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Introduction
The dimensions and degrees of freedom of system underlie many natural phenomena. Dimensional capacity, implicit in Galileo's scaling, appears to play a role in biological scaling including metabolic scaling, collective intelligence, black body radiation, wind gust scaling, Brownian motion, dark energy, etc. Models for diverse systems discussed in the various articles on RG rely on dimension and degrees of freedom.
Skills and Expertise
Education
September 1973 - June 1976
September 1969 - May 1973
Publications
Publications (173)
Repeated incremental application of reductionism to a cluster of lexical, allometry, radiation and dark energy scaling ideas from 2005 until now leads essentially to Galileo's scaling induced by dimension notched up from 3D to 4D. The result gives a theoretical explanation of 3/4 metabolic scaling, dark energy and other phenomena.
Physics World on September 27, 2024 referred to a 2023 Nature paper, Park, M., Leahey, E. & Funk, R.J. Papers and patents are becoming less disruptive over time. Nature 613, 138–144 (2023). https://doi.org/10.1038/s41586-022-05543-x.
That led to a paper on arxiv, Kang, Huquan / Fu, Luoyi / Funk, Russell J. / Wang, Xinbing / Ding, Jiaxin / Liang, Sh...
This is a revision of the preceding RG article I posted, On Galileo, Clausius, et al. explaining dark energy. The main conceptual change is using mathematical induction on the number of dimensions to move from 3D to 4D systems. The idea of adding mathematical induction occurred to me after posting the previous article. I think of this as bootstrapp...
This is a provisional draft of article on dark energy.
An explanation for dark energy has eluded physics since it was discovered in 1998. Here astronomy's assumed equality of redshift and luminosity supernovae distance measurements of is assumed to be false. The assumption replacing it is a generalization of principles of dimensional capacity implicit in Galileo's \textit{Two New Sciences}: luminosity...
The June 19, 2024 newsletter from The Economist says that particle physicists and theoretical physicists dislike dark energy. The reason is that `No-one really knows what dark energy is'. Suppose dark energy can be explained by an approach based on Galileo. Then the conundrum dark energy so far poses for science may be more significant for revealin...
Differential scaling applicable to 3D weight M relative 2D area A in Galileo's Two New Sciences, extended to include rates by Sarrus, Rameaux, leads to 4/3 scaling and possible modeling of dark energy.
In allometry generally, on an increase in animal size, $(D+1)/D$ disproportionally scales an invariant ratio's $D+1$ dimension numerator compared to its $D$ dimension denominator. Allometric scaling reinstates invariance. In particular, 3/4 does not scale metabolism; it allometrically scales 4/3 differentially scaled oversupply of materials transpo...
Principles of differential scaling implicit in Galileo's Two New Sciences, expressed by an equation in a recently posted article, provide an explanation for dark energy.
Galileo I's principles of differential and allometric scaling are used to derive differential scaling principles for distance, energy time and entropy in dual reference frames.
Principles of 4/3 differential scaling in Galileo I and Galileo IIIa are applied to cosmology. Cosmological theories and astronomical observations support the validity of Galileo I and Galileo IIIa.
Principles in Galileo I on differential and allometric scaling and in Galileo IIIa are here applied to some cases in physics.
Principles in the article Galileo I: Principles of differential scaling and of allometry are here applied to Galileo's animal bone scaling, Kleiber's Law, brain weight scaling and Peto's Paradox.
This article intends to provide a summary of current principles of differential scaling and of allometry, based on Galileo's scaling in his Two New Sciences.
At a session on January 8, 2024, DES released its astronomical findings at the 243rd AAS meeting being held January 7 to 11, 2024. For the LambdaCDM model, DES found Omega_M = 0.291, close to 0.2967 implied by a theoretical 4/3 scaling of cosmological space.
Galileo's scaling in Two New Sciences is the basis for a general model of allometric scaling that applies to Kleiber's Law. The general model of allometric scaling based on Galileo is inconsistent with WBE, and contradicts WBE. Generalizing 4/3 scaling founded on Galileo's scaling has applications in biophysics and in physics generally.
