One very old and pervasive habit of thought is to imagine that the true answer to whatever question we are wondering about lies out there in some eternal domain of "timeless truths." The aim of re-search is then to "discover" the answer or solution in that already existing timeless domain. For example, physicists often speak as if the final theory of everything already exists in a vast timeless Platonic space of mathematical objects. This is thinking outside of time.
Scientists are thinking in time when we conceive of our task as the invention of genuinely novel ideas to describe newly discovered phenomena, and novel mathematical structures to express them. If we think outside of time, we believe these ideas somehow "existed" before we invented them. If we think in time we see no reason to presume that.
The contrast between thinking in time and thinking outside of time can be seen in many domains of human thought and action. We are thinking outside of time when, faced with a technological or social problem to solve, we assume the possible approaches are already determined by a set of absolute pre-existing categories. We are thinking in time when we understand that progress in technology, society and science happens by the invention of genuinely novel ideas, strategies, and novel forms of social organization.
The idea that truth is timeless and resides outside the universe was the essence of Plato's philosophy, exemplified in the parable of the slave boy that was meant to argue that discovery is merely remembering. This is reflected in the philosophy of mathematics called Platonism, which is the belief that there are two ways of existing. Regular physical things exist in the universe and are subject to time and change, while mathematical objects exist in a timeless realm. The division of the world into a time-drenched Earthly realm of life, death, change and decay, surrounded by a heavenly sphere of perfect eternal truth, framed both ancient science and Christian religion.
If we imagine that the task of physics is the discovery of a timeless mathematical object that is isomorphic to the history of the world, then we imagine that the truth to the universe lies outside the universe. This is such a familiar habit of thought that we fail to see its absurdity: if the universe is all that exists then how can something exist outside of it for it to be isomorphic to?
On the other hand, if we take the reality of time as evident, then there can be no mathematical object that is perfectly isomorphic to the world, because one property of the real world that is not shared by any mathematical object is that it is always some moment. Indeed, as Charles Sanders Pierce first observed, the hypothesis that the laws of physics evolved through the history of the world is necessary if we are to have a rational understanding of why one particular set of laws hold, rather than others.
Thinking outside of time often implies the existence of an imagined realm outside the universe where the truth lies. This is a religious idea, because it means that explanations and justifications ultimately refer to something outside of the world we experience ourselves to be a part of. If we insist there is nothing outside the universe, not even abstract ideas or mathematical objects, we are forced to find the causes of phenomena entirely within our universe. So thinking in time is also thinking within the one universe of phenomena our observations show us to inhabit.
Among contemporary cosmologists and physicists, proponents of eternal inflation and timeless quantum cosmology are thinking outside of time. Proponents of evolutionary and cyclic cosmological scenarios are thinking in time. If you think in time you worry about time ending at space-time singularities. If you think outside of time this is an ignorable problem because you believe reality is the whole history of the world at once.
Darwinian evolutionary biology is the prototype for thinking in time because at its heart is the realization that natural processes developing in time can lead to the creation of genuinely novel structures. Even novel laws can emerge when the structures to which they apply come to exist. Evolutionary dynamics has no need of abstract and vast spaces like all the possible viable animals, DNA sequences, sets of proteins, or biological laws. Exaptations are too unpredictable and too dependent on the whole suite of living creatures to be analyzed and coded into properties of DNA sequences. Better, as Stuart Kauffman proposes, to think of evolutionary dynamics as the exploration, in time, by the biosphere, of the adjacent possible.
The same goes for the evolution of technologies, economies and societies. The poverty of the conception that economic markets tend to unique equilibria, independent of their histories, shows the danger of thinking outside of time. Meanwhile the path dependence that Brian Arthur and others show is necessary to understand real markets illustrates the kind of insights that are gotten by thinking in time.
Thinking in time is not relativism, it is a form of relationalism. Truth can be both time bound and objective, when it is about objects that only exist once they are invented, by evolution or human thought.
When we think in time we recognize the human capacity to invent genuinely novel constructions and solutions to problems. When we think about the organizations and societies we live and work in outside of time we unquestioningly accept their strictures, and seek to manipulate the levers of bureaucracy as if they had an absolute reason to be there. When we think about organizations in time we recognize that every feature of them is a result of their history and everything about them is negotiable and subject to improvement by the invention of novel ways of doing things.