Ordered in sequence of presentations
|slides||Garnet Ord: The superposition principle and images in spacetime
Feynman’s path integral approach to the Young double-slit experiment makes it clear that phase and the superposition principle are necessary to obtain interference fringes. However, the origins of phase and superposition are not considered in the PI approach, and the relation to classical physics remains elegant but formal. In this work we show that both phase and superposition emerge from special relativity extended to account for binary periodic clocks in piecewise inertial frames. This pushes the peculiarities of quantum propagation back to the interaction of the two relativity postulates. The effects discussed are illustrated by considering images of binary clocks in spacetime diagrams.
|slides||Nick Greaves & Stephen Fry: Duplication theory
(A homage: “ALWAYS in the history of science when on the brink of a paradigm shift it is relatively impossible to teach anybody anything when so entrenched in career-long status quo”. — RL Amoroso, June 2015)
Nicholas Greaves (in a brief presentation by Stephen Fry) proposes a mechanism that postulates a common basis for three of the most blatantly unexplained phenomena confronting science:
– electromagnetic induction,
– morphic transmission in life forms, and
– memory (and even, by simple extension of memory: telepathy/ESP)
These are cases of transmission of form; of order-forming fields (EMF, etc); or, to generalize, of transmission of ‘order’ or ’arrangement’.
This powerful conjecture raises thrilling possibilities. It is based on consideration of degrees of similarity of patterns, structures, and/or events across time and/or space or both (T and S being initially approached as equivalent-base dimensions).
Scientists ask for ‘some mathematics to describe it’. In SF’s opinion it requires a new mathematics to deal with quantifying its terms and phenomena. This would be the mathematics of similarity – hoping one can approach quantification of the effect by quantification / classification of the degree of similarity of the cause. Reflecting Heisenberg, similarity of events at sub-atomic scale has a powerful effect; but similarity at macro scale on a vast numerical scale also has effect. The motivating factor is how close the Total Degree of Similarity (TDS) comes to absolute similarity – ‘Counter-Heisenberg Singularity’[CHS]). This similarity can take the form of repeat of arrangement in a physical system, events of change in that arrangement, repetition of individual events, or of vast events – all can become events with repetition close to singularity, and thus generate the effect; but to discuss the effects we need a mathematics to express the quantification and perhaps the interactions.
. . .
[An aside: Referring to the opening quote above, Greaves has always said his conjecture explains the immovability of established opinion in a population).
(A. Koestler wrote to encourage Greaves to keep going with his initial conjecture, about 2 years before R. Sheldrake first published Sheldrake makes a similar comment).
|slides||Anton Vrba: Are we limited to a mere relative reality?
According to H. Poincaré, only the purport of physical laws (P) and the geometry (G) combined as a whole can describe nature (N). Equally well, the expression (Nr)=(Gr)+(Pr) symbolically describes the relative reality as we understand it. The question that needs to be answered, is: Can we reverse engineer, by logical deduction, an alternate set of physical laws (Pa) if (Ga) is set to an Euclidean geometry? This talk investigates if an absolute reality (Na) is physically possible that correctly describes the observed.
|slides||Peter Rowlands: A Hierarchy of Symmetries|
|slides||Richard Amoroso: Goedelizing Fine Structure
Refer to this PDF document
|Anthony Booth: Stochastic wave process on Minkowski space – Lepton masses and possible baryon structure.
Following on from earlier reading to the ANPA group regarding continuum modelling of electrons (see ripple.pdf), a lower level of causal continuum model reaching into the general basis for leptons and thereby into possible hadron structures becomes possible. This same lower level model also produces a gravity that is Newtonian for short range but modifies in the long range as supports cosmological phenomena such as the galactic dark matter effect.
|slides||Nick Rossiter: Abstract Relations and Allegorical Categories
Representing relationships is a key activity in the physical sciences. Mathematically relations can be represented as a generalisation of the function in sets. There are a number of problems with such a treatment: the fundamental basis of set theory is discrete elements rather than morphisms between sets and there is no natural way of employing higher-level mappings as is often required for a full solution to real-world problems.