Why scale factors have no role at all in allometric scaling.
Writing the recently posted article on why WBE is not correct illuminated the question of why allometric scaling does not account for the hierarchical scaling of the circulatory system. I have wondered about that for about 15 years. But on completing the WBE article, the solution presented itself in a minute. Leading to this article.
This article explains why West, G. B. / Brown, J. H. / Enquist, B. J., A General Model for the Origin of Allometric Scaling Laws in Biology, 1997 Science , Vol. 276, p. 122-126 is wrong in principle, theory, method and inferences, mainly because a geometric series is the wrong model, scale factors are the wrong method, and the dimensions of scale f...
Principles of dimensional capacity supply means for a small window of radiation that Thomas Gold conjectures in his 1962 article on the arrow of time.
Galileo showed that magnitudes of a beam's volume and cross-sectional area scale differently due to their different dimensions. But physical dimension is more fundamental than the mathematical scaling it induces. Some twentieth century problems unsolved using scaling --- metabolic scaling and dark energy are examples--- can be solved using dimensio...
This article gives online locations of the Bulletin de l'Acad\'emie Royale de m\'edecine de Paris, 1838, containing the synopsis of a submission to the Academy by Sarrus and Rameaux.
Changing the conceptual reference frame from energy use to energy supply gives a derivation of Kleiber's Law.
Translation into English of a report about a physiological study of soldiers by Sarrus and Rameaux related to their 1838 article on the rate of breathing.
If you wish to read this article, please download it. The appended excerpt from the 1839 Archives General journal does not, in the online reading version under the Overview tab, appear, at least...
Since 4/3 scaling, which applies to bounded, finite systems, as in metabolic scaling, Peto's paradox and brain weight scaling, also applies to unbounded expanding cosmological space, 4/3 scaling is probably valid and the mathematics of WBE 1997 is probably wrong.
A flowchart display of the logical steps.
A reasoning flowchart shows the pivotal extension from 3D to 4D in the argument for universal 4/3 scaling.
This paper intends to fill in a logical gap in a 2009 paper, A theory of intelligence. The mean path in a social network measures degrees of separation, or social distance, in steps or social connections, between pairs of people in the same generation --- horizontally. The principles underlying mean path length between contemporaries apply for cons...
4/3 scaling applies to Kleiber's Law and the expansion of cosmic space.
A one page (nutshell) derivation of Kleiber's Law based on degrees of freedom.
Generalizing Galileo's strength of materials scaling implies 4/3 scaling is a universal physical law, arising in brain weight / body weight scaling, metabolic scaling, Peto's paradox, black body radiation, the fractal envelope of Brownian motion, the expansion of space in cosmology and so on.
PDF of some of the original emails. Printed using an outlook reader evaluation copy from https://www.coolutils.com/TotalMailConverter.
In July 2005, after studying inference and language, I hypothesized that average IQs increase because the compression of information in ideas increases. In September 2005, I emailed James Flynn, of the eponymous Flynn Effect, about this hypothesis. After the September exchange of emails, I tried to find evidence for the hypothesis and an equation a...
Numerous instances of allometric quarter scaling occur in plants and animals. This article makes the case for quarter scaling and related 4/3 scaling as universal physical laws.
Mathematics implicit in allometric and similar scaling is here made explicit. Explicit mathematical modeling implies the physics applicable to phenomena that scale. The mathematics is demonstrated using examples from Galileo's \textit{Dialogues Concerning Two New Sciences} and Sarrus and Rameaux's work on how rates of heart beating scales with size...
An equation based on network entropy predicts a national economic growth rate from the rate at which national average IQs increase.
A society's problem solving intelligence can be quantified using its mean path length $\mu$ and clustering coefficient $C$. Societies and their ideas are small world networks. Knowledge transmission, acquisition and exchange occurs in human societies and from stored written records. $\mu$ and $C$ together with the principle that network degrees of...
The speculation by some philosophers and physicists that consciousness is unsolvable using physics can be refuted by the statistical mechanics of problem solving.
