I have taken for granted that our sense of time is founded on our sense of space and that this is an example of embodied thought. A recent paper (citation below) examines this assumption and shows it far from clear.

Kranjec and Chatterjee say:

Is time an embodied concept? People often talk and think about temporal concepts in terms of space. This observation, along with linguistic and experimental behavioral data documenting a close conceptual relation between space and time, is often interpreted as evidence that temporal concepts are embodied. However, there is little neural data supporting the idea that our temporal concepts are grounded in sensorimotor representations. This lack of evidence may be because it is still unclear how an embodied concept of time should be expressed in the brain. The present paper sets out to characterize the kinds of evidence that would support or challenge embodied accounts of time. Of main interest are theoretical issues concerning (1) whether space, as a mediating concept for time, is itself best understood as embodied and (2) whether embodied theories should attempt to bypass space by investigating temporal conceptual grounding in neural systems that instantiate time perception.

In their analysis they stick very tightly to two theoretical ideas. The first is that simulation is the method of embodiment. To prove an embodied representation, one needs to find sensory or motor neurons whose activity is grounding the representation. The second is that abstraction of concepts relies on relational schema as outlined by Lakoff and Johnson. These schema can either be verbal in nature (and left hemisphere in location) or analog in nature (and right hemisphere in location). They use the research of Kemmerer is show some neural differences in processing space and time

In the end the question is left open – Is space embodied? Is time embodied through space? This is not surprising given their assumptions of embodiment necessarily implying simulation and schema. But if we think about it, what is there of a primary sensory nature or of a primary motor nature to ground space or time in the sense of motor and sensory neuron activity? We do not directly physically sense space or time nor do we use our muscles to directly affect them. They are part of the framework and not things perceived, except as the where and when other things are perceived. And they are not things done, except as the where and when of actions done.

Instead space seems grounded in the activity of the hippocampus and nearby cortex, in the form of activity of space cells, grid cells, heading cells, border cells and a library of location maps. And time seems grounded in the sequential moments of memory, again in the form of the hippocampal and related activity. In seems a reasonable idea to include the machinery of memory along with the machinery of the senses and of muscular activity as part of the body that gives cognition its grounding. It is the process of consciousness that is likely to create not only the ‘self’ and the ‘world’ but also the ‘here’ and the ‘now’ as a structure, a model of reality, into which objects and movements can be placed and which the hippocampus can remember.

Kranjec, A., & Chatterjee, A. (2010). Are Temporal Concepts Embodied? A Challenge for Cognitive Neuroscience Frontiers in Psychology, 1 DOI: 10.3389/fpsyg.2010.00240