals that a member borrowed—is tracked solely on lending library cards, and only a small portion of members have surviving lending cards, with a larger portion of the cards surviving from the 1930s than the 1920s (Kotin and Koeser, “Cards in Context”). Based on the extent of missing cards, we know that this is the most incomplete portion of the datasets in the Project.

To estimate missing borrowing activity, we focused on modeling the behavior of the members with borrowing records and the subscription information in the logbooks, specifically how members utilized their subscriptions.15 Unlike modern libraries, which usually allow many books to be checked out at the same time, subscriptions to Beach’s lending library included specified limits. The basic subscription allowed members to borrow one volume at a time; members could pay more to borrow two volumes at a time; or could purchase a supplement to increase the volume limit (Kotin and Koeser, “Data Sets” 4, 30).

We can think of the number of subscriptions as a window into the “borrowing capacity” of the library and use that to estimate the missing borrowing activity (fig. 7). Because subscriptions were expensive, members typically took full advantage of their privileges, borrowing a book the same day they subscribed and borrowing a new book on the same day they returned an old one. In fact, our analysis indicates that members were more likely to go over their subscription volume limits than underutilize their privileges and that Beach became much more permissive in the later years of the lending library (fig. 8). We can illustrate this by comparing numbers from Project data with a handwritten tally from February 28, 1931, which notes that seventy-five books were checked out (see fig. 9). On that date, there are thirty-one active subscriptions documented and thirty-two borrowing events recorded; because a few of those subscriptions were for more than one volume at a time (three subscriptions for two volumes each and one subscription for three), we calculate that based on these subscriptions there should be a maximum of thirty-six volumes checked out.16 The seventy-five checked out books documented on that hand-written tally are double what we would estimate based on subscriptions.

Yet even this tally, which is much higher than we would estimate based on Project data, might be less than the actual activity of the lending library, given Beach’s propensity not to document free subscriptions. For instance, Fitch relates that when the composer and critic Virgil Thomson was “too poor to buy a subscription, Sylvia waived her fee,” so that he could still use the library (151). Therefore, even if we assume that members fully utilized their subscription volume limits, we can only estimate a minimum for the missing borrowing activity. Nonetheless, we believe that this lower bound is still useful. To calculate this missing activity, we assume a volume limit of one (again, a minimum) for all subscriptions, renewals, and supplements without documented volume limits. When compared to the known borrowing activity, we calculate a ratio of 0.64 borrow events per week. During the week of December 5, 1920, for example, the active subscriptions with documented borrowing would indicate that at least nineteen volumes were checked out, and there are twelve borrowing events recorded that week. When we apply this ratio to the records of subscriptions without documented borrowing activity, we arrive at an estimate of 63,330 missing borrowing events, without accounting for undocumented subscriptions due to logbook gaps. This means that the 20,597 documented borrowing events provide at best twenty-six percent of the full activity of the lending library.

Applying this method to specific time periods with reliable logbook data demonstrates the high variation in the available data. From the beginning of the lending library through the end of 1927, before the first logbook gap, we estimate at best ten percent of borrowing activity is documented (4,459 borrows; estimated total 46,025). The later periods are substantially better documented: between 1932 and 1937, fifty percent of activity is documented (5,003 borrows; estimated total 10,111) and fifty-three percent of activity after September 1939 (3,436 borrows; estimated total 6,503).

While we expect many scholars will be interested in members and their activities, there is also a fourth set of information that is incomplete in the Project—records of books available in the library. The extant borrowing records include numerous book titles, which have been identified and regularized by Project team members.17 But if we have at best twenty-six percent of the full borrowing activity, how accurately do the books in the published dataset reflect the lending library’s actual holdings? The book dataset includes 6,020 records; 5,683 of them were borrowed at least once (some purchases were tracked on lending library cards, but the books were not necessarily lending library titles). If we exclude the 475 titles that the Project team has not been able to definitively identify, we arrive at a total of 5,208 books with validated bibliographic metadata in the lending library.18

