Journal of creation 5(3) 2011 p art of this paper
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- Bu səhifədəki naviqasiya:
- A mathematical test
- The origin of the Carboniferous coal measures—part 3: a mathematical test of lycopod root structure
- Typical misleading representations of stigmaria and lycopods
- Acknowledgments
| Papers 74 JOURNAL OF CREATION 25(3) 2011 P art 1 of this paper 1 noted how uniformitarians thought the Paleozoic coal deposits of the northern hemisphere formed in swamps. This was despite the plethora of evidence they uncovered which presented problems for their surrounding the incredible biodensity of fossils in the coal measures coupled with a lack of biodiversity;; the disarticulation of the fossils coupled with their excellent preservation;; and the separation of different fossilized parts geographical extent of the coal seams, the high purity of the coal seams with minimal contamination from mud and sand, silvomarine origin of the Paleozoic coal deposits. This hypothesis by biologists is supported by their paleontological and chemical evidence that the dominant Paleozoic fern tree plants were structured for a water environment. In line with this, the second part of this paper 2 concentrated on on the elastic and vacuous nature of those fern trees. The author’s calculations concerning their root structures, their unusual ontogeny and radiating rootlets and other evidence The silvomarine hypothesis for the formation of Kuntze. His concept was that the Paleozoic coal beds formed addition to a phenomenal breath of quantitative analyses (e.g. on coal bed chemistry). hypothesis. Where did the intervening limestone, shale, sandstone, and clay layers come from? Why are the fern tree roots that form the base of this forest almost always separated from their trunks? How do you account for the large number of coal layers in cyclothems? Why is the biodiversity so low? And so forth. questions, a mathematical model of the dominant vegetation in the Paleozoic coal beds should be made. This is of much biodiversity seen in the coal beds. This paper presents a mathematical model of a lycopod or fern tree, concentrating
A reasonable assumption for the spread of a lateral Paleozoic lycopod root system in an aqueous environment would be that at its termini for the mature Stigmaria, and perhaps in its intermediate stages at the points where its roots bifurcate, its roots should be equidistant from each other. That is, they would be distributed equally around a circle centered at their genesis point. This is certainly the 3
Stigmaria, then there would be a uniquely determined angle between them if the roots are equidistant from each other at the termini of both stages. If ‘a’ is the common length of
‘b a = b Therefore any previously published example of such a The origin of the Carboniferous coal measures—part 3: a mathematical test of lycopod root structure Joanna F. Woolley The notion of the compatibility of form and function in plant organisms is used as a guide to mathematically predict the geometrical shape of Carboniferous Stigmaria (i.e. lycopod roots). It is assumed that Stigmaria were created to be in an abundant fluid environment. The analytical predictions resulting from this assumption are compared to the Paleozoic fossil evidence. This mathematical model is part of a complete lycopod model that is outlined in enough detail to be reproduced. Finally a rationale for the discrepancies in the depiction of Stigmaria in popular and scientific venues versus what has been used in this model developed is given. Agreement between predicted stigmarian structure and the fossil evidence strongly supports an abundantly fluid environment for them. It favors the floating forest, catastrophic paradigm of Paleozoic coal formation.
