How do you measure a year? Simply as “five-hundred-twenty-five-thousand-six-hundred minutes”?1 From the perspective of a clock, sure, a year is just a collection of identical minutes. But we are not clocks.
Time, as experienced, is less like a linear arrow and more like a sequence of moments of connection: time spent alone – even in a crowd – seemingly compresses down to a blur, while moments that are shared with others – addressing them as ‘you’ – can feel like “a glimpse through to the eternal”.2 This is because shared experiences connect us to something beyond ourselves, and the memories soothe the existential anxiety experienced in isolation.
In isolation, one is confronted with the fact that all the time that one spends alone in life dies with them. In contrast, the time that one spends with others persists; it is connected to a vast network with unfathomably deep roots and an indeterminate future: the world. Fleeing from the face of the fear of non-being, one goes into the world to share it with others.
Therefore, shared experiences have intrinsic, existential value. And what is valued is desired: people long for the belonging that comes from being able to say “remember when ___?”. This drive for human connection underpins entire industries, from live entertainment to dating apps to college campuses. The corporate office is no exception – workers care about feeling connected.
Connecting at Work
The workplace is, for many, a main source of human interaction; an employee working 40 hours a week spends over 1/3 of their waking hours “on the clock”.3 For this reason, shared experiences in the workplace, created through working together on teams or attending the same events, are especially critical for human well-being.
But what about the bottom line? Businesses are in the business of making money, not necessarily making their workers happy. While many HR professionals may truly care about the well-being of their employees, there are still fiduciary responsibilities to consider. So what is in it for the balance sheet? Reducing voluntary turnover.
Workforce turnover costs US businesses a trillion dollars a year, and in many cases it is entirely preventable.4 One of the biggest reasons for voluntary turnover is that workers feel disconnected. In fact, a study by ADP showed that workers who feel disconnected are four times more likely to leave.5 A corporate culture that prioritizes shared experiences, therefore, could increase the ROI of a company’s hiring and training program.
In addition to creating a sense of belonging and connectedness that keeps people engaged, shared experiences can also help reduce turnover by creating social capital. Social capital, which can be defined as the resources that one can access through their network,6 requires trust. Trust requires opportunities for people to display trustworthiness,7 and these opportunities take place in the context of shared experiences.
Social capital, like the experiences it is formed out of, is shared. It is a non-transferable source of value for those who hold it; you can’t leave a company and still maintain full access to the skills and resources of the people there. Employees stay partly because they do not want to leave their social capital, formed through time spent with co-workers, on the table.
Therefore, prioritizing shared experiences in the workplace is a win-win, for both the well-being of the employees and the bottom line of the company. Employees feel more connected and gain social capital, and employers save on hiring and training.
The Basis of Shared Experience
In today’s data-driven era of HR, metrics are vital for assessing the effectiveness of various management strategies. So, how would one go about quantifying shared experiences for the purpose of reducing turnover? Going further, how could shared experiences be factored into things like performance evaluations? Before answering any of these questions, we need to establish a measurement basis for shared experience.
To measure something, you need to know the unit of measurement. So, what is a unit of shared experience? Time seems to be the obvious choice here, because it is through spending time in shared contexts with others that shared experiences happen. Therefore, shared experience can be seen as a sort of overlap of one’s time and attention with others.
But this concept needs a bit of refining. For example, is going to a concert for two hours with 5,000 people the same amount of shared experience as spending 10,000 hours with one other person? Time spent in large groups is not the same as time spent in intimate settings.8 While large events can be a valuable source of solidarity for a community or organization, the time one spends in a crowd is diluted among the throng. Time is a limited resource; you can really only give your full attention to one person at a time.
Attention by itself does not create shared experience, but rather it is joint attention – knowingly experiencing the same thing – that creates the sense of belonging people long for.9 When two people acknowledge to each other that they are seeing or otherwise experiencing the same thing, their mental worlds intertwine. It is the fundamental phenomenon that enables people to understand each other.10
So, that concert with 5000 people? While the 5000 people may have all been gazing upon the stage, taking in the same sights and sounds, it is really only shared experience for people who have a mutual awareness that they are experiencing the same thing. They look to the stage, then to each other, and smile, knowing that they are not alone.