This number sounds plausible but based on a handwritten tally in the Beach papers, we know that there were 4,600 books in the lending library in February 1931 (Beach, “Total”). Rather than removing unlisted books, we can use the 1931 total as a starting point. If we identify all borrowing events that started on or before February 28, 1931, we find 2,874 titles. By looking at the last borrow status for each item and filtering out the 109 items that were not returned, we arrive at a total of 2,765 items, or sixty percent of the total tallied by Beach. While this percentage is lower than we might expect, it is important to keep in mind that this is based on the earlier time period, when a much smaller proportion of the borrowing history is documented, and we expect that many of the borrow events that occur after this date add to our knowledge of these 4,600 books.

While Beach’s tally is useful, predicting missing books is also a research problem that transcends the lending library. We can also treat missing books as analogous to an unseen species, which is a common challenge for ecologists, who have developed statistical methods to correct for bias due to samples that exclude species that are difficult to observe or extinct. This approach has been applied to estimate missing portions of medieval music scores, digitized books, Shakespeare’s vocabulary, and most recently manuscripts from medieval European literature, where Kestemont et al. argue that “parallels between cultural and ecological diversity” mean these models can and should be applied to cultural artifacts (765; Cuthbert; Riddell and Bassett; Efron and Thisted).

To create an ecological statistical model of the lending library, we treat each book title as a unique “species” and the “sightings” of each title is the total number of times it was borrowed (fig. 10). This approach results in estimates of total books that vary from 6,768 to 8,102, depending on the method used.19 Based on these numbers, the Project is missing somewhere between 1,560 and 2,894 titles; this means the 5,208 certain titles provide somewhere between sixty-four percent and seventy-six percent of the total books held by the lending library.

It might seem surprising that such a small portion of the borrowing activity (at best twenty-six percent) would provide evidence for the majority of the books that circulated in the lending library (an estimated sixty-four percent to seventy-six percent). Yet since book popularity distribution follows a power law, much of the missing borrowing activity would most likely provide additional evidence for the more popular titles, rather than borrowing records of these missing books.

Although we find these estimates useful, we recognize that this approach is not a perfect fit for lending library books. Our estimates treat individual books as “species,” but it’s likely that many books were only borrowed once, which differs from some of the assumptions in the unseen species model.20 We also know the collection changed over time as Beach acquired new books, and as older books were purchased, went missing, or became damaged, and this rate of change is surely different than that of species in an ecosystem. The behavior of lending library members borrowing books is likely more complicated than these models account for, since we know that the actions of one member could easily impact others: whether waiting for a book to be returned or recommending books to another reader with similar taste.21

There’s one additional resource that might inform our estimate of missing books, which is a catalog of lending library book acquisitions from March 1933 to May 1940 (New Library Books Beach Papers).22 Of the 1,055 books included in this catalog, only 106 of them (ten percent) are not included in the published datasets, which suggests that our estimates of missing books might be slightly inflated. However, relying on this acquisition catalog data to estimate the full library holdings is difficult, since we ultimately don’t know what proportion of the total these items represent. If we examine the borrowing activity during the dates covered by the catalog, the books in this catalog account for only forty-one percent of borrowing events and twenty-eight percent of the identified items in circulation; so unfortunately, the ten percent of unknown titles within the catalog can’t be applied to the lending library collection at large.

Before speculating, we look to the available data to see what we can learn about Hemingway’s interactions and behavior as a member of the lending library (fig. 11). He first subscribed to the library in late December 1921 for just one month, then had two successive three-month subscriptions in February and August 1922, with gaps of a month or more in between subscriptions. After another gap of several months, he renewed again in March 1924 and held three successive year-long subscriptions. His last documented subscription ended in March 1927, but he continued to borrow books through the 1930s without an active subscription, likely a reflection of his special relationship with Beach. There are 117 borrowing events on his extant lending library cards (132 book events total, with 112 unique titles) but the earliest one is only from October 1925; none of the activity from 1922 and early 1925 survives.