Papers 75 JOURNAL OF CREATION 25(3) 2011 measured and that of the bifurcation angle between them. The lengths could then be put into the eq uation that calculated the ideal bifurcation angle under the given assumptions. The calculated and measured angles could then be compared to see how valid the assumption is in practice. Take the example from the literature note that there is considerable variation in the lengths of the root sections (the averaged values were used), apparently because some suffered from adverse the averaged measured angle between have reasonable agreement, though it is root growth in this specimen is far more interesting. Given the lengths and the analytically determined angle from the example under discussion, an iterative mathematical procedure can be used to calculate the the roots and their lengths if they must be equidistant from each other. The calculations showed that every second pair of terminal roots has to cross each other. That the terminal roots have to cross each other can also be shown the stigmarian branches make an equal angle of 90° with any circle centered at new outwardly progressing branches then make the same angle in absolute magnitude (but not 90°) with any circle of expansion. However, these angles have opposite signs at alternate positions around the periphery of any of these circles. When the branches have grown to where they are equidistant from each other, the second point of bifurcation two new branches in the next bifurcation then have to be expansion at a more tangential aspect, while the other one approaches at more of a normal aspect. Therefore, the must necessarily cross each other eventually, because they are rapidly approaching each other while the other pair is on a more nearly parallel course. Thus the distance between them closes as they grow outward before they cross. They have to cross in order to put distance between themselves equal to that of the more nearly parallel branches. This is a most unnatural circumstance if the roots are embedded 4 This was consistent with the calculated angle for the crossing of the stigmarian roots of 58.06°. The author also collected one sample of fossil stigmarian roots measured at it was 53°. Another sample, from southeastern Kentucky’s Bryson Formation, was also located. It again had an angle that measured 53°. These three in the mathematical model, though the agreement could be better. and bifurcation angles were considered, but found wanting. For instance, retaining the assumption of the equal separation before they bifurcate or at their maximum extent), but adding the requirement that the bifurcation angles between all the sets of roots for all bifurcations be equal, will not allow the branches to cross each other and remain equidistant. That mathematically excluded when the angles are required to be equal. Furthermore, for the case where the terminal branches are not allowed to cross but the equal bifurcation angles requirement is retained, to 60°, which is below the value of any bifurcation angle seen in fossil evidence the author is aware of. Finally, the ratios far from those observed in real fossil remains. This all strongly suggests that such a root system was indeed designed for a watery environment. If it were not, then the plant would have, at one point in the terminal stage of its roots’ growth, a situation where every second pair of root tips of the plant would be nearly coincident. This limited environment. When this prediction is compared to the photographs of the few existing extant stigmarian root systems available to the author, good agreement is found. The mathematical model of a Stigmaria part of a complete lycopod mathematical model outlined here. 5
those concerning the large number of layers in Paleozoic cyclothems;; the biodensity and particular spacing of lycopods;; and the origin of the limestone, shale, sandstone, and clay layers in cyclothems. These questions and others, like why Stigmaria are nearly always found separated from c a b β α Alpha = 78.86 degrees, beta = 69.2 degrees,; for a 9-meter diameter: a = 0.716829006 m, b = 0.942453873 m, c = 2.98482897578 m; for a 6.7-meter diameter: a = 0.533639371 meters, b = 0.7016045499 meters, and c = 2.22203934863. Figure 1. [Above] A Stigmaria ficoides Brongniart from the Middle Pennsylvanian of the Piesberg near Osnabruck, Germany; [Below] a schematic configuration (top view). Papers 76 JOURNAL OF CREATION 25(3) 2011 their lycopod trunks, will be answered in forthcoming articles. The answers are both intriguing and surprising, providing good reasons to believe the superior merit of the silvomarine hypothesis. Typical misleading representations of stigmaria and lycopods evidence to use in reconstructing lycopod root systems, especially the crossing of their roots, accurate portrayals of them are exceedingly rare. 6 What reconstructions are attempted usually mimic the roots of contemporary trees with shallow roots splayed out radially from the base, with a notable absence of any root crossings. A few typical examples of this tendency follow. The University of California at Berkeley paleontology department’s web site reproduces a representation of Stigmaria consistent root crossings of Stigmaria. In addition, the height of the Lepidodendron lycopod is distorted by a factor this is not the case). All these gross distortions help hide 8 as are similar misrepresentations of the Stigmaria. Pennsylvania contains some of the world’s best examples of Upper Carboniferous strata. Accordingly, the Pennsylvania producing Carboniferous vegetation. This vegetation is dominated by the lycopod fern trees, shown uprooted in the three accompanying photographs of paintings and