Papers by Blair Macdonald
'Fractals are everywhere'; but for the large-scale galaxy distribution in observable universe, by... more 'Fractals are everywhere'; but for the large-scale galaxy distribution in observable universe, by the 2012 WiggleZ Dark Energy Survey, they were ruled out. They were however, granted on small cosmic scales, as claimed by proponents, and notwithstanding the ensuing enigma of explaining the standard model of cosmology 'very large' cosmic structures (LQGs) have indeed-as predicted-have been observed in the large-scale universe since the WiggleZ survey. Can a (different) fractal model explain all these cosmological observations and conjectures, and if so, are we are modeling the fractal the universe incorrectly? An experiment was conducted on a 'simple' (Koch snowflake) fractal from the perspective of an observer within a growing/emergent fractal-'looking' in iteration-time. The fractal was inverted-to show what the fractal looks like back to its origin; new triangle sizes were held constant allowing earlier triangles in the set to expand as the set iterated. Classical kinematic equations of velocities and accelerations were calculated for total area total and the distance between points. Hubble-Lemaitre's Law and other cosmological observations and conjectures was tested for. Results showed area(s) expanded exponentially from an arbitrary starting position; and as a consequence, the distances between pointsfrom any location within the set-receded away from the 'observer' at increasing velocities and accelerations. It was concluded that the fractal is a geometrical match to the cosmological problems. It explains: Hubble-Lemaitre and accelerated expansion; inhomogeneous (and said fractal) galaxy distribution on scale and large scales; and other problems-including the cosmological catastrophe and the early inflationary expansion epoch of the universe. Also, the fractal offers a direct mechanism to the cosmological problem and can further explain the quantum problem-unifying the two realities as being two aspects of the same geometry.
viXra, Sep 1, 2021
Fractal geometry is an accepted mathematical description of nature. One of the great questions in... more Fractal geometry is an accepted mathematical description of nature. One of the great questions in cosmology-along with what is the 'dark energy' and the other cosmic anomalies-is whether the universe is also fractal? The 2012 WiggleZ Dark Energy Survey found, in agreement with fractal-cosmology proponents, the small-scale observable universe is fractal, the large-scale is not fractal. Fractals have not been modelled from the perspective of being within a growing one. Can a (different) fractal model explain all cosmological observations and conjectures, and if so, are we are modelling the fractal universe incorrectly? An experiment was conducted on a 'simple' (Koch snowflake) fractal, testing the perspective of an in-situ observer within a growing/emergent fractal-'looking back' in iteration-time to its origin. New triangle sizes were held constant allowing earlier triangles in the set to expand as the set iterated. Classical kinematic equations of velocities and accelerations were calculated for the total area total and the distance between points. Hubble-Lemaitre's Law and other cosmological observations and conjectures were tested for. Results showed area(s) expanded exponentially from an arbitrary starting position; and as a consequence, the distances between points-from any location within the set-receded away from the 'observer' at increasing velocities and accelerations. It was concluded, at the expense of the cosmological principle, that the fractal is a geometrical match to the cosmological problems, including the inflation epoch, Hubble-Lemaitre and accelerated expansion; inhomogeneous (fractal) galaxy distribution on the small and homogenous on large scales; and other problems-including the cosmological catastrophe. The fractal may offer a direct mechanism to the cosmological problem and can further explain the quantum problem-unifying the two realities as being two aspects of the same geometry.
viXra, 2015
Global income has increased exponentially over the last two hundred years; while, and at the same... more Global income has increased exponentially over the last two hundred years; while, and at the same time respective Gini coefficients have also increased: this investigation tested whether this pattern is a property of the mathematical geometry termed a fractal attractor. The Koch Snowflake fractal was selected and inverted to best model economic production and growth: all triangle area sizes in the fractal grew with iteration-time from an arbitrary size – growing the total set. Area of triangle the ‘bits’ represented wealth. Kinematic analysis – velocity and acceleration – was undertaken, and it was noted growing triangles propagate in a sinusoidal spiral. Using Lorenz curve and Gini methods, bit size distribution – for each iteration-time – was graphed. The curves produced matched the regular Lorenz curve shape and expanded out to the right with fractal growth – increasing the corresponding Gini coefficients: contradicting Kuznets cycles. The ‘gap’ between iteration triangle sizes (...