Building off the concept of joint attention, it follows that as you pass through time you are either knowingly sharing a moment with other people, or you are in your own world. Thus, the total time one spends in life (or in an organization) can be divided up into the cumulative time that one shares with others and the cumulative time that one spends alone, where the portions of one’s time that are attributed to others are matched one-to-one with the corresponding histories of the people that one shares it with.
This is the time-network: how one’s time is split up and shared mutually with others. It is formed out of shared history, contains both active and dormant relationships, and is continuously evolving with every encounter and tick of the clock. It is the social dimension of time; and it underpins the very fabric of our shared reality. Using the time-network as a framework, shared experience can then be quantified.
The Time-Network
The time-network is a type of weighted social network, where the amount of time spent in joint (or mutual11) attention represents the strength (depth of shared history) of the relationship. Because each person can have a relationship with every other person, this is best represented with a matrix, where the rows and columns represent the people, and the values in the cells represent the relationships.
The matrix that represents the time-network is illustrated in Figure 1. The values in the matrix are represented by \(\tau_{ij}\), where \(i\) and \(j\) (the row and column indices) represent actors (i.e. people) in a network of \(N\) actors (\(N = 3\) in the figure).
Each row in the matrix is an actor’s time-network profile, or how their time and attention has been distributed throughout the network. It shows how they share their time with others.
The sum of an actor’s time-network profile is their tenure, or how much time they have spent in total (no double-counting of hours). Actor \(i\)’s tenure is represented by \(T_i\) and calculated as shown in Eq. \eqref{T1} below.
$$ T_i = \sum_{j=1}^N \tau_{ij} \tag{1} \label{T1} $$
The diagonal of the matrix \((i = j)\) is each actor’s self-time, i.e. cumulative time in one’s own world, while the off-diagonal of the matrix \((i \ne j)\) is the mutual-time between actors, i.e. cumulative time engaged in joint attention. Because joint attention is marked by a mutual awareness and understanding of attending to the same thing, actor \(i\)’s mutual-time with actor \(j\) is the same as actor \(j\)’s mutual-time with actor \(i\). Therefore, the matrix is symmetric, such that \(\tau_{ij} = \tau_{ji}\).
Time-Network Overlap
If actors \(i\) and \(j\) spent a lot of time together, their mutual-time, \(\tau_{ij}\), would be large, reflecting the strength/depth of their relationship. But this does not account for whether the two actors have mutual connections, which is a critical factor in relationships.
Mutual connections make it easier for people to trust each other.12 For example, if I met a stranger who asked me for help, I would be more inclined to help them if I learned that we had a few friends in common. But if I had nothing in common with them, it would be rational to be more cautious. Rational behavior in relationships changes based on the level of embeddedness around the relation.13 So, if the goal is to create a culture rich in social capital, where trust is the norm, embeddedness must also be considered.
Using traditional social network analysis, embeddedness is determined by simply counting up the number of mutual connections that two actors share.14 But time-networks do not measure relationships in a binary ‘yes/no’ kind of way. The time-network is a sliding scale, a weighted network measured in units of time. So, embeddedness must be calculated using a different method, such as the sum of minimums shown in Eq. \eqref{Overlap},
$$ \Omega_{ij} = \sum_{k=1}^N \min(\tau_{ik},\tau_{jk}) \tag{2} \label{Overlap} $$
where \(\Omega_{ij}\) is the time-network overlap between actors \(i\) and \(j\), added up over all mutual connections.
Using this equation, an actor’s overlap with themselves is simply their tenure, i.e. \(\Omega_{ii} = T_i\), while the overlap between two actors ranges from zero to the minimum of both actors’ tenures, as shown in Eq. \eqref{Overlap_limits}, and illustrated in Figure 2.
$$ 0 \le \Omega_{ij} \le \min(T_i,T_j) \tag{3} \label{Overlap_limits} $$
Additionally, just like with the time-network matrix, the time-network overlap matrix is symmetric, i.e. \(\Omega_{ij} = \Omega_{ji}\).
Fragmentation and Resilience
Now that we have established a formal definition of the time-network (and its corresponding metric for embeddedness), what would it look like if it was actually measured and factored into incentives? What would be the implications? Specifically, what would it look like if people were encouraged to maximize their time-network overlap with everyone?
