The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann
|See Water in Zero Gravity, by Backreaction|
Is it possible for us to get this “sense of being” without understanding what momentum is? Do we say it just feels right or do we say that something flows according to the way in which we think about time? If you were to say things must be discrete by nature then how would any logic flow from the idea of such particularization?
Can I realistically call such a sphere in space a spherical cow? For a moment consider that such a collapse will be of acoustical variety type that we can say in the absence of earths constraints we can see how the universe likes to appeal to our nature of particularization by producing particles for which we can examine the substructure of the world we live in, in science?
In the case of discrete measure how is it such a transfer can take place in mind that the experience becomes part and parcel of the greater reality “of moving in abstract spaces?” Do we say this is reality but one as such configured and mathematically devised so as to seek correlations in the world that make sense?
Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulationFrom Flatland to Hypergraphics: Interacting with Higher Dimensions
I am trying to formulate a response in regard to the opening question in title. So please be patient with me as things appear in this blog posting.
|Title page of the 1st edition of Isaac Newton‘s Principia defining the laws of motion.|
Mōmentum was not merely the motion, which was mōtus, but was the power residing in a moving object, captured by today’s mathematical definitions. A mōtus, “movement”, was a stage in any sort of change, while velocitas, “swiftness”, captured only speed. The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists. The first of these was Byzantine philosopher John Philoponus, in his commentary to Aristotle´s Physics. As regards the natural motion of bodies falling through a medium, Aristotle’s verdict that the speed is proportional to the weight of the moving bodies and indirectly proportional to the density of the medium is disproved by Philoponus through appeal to the same kind of experiment that Galileo was to carry out centuries later. This idea was refined by the European philosophers Peter Olivi and Jean Buridan. Buridan referred to impetus being proportional to the weight times the speed. Moreover, Buridan’s theory was different to his predecessor’s in that he did not consider impetus to be self dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus.
Of course I am always interested in the history of what Momentum might mean. How this is built conceptually and historically so as to define this by a method by which we may measure some thing realistically.
The somatosensory system is a diverse sensory system composed of the receptors and processing centres to produce the sensory modalities such as touch, temperature, proprioception (body position), and nociception (pain). The sensory receptors cover the skin and epithelia, skeletal muscles, bones and joints, internal organs, and the cardiovascular system. While touch (also, more formally, tactition; adjectival form: “tactile” or “somatosensory”) is considered one of the five traditional senses, the impression of touch is formed from several modalities. In medicine, the colloquial term touch is usually replaced with somatic senses to better reflect the variety of mechanisms involved.
The system reacts to diverse stimuli using different receptors: thermoreceptors, nociceptors, mechanoreceptors and chemoreceptors. Transmission of information from the receptors passes via sensory nerves through tracts in the spinal cord and into the brain. Processing primarily occurs in the primary somatosensory area in the parietal lobe of the cerebral cortex.
At its simplest, the system works when activity in a sensory neuron is triggered by a specific stimulus such as heat; this signal eventually passes to an area in the brain uniquely attributed to that area on the body—this allows the processed stimulus to be felt at the correct location. The point-to-point mapping of the body surfaces in the brain is called a homunculus and is essential in the creation of a body image. This brain-surface (“cortical”) map is not immutable, however. Dramatic shifts can occur in response to stroke or injury.
Haptics are gaining widespread acceptance as a key part of virtual reality systems, adding the sense of touch to previously visual-only solutions. Most of these solutions use stylus-based haptic rendering, where the user interfaces to the virtual world via a tool or stylus, giving a form of interaction that is computationally realistic on today’s hardware. Systems are also being developed to use haptic interfaces for 3D modeling and design that are intended to give artists a virtual experience of real interactive modeling. Researchers from the University of Tokyo have developed 3D holograms that can be “touched” through haptic feedback using “acoustic radiation” to create a pressure sensation on a user’s hands. (See Future Section) The researchers, led by Hiroyuki Shinoda, currently have the technology on display at SIGGRAPH 2009 in New Orleans.