The Koch snowflake fractal attractor was analysed by Lorenz and Gini methods. It was found the fr... more The Koch snowflake fractal attractor was analysed by Lorenz and Gini methods. It was found the fractal Lorenz curve fits the wealth (stock) distribution Lorenz curve. Gini coefficient analysis showed an increasing coefficient by iteration (time). It was concluded the Lorenz distribution is a property of the fractal and inextricably linked to (fractal) growth and development.
Fractal geometry is found universally and is said to be one of the best descriptions of our reali... more Fractal geometry is found universally and is said to be one of the best descriptions of our reality-from clouds and trees, to market price behaviour. As a fractal structure emerges-the repeating of a simple rule-it appears to share direct properties familiar to classical economics, including production, consumption, and equilibrium. This paper was an investigation into whether the mathematical principles behind 'the market'known as marginalism-is an aspect or manifestation of a fractal geometry or attractor. Total and marginal areas (assumed to stand for utility) and the cost of production were graphed as the fractal grew and compared to a classical interpretation of diminishing marginal utility theory, and the market supply and demand. PED and PES was also calculated and analysed with respect to (iteration) time and decay. It was found the fractal attractor demonstrates properties and best models classical economic theory and from this it was deduced the market is a fractal attractor phenomenon where all properties are inextricably linked. The fractal, at equilibrium, appears to be a convergent-zeta function-series, able to be described by Fourier analysis, and involves Pi, i, e, 0, and 1 (of Euler's identity) in one model. It also demonstrated growth, development, evolution and Say's Law-production before consumption. Insights from the fractal on knowledge and knowing are also revealed, with implications on the 2 question of what exactly is 'science'-and what is 'art'? A connect between reality and quantum mechanics was identified. It was concluded marginal, classical economics is an aspect of a universal fractal geometry.
Making sense of the nearly 100-hundred-year-old quantum nature of light and matter, with its-to n... more Making sense of the nearly 100-hundred-year-old quantum nature of light and matter, with its-to name a few-wave-particle duality, measurement problem, and entanglement 'spooky action at the distance'-remains the greatest questions to physics. Since the 1980s, fractal geometry, a new and exciting field of mathematicsthat the fathers of quantum mechanics did not have and has not been tested for quantum properties-has developed. Can the isolated fractal explain the quantum? An experiment was conducted on a simple-but isolated-fractal testing whether the geometry of fractals corresponds to quantum enigmas. It was found the isolated fractal emerges by a duality of propagation-of an oscillating sinusoidal wave-of 'bits'-of information-iterating in a superposition of time, scale, and symmetry, with a possible constant speed, demonstrating all the hypothesised. The quantum 'measurement problem' was addressed as being a problem of isolated scale-invariant fractals-or fractal landscapes-where position is only 'known' when additional (fractal) information is added-which 'equally' gives rise to a (quantum-like) 'uncertainty' problem. Also, quantum entanglement and other quantum features were explained by the fractal model. Consequences of the model were discussed, notably to its relevance to the nature of light (the speed of it etc.), the behaviour of the atom, time, knowledge and our reality, and the model's direct inextricable connection with cosmological observations and conjectures. Finally, it was concluded that the model is preliminary but fundamental.