The way the math works out, the fastest way for a person to increase overlap with everyone is to spend time with well-connected individuals that they do not know very well. This sort of behavior, adopted across a network, would first prioritize building bridges between the most disconnected clusters of individuals, and then would strain towards a point in which everyone in the network has spent equal time with everyone. So, incentivizing this behavior would counteract the tendency of networks to become fragmented.
Fragmentation is a natural process in an institution, driven by individuals’ desire for security through irreplaceability. To avoid being replaced, people hoard knowledge, seek out positions of power, and resist change. This process can lead to stagnation and fragility at the group level, ultimately jeopardizing the security of the group (and the individual as a result). For example, a company with a fragmented and rigid internal network may not be able to pivot fast enough to compete with shifting market conditions. Internal conditions change unexpectedly as well: people get sick, go on vacation, or leave for different opportunities. Without a replacement, those who have made themselves irreplaceable will either feel chained to their position or will derail the entire operation when they step away.
The opposite of fragmentation is redundancy. While redundancy is often seen as something negative, something to eliminate in the name of efficiency, some level of redundancy is necessary to remain resilient and adaptable in the face of changing and uncertain conditions.15 If there is no redundancy, the whole operation can come grinding to a halt at a moment’s notice. Therefore, prioritizing time-network overlap (a form of redundancy) is a preventative measure that could increase the resilience of one’s organization.
Measuring the Time-Network
Theoretically, this sounds great. Resilience is a good thing, and is critical in unprecedented times. But how would one go about incentivizing time-network overlap for the purpose of ‘de-fragmenting’ one’s organization? While the time-network is definitely real (rooted in the fundamental phenomenon of joint attention), it is not clear how one could actually measure it. Its continuous nature (cumulative time engaged in joint attention) seems to imply the need for continuous measurement – continuous measurement of everyone’s attention.
Would employees be issued special glasses that monitor eye contact on shifts? Or would brain chips be implemented that scan for synchronized neural activity in meetings? Even if such technologies existed, they would nullify the express purpose of this proposed methodology: increasing employee retention rates. Employees likely would not want to be subjected to continuous monitoring of their interactions with others and would seek work elsewhere to avoid being ‘nano-managed’. Humans aren’t machines; incentive schemes can backfire if they send the wrong signal.
There is a famous ‘law’ in management that explains this phenomenon: “when a measure becomes a target, it ceases to be a good measure.”16 Unlike a piece of lumber which does not care if one measures its length with a ruler or tape measure, in inches or in centimeters, human behavior can change in unpredictable ways when measured. So, if the modes of interaction, the ways in which relationships play out within a specific culture, were measured and targeted directly, it may take away from the spontaneity and freedom that is necessary for genuine interaction. Measurement can destroy the very thing it was supposed to measure.
The time-network is no exception. Its basis – joint attention – is extremely elusive and resistant to measurement. To be confident that two people are engaged in joint attention over a duration of time, one would have to know the inner thoughts of both individuals over the entire duration. Attempting to precisely measure this would be highly invasive and would disrupt the actual process of joint attention. Additionally, joint attention impairment is one of the defining features of autism,17 so even if direct measurement of the time-network was feasible, it would likely discriminate against neurodivergent individuals. Direct measurement of the time-network is not only basically impossible, but also should not be attempted for ethical reasons.
For these reasons, the method presented in this article (the harmonic reciprocity method) takes an indirect approach to measuring the time-network. Instead of directly measuring moments of joint attention, it estimates potential for joint attention. Joint attention requires some level of communication, and communication frequency directly correlates with time spent towards shared focal points of attention, or ‘events’.18 So, rather than monitor people’s attention or communication (which violates people’s privacy), the time that actors spend towards the same ‘events’ is taken to be the basis for measuring the time-network. This approach was selected because it is relatively non-invasive and in many cases uses already-existing data, such as time-sheets or attendance records.
