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Weibull Analysis of Arch Collapses
Get PDFArches are one of the wonders of nature. Their seemingly physics-defying appearance has made them a popular attraction all over the world. Though these enigmatic structures are made of rock, they are fragile and are likely to collapse at some point due to several environmental factors associated with physical and chemical erosion, or even arson. Arch collapse is specifically interesting to the creation model as an indicator of youth, since they collapse regularly but are not presently forming at great rates. Arches have been discussed by Faulkner (2024) and others, but there is not a comprehensive explanation of the mechanism, age, and evolution of arches in the young earth creation model. This could give us insight into post-Flood processes.
We are left with a quandary. Statistically, we are dealing with the population of arches, rather than a single arch. This distinguishes this study from the few conventional studies that examine the degradation of a single arch. The question remains: how should we aim to understand the lifespan of the population of arches?
Weibull analysis is a statistical engineering technique used to understand failure characteristics in populations which experience aging processes. This paper applies Weibull analysis to arch collapses to constrain the total lifetime of a population of arches under the assumption that they formed around the same time. This is expected to better reflect the physical changes that arches undergo than the constant failure rate model assumed by Faulkner (2024).
An unsuccessful attempt to validate the total count of arch collapses in Morton (2020) was made, including scholarly articles, two online arch databases, and inquiries to Arches National Park. Therefore, four synthetic arch collapse datasets were created to validate the Weibull analysis methodology. The datasets consist of collapse dates of arches, which are used to derive total lifetimes.
The failure analysis yields two parameters, the shape (β, determines how the failure rate changes over time) and scale (η, represents characteristic lifetime), which define the distribution of failure ages (in this case an arch collapse). One of the things to determine is how much collapse data is necessary to be able to separate different failure models. We also created a failure probability calculator, which can provide forward-looking predictions of failure rates based on model parameters and applied it to a scenario like the arches at Arches NP. Predictions of the next likely arch collapse, and the total lifespan of remaining arches were made for each synthetic model.
Weibull analysis was successful in finding the statistical parameters of the synthetic datasets. It was able to distinguish between distinct populations with only 50 years of arch collapse observations, so can potentially be used with real-world collapse observations. The precision of the estimated parameters is dependent on the number of collapses observed during the timeframe. If the real formation date is unidentifiable, then potentially geological context and collapse comparisons can be used to find it. An estimate of the number of prior collapses improved accuracy and might be needed for real-world analyses. Analyzed lifespan error in real arch populations may be governed by differing formation dates, and the number of unknown prior collapses.
Weibull analysis is useful for understanding the history of arches. By determining arch population lifetime parameters, it can constrain “backwards” the number of arches that have existed and can help constrain the time of formation. A Weibull model can be used to integrate observations of multiple parameters, e.g. comparing measured and modeled modern day collapse rates. This model can be tested on real arch populations through predictions of the rate of future arch collapses. The analysis could be improved by estimating the Weibull shape parameter by the method of moments. Future studies of arch collapse will focus on finding more verifiable arch collapses and integrating seismic and weather data to parameterize arch collapse rates. This model works and can be applied to real datasets to estimate formation dates, collapse dates, and future lifespan of arches.
REFERENCES
Faulkner, D. R. 2024. How long have arches been around? Answers In Depth 19. https://answersingenesis.org/geology/how-long-have-arches-been-around/. Accessed 2024-09-27.
Morton, M. C. 2020. The delicacy of arches. Eos 101. DOI: 10.1029/2020EO146523
Potential Flood Boundary Implications of the Superfamily Djadochtatherioidea in the Extinct Multituberculata Order Relating to the K-Pg Boundary Using the PBDB
Get PDFDefining the flood boundary in the fossil record has immense creation narrative value. Global extinction events are of major importance in identifying trends in the fossil record because a global flood would clearly cause major biotic turnover. Organisms which appear on either side of a major extinction event can reveal patterns of their dispersion given the event in question is the end of the flood. This idea ties closely to Arment’s Marsupial investigation, which demonstrates that Marsupials appear almost exclusively in Australia, suggesting a flood boundary after their appearance in the fossil record asserts that they migrate to the Ark and then immediately back to the same geographic location (2020). Studying other trends around proposed flood boundaries can reveal the unlikelihood of such chance migration.