Scaling ideas of Galileo and of Sarrus and Rameaux translate, using ratios of dimensions, into an algebra of compared scale factor exponents. That algebra reveals that the scaled circulatory system of a similar larger animal has dimensional capacity to distribute energy that is 4/3 greater than the animal's scaled dimensional capacity to use that e...
Scaling ideas of Galileo in 1638, Sarrus and Rameaux in 1838 and West Brown and Enquist in 1997, modified and generalized, derive Kleiber's Law.
Comparing scale factors may help analyze metabolic scaling. This approach implies circulatory systems distributing blood-energy-scale by a 4/3 power of body mass. Invariance of the rate of energy use per cell, regardless of mammal size, requires 3/4 scaling of 4/3 scaled energy distribution. Summary
By analogy to the findings of Swadesh's glottochronology, facial expressions used by members of society likely diverge from the expressions used by the ancestral society at the rate of 5.6% per thousand years. If so, that slow rate and the difficulty of detecting it would explain the suggestion that facial expressions relating to emotion are innate...
Estimates of Omega_m after Betoule 2014 are also consistent with a 4/3 ratio of dimensions accounting for dark energy.
A 4:3 ratio of dimensions can account for expansion of the universe. Supportive astronomical theory and data are outlined.
The article, Deriving Kleiber's law from its history, recently posted, lays foundations for this article and would be good to read first.
A succinct derivation of Kleiber's Law.
More detail can be found on RG, including in Deriving Kleiber's law from its history
Scaling ideas used by Galileo in 1638, by Sarrus and Rameaux in 1838 and by West Brown and Enquist in 1997 help derive Kleiber's Law.
The paper is less than 5 1/2 pages.
Ideas in this paper lay the foundation for the more recent: RG article, Dark energy modeled by scaling
4/3 laws are often based on a ratio of the degrees of freedom of two systems. Applicable phenomena include dark energy, 3/4 scaling of metabolism (Kleiber's Law) and of brain weights, 4/3 scaling of wind eddies, isotropically radiated energy, Peto's cancer paradox, information distribution in social networks. How should 4/3 laws be introduced? By g...
This is a critique of Hayflick’s limit and the allometry of mammalian aging DOI: 10.13140/RG.2.2.33994.49609/4.
This is a revision of an article first posted on RG in December 2020 on the individual’s rate of thought, clarified, reorganized, and (hopefully) improved.
Heinrich Hertz observed that an equation, once discovered, sometimes seems wiser than its discoverer. E. T. Bell's paraphrase of Hertz's observation is often cited. This article gives the provenance of Hertz's original remark: ``Man kann diese wunderbare Theorie nicht studieren ohn bisweilen die Emfindung zu haben wohne den mathemitschen als seien...
The degrees of freedom of a network that distributes energy measures network output capacity. The degrees of freedom of a network using that energy measures use capacity. The ratio of degrees of freedom --- 4 --- of a system distributing energy and the corresponding system using energy --- with 3 degrees of freedom --- gives a 4/3 ratio of capaciti...
Degrees of freedom of an energy transmitter quantifies its capacity to distribute energy. Degrees of freedom of an energy receiver quantifies its capacity to use energy. The degrees of freedom of a transmitter increases with size by 4/3 times the degrees of freedom of the receiver: there are economies of scale, because transmitting capacity grows w...
English translation from the original German of Ludwig Boltzmann's 1884 article deriving Stefan's Law.
If the Hayflick limit is approximately invariant for normal mammalian cells for all mammalian species, Kleiber's Law applied to the Hayflick limit suggests an allometric scaling applies to mammalian ageing. In particular, human longevity can be allometrically estimated based on mouse longevity.
Dimensional capacity and its corollary 4/3 scaling laws can resolve Peto's 1977 cancer paradox.
The same universal 4/3 law, itself a consequence of the principle of dimensional capacity, underlies 3/4 scaling of brain weights and metabolisms.
English translation from the original German of Otto Snell's 1892 article.
The average individual human problem solving rate contradicts existence of a language organ or instinct.