models the exterior dimensions and morphology of the lycopods are well known, they are grossly misrepresented in the museum. For example, the roots are only one fourth the size they should be, the rootlets are one twelfth the size they should be (the equivalent of pretending a six foot man is only six inches high!), and they are missing on the top of the roots (except at the tips of them) and shown bending downward rather than radiating straight out from the root. All of these disingenuous representations are necessary, along with other ones concerning the biodiversity and biochemistry of the that Pennsylvanian coal was produced ments cannot be expected to get things of a technical nature correct. However, the Pennsylvania State exhibit was Figure 2. Reproduction of an unrealistically distorted depiction of a Lepidodendron and its roots, abstracted from the University of California at Berkeley’s department of paleontology website. Baird as a consultant. 9 Although his expertise centers on tetrapods (i.e. amphibians and lepospondyli), it would be logical to assume that he was aware and approved the presentation of lycopods at the museum. There were several species of Stigmaria named before 1820. However, these names are not given scientific credence because they occur before the date an international commission on botanical names was established. 10 After that date various researchers began to produce descriptions of new species and otherwise add to our knowledge of Stigmaria. Because this data was scattered throughout William G. Chaloner writing it. 11 Chaloner is noted for his work on fossil spores, not on lycopods. Perhaps because of this his review was all the more candid than it would have been otherwise. He noted species of Stigmaria that had been described. This was because some of them had been established only after a few transverse cuts had been made on fossil specimens and stages of stigmarian ontogeny. In fact, it is likely the three of taphonomic disturbances rather than speciation. More on this topic will be given after the following discussion. Similarly, the author has seen a complete gradation between smooth and grooved stigmarian steles, so this may also be a taphonomic development that is not related to differences in Stigmaria species. Note that Chaloner fails to even mention the two books written by the botanist work is far broader in scope of specimens considered and had far more empirical rigour than any reference Chaloner chose to cite. Figure 6 is from Chaloner’s review. 12
gives a typically disingenuous, crossing Stigmaria. The distortions of the fossil evidence all tend to hypothesis at the expense of the silvomarine one. The lower part of the diagram is much worse. The rootlets are shown visibly tapering with one of them bifurcating. They are noted as being 40 cm long, one fifth of the length reported elsewhere. They are shown bending 100,000 rootlets seen by the author, none have been visibly tapered, Lepidostrobus Lepido- phylloides Lepidodendron Stigmaria Papers 77 JOURNAL OF CREATION 25(3) 2011 Figure 5. A questionable reproduction of an uprooted Stigmaria with rootlets (note absence of rootlets on most of the top [left] side) as displayed at the Pennsylvania State Museum in Harrisburg, Pennsylvania. Figure 6. The details, as well as the overall picture, of Stigmaria are misrepresented in the above diagrams abstracted from an encyclopedic review of lycopods. Figure 3. A questionable reproduction of the Upper Carboniferous forest, as displayed at the Pennsylvania State Museum in Harrisburg, Pennsylvania. Figure 4. A questionable reproduction of an uprooted Stigmaria with rootlets, as displayed at the Pennsylvania State Museum in Harrisburg, Pennsylvania. bent downward instead of radiating out perpendicularly to the surface of the Stigmaria, bifurcated, or been as short as represented here when their lengths could possibly be traced that far. 13 space in the interior of the Stigmaria. However, the rootlets are shown as traversing parallel to the stele in this space before they enter it. This has never been observed by the author. Numerous examples of the rootlets entering the stele perpendicularly—without undergoing any bends in the interior of the Stigmaria have been seen. The case of usually broken rootlets being swept in one direction along the axes of the stele has also been observed. Could it be that the few cuts examined by other researchers on a simple Stigmaria are running into this phenomenon without correctly interpreting it? Are Stigmaria structural disturbances having nothing to do with evolutionary differentiation and everything to do with a violent placement they have been too preoccupied with the quest to prove an untenable guess to have noticed the true macroscopic nature of lycopod fern trees?
The Paleozoic fern tree root model is an integral part of a more extensive model of the entire lycopod. Such a model is necessary to quantitatively examine the various aspects of the hypothesis that the Carboniferous coal measures were Paleozoic fern tree model is contrasted to the input that would have been derived if the contemporary consensus depiction that arguments about homologous structures and evolutionary adaptive reduction, the dwelling on evolutionary expectations rather than on observations, has steered researchers away 2 metres R f 10cm Camb
X2 PX Mid C Phell Papers 78 JOURNAL OF CREATION 25(3) 2011 from a more realistic appreciation of Paleozoic lycopod examples of dubious depictions of lycopod structures, ones showing gross distortions from the fossil evidence, are given. forest hypothesis of Kuntze at the expense of the swamp hypothesis for the genesis of Paleozoic coal beds.