On average, Hemingway kept books out for thirty-two days (fig. 12). Sometimes he returned books after only a few days; he returned Wyndham Lewis’s Time and Western Man (1927) after only a single day in October 1927, and David Garnett’s Go She Must! (1927) was borrowed and returned on the same day.25 But there are some books he kept out over a hundred days; a number of books checked out in May 1926 were not returned for months that year, including Ivan Turgenev’s Knock Knock Knock and Other Stories (1921), out 176 days, returned in November; W. H. Hudson’s Far Away and Long Ago (1918), out 150 days, returned in October; and Nietzsche’s Thus Spake Zarathustra (1883), out 131 days, returned in September.

The subscriptions with missing borrowing activity span a total of nineteen months, and in all but one three-month subscription Hemingway subscribed for two volumes at a time. Based on Hemingway’s typical borrowing behavior, and assuming full utilization of two volumes at a time when he had them, he would have borrowed around thirty-three books during these nineteen months; if we use the library-wide average of eighteen days, he could have borrowed as many as fifty-nine titles.

To generate these missing books for Hemingway, we utilized the periods when he subscribed to the library but for which we have no documented borrowing activity, and then created a list of recommendation candidates based on books published before or during the subscription period and held by Shakespeare and Company. We then ranked these titles for each subscription period, and in figure 13 show the top ten recommendations generated by our two different approaches, alongside the overall most popular titles in the lending library (both for all time and within that specific circulation window).26

In figure 13, the top predictions on the left are the results of the implicit feedback approach, sorted by the coefficient of variation and then median score for the model. Next are the top recommendations for the memory-based approach, sorted by median score and then coefficient of variation. We include in our summary the most popular books during the period of Hemingway’s undocumented borrowing, as well as most popular over the entire lifetime of the lending library, to demonstrate that our predictions are surfacing something other than simply popularity. We are intentionally only reporting scores for books and not periodicals, which, though very popular in the library, do not have data about individual issues. Figure 14 helps further elucidate these book predictions by visualizing the individual scores for each title and providing a longer list of recommended titles using the more conservative estimate that Hemingway likely read thirty-three books. On the right are the scores for the implicit feedback approach, with the scores increasing in confidence from left to right. Each of the ticks in the plot represents one iteration of the model, which we ran one hundred times to provide the most consistent sample for scores. Notably, the dispersion of ticks is not consistent across subscription periods, and there are also some books that appear in both periods but with differing scores from the model. We specifically report the coefficient of variation in our table to account for this dispersion, since we want to recommend books that the model is more consistently confident about rather than those that might have sporadically high scores. On the left, we show the scores for the memory-based approach, which was based on three methods: cosine similarity, Euclidean distance, and Pearson correlation coefficients. All three methods use the same principle of comparing borrowers’ preferred books to find the most similar books to recommend. While many of the scores are consistent, there are some outliers where one or two of the methods are much more confident in their predictions; for example, Charles Dickens’s David Copperfield (1850) is the top recommended book for the Pearson correlation but is ranked much lower by cosine similarity and Euclidean distance.

Some of our recommendations can be confirmed by Hemingway’s letters and library catalogs. Hemingway certainly read Willa Cather’s One of Ours (1922), although he didn’t think particularly highly of it: in a June 1923 letter to Gertrude Stein, he writes that it “starts getting really good about page 425” (the first edition was 459 pages), and in a November 1923 letter to Edmund Wilson, he disparages the battle scenes as drawn from Birth of a Nation. (“I identified episode after episode, Catherized,” he writes [Letters 2: 29, 80].) His library in Cuba included Norman Douglas’s South Wind (1917), along with three other Douglas titles, and David Garnett’s Lady into Fox (1922) and a Man in the Zoo (1924) (Brasch and Sigman 129, 156). Hemingway’s library included twelve books by Garnett, some of them duplicate copies, and he borrowed two Garnett titles from Shakespeare and Company in late 1926 and early 1927. Recent scholarship suggests that not only was Hemingway a fan of his books, but that perhaps “Garnett has been overlooked as one of Hemingway’s influences” (Kale).