This article adopts and expands on ideas in a book, The Intelligence of language, in a 2008 article on Lexical growth, and in a 2009 article on a Theory of intelligence to ground an argument against the hypothesis of a language organ.
Society's rate of collective problem solving R can be approximated using outputs such as lexical creation and improvement, technologies and economic growth. Three factors generate society's collective problem solving capacity: networked brains, concepts and average individual problem solving capacity r. If multiplicative factors representing networ...
Average IQs since about 1970, lighting efficiency expressed in lumens per labor cost per hour from 1750 B.C.E. to 1992, and the English lexicon from 1657 to 1989 all increased at similar rates, about 3.41% per decade. PGA Tour average drive distances from 1980 to 2018 increased by about 3.66% per decade. Are the rates measuring the same effect? The...
Here outlined are possible problems with a 4/3 law based on dimensional capacity and possible tactics for addressing those problems. 4/3 scaling relates to metabolic scaling, wind eddy scaling, Brownian fractal envelope and astronomical observations denoted dark energy, among other phenomena.
A society's management of its problem solving resources is analogous to management of financial assets. And vice versa.
The principle of dimensional capacity may qualify as one of `other laws of physics hitherto unknown' referred to in Schrodinger's What is Life?
Inferences implying the existence of dark energy are based on astronomical observations. The elusiveness of an explanation is due to the current omission from physics of principles based on dimensional capacity. Those principles imply that the same energy appearing in four dimensions has 4/3 as much energy per dimension in three dimensional space.
Society having a whole generation educated in school to be informed might improve society's ability to respond to a pandemic and collectively solve problems a pandemic raises.
Metabolism is slower for larger organisms than for small ones. Since the 1880s, if not earlier, a fractional exponent $b$ of organism mass $M$ has mathematically represented this physiology as metabolism $Y \propto M^b$ with $b<1$. Researchers since then have attempted to determine what value $b$ has and why. Instead of starting from $M^b$, after l...
The concepts of network entropy and clustering coefficient may assist in modeling virus transmission within societies.
Mathematical concepts compress solutions to problems involving natural and other phenomena. Hundreds of generations of human society have tested those solutions for their accuracy and utility and have continuously refined them. Those concepts likely often reflect fundamental aspects of the universe including phenomena not yet modeled, perhaps not y...
Astronomy infers existence of an unknown force denoted `dark energy' accelerating the expansion of space. Astronomy assumes matter decelerates expansion. Instead, apply by analogy the method of inverting conceptual reference frames and treat expanding space as the inertial reference frame. Gravitation appears as an apparent force because matter coh...
An animal's circulatory system and system of alveoli by theory should both scale with size by a 4/3 exponent.
The network effect of sharing losses among economic actors might increase chances of keeping more of the economy intact until the COVID-19 epidemic has run its course. The concepts of network entropy and dimensional capacity assist analysis.
In poetry, sometimes there are parallel structures and patterns based on words, phrasings, appearance (thinking of e. e. cummings): rhyming words, syllables per line, word play, witty and unexpected word pairings and contrasts, and so on. In physics there are also parallel patterns and structures, but instead of rhyming words, there are general or...
This about someone's great idea: a heat map to track the whereabouts and potential whereabouts of the virus.
Cell phones are almost ubiquitous. Soon, COVID-19 might also be ubiquitous? Can we use cell phones to fight epidemics?
Identifying everyone who is infectious is arguably our best strategy now. Universal and ongoing identification with enforced isolation of infectious persons might allow resumption of social and economic life.
This article raises questions: is identification, detection and isolation superior to mass social distancing? And is it feasible at this advanced stage of epidemic spread?
The role of the formula for network entropy suggests a way for the concept of the soul to arise. The word `soul' reifies absence, upon death, of a person from a social network. The effect of a person after they are absent from a network persists: soul.
This article gives an over view of, and references, several papers that provide an explanation of dark energy. A constant $4:3$ ratio of dimensions for contemporaneous spatial reference frames can account for expansion of the universe.