The Harmonic Reciprocity Method
To estimate the time-network using the harmonic reciprocity method, you need a ‘time-sheet’ where actors log their hours towards ‘events’ such as projects or meetings, where \(x_{ie}\) is the cumulative amount of time that actor \(i\) has spent towards event \(e\). Additionally, there can be no double-counting of an actor’s time to multiple events, such that actor \(i\)’s tenure \(T_i\) can be calculated by adding up their time spent over all \(M\) events, as shown in Eq. \eqref{T2} below:
$$ T_i = \sum_{e=1}^M x_{ie} \tag{4} \label{T2} $$
This definition of a time-sheet is typical of time-sheets in organizations, where double-counting one’s time to multiple projects is not allowed. Using this type of dataset, the time-network can then be estimated using the following equation:
$$ \hat\tau_{ij} = \sum_{e=1}^M h_{ije} \tag{5} \label{hattau} $$
where \(\hat\tau_{ij}\) is the estimated time-network value between actors \(i\) and \(j\), \(M\) is the number of events used for analysis and \(h_{ije}\) is the harmonic reciprocity of actors \(i\) and \(j\) over time spent towards event \(e\), calculated with Eq. \eqref{hr}, where \(\Sigma\vec{x}_e\) is the sum of all actors’ time spent towards event \(e\):
$$ h_{ije} = \frac{x_{ie} x_{je}}{\Sigma\vec{x}_e} \tag{6} \label{hr} $$
In words, Eq. \eqref{hattau} adds up the ‘harmonic reciprocity’ between two actors for every event, which is calculated, per Eq. \eqref{hr}, as the product of two actors’ time spent towards an event divided by the sum of all actors’ time spent towards that event. This calculation, which is rooted in time spent towards shared focal points of attention, results in a matrix that has the same properties as the actual time-network: the matrix is symmetric, as in \(\hat\tau_{ij} = \hat\tau_{ji}\), and the sum of each row or column (each actor’s estimated time-network profile) equals each actor’s tenure as in \(T_i = \sum_{j=1}^N \hat\tau_{ij}\).
Thus, the harmonic reciprocity method provides an easy way to calculate some semblance of the time-network. This is convenient, because, as previously explained, actually measuring the time-network is fraught with ethical and logistical hurdles. Therefore, while it is not exactly mathematically rigorous, it is more of an practical necessity to assume that \(\hat\tau_{ij} \approx \tau_{ij}\). The limitations to this assumption are discussed later in this article, but for now let’s look at some basic examples.
Alice and Bob
For only two actors and one event, Eq. \eqref{hattau} simplifies down to the example of Alice and Bob shown in Figure 3, where Alice spent \(A\) hours and Bob spent \(B\) hours towards an event. This time is then transformed from time attributed to events to time attributed to people, illustrated with dashed lines in the figure and calculated as shown in the accompanying table.
In the figure, Alice’s tenure of \(A\) is split into parts \(\frac{A^2}{A+B}\) and \(\frac{AB}{A+B}\), and similarly Bob’s tenure of \(B\) is split into parts \(\frac{B^2}{A+B}\) and \(\frac{AB}{A+B}\). The part of Alice’s tenure that is attributed to herself is her self-time, while the part that is attributed to Bob is Alice and Bob’s mutual-time (and in this example with only one event, it is also their harmonic reciprocity from the event). These parts constitute each actor’s time-network profile, or how their tenure is distributed among everyone in the network, including themselves.
The mutual-time between Alice and Bob in Figure 3 is similar to the harmonic mean: a measure of average that gives weight to smaller numbers. In fact, in this example, where there are only two people and one event, the sum of their ‘off-diagonal’ \((i \ne j)\) time-network values is exactly equal to the harmonic mean of \(A\) and \(B\): \(\frac{2AB}{A+B}\).
The nature of the harmonic mean is such that if \(A\) is kept constant, it doesn’t matter how large \(B\) is: the harmonic mean of two numbers cannot be any larger than twice the value of the smallest number. So, if Alice and Bob’s mutual-time (calculated with the harmonic reciprocity method) was incentivized in some way, it would encourage them to synchronize their time-investments into events, reinforcing the assumption that the events are focal points of joint attention. This is why this method is called the ‘harmonic reciprocity’ method: it is related to the harmonic mean and, if prioritized, should encourage people to reciprocate with each other with how they spend their time.