Multituberculates are an extinct group of mammals which appear on either side of the K-Pg boundary. Because the K-Pg is often proposed as the end flood boundary, the pattern of this order reveals the likelihood of this boundary given dispersion patterns. The Multituberculate order has several superfamilies, the focus of which is Djadochtatherioidea. There is a large amount of undetermined phylogeny in the order, lending the opportunity for analysis of past taxonomical decisions and some regrouping. The first goal was to locate the global occurrences of the Djadochtatherioidea superfamily in the Paleobiology Database. The papers corresponding to the database entries were then used to study the specimens, as well as local stratigraphy, to determine the validity of the specimen and the validity of its date relative to the K-Pg boundary. The largest family in Djadochtatherioidea is Eucosmodontidae, found throughout North America on both sides of the K-Pg, and in Mongolia. Flynn describes specimens from the Cretaceous of New Mexico which are morphologically identifiable as Eucosmodontidae (1986). Krause similarly describes specimens from the early Eocene of Wyoming (1982). Both papers demonstrate the presence of Eucosmodontidae and Djadochtatherioidea on both sides on the North American K-Pg boundary. Lesser specimens are found in Mongolia. Analysis of papers linked with the PBDB localities of Djadochtatherioidea in Mongolia reveal only Cretaceous specimens.
These patterns demonstrate that the Djadochtatherioidea superfamily is likely a baramin which occupied modern North America and Mongolia and then dispersed to North America after the flood. The morphological similarity of the superfamily lends itself to single baramin classification, though more detailed work needs to be done to verify this. The global distribution of the superfamily does not prohibit the K-Pg boundary from being the end flood boundary, as it is entirely feasible that the kind existed in a few places, migrated to the ark, stayed morphologically similar during the flood years, and then the surviving individuals migrated to North America where some radiation occurred. Given the lack of return to Mongolia for the superfamily, it is not a case of unlikely remigration. It is important to note that this is a preliminary report on such findings. First, greater analysis of specimens must be done, Principal Component Analysis being the most obvious, before complete conclusions can be drawn on the baraminology of the group. Further, the order Multituberculata contains more superfamilies than Djadochtatherioidea, meaning more research regarding these other superfamilies must be conducted to determine if different patterns are present. However, this serves as a solid starting point regarding the Multituberculates and their story in the flood and its potential boundaries.
Arment, C. 2020. To the Ark, and Back Again? Using the Marsupial Fossil Record to Investigate the Post-Flood Boundary. Answers Research Journal 13: 1-22.
Flynn, L. 1986. Late Cretaceous Mammal Horizons from the San Juan Basin, New Mexico. American Museum Novitates no. 2845:1-30.
Krause, D. 1982. Multituberculates from the Wasatchian Land-Mammal Age, Early Eocene, of Western North America. Journal of Paleontology 56, no. 2:271-294
Does Biostratigraphy Work without Faunal Succession?