Current greenhouse theory is incomplete: it does not include Raman spectroscopy and is incorrectl... more Current greenhouse theory is incomplete: it does not include Raman spectroscopy and is incorrectly based on the special group of 'Tyndall' greenhouse gases, which are really the thermoelectric (TE-IR) gases, as detected only by thermoelectric transducers. It's premise: 'the non-GHGs Nitrogen and Oxygen do not absorb or emit infrared radiation' presents a paradox, it contradicts both quantum mechanics and thermodynamics-where all matter above absolute 0 0 Kelvin radiates IR photons. These (above) molecules possess quantum predicted emission spectra within the IR range of the EMS-at 2338cm-1 and 1556cm-1 respectively-but are only observed, and temperatures from them measured, by Raman Spectrometers, 'IR spectrometers' complement instrument. This was investigated by quantum and thermoelectric theory and application. A report of Raman spectrometer measurements on jet engine outlet temperatures and gas concentrations was referring to, and the following conclusions made: 1) all Raman modes (the non-GHGs) are temperature/radiation equivalent to 'IR-active modes with respect to-and complying with-the Boltzmann and Planck's constant, and quantum spectroscopy theory; 2) in support, H2O's 3659cm-1 mode is both TE-IR and Raman equivalent-supporting the 'equipartition' principle; and CO2's temperature can be measured by both instruments independently through its shared modes; 3) the special (1%) greenhouse gases, discovered by Tyndall in ca. 1859, are really the thermoelectric gases, detected only by receiving (nonradiating) thermo-electric transducers; 4) 'IR' spectroscopy is also based on these thermoelectric transducers, and as a consequence 'IR' spectrographs show only the spectra modes with electric dipoles and not Raman; 5) N2 , when radiated at it's 2338cm-1 mode, is (long lasting) metastable, and is essential to the operation of a CO2 Laser: from this mechanism, it was concluded-contrary to current greenhouse theory-atmospheric CO2 is heated by the same mechanism; 6) all the atmosphere absorbs heat directly from the Sun-just as with the oceanic euphotic layer.
This spreadsheet model is to complement publications relating to the fractal.
Greenhouse theory has at its foundation a special group of trace gases and molecules. Together th... more Greenhouse theory has at its foundation a special group of trace gases and molecules. Together these gases are claimed to be the only ones that absorb infrared radiation. The assumption that the remaining gases, nitrogen and oxygen, do not absorb or emit infrared radiation presents a paradox; it contradicts both quantum mechanics and the laws of thermodynamics which prescribes that all matter above absolute zero degrees Kelvin radiates infrared photons. In this study the role of thermoelectric detectors as used to determine the 'infrared atmosphere' was investigated. This study hypothesises that current greenhouse theory has misinterpreted the significance of those special greenhouse gases (CO2 etc.) since they and their spectral 'modes' are detected only by thermoelectric transducers: that they are the thermoelectric gases. It was concluded that the special (1%) greenhouse gases, discovered by Tyndall in ca. 1859, are really only those detected by thermo-electric transducers. 'IR' spectroscopy is also based on these thermoelectric transducers, and as a consequence 'IR' spectrographs show only the spectral modes with electric dipoles and not Raman modes. All current Blackbody radiation theory is determined from thermoelectric measurements alone and requires revision in light of complementary modern Raman laser Spectroscopy measurements. From this thermoelectric understanding in conjunction with modern Raman Spectroscopy, it was concluded that current greenhouse theory is incomplete and misconceived. All of the atmosphere radiates IR radiation in compliance with the said laws. The only thing separating the gases are the instruments detecting them.
viXra, 2016
Continuing the debate on whether the universe is fractal by nature: an experiment was undertaken ... more Continuing the debate on whether the universe is fractal by nature: an experiment was undertaken on the ‘simple’ Koch Snowflake fractal to test whether fractal geometry matches observations and conjectures. The Koch Snowflake was inverted to model observations from within an iterating fractal set it: simulating a static or ‘measured’ position. Converse to the fractal snowflake emergence – where triangle sizes diminish; the sizes of new triangles were held constant, and earlier triangles in the set expanded as the set iterated. Kinematic velocities and accelerations were calculated for both the area expansion of the total fractal, and the distance between points and the ‘observer’ within the fractal set. The inverted fractal was tested for the Hubble's Law. It was found area(s) expanded exponentially; and as a consequence, the distances between points – from arbitrary locations within the set – receded away from the ‘observer’ at increasing velocities and accelerations. The model...