Beyond only two actors, the calculation gets a bit more complex, as shown in Figure 4. In this figure, not only does the network size increase (number of nodes and edges), but the denominator of the harmonic reciprocity equation also expands to include the time that everyone spent towards the project or event. For example, the harmonic reciprocity/mutual-time between actors Alice and Bob, with their friend Charlie added to the picture, would be \(\frac{AB}{A+B+C}\). So, it no longer is equal to the harmonic mean, but rather is a proportion of the harmonic mean. In these cases, a different explanation of the harmonic reciprocity equation may be helpful.
In networks of more than two actors, the harmonic reciprocity equation may be better thought of as distributing one’s time spent towards an event in accordance with the proportion of the event attributed to each actor. For example, notice that the harmonic reciprocity between Alice and Bob is also equal to \(\small A\left(\frac{B}{A+B+C}\right)\), or actor A’s time multiplied by actor B’s proportion of the entire project/event. Essentially, the harmonic reciprocity equation assumes that each event is a weighted composite of all the people involved in it, weighted by time investment.
Easy as ABC
To show what this looks like with numbers, let’s consider three actors who worked on one project together: actors A, B, and C. In this example, actor A worked 30 hours, actor B worked 12 hours, and actor C worked 58 hours. In total, they worked 100 hours on the project, so actor A worked 30% of the hours, actor B 12%, and actor C 58%. These proportions are then used to distribute each actor’s time to the other actors.
This calculation is demonstrated in Table 1 below, where the rows represent the actor being considered, and the columns represent the actors that they are in relation with. The values in the cells represent how much of each actor’s time spent on the project would be attributed towards their relationship with others, including themselves.
Table 1: Harmonic Reciprocity Calculation
| Actor | A | B | C |
| A | 30 x 30% = 9 | 30 x 12% = 3.6 | 30 x 58% = 17.4 |
| B | 12 x 30% = 3.6 | 12 x 12% = 1.44 | 12 x 58% = 6.96 |
| C | 58 x 30% = 17.4 | 58 x 12% = 6.96 | 58 x 58% = 33.64 |
For illustration purposes, the time-network values in Table 1 are also represented by connected donut charts in Figure 5. In the figure, each person’s time is split up into parts that are shared with the other actors (illustrated with matching colors and connecting arrows), with the exception of their self-time (in white), which is unique to them.
Notice that the sum of each row (or column) of Table 1 and each pie chart of Figure 5, i.e. the sum of each actor’s time-network profile, adds up to that actor’s total time spent on the project. For example, for actor A, 9 + 3.6 + 17.4 = 30. In other words, this transformation preserves the time that each actor spends in total.
As demonstrated by the examples above, the harmonic reciprocity method estimates the time-network indirectly through time spent towards ‘events’ that are focal points of attention for everyone involved, bypassing the aforementioned ethical and logistical issues with direct time-network measurement. This is convenient, but the indirect approach introduces another problem to solve. How does one determine the set of ‘events’ used for the analysis?
Selecting the Set of Events
At its core, the harmonic reciprocity method is a transformation or projection of a two-mode matrix (actors → events) to a one-mode matrix (actors → actors). Inherent in such a transformation is some loss of fidelity.19 For example, consider if only one ‘event’ was used for analysis. In this case, an actor’s overlap with another actor would simply be the same as the minimum of both actors’ tenures. Mathematically speaking, if \(M=1\), then \(\Omega_{ij} = \min(T_i,T_j)\). So, using the harmonic reciprocity method, the limits described in Eq. \eqref{Overlap_limits} are really only relevant when multiple events are considered in the analysis.
Not only does the number of events matter, the boundaries of events also has impact. For example, if exactly \(N\) events are used, and the boundaries of these events are such that each person’s time is logged only into their own personal event, then \(\Omega_{ij} = 0\) for all \(i \ne j\). Therefore, for a given network, the calculated overlap values are maximized when one common event is used for everyone’s time, and minimized when each actor is siloed into their own individual ‘event’.
Overlap in the time-network, as calculated with the harmonic reciprocity method, depends on the granularity and focus of the events used. If time was logged on a task-wise basis, the overlap would be sparse, as tasks are typically individual in scope. On the other hand, if time was logged on a department/team basis, the resulting image of the network would be quite fuzzy, and may not be very useful. The set of events used has a significant, yet bounded, effect on the results.