Get PDFBiostratigraphy is a methodology for determining relative timing of sedimentary deposits based on their fossil content. It foundationally assumes faunal succession—that fossil ordering arises because different organisms lived exclusively in different eras of history. Accordingly, first appearances and extinctions would be globally unique single moments in time. The highly dynamic Genesis Flood violates this assumption with all fossilized forms existing simultaneously at the beginning of the Flood and burial potentially occurring at any time dependent on specific process. To date, no one has simulated the fossil record under conditions expected during the Flood to test the effectiveness of biostratigraphic methods on the Flood-deposited fossil record when the fundamental assumptions have been transgressed. Can this lead to distorted interpretations of relative timing in some cases? Differences in character between Flood and post-Flood fossil assemblages could be used as a criterion for identifying the Flood terminal boundary (Whitmore and Garner, 2008). In this study, I simulate fossil records with different ordering style (true order, process order, successive inundation, endemism, and random), degree of ordering, and per-column fossil density. I then statistically compare the resulting timescales generated by automated graph-based biostratigraphic analyses. An additional set of experiments was run which compared the compatibility of geographically restricted biostratigraphic analyses with ones produced with full global knowledge. This simulates the historical development of the geologic column framework in Europe being later applied to new discoveries across the globe. The results of the simulations show that biostratigraphy consistently recovers the correct ordering of the fossil record when one exists. However, the method will also reliably produce a self-consistent global ordering even in cases where one does not exist, leading to timing distortions between distant columns. Higher precision in the interpreted biostratigraphic timescale increases time distortions. This timing distortion comes from having only a small number of index assemblage permutations preserved in direct relationship with each other in particular locations—an extremely stringent notion of the “completeness” of the fossil record. When such combinatorial completeness is low, as it is in the real fossil record, then global consistency of observed fossil “aboveness” cannot distinguish between a highly ordered and unordered fossil record. The experiments also show that fossil range extensions are positively correlated with timing distortions, as they represent inconsistencies between the interpreted biostratigraphic timescale and the actual fossil record. In the experiments testing the expansion of an initial framework to the global set of observations, the majority of simulations show complete consistency between restricted framework and global framework for all styles and degrees of ordering. The random and process order cases had significant minorities of simulations result in inconsistencies between frameworks, which could be manifest in reality as region-specific index taxa or initial index taxa becoming superseded. Zeller (1964) showed that both correlations of sections and interpretation of cyclicity could be made for sequences that had been generated from completely random data. Far from suggesting that these interpretations were always spurious, he provided a warning of applying interpretive methods in situations where they are inapplicable. He exhorted his readers to distinguish random events versus the necessary consequences of events, which are non-random, as a guide to careful interpretation of correlations. Similarly, biostratigraphy should be reliable when core methodological assumptions are met, but can yield false correlations otherwise. I consider several possible independent lines of evidence for relative timing that could validate the conditions necessary for successful biostratigraphic interpretations including radiometric methods, global isochronous events (e.g. impacts, megasequence boundaries), distant fossil-strata correspondences, and stratomorphic series. Currently, these independent chronometers can support coarse ordering consistent with the various creationist proposals for generation of fossil ordering during the Flood, but cannot distinguish between them. Further research in these areas may be able to test for more fine-grained precision in fossil ordering. REFERENCES Whitmore, J.H., and P.A. Garner. 2008. Using suites of criteria to recognize pre-Flood, Flood, and post-Flood strata in the rock record with application to Wyoming (USA). In A.A. Snelling (editor), Proceedings of the Sixth International Conference on Creationism, pp. 425–448. Pittsburgh, Pennsylvania: Creation Science Fellowship; Dallas, Texas: Institute for Creation Research. Zeller, E.J. 1964. Cycles and psychology. Kansas Geological Survey Bulletin 169:631–636
Gravitational Waves as Vibrations on the Cosmic Fabric
Get PDFThe Cosmic Fabric Model (CFM) (Tenev and Horstemeyer 2018a; Tenev 2018) considers the universe as a solid, elastic, thin ether existing in four spatial dimensions. Matter is postulated to prescribe volumetric strain on the fabric, and the lapse rate of time is postulated to dilate in the presence of strain (Tenev and Horstemeyer 2018a). By applying continuum mechanics to the fabric of space, Tenev and Horstemeyer (2018b) derived that the linearized action of the fabric is equivalent to the linearized Einstein-Hilbert Action, resulting in the Einstein Field Equations from a continuum mechanics standpoint. Further, the linearized Schwarzschild metric was also derived from the continuum mechanics of the fabric (Tenev and Horstemeyer 2019a). CFM then provided an elegant solution to the dark matter effect (Tenev and Horstemeyer 2019b; Tenev 2018) where additional gravitation is caused by the inherent structure of the fabric.
Using the simplifying assumption of near-static fields (low strain rates), Tenev and Horstemeyer (2018a) applied Hooke’s Law in the case of bending plates to decompose the total elastic energy of the fabric into the bending energy and membrane energy of the hypersurface. The membrane energy vanished, and the bending energy was shown to equate to the Lagrangian of the linearized Einstein-Hilbert Action.