Two assumptions, the rate of spread and when diagnosis is possible permit a simplified model of an epidemic. The simplified model facilitates consideration of policy options for containment of the epidemic. The simplified model implies that international travel restrictions for a virus like COVID-19 can help slow the spread of the epidemic.
Network effects arising from individual action raise hope that in those actions individuals collectively and emergently will help limit the spread of COVID-19.
Actions by individuals to inhibit the transmission of COVID-19 may have substantial collective effects. The concepts of dimensional capacity and network entropy play a role in reaching that conclusion. In the case of person to person or proximity disease transmission, increasing COVID-19 transmission path length might reduce the rate at which the d...
This article compares COVID-19 transmission means to the dissemination of information over the internet as a means of combating COVID-19, not from the perspective of a health professional, but from a network perspective.
This paper is intended to lay out a theory that accounts for the expanding universe and provide reasons for the plausibility of the theory. The theory is based on dimension. Justification in part arises from noting that the 4/3 scaling that accounts for cosmological expansion is a universal law of nature, based on dimensional capacity, a fundamenta...
The formula for network entropy enables calculation of the average rate of individual human problem solving, absent language and social networking, about 5.6\% per thousand years. This article discusses some implications of an individual rate that low.
A formula for network entropy is analogous to the formula for thermodynamic entropy. Network entropy relates the rate of collective problem solving to the average rate of individual problem solving. By analogy network entropy can be applied to the genius concept in two ways. The first analogy is based on the relationship of the component factors in...
The principle of dimensional capacity observes that the capacity of a system to contain weight, heat, energy or information is proportional to its dimension, and more generally, to the system's degrees of freedom. The principle of dimensional capacity provides an alternative explanation to the many worlds hypothesis. The capacity exists for many wo...
Clausius named entropy, a concept he derived, in 1865. Ideas that arose after 1865, namely (1) mean path length in steps, (2) Boltzmann's logarithmic characterization of entropy, (3) Jensen's inequality and (4) dimensional capacity, help simplify the concept of entropy as it was originally presented by Clausius. Simplification has conceptual and pe...
A problem in the modeling of 3/4 metabolic scaling is analogous to the problem addressed by cosmological inflation. Perhaps both are resolved by the principle of dimensional capacity.
The principle of dimensional capacity relates to Shannon's definition of the capacity C of a discrete channel in his 1948 article on the mathematical theory of communication.
In Clausius's definition of entropy, he divides heat change by temperature. Why? This article attempts to address that question. The reasons appear to be: more degrees of freedom increases the capacity of a system (the principle of dimensional capacity). By assumption, an ideal heat engine is optimally efficient. Jensen's inequality implies that a...
The principle of dimensional capacity is not part of physics at December 2019. However, the principle of dimensional capacity seems to underlie simple modeling of 3/4 metabolic scaling, the 4/3 fractal envelope of Brownian motion and (so-called) dark energy. Perhaps convenience afforded by the principle of dimensional capacity outweighs the skeptic...
A very short paper.
An analogy of the universe to a Carnot ideal heat engine without the piston, so that the "working substance" in the heat engine "chamber" expands in an unbounded way when energy is added to the heat engine chamber.
An average individual rate of problem solving helps estimate that language is about 150,000 years old. Estimates of the average individual problem solving rate derive from glottochronology, the rate of phonemic change, and, using a statistical mechanical method, indirectly from society's collective problem solving rate.
Earlier papers considering n...
Lengths, areas and volumes scale differently because of their different dimensionality. A dimensional point of view provides a perspective different than that of scaling on the effect of an increase in size of a system having length, area and volume. Dimension is more fundamental since it is dimension that induces scaling when length increases in a...
This article reviews different, but not all independent, ways to arrive at the role of a network's mean path length as scale factor for network distribution of energy or information. Quantitative and theoretical uses of mean path length are briefly summarized in a separate paper posted in August 2019 on ResearchGate.
This paper therefore sets out...
A recent study finds that, based on a sample of 17 languages, the average rate of transmission of information is the same for all languages. That average rate of transmission of information and the rate of English lexical growth both appear to be instances of a universal collective problem solving rate. This paper explores qualitative reasons for i...
