Department of Education estimates that 60 percent of all new jobs in the early 21st century will require skills that only 20 percent of the current workforce possesses. Collectively, we call these changed ways of thinking and acting the “lattice ways” as shown in Figure 2. And it marks an inflection point in the ways careers are built, work is done and participation in organizations is fostered. It represents the multidirectional, flexible and expansive nature of how successful organizations work today. The corporate lattice metaphor signals a shift in mindset and outlook as we cross the chasm from the Industrial Age to the knowledge economy. In the real world, lattice structures are evident everywhere from a garden’s wooden trellis to the metalwork of the Eiffel Tower to the emerging matrix structures and network models companies are adopting. In mathematics, a lattice is a three-dimensional structure that extends infinitely in any direction. The corporate lattice model, in contrast to the traditional ladder, is more adaptive, and therefore better suited to align with the changing needs, norms and expectations of today’s workplace. The convergence of these trends, summarized in Figure 1, irreversibly alters the corporate landscape.įigure 1: Forces driving the changing world of work From ladder to lattice
In just about every way, employees are more diverse than ever – including their very definitions of success.
6 Younger generations are bringing different attitudes about what it takes to motivate them at the same time older workers are looking for flexible options to stay in the labor market. 5 Men in dual-career couples now report one-third greater work-life conflict than women. workforce and are the primary breadwinners in 40 percent of U.S. families mirroring the “traditional” structure upon which the ladder model was built, where Dad works and Mom stays at home. Family structures have changed markedly, with a mere one in six U.S. The workforce isn’t what it used to be either. 3 Project work, one example of nonroutine activity, has increased 40-fold over the past 20 years, making collaboration and teamwork more important than ever. And the work itself is less routine, with the growth in nonroutine tasks outpacing routine tasks by 20 percentage points since 1960. 2 Technological advances, globalization and the rise of knowledge work have resulted in work and workers being less bound to physical locations or set hours teams are often dispersed across locations and time zones. 1 Organizational structures are, on average, 25 percent flatter than they were 20 years ago. While 60 percent of corporate value creation once depended on hard assets, now more than 85 percent relies on the intangible assets of brand, people and intellectual property. Ultimately, the ladder’s one-size-fits-all approach assumes employees are more alike than different, and want and need similar things to deliver results.īut the workplace isn’t what it used to be. It defines career success as a linear climb to the top. Its hierarchical structure governs how information flows and whose ideas matter. The ladder proffers a worldview in which power, rewards and access to information are tied to the rung each employee occupies. See also the ProofWiki definitions of Convex set and Interval (coincide with the ones I referred to).The corporate ladder model took hold at a time when the central business goal in the emerging industrial economy was achieving economies of scale. While the closed interval is, of course, defined as in the other answer.Īpparently the definition is not standard. (I think that Davey and Priestley only refer to closed intervals, but I'm not sure.) These references seem never to define formally what is an interval, but always refer to an interval as a closed interval, $$, an open interval, $(a,b)$ or an half-open interval, $(a,b]$ or $[a,b)$, where $a\leq b$. This is the definition given in Introduction to Lattices and Order, by Davey and Priestley, page 63 (in the second edition) and also in General Lattice Theory, by Grätzer, page 21 (in the second edition too). I was amazed that people call intervals to such subsets of posets Īs far as I am concern, a subset $C$ of a poset $P$ satisfying the property $p \in C$ whenever $a,b \in C$, $p \in P$ and $a\leq p \leq b$ is called a convex set. The answer given (and already accepted) gives what seems to be the definition of interval of a poset, according to its Wikipedia article which is also linked to in a comment.
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