About Aristotle’s ;point of view and `development’ up to Boyle
A readable summary is
Jennifer Rampling
More than 2,000 years of elements: a prehistory of the periodic table
Nature 565 563 (2019) Jennifer Rampling traces how ideas of material essence and indivisibility evolved in the centuries before modern atomic theory. It is a part commemorating the 150th
anniversary of the Periodic Table.
Archimedes
Galileo and Descartes were mathematically awaken by Archimedean `mathematical physics.’ Archimedes gave them the conviction that the world could be understood in terms of mathematics. Descartes wished to establish mathematical understanding of the world free from any (not so-reliable) empirical input. To this end, he wished to free our spirit from any worldly experience: `I think, therefore I am’ was intended to establish `