Last week … Volume : The volume of a solid object measures how much space it occupies.

1. Last week … • Volume: • The volume of a solid object measures how much space it occupies. • The volume of irregularly shaped objects can be determined by their displacement of a liquid. • Density: • The densityof a material is the mass per volume Lecture demo: Displacement of water by a butterfly and a sponge. density = mass / volume

2. Position • Context: Where are you? • Where are the keys? • Definition: • The position is the location in a • coordinate system, usually in two • or more dimensions. Location in a coordinate system • The position of an object is the • location of the center of the object. • The position of a person is a point • between the eyes. • Discussion: -Center means geometrical center or center of mass, … • - Position vs. Time graphs; symbol for position: x, symbol for time: t Lecture demo: Pendulum, Motion Detector and Computer

3. Out-of-body experiences with video feedback - Subject sees video image of itself with 3D goggles - Two sticks, one strokes person's chest for two minutes, second stick moves just under the camera lenses, as if it were touching the virtual body. - Synchronous stroking => people reported the sense of being outside their own bodies, looking at themselves from a distance where the camera is located. - While people were experiencing the illusion, the experimenter pretended to smash the virtual body by waving a hammer just below the cameras. Immediately, the subjects registered a threat response as measured by sensors on their skin. They sweated and their pulses raced. Real system & similar virtual system & bi-directional instant. coupling = mixed reality Blanke O et al.Linking OBEs and self processing to mental own body imagery at the temporo-parietal junction. J Neurosci 25:550-55 (2006).

4. Experimental evidence for mixed reality states in physical systems Objective: Understand synchronization between virtual and real systems. Approach: - Couple a real dynamical system to its virtual counterpart with an instantaneous bi-direction coupling. - Measure the amplitudes of both systems and their phase difference, and then detect synchronization.

5. Experimental evidence for mixed reality states in physical inter-reality systems Results: - Experimental evidence for a phase transition from dual reality states to mixed reality states. - Phase diagram of the inter-reality system is in good agreement with the phase diagram of the simulated inter-reality system. Phase diagram of the inter-reality system: amplitude of the coupling versus the frequency ratio of the real and the virtual system. The phase boundary between mixed reality states (I) and dual reality states (II). The solid, dashed, and dotted lines indicate the critical points in the experiment, simulation, and analytic theory, respectively.

6. Mixed reality states in physical systems: Why are they important? - Virtual systems match their real counter parts with ever-increasing accuracy. - New hardware for instantaneous bi-directional coupling - In mixed reality states there is no clear boundary between the real and the virtual system. Mixed reality states can be used to analyze and control real systems with high precision. And then there is the possibility for time travel … by the virtual system. Publication: The paper "Experimental evidence for mixed reality states in an inter-reality system" by Vadas Gintautas and Alfred Hubler, in Phys. Rev. E 75, 057201 (2007), was selected for the APS tip sheet: http://www.aps.org/about/tipsheets/tip68.cfm Photo: A. Hubler and V. Gintautas at the inter-reality system

7. DisplacementContext: Where are we going?Definition: • Displacement describes the change in • Position • Discussion: • Distance is the magnitude of the displacement • Velocity is the rate of change in position • Symbol for displacement: Δx Displacement and Distance Traveled

8. VelocityContext: Where are we going?Definition: • Velocity is the rate of change in position. • Velocity describes how fast something moves. • Discussion: • - Symbol for displacement: v = Δx / Δt • whereΔx is displacement and Δt is time lapsed • - Units: mph, m/s, km/h • Velocity = 0 => object at rest • Motion with constant velocity: • + frictionless horizontal motion • + sinking object in viscous fluid • + parachute • + motion without push or pull • Speed is the magnitude • of the velocity

9. Acceleration • Context: A car accelerates. • I am speeding up. • Definition: • Acceleration how fast does fast • change. • Acceleration the rate of change of the velocity. • Discussion: • Symbol: a, Units: m/s2 • Acceleration = 0 => velocity =constant • Motion with constant acceleration: free fall in vacuum, rolling • down an incline, washers on a string, circular motion with const. speed

10. Position, velocity, acceleration • The position of an object is the • location of the center of the object. • The position of a person is a point • between the eyes. • Velocity is the rate of change in • position. • Velocity describes how f ast • something moves. • Acceleration describes how fast • does fast change. • - Acceleration describes how rapidly an object is speeding up. • - Acceleration the rate of change of the velocity.