Many of the other recommended titles are by authors whose books Hemingway read or owned. He owned five books by Joseph Conrad and borrowed one from Shakespeare and Company in 1926. In a 1922 letter, Hemingway writes, “I read the Roosians and Joe Conrad pretty near always in the country—because they’re so long” (Letters 1: 375). He owned two books by Joseph Hergesheimer, who he refers to as “Hergo” in a 1925 letter and alludes to in The Sun Also Rises (1926) (Letters 2: 422–423). He owned two books by Samuel Butler, and mentions Hudibras (1663) in a 1926 letter (Letters 3: 41). He borrowed one title by Eugene O’Neill, owned Frank Swinnerton’s autobiography, read Lord Dunsany’s Fifty One Tales (1915), owned two titles by G. K. Chesterton, and read Chesterton’s The New Jerusalem (1920) in 1925. He was certainly familiar with Vachel Lindsay’s work—in January 1924 he cabled Ezra Pound to say he was rushing “two hundred pound California bathing beauty” to Pound’s bedside, probably referring to Vachel Lindsay’s recently published Collected Poems (1923), which was 390 pages long, and elsewhere refers to Lindsay as “the golden whale” (Letters 2: 96, 97–99).

These recommendations also surface authors that Hemingway was known to have had strong feelings about. He owned six titles by Max Eastman, but described The Literary Mind (1931) as “pretentious rubbish” (Reynolds 120; Letters 4: 615).27 He owned eleven titles by Henry James, two of them in duplicate, but Reynolds includes Hemingway’s comment about The Awkward Age (1899)—“an enormous fake” (Hemingway’s Reading, 141; Brasch and Sigman, Hemingway’s Library, 202).

Despite Hemingway’s known interest in Russian literature, which is clearly reflected in his available borrowing record (twelve borrows of Turgenev, some of them repeats; three of Dostoyevsky, and a collection of Russian literature from Mirsky), our recommendations only include one title by a Russian writer, Nikolai Leskov. Perhaps this is because there are so few borrowing events recorded for Turgenev: the most activity recorded for any of the ten Turgenev titles is three events, and for four of these titles Hemingway is the only known borrower.

While we have delved into some of the specific recommendations, in figure 13 we also included the most popular titles for Hemingway’s subscription periods and the library overall, since popularity is a naive but often effective metric for recommendations. Many of the listed titles are in fact plausible—if unsurprising—recommendations for Hemingway. For instance, we see that titles by James Joyce feature heavily. Hemingway’s extant borrowing records don’t include any books by Joyce, but Reynolds’s list includes six Joyce titles, three of which were purchased from Shakespeare and Company in March 1934: Two Tales of Shem and Shaun (1932), Chamber Music (1907), and A Portrait of the Artist as a Young Man (1916).28 Reynolds notes that Dubliners (1914) was “probably read by 1924” and Portrait was “probably read in the 1920s” (Hemingway’s Reading, 143). Dorothy Richardson’s Pointed Roofs (1915) and Honeycomb (1917) were both popular in the lending library, and while Hemingway’s borrowing records don’t include any Richardson titles, he owned Dawn’s Left Hand (1931), the tenth and final novel in the Pilgrimage series, and Reynolds indicates he read it in 1934. He was certainly familiar with Richardson’s work, since in 1924 he wrote a letter to her requesting a short story, which was published later that year in the Transatlantic Review (Hemingway to Richardson, Letters 2: 126).

Though popularity provides some likely insights into Hemingway’s reading habits, this approach would overlook titles like Hergesheimer’s Mountain Blood (1915), which was only checked out twice in the entirety of the library’s history but was highly recommended in our models. Not only does our speculative approach move beyond simple popularity; many of the recommended titles and authors that are confirmed or partially confirmed by Hemingway’s letters and libraries are not authors included in his documented borrowing history—indicating that these recommendations are based on commonalities between his borrowing activity and other members of the library. This finding requires further analysis beyond the scope of this paper, but we believe even this initial exploration presents the value of speculative reading, which not only helps confirm the work of previous scholars, but also opens new research avenues for conceptualizing and studying reading communities and individual members of the library.