Using the mean path length as a scale factor leads to a formula for network entropy. Mean path length scaling has uses both quantitative and theoretical. Quantitative uses are available because the mean path length can be measured and in some cases can be estimated based on theoretical considerations. Theoretical uses mostly relate to the idea of d...
Ever so slightly changing Galileo's conceptual reference frame for explaining the effect of increased animal weight on the cross-sectional area of weight-bearing bones leads to a possible explanation of dark energy.
Ever so slightly changing Galileo's conceptual reference frame for explaining the effect of increased animal weight on the cross-sectional area of weight-bearing bones leads to a possible explanation of dark energy.
Questions
Questions (477)
Published 1934.
Teissier and Huxley coined allometry in 1936.
This is the French version of the article that appeared in Nature magazine in 1936, co-authored with Huxley.
I Googled this question on November 24, 2024.
The AI Google answer was:
"No, allometric scaling is not the inverse of Galileo differential scaling, but rather a change that deviates from isometry."
I think the AI answer is wrong. Reasons are in various RG articles, such as
Suppose the AI Google answer were correct. Why would an organism deviate from isometry? Are there articles that support the deviation from isometry point of view?
Fourier’s invention of Fourier series probably qualifies as a method that exceeded in importance the theory of heat in which it was developed.
Carnot’s idealized steam engine is another example.
I think extending Galileo’s 3D/2D differential scaling to 4D/3D is more important than problems for which it was developed, Kleiber’s Law and dark energy:
Can you give instances of where the method found assumed more importance than the problem to which the method was addressed?
And references?
Or some other mechanism?
As a response to Galileo differential scaling, metabolic scaling might best be characterized as a pull. The cell pulls in the resources it needs, and no more. The pull differentially scales down on an increase in animal size.
As in:
Are there articles about this?
His article is described as:
Cannon, W. B. (1926). Physiological Regulation of Normal States: Some Tentative Postulates Concerning Biological Homeostatics. Paris: Editions Medicales.
or,
Cannon, W.B. (1932) Physiological Regulation of Normal States: Some Tentative Postulates Concerning Biological Homeostatics. In: Pettit, A., Ed., A Charles Richet: Ses amis, ses colléges, ses eléves, Les Editions Medicales, Paris, 91-93. (In French)
Assuming that dark energy is resolved by Galileo 4/3 differential scaling, can resolution of dark energy be used to solve other cosmological problems? Problems for which that might be possible might include:
(1) Hubble tension
(2) Cosmic constant
(3) Cosmological inflation
(4) Gravity.
(5) Cosmic constant
If you solve these problems using Galileo 4/3 differential scaling, please advise where you have posted your answer.
Galileo 4/3 differential scaling is described in various RG papers, recently and mainly
and also
.
Hubble tension is the name given to a conflict of measurements of the Hubble constant that do not agree with each other. Using SN gives 73 km/sec per Mpsec, using CMB gives 67, all roughly.
If so how? And if it does, could it resolve the Hubble tension?
What the citations for the best resources for answers to this question?
This is a follow up question to: Are there any theories of dark energy that predict the value of omega_M? asked on RG on Oct 21, 2024.
Harri Shore kindly provided a comprehensive answer on RG the same day, explaining that Omega_M Is Typically Derived from Observations.
Scolnic, D. M. / Jones, D. O. / Rest, A. / Pan, Y. C. / others, in The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample 2018-06 ApJ , Vol. 859, No. 2 p. 101, estimated Omega_M. NASA (https://lambda.gsfc.nasa.gov/education/graphic_history/matterd.htm) describes Scolnic et al. study as “providing the tightest uncertainty obtained from this method in the plot”. The Pantheon 2018 estimate for Omega_M is 0.298 plus/minus 0.022.
The 4/3 theory predicts Omega_M as the denominator value in 4^3/3^3, which is 0.2967, very close to 0.298. For example, a recent discussion of 4/3 scaling based on Galileo is at:
Are there any articles laying out the math? If so, what are the cites for those articles?