Clearly, a set of events somewhere between the universal and the individual will give the best results, so that the assumption \(\hat\tau_{ij} \approx \tau_{ij}\) is acceptable, but it may be difficult to determine where that line is. Therefore, it may be beneficial to compare the time-network under different event sets, such as time spent working for the same clients, or in the same region, or on the same shift. No matter what set of events is selected, the resulting overlap will still be bounded by the limits in Eq. \eqref{Overlap_limits}, but there is a lot of room for variation.
Another point of consideration is that the set of events used for the analysis should be relatively equal in scope. Using both general and specific events in the same analysis will skew the results. If, for example, one wanted to portray one group as more connected than another, they could lump all of that group’s time into a single, general ‘event’, while breaking up the other groups’ time into smaller, more specific events. To protect against this type of bias, the set of events selected for time-network analysis using the harmonic reciprocity method should be from the same strata of event sets, as illustrated in Figure 6.
In summary, the harmonic reciprocity method for constructing the time-network is sensitive to the number and scope of the events used for analysis: the method works best when the events encapsulate the contexts in which interaction actually takes place, and that the events have roughly equal levels of interaction. Therefore, to ensure fidelity of results and buy-in from employees, the set of events used for analysis should be agreed upon by everyone involved so that the conclusions are grounded in the culture it is a part of.
Modifications to the Method
No dataset is perfect. Your existing time-sheet records probably were not recorded with strict adherence to the above recommendations about event sets. In practicality, no time-sheet, existing or future, will perfectly follow the recommendations. That is because time-sheets are primarily for the purpose of billing a client, not for internal record-keeping of the time-network. So, to accommodate an imperfect event set, one could assign an interaction coefficient, \(0 \le \alpha_e \le 1\), to each event, where a value of 1.0 implies maximum interaction. This way, more intimate events like tasks and meetings, where joint attention is more likely, can be weighted accordingly with a coefficient close to 1.0, while larger, less interaction-intensive events (or events that are more spread out) can be assigned smaller coefficients.
In this case, if an interaction coefficient was less than 1.0 for a given event, a portion of an actor’s time spent towards that event, \((1-\alpha_e)x_{ie}\) to be exact, would get redirected into a separate, individual ‘event’ for that actor. For example, if one worked eight hours towards a project with a coefficient of 0.25, two hours would be logged to the shared project event, while six hours would be funneled into the actor’s personal event. This modification to the method is a pre-processing step that adds personal ‘events’ for each actor, and if this step is taken, it results in an augmented time-sheet with \(M^* = M + N\) events.
Additionally, for events with high degrees of interaction but multiple focal points of attention, such as a party, treating it as a single focal point will overestimate overlap, but adjusting it with a simple interaction coefficient would under-estimate interaction. To increase the accuracy of the results for these types of events, where the focal point of attention is not clear, one could give actors the option to mutually modify the time-network.
Consider a party with 30 people that lasted two hours. Using the harmonic reciprocity method (with an interaction coefficient of 1.0), each person’s time would be split evenly with everyone else, i.e. four minutes of ‘mutual-time’ with each other person, and four minutes attributed to ‘self-time’. But at parties, while there is a lot of mixing; people tend to clump together into small groups.
So, to capture this localizing effect, actors could mutually modify the time-network. The way this would work is that if actor A said that they spent 25 minutes with actor B, but actor B only wrote down 15 minutes, their mutual-time would be 15 minutes, and the 10 extra minutes that actor A thought they spent with actor B would be transferred to their ‘self-time’. Only the reciprocated amount would get counted as ‘mutual-time’, preserving the symmetric structure of the time-network. Thus, if mutual-time and/or time-network overlap were incentivized, adjusting one’s time-network values from an event would only be advantageous if the change was coordinated with the other people involved.
Example Application
So far, the examples explored in this article only involve up to three actors and one event. To demonstrate what a larger time-network would look like, such as what would be more typical in an organization, let’s take this a step further. Let’s say instead we have a time-sheet of seven employees working on four projects: employees E1 through E7, and projects P1 through P4, with the cumulative time-sheet history as shown in Table 2 below.