French language translations found necessary to complete the background upon which this article is based.
logic of lycopod root structure, J. Creation 25 3. The measurements of a Piesberg, Germany, Stigmaria were taken from a
5. The modeling assumptions for the Stigmaria were considered as being neutrally buoyant in water (based on the author’s observations of the fossil evidence of their ease of pliability relative to their assumed rootlet solid structure to be 2.62 g/cm 3 the rootlets of Brongniart from Westfalen, Germany (Middle Pennsylvanian) as presented in Hirmer, ref. 3, p. 294, bottom right 3 . The roots were taken averaged dimensions from a Brongniart from Piesberg, Germany (Middle Pennsylvanian), Hirmer, ref. aufgestellte Baumstumpf mit Wurzeln aus dem Carbon des Piesberges, Jahrbuch d. k. Preuß. Geol. Landesanst. für das Jahr, 1889, Berlin, 1892. The lengths of the roots from their genesis point were normalized to be 4.5 m (9 m in diameter) for a mature specimen, as reported in Williamson, W.C.,
,
It was assumed that the root development paralleled the development of the trunk, including that of its pith. Therefore, the trunk development will now be discussed. The height of a modeled Sigillaria was taken to be 30 m, a generally accepted maximum value (although higher estimated and actual values have been reported). The pith of the trunk was taken to follow a third literature) and allowed to asymptotically converge to its genesis point on the origin. This equation (in meters with y being the vertical distance) is
3 – 191.38 x 2 + 94.61 x for a Lepidodendron Sigillaria up to its maximum was taken as representing the mature interior development of the roots up interior narrowing was taken as being linear. The spacing density of rootlets on the roots was taken as uniform but rootlets were assumed not to remain on the mature Stigmaria before its branches became horizontal. A better, consistent estimate of the spacing density as a function of root diameter is possible only if the effects of elastic distortion due to the crushing of the roots can be adequately taken into account—something the author has yet to accomplish. The spongy material in the roots was taken to cover 30% of the remaining interior space, with the low density of 0.1 g/cm 3 . This estimate is predicated upon measurements taken on a Stigmaria from the Scrubgrass coal layer of western Pennsylvania collected by the author. The Stigmaria sample underwent an unusual electrochemical taphonomy, preserving the interior of the Stigmaria. Rootlets are taken to be uniformly 2 meters long (with the density as noted above), a calculational consideration only when they are exposed out of the water. The exterior of the tip of the Stigmaria was taken to be a right circular cone tapering from a radius of 2.60238226322 cm to a radius of zero in the last 10.16 cm of its length, following the formula
2
implicitly giving the radius of the circular cross section r as a function of y, the start of the last 10.16 cm of the root (y = 0) to its termination (y = 10.16), as averaged from measurements on specimens collected by the author [not believed by the author to have undergone much, if any, crushing]. 6. However, note that root crossings were obviously known to leading researchers Kuntze, Brongniart and Williamson over a century ago. The early and ubiquitously copied misrepresentation of the appendices or rootlets on the Stigmaria page 50 of his booklet Geogenetische Beitrage, Gressner and Schramm, where the break in the lower, mature lycopod has been omitted, making it
PA, p. 26, 2005, as seen at www.portal.state.pa.us/portal/server.pt/ document/1009151/100years_pdf, accessed 1 May 2011.
edn), International Association for Plant Taxonomy, Vienna, Article 13, 2006;; ibot.sav.sk/icbn/main.htm.
Comparative Study of Stigmarian Appendages and Isoetes Roots, American J. Botany 34 takes great pains to argue along the lines of homologous development and adaptive reduction, using detailed microscopic evidence to argue its case, its phenomenal distortion of the macroscopic physiology of lycopods typically mirrors its evolutionary myoptism. 13. The author has observed considerable taphonomic variation in rootlet diameter and great variation—including wrapping around the root—in rootlet direction. The rootlets are usually observed as being stiff, but they can also be undulating. The author does not discount the possibility of rootlet bifurcation. Joanna F. Woolley is a store manager for a national jewelry store chain. She has an avid interest in gemstones, minerals, and fossils. This article is an outgrowth of a home school science project by Joanna F. Woolley. In addition to an avid interest in fossils, minerals, and gemstones, she is active in church work. Yüklə 81,32 Kb. Dostları ilə paylaş:
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