We seek to lift the near-static field assumption and to generalize CFM to high strain rates. To demonstrate the high strain rate effect, we first note a key connection between the metric tensor and the strain tensor from continuum mechanics. This allows us to model time derivatives and four-dimensional shear terms. What looks like shear terms with the time axis is shown to be three-dimensional velocity-related terms. Applying only the assumption of small strains (the weak gravity regime), we obtain an equation that extends the behavior of the fabric to now include the case of high strain rates.
We then verify CFM’s compatibility with gravitational waves. This validates the analysis already completed by Tenev (2018; Tenev and Horstemeyer 2018a) who showed that the harmonic gauge condition is satisfied and that the linearized Ricci scalar can be employed. A wave equation for gravitational waves was derived, showing that the maximum shear wave speed is the speed of light. They demonstrated that the waves would exist with two degrees of freedom which corresponds to the polarization of gravitational waves.
Previously, the kinetic energy term of the Lagrangian was ignored, but it needs to be accounted for now that we consider high strain rates. However, in relativity, kinetic energy is relative to the observer and thus not Lorentz invariant. A relativistic formulation of the fabric’s Lagrangian is considered where the role of the “kinetic energy” is represented by a rest mass-energy term. A density for the fabric of space is considered and presently taken as a parameter of the model. We discuss how the physical meaning of this term is likely related to the Cosmological Constant. However, a formal interpretation of this term will require rigorous analysis that is outside of the scope of this research.
This analysis illustrates that CFM is a viable model in more general cases than was previously considered. Our analysis demonstrates the ability of the model to represent gravitational waves as mechanical propagation through the fabric at the speed of light. It also offers some hints to a mechanical understanding of the Cosmological Constant. The idea that human-relatable concepts, such as fabrics and engineering principles, can be leveraged to understand the universe is indicative that God designed and optimized the cosmos for comprehension. CFM is developed from the viewpoint that the universe was engineered by God, the ultimate Creationeer®, for mankind to behold the greatness of their Maker.
References
Tenev, T.G. 2018. An Elastic Constitutive Model of Spacetime and Its Applications [dissertation]. Starkville, Mississippi: Mississippi State University.
Tenev, T.G. and M.F. Horstemeyer. 2018a. Mechanics of spacetime — A solid mechanics perspective on the Theory of General Relativity. International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology 27, no. 1850083. DOI: 10.1142/S0218271818500839.
Tenev, T.G. and M.F. Horstemeyer. 2018b. Recovering the principle of relativity from the Cosmic Fabric Model of space. Reports in Advances of Physical Sciences 2, no. 1850011–13. DOI: 10.1142/S2424942418500111.
Tenev, T.G. and M.F. Horstemeyer. 2019a. The spacetime metric of a spherically symmetric deformation of space derived from the Cosmic Fabric Model of gravity. International Journal of Modern Physics. D, Gravitation, Astrophysics, Cosmology 28, no. 1950096. DOI: 10.1142/S0218271819500962.
Tenev, T.G. and M.F. Horstemeyer. 2019b. Dark matter effect attributed to the inherent structure of cosmic space. International Journal of Modern Physics D, Gravitation, Astrophysics, Cosmology 28, no. 1950082. DOI: 10.1142/S0218271819500822.
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Centennial Library ShelfLife, September/October 2025
Get PDFArticles in this issue: CU Discover and Alma/Primo platform, 2025 Library STAR Award, Biblical Heritage Gallery, 2025 Library Internship, Course Reserves, Research Librarians, Library Locker, Digital Services Publishing Cornerhttps://digitalcommons.cedarville.edu/library_enews/1133/thumbnail.jp
Life After Work: Insight into the Social Life and Leisure of Martha McMillan
Get PDFThis essay discusses the social life of the McMillan family, recorded in Martha McMillan\u27s journal. Martha\u27s journals provide key insights into her Christian values of hard work and her intentionality in serving the community, while also finding rest and enjoyment. Her writing catalogs the many social events and leisure activities of her family and community in rural Ohio