Table 2: Example Time-Sheet Matrix
Assuming that the set of events used (P1, P2, P3, and P4) adequately captures the focal points of attention, such that \(\hat\tau_{ij} \approx \tau_{ij}\), the time-network matrix \(\mathbf{\tau}\) can be estimated using the harmonic reciprocity method.
Excel Application
To estimate the time-network matrix index in Excel, apply the following LAMBDA function to the time-sheet matrix in Excel:
=LAMBDA(x,MMULT(x,TRANSPOSE(x/BYCOL(x,SUM))))UCINET Application
Alternatively, in UCINET, a commonly-used software for social network analysis,20 this can be done via the command line interface with the following command, where “x” is the dataset with the time-sheet records oriented as in Table 2:
tau = product(x,transpose(colstoch(x)))The rows (or columns) of the resulting time-network, shown in Table 3 below, are the time-network profiles of the employees, and the sum of each employee’s time-network profile is equal to their corresponding row sum in the time-sheet (Table 2).
Table 3: Example Time-Network Matrix
Comparing time-network profiles can reveal interpersonal patterns. For example, by examining the bar-chart of the time-network profiles of employees E1 & E7 shown in Figure 7, it is immediately clear that they do not have very much overlap. This may be because these two employees were working on different teams, or perhaps because of hidden interpersonal conflict.
This analysis admittedly does not reveal the underlying causes of any problems in the network, but it can serve to guide an HR practitioner to potential points for intervention. For example, the only noteworthy overlap between employees E1 & E7 is their shared experience with employees E5 & E6. Knowing this, one could hypothesize that employees E5 & E6 act as an intermediate link between employees E1 & E7. Insights like this, drawn from the time-network, could help HR practitioners understand the hidden structure of their organization and make better decisions in times of crisis.
In contrast to employees E1 & E7, the time-network profiles of employees E1 & E3 overlap a lot. This overlap, clearly visible in Figure 8, is evidence that these two actors likely work closely together. But exactly how much overlap do they have? To calculate the precise amount of overlap between any two actors, follow the instructions below:
Excel Application
In Excel, apply the following LAMBDA function in Excel to the previously calculated time-network matrix.
=LAMBDA(tau,MAKEARRAY(ROWS(tau),ROWS(tau),LAMBDA(i,j,SUM(MAP(CHOOSEROWS(tau,i),CHOOSEROWS(tau,j),MIN)))))UCINET Application
Or, if you are using UCINET, this can be done directly with the “Data → Affiliations (2 mode to 1 mode)” tool, with the “Sum of cross-minimums” method applied to the time-network matrix as shown in the dialog box below:
The results, using the example time-network in this article, should match the values in Table 4 below:
Table 4: Example Time-Network Overlap Matrix
The resulting matrix is called the ‘time-network overlap matrix’, or ‘overlap matrix’ for short. Note that the diagonal of the overlap matrix (and the maximum value of each column) is equal to each actor’s tenure, also shown by the column totals in Tables 2 & 3. This part of the overlap matrix, one’s overlap with oneself, exists regardless of the level of interaction. Additionally, it is already incentivized in organizations, as people are paid for their individual hours. So, if the goal is to create a workplace where people feel connected, it is the overlap between actors that matters.
As was demonstrated in this example, time-network analysis can be easily implemented with existing spreadsheet or social network analysis software, regardless of the number of actors or events. Using the provided Excel LAMBDA functions (or the corresponding UCINET features), you can estimate the time-network and overlap matrix of your organization today!
For convenience, the example above is provided in an Excel file at the bottom of this article.
Limitations and Future Research
Time-network analysis is a new method for analyzing social networks, and could potentially be a new paradigm for the field. But every model has its limitations. Specifically, the ‘harmonic reciprocity’ method presented in this article for constructing the time-network is sensitive to the set of events used for analysis. The results also only estimate potential for interaction between actors, as direct measurement of joint attention would take away from the spontaneity needed for genuine human connection.
For these reasons, making decisions based on the time-network alone is not recommended. Multiple sources of data, both qualitative and quantitative, are needed to ground the analysis in the multidimensional nature of lived experience. For example, one could analyze the time-network in conjunction with a ‘trust network’ constructed through a qualitative survey, and analyze the correlations between the two. Or one could compare the time-network and the ‘communication network’ to see how time spent on projects together affects communication patterns.21 The time-network is only one piece of the puzzle, and future research is required to determine exactly what it can and cannot reveal about an organization.
