Our most cutting-edge virtual reality remains focused on visual perception over embodiment. This article presents a dance performance project that stems from a foundation in somatics, creative dance, and HCI to embrace the challenge of centering bodies and embodiment within virtual reality. Our team of choreographers, dancers, and technologists recount the two-year development of the 360 video through ideation, movement tracking workshops, prototyping, process share-outs, to a final performance, to reflect on how our goal to centre bodies guided our artistic and technology choices throughout the entire process of making. Space became a key theme as we refined the choreography and design to use the full potentialities of the immersive environment. Place became a key theme as we prioritised configurations that enabled the performance to be showcased in the Pacific, Eastern Europe and Latin America. We discuss challenges and opportunities for supporting embodiment in virtual reality dance performance.

There are decades of work investigating how to support users in inhabiting avatars’ bodies in immersive experiences, however we are still learning about how Virtual Reality (VR) can support people in more deeply inhabiting their own bodies. Over the course of five action research workshops, we explored the design space for how VR can support feeling embodied and generating movement within a dance context. We explored design factors and participants’ experiences within: games intended to stimulate physical movement, single player and multiplayer 3D painting, 360 live video, and custom real-time audio and visual feedback based on motion capture. We found that participants spontaneously explored collaboration including synchronous, asynchronous, remote and collocated. Where there were mismatches between visual and kinesthetic perceptions, participants explored how to recalibrate, alternate between, and integrate perceptions. Participants were compelled to explore their control of real-time effects, which led to rich movement generation as we iterated through the effects’ parameters. We present a design space that encapsulates the insights of our action research, with axes for control, collaboration, auditory and visual feedback. We discuss implications for the support of immersive embodiment in dance.

Mid-air arm movements are important for various activities. However, common resources for their self-directed practice require practitioners to divide their focus between an external source (e.g., a video screen) and moving. Past research found benefits for egocentric guidance visualizations compared to common resources. However, there is limited evidence about how such visualizations should look and behave. EGuide supports the investigation of different egocentric visualizations for the guidance of mid-air arm movements. We compared two visual appearances for egocentric guidance visualizations that differ in their shape (look), and three guidance techniques that differ by how they guide a user (behavior). For visualizations with a continuously moving guidance technique, our results suggest a higher movement accuracy for a realistic than an abstract shape. For user experience and preference, our results suggest that visualizations with an abstract shape and a guidance technique that visualizes important postures should not pause at important postures.

Abstract Let denote the collection of all Π10 classes, ordered by inclusion. A collection of Turing degrees in is called invariant over if there is some collection of Π10 classes representing exactly the degrees such that is invariant under automorphisms of . Herein we expand the known degree invariant classes of , previously including only {0} and the array noncomputable degrees, to include all highn and non-lown degrees for n > 2. This is a corollary to a very general definability result. The result is carried out in a substructure G of , within which the techniques used model those used by Cholak and Harrington [6] to obtain the same definability for the c.e. sets. We work back and forth between G and to show that this definability in G gives the desired degree invariance over .

We investigate the notion of K-triviality for closed sets and continuous functions in 2ℕ. For every K-trivial degree d, there exists a closed set of degree d and a continuous function of degree d. Every K-trivial closed set contains a K-trivial real. There exists a K-trivial Π10 class with no computable elements. A closed set is K-trivial if and only if it is the set of zeroes of some K-trivial continuous function. We give a density result for the Medvedev degrees of K-trivial Π10 sets. If W ≤TA′, then W can compute a path through every A′-decidable random closed set if and only if W ≡TA′.

We investigate notions of randomness in the space C[2 N] of nonempty closed subsets of {0, 1} N. A probability measure is given and a version of the Martin-Löf test for randomness is defined. Π 0 2 random closed sets exist but there are no random Π 0 1 closed sets. It is shown that any random 4 closed set is perfect, has measure 0, and has box dimension log2. A 3 random closed set has no n-c.e. elements. A closed subset of 2 N may be defined as the set of infinite paths through a tree and so the problem of compressibility of trees is explored. If Tn = T ∩ {0, 1} n, then for any random closed set [T] where T has no dead ends, K(Tn) ≥ n − O(1) but for any k, K(Tn) ≤ 2 n−k + O(1), where K(σ) is the prefix-free complexity of σ ∈ {0, 1} ∗. 1

Abstract We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.