<p>Figure 13. Acceleration the inverted fractal at each corresponding iteration time (t): (... more <p>Figure 13. Acceleration the inverted fractal at each corresponding iteration time (t): (A) expansion of total area, and (B) distance between points. u = arbitrary length.</p> <p>The fractal demonstrates Hubble's Law and accelerating expansion (cosmological constant). All fractals expand at accelerating rates - trees are the best example.</p> <p>Publication pending.</p
viXra, 2015
In a recent publication it was discovered trees growth rate accelerates with age. Trees are descr... more In a recent publication it was discovered trees growth rate accelerates with age. Trees are described as being clear examples of natural fractals. Do fractals offer insight to the accelerating expansion? In this investigation the classical (Koch snowflake) fractal was inverted to model the growth of a fractals seen from a fixed – new growth – perspective. New triangle area sizes represented new branch volume; these new triangles were held constant allowing earlier triangles in the set to expand as the fractal set iterated (grew) through time. Velocities and accelerations were calculated for both the area of the total fractal, and the distance between points within the fractal set using classical kinematic equations. It was discovered that the area(s) of earlier triangles expanded exponentially, and as a consequence the total snowflake area grew exponentially. Distances between points (nodes) – from any location within the fractal set – receded away at exponentially increasing veloci...
viXra, 2018
Greenhouse theory (and radiation theory as a whole) presents a paradox and contradicts both quant... more Greenhouse theory (and radiation theory as a whole) presents a paradox and contradicts both quantum mechanics and thermodynamics. Its premise claims molecular nitrogen and oxygen (99 percent of the dry atmosphere) do not transfer (emit or absorb infrared) radiation at any temperature; however, all matter above absolute zero Kelvin radiates IR photons, and ‘air’ is a very poor thermal conductor of heat (0.0262 W/(m K)) – so how does it transfer heat? It was hypothesised these gases do radiate IR photons at their quantum mechanics predicted spectra at 2338cm-1 and 1556cm-1 respectively, and these predicted spectra are observed by (thermoelectric based) IR spectroscopy’s complement instrument, the Raman Spectrometer. It was found the nitrogen and oxygen do possess quantum predicted emission spectra both within the IR range of the EMS, and these are only observed – and their respective temperatures and concentrations accurately measured – by Raman laser Spectrometers. It was concluded: ...
Climate science's fundamental premise-assumed by all parties in the great climate debate-says the... more Climate science's fundamental premise-assumed by all parties in the great climate debate-says the greenhouse gases-constituting less than 2% of Earth's atmosphere; first derived by John Tyndall's in his 1859 thermopile experiment, and demonstrated graphically today by infrared IR spectroscopy-are special because of their IR (heat) absorbing property. From this, it is-paradoxicallyassumed the (remaining 98%) non-greenhouse gases N2 nitrogen and O2 oxygen are non-heat absorbent. This paper reveals, by elementary physics, the (deceptive) role thermopiles play in this paradox. It was found: for a special group substances-all sharing (at least one) electric dipole moment-i.e. CO2, and the other greenhouse gases-thermopiles-via the thermoelectric (Seebeck) effect-generate electricity from the radiated IR. Devices using the thermopile as a detector (e.g. IR spectrographs) discriminate, and have misinterpreted IR absorption for anomalies of electricity production-between the sample gases and a control heat source. N2 and O2 were found to have (as all substances) predicted vibrational modes (derived by the Schrodinger quantum equation) at 1556cm-1 and 2330cm-1 respectively-well within the IR range of the EM spectrum and are clearly observed-as expected-with Raman Spectroscopy-IR spectroscopy's complement instrument. The non-greenhouse gases N2 and O2 are relegated to greenhouse gases, and Earth's atmospheric thermoelectric spectrum was produced (formally IR spectrum), and was augmented with the Raman observations. It was concluded the said greenhouses gases are not special, but typical; and all substances have thermal absorption properties, as measured by their respective heat capacities.