It is also currently an open question as to how the time-network could effectively be factored into incentives, and what effect it would have on an organization. For example, if time-network overlap was incentivized, it would encourage employees to work with people they are not familiar with, breaking down silos. But silos can provide stability, so an over-emphasis on overlap may result in a chaotic, overly redundant system. Therefore, not only should the time-network be paired with other network measurement approaches for grounding the analysis, but the time-network also should not be used as the sole basis for performance evaluation. It should be paired with qualitative evaluations and quality of work.
Nevertheless, the time-network represents an important dimension of organizational life. Those with substantial amounts of time-network overlap with others are critical for maintaining a sense of cohesion and unity in a complex organization. They are the connectors, the team players, the cornerstones of corporate culture.
Conclusion
If time is money, time spent with others is a shared asset. This is why shared experiences are so important for employee retention. The more that people feel invested in the people they work with, the less likely they will want to leave. So, if you want to slash turnover rates and create a workplace where people feel connected, you should care about the social dimension of time: the time-network.
The time-network estimates how much time people invest in others around them, and can easily be calculated with existing time-sheets using the method presented in this article. Future research is needed to determine exactly what the time-network can and cannot reveal, and how it can effectively be implemented in incentive systems, but its ease of measurement and explanatory power makes it an attractive candidate for monitoring the health of an organization.
- Original Broadway Cast of Rent, Seasons of Love, Rent (Original Broadway Cast Recording), 1996. ↩︎
- The dualism presented in this article, of self-time and mutual-time, is inspired by the philosopher Martin Buber’s dualism of “I-It” and “I-Thou”. Self-time would correspond to time spend in the world of “I-It”, while mutual-time would represent time spent in the reality of “I-Thou”. Buber argues that it is through mutual relations that one accesses and addresses the “eternal Thou”.
Martin Buber, I and Thou, trans. Ronald Gregor Smith (Martino Publishing, 2010), 75. ↩︎ - Assuming eight hours of sleep a night, the 40 hour workweek takes up 35.7% of a worker’s conscious life. ↩︎
- Shane McFeely and Ben Wigert, “This Fixable Problem Costs US Businesses $1 Trillion,” Gallup Workplace, 2019. ↩︎
- Marcus Hayes et al., “Measuring the ‘I’ in DE&I,” ADP Research Institute. United States of America, 2021. ↩︎
- Nan Lin, Social Capital: A Theory of Social Structure and Action, Repr, Structural Analysis in the Social Sciences 19 (Cambridge Univ. Pr, 2007). ↩︎
- Elinor Ostrom, ed., Trust and Reciprocity: Interdisciplinary Lessons from Experimental Research, 1. papercover ed., 2. [print.], The Russell Sage Foundation Series on Trust, vol. 6 (Russell Sage Foundation, 2005), 8. ↩︎
- Phillip Bonacich, “Technique for Analyzing Overlapping Memberships,” Sociological Methodology 4 (1972): 176–85, JSTOR, https://doi.org/10.2307/270732. ↩︎
- Wouter Wolf et al., “Joint Attention, Shared Goals, and Social Bonding.,” British Journal of Psychology (London, England : 1953) (England) 107, no. 2 (2016): 322–37, https://doi.org/10.1111/bjop.12144. ↩︎
- “Joint Attention and the Problem of Other Minds,” in Joint Attention: Communication and Other Minds: Issues in Philosophy and Psychology, ed. Naomi Eilan and Johannes Roessler (Clarendon Press ; New York : Oxford University Press, 2005). ↩︎
- Mutual attention is the basic phenomenon of eye-contact: A is attending to B and B is attending to A. Joint attention is more flexible: A and B are both attending to X, and A and B are mutually aware of each other’s attention. Joint attention can be sustained for longer periods of time and therefore is the primary basis for the concept of mutual-time, but time spent in mutual attention is also fully mutual. Additionally, moments of mutual attention are required to establish and sustain joint attention with another person. Therefore, for completeness, mutual-time includes both joint and mutual attention.
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