Category theory with its emphasis on morphisms and multilevel architecture is a promising candidate for representing relations. In recent ANPA proceedings the author has emphasised the potential of the Cartesian closed category, including the topos, in this respect. While the topos has emerged as the leading contender in meeting requirements for handling relations, there is discussion over whether the approach could be augmented by the use of the category REL (relation) as a categorification of the set theory concept. REL is not Cartesian closed, severely limiting its usability. Recognising the limitations of REL Freyd and Scedrov, working in pure category theory, have developed the category of allegories.
The purpose of the current presentation is to understand the limitations in REL, to describe allegorical categories and to explore and evaluate their use in conjunction with the topos approach described earlier.
|slides||Louis Kauffman: Braiding, Fermions and Physics
We begin with ideas from discrete physics and show how the complex numbers, the split quaternions and indeed all of matrix algebra arises from observing simple discrete dynamical systems. We show how the Schrodinger equation and the Dirac equation can be viewed in this context and how the Rowlands Nilpotent aproach to the Dirac equation fits into this way of thinking. We then concentrate on Majorana Fermion operators and their relation to topological braiding.
|slides||Louis Kauffman: Knots and Higher Categories
This talk will be an introduction to category theory by way of knots and diagrams. A knot diagram is an example of an infinitely high category. Space is based on knots. Lets see where we can go from there.
|Stephen Wood: Triads of Life
The first half of the talk deals with phenomenological ecology and starts with certain personal encounters with birds in the field. These encounters illustrate the ornithological notion of ‘jizz,’ the characteristic way a bird appears to the watcher. I argue that jizz captures the notions of the ‘inscape’ and ‘instress’ proposed by Gerard Manley Hopkins and that Hopkins is in turn addressing the innate expressiveness of living beings, as described by Maurice Merleau-Ponty.
The second half of the talk deals with the systematics of John Bennett, where the qualitative significance of the numbers is seen to yield a series of complementary interpretations of a phenomenon. I briefly describe the progression of the systems, from monad to hexad, before focusing on the triad, where phenomena are seen as systems of process and relation. The triad consists of three impulses and six triads arise from their possible permutations, namely interaction, identity, creation, concentration, order and freedom. I draw together James Patton’s description of the general character of living processes with Hopkins’ identification of the three impulses, to sketch out the six triads of life. Particular emphasis is given to identity and freedom, which have no equivalent in mainstream science.
|write up||Anthony Blake: Dynamic systems of awareness
The most abstract and the most concrete may be closer than they seem. The link is dynamism, the structure of change. In mathematics we have operators and functions; in the physical body, dance. Bohm spoke of a proprioception of thought equivalent to that of bodily knowledge of position and movement. Structure involves at least two levels. A basic form is that one level is in a state of unity and the other in a state of multiplicity. In human experience they come together in what is often called ‘awareness’. The session will be largely experiential. People participate as they find fit. You are invited to move to patterns and music in a precise way. The movements used are derived from the work of G. I. Gurdjieff. The sensate experience of dynamic systems may help to illuminate abstract operations, though this cannot be predetermined.
|No Slides||Nicky Graves Gregory: Living Mathematics: n introductions
I shall introduce some of the notions of living mathematics in a number of ways, where n is a whole number greater than or equal to one. The introduction(s) may or may not come from the following list, in non-hierarchical order:
1. The circle and the vesica piscis
2. Truth, Beauty, the Good
3. The 5 perfect solids
4. 3 dimensions, 6 directions, +2
5. Is space more mysterious than time?
6. Mathematical grammar, including mathematics of gesture, mathematics of questions, 2nd person mathematics
7. Oneness is no-thingness – the mathematics of heterogeneity, quality and quantity
8. Is the human the measure of all things? Visual measure, aural measure.
9. Discreteness and integrity, integers and cell membranes, leaf light and rotting spinach.
10. Mathematics has meaning – the morality of knowing
There may be a practical component to my presentation.
|slides||Dino Buzzetti: Frederick Parker-Rhodes’ “Inferential Semantics”
An examination of the merits and limitations of Parker-Rhodes’ formalism to represent the deep semantic structure of empirical languages is attempted. In the face of a fruitful endeavour to formalise the context conducive to the listener’s interpretive act, the major drawback of Parker-Rhodes’ proposal lies in its concern to keep out self-reference phenomena. Various approaches to formalise self-reference are then considered and special attention is paid to control and self-organisation processes. In this respect, Kálmán’s realisation theory of dynamic control systems and Spencer Brown’s calculus of indications prove to be particularly relevant.
|withheld||Michael Heather: Euler’s Identity as the signature of the Topos or the (so called) beauty of mathematics|
|slides||Paul Mountcastle: Radar and Quantum Mechanics
Radar signal processing has become very sophisticated in the last fifty years, fueled in part by discovery of the fast Fourier transform in 1965, and with it the field of digital signal processing. Fundamentally, we now look at the radar instrument as something that acquires and processes the transfer function of the world, in a sense that I will try to communicate concretely via examples. Something (an electromagnetic signal or signals) is transmitted. This object admits a finite operational description in terms of a set of Fourier coefficients labeled by some indices that are discrete and finite in number. Something of exactly the same kind is received by the instrument. In the signal processor, even the ideas of “the signal transmitted” and “the signal received” lose genuine operational significance. The instrument measures and places side-by-side in its local memory bank the elements of a complex vector-valued transfer function, the quotient of these two signal objects. The processor then performs certain definite arithmetic operations on this quotient vector to obtain quantities that we (classical observers) consider to have physical sense. The arithmetic operations constitute in all cases projection from a discrete complex vector space of measurement onto a real, positive, continuous space of generalized coordinates that may (without sacrificing logical sense) be identified as a probability density. The dimensions of this projective space are just the parameters that are needed to specify a physical model of phase of the transfer function.
I will describe the radar measurement process and the associated signal processing in a general language. To correctly capture polarization effects, the vector space ought to be promoted from complex to complex quaternion-valued. This is known to radar people, but is usually considered too much trouble to bother with from the purely practical point-of-view. The elements of the polarized transfer function each contain an amplitude and a phase factor (the determinant), but also factors belonging the six-parameter group SL(2,C) of 2×2 complex matrices with determinant unity. We know that objects of that kind are capable of representing classical rotations and boosts in a very definite way. The group SL(2,C) is said by mathematicians to be isomorphic to the Lorentz group in the same way that SU(2) elements are isomorphic with the three-parameter rotation group. The radar description of measurement appears to correspond to quantum mechanics in all significant respects, except that the frequencies of the signals are regarded classically either as occupying a continuous band of the electromagnetic spectrum, or as occupying a lattice with uniform spacing in frequency. This assumption is violated by the quantum phenomena. From the radar view, it can be relaxed without modifying much of anything else. A program is suggested for identifying all of the conventional classical quantities as model parameters.
|slides||Geoffrey Constable: Rotations
Linear velocity is relative but angular velocity is absolute – an apparent paradox and one that is addressed in this presentation.
In earlier ANPA presentations it was argued that Quantum Jelly (QJ) is the ether that facilitates the transmission of electromagnetic radiation. It was also argued that, in order to overcome difficulties associated with ‘ether wind’, QJ is insensitive to relative linear velocity.
In this presentation it will be shown that QJ consists of short-lived, transient, entities generated by particles with half-integral ‘spin’, such particles being located predominantly at the extremities of the universe. It will be proposed that, irrespective of whether the universe itself rotates, QJ establishes a datum whereby any rotation within the universe can be detected and measured.
It will also be proposed that, as a mathematical device, the ‘short-lived and transient entities’ that constitute QJ possess mass and locations that can be described as almost entirely ‘imaginary’, time within QJ remaining ‘real’. As a consequence of this device, the velocity of QJ components becomes imaginary, while angular velocity remains real. Force can be exerted by such entities but in reverse to associated accelerations.
By the use of proposals such as these, the paradox is resolved. Angular velocity, as measured against QJ and thus the universe as a whole, is as relative as linear velocity. Moreover, QJ can exert the forces whereby rotation can be measured (as with a tuning fork gyro) or observed (as with a precessing flywheel gyro).