Is the universe a fractal? This is one of the great-though not often talked aboutquestions in cos... more Is the universe a fractal? This is one of the great-though not often talked aboutquestions in cosmology. In my earlier publication where I inverted (Koch snowflake) fractal I showed the fractal demonstrated: Hubble's Law, accelerating expansion, and a singularity beginning. Surveys of the universe-the most recent and largest, the 2012 WiggleZ Dark Energy Survey-show, galaxy distribution on small scales to be fractal, while on large-scales, homogeneity holds. There appears to be new anomaly to explain: a galaxy distribution transition from rough to smooth with cosmic distance. From my model I derived a Fractal-Hubble diagram. On this diagram, measurement points along the curve are clustered near the origin. This clustering was not addressed in discussions or part of the conclusion of my earlier experiment. Can this clustering of points account for the observed galaxy distribution transition? Could this transition be another property of fractals, and therefore could the universe-itself-be fractal? It was found, yes they do. Clustering of measurement points (and of galaxies) is as a result of observation position in the fractal. On small scales-relative to large scalesthe cosmic surveys are what one would expect to see if one were viewing from within an iterating-growing-fractal. If trees-natural fractals that have also been found to grow at accelerating rates-are used to demonstrate this fractal: the large-scale smoothness maybe akin to a tree's trunk; and the rough (fractal) on small-scales, to its branches. This discovery unifies the anomalies associated with the standard cosmological model. Together they are-through the mechanics of the fractalinextricably linked.
<p>Figure 12. The Fractal/Hubble diagram: recessional velocity vs. distance between triangl... more <p>Figure 12. The Fractal/Hubble diagram: recessional velocity vs. distance between triangle geometric centres points. As distance increases from a fixed observation point, the recession velocity of the points increases. u = arbitrary length unit. t = arbitrary time unit.</p> <p>Publication pending.</p
This diagram shows the quantum predicted spectra of the infrared atmosphere. It distinguishes bet... more This diagram shows the quantum predicted spectra of the infrared atmosphere. It distinguishes between the thermoelectric (IR) and the Raman active spectra. It also shows the 19th century derived 'blackbody' curve for the Sun (b) and the Earth (c). The curve 'a' is the 20-century correction curve derived by Raman spectroscopy. This curve is my work and I aim to change radiation and greenhouse theory with it. Raman spectrometers through the Boltzmann constant measure the temperature of the shown molecules. All matter radiates and that includes the gases of the atmosphere.<br>In my two papers( Quantum Mechanics and Raman Spectroscopy Refute Greenhouse Theory and The Greenhouse Gases and Infrared Radiation Misconceived by Thermoelectric Transducers ) I expose and address this discrepancy. I call it a systematic error that has played itself out over the last 160 years; Raman spectroscopy had solved it.
This spreadsheet model is to complement the publication 'Fractal Geometry a Possible Explanat... more This spreadsheet model is to complement the publication 'Fractal Geometry a Possible Explanation to the Accelerating Expansion of the Universe and Other Standard ΛCMB Model Anomalies'.
The (Koch Snowflake) fractal (above) is a wave like object.<br>As can be seen that the peri... more The (Koch Snowflake) fractal (above) is a wave like object.<br>As can be seen that the perimeter of the formed fractal is made-up of an infinity of triangles/'particles' and these together act as or form a wave. When a change is made to one of the triangles (the red dot on iteration 0) and this change iterated, as demonstrated, the wave is revealed. Any change to the triangles/ particles will 'mutate' or change the shape of the fractal and be viewed as a pulse, propagating, cycling round and round every 6 iterations (in the case of the Koch Snowflake), forming, if one were to view a change made to the fractal from a Front Elevation view, a pulse in the form of a classic wave.<br>The wave will range through an infinitely of scales: from infinitely large amplitudes, frequencies, and wavelengths, – down to, but never reaching zero. The wave will move or be produced at fractal production speed.There are issues of spin direction too. The spiral can spin in both directions, clockwise and or anti-clockwise.
<p>All is described on the diagram itself.</p
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Papers by Blair Macdonald