Teleological theories are often dismissed in the study of animal behaviour, because of both the anthropomorphic element, and the paradox of retro-causation. Instead, emergent properties of animal systems, such as those which drive behaviour and decision making, are generally deemed to be non-purposeful. Nonetheless, organisms’ interactions with the environment, including sensory processing, have long been subject to biological study, and the resulting models include Jakob von Uexküll’s functional circle (part of his ‘Umwelt Theory’). The functional circle is modelled on an (...) assumption of three- dimensional space containing matter and energy, and one-dimensional, linear time. Moreover, the function of such models relies upon feedback within biological systems, and generally assume that the functional feedback loops close. I argue that this is impossible, because a feedback loop cannot go back intime to close itself, and so whilst it may approximate closure in space, it does not close in the dimension of time. To address this problem, I propose a conceptual model where time is treated as having a three- dimensional structure, and is measured in terms of past, future, and subjective present, termed the ‘period,’ ‘present’ and ‘phase,’ respectively. Space and matter, meanwhile, occur as a two- dimensional intersect, in which three-dimensional emergent properties which occur ion time are embedded. The model relies on functional helices rather than circles, and the loops of each helix (unlike circular loops) never achieve closure. I explain how this therefore results in a biological system, based on both feedback and anticipatory probabilities, which is both autopoietic and teleological. I also provide examples of how the concept can be applied, using foraging behaviour as an example. I further propose the theoretical origin of such a system is ‘timing’ and ‘rhythm,’ both of which I argue have their origins in single cellular organisms’ chemotaxis and the associated gradient descent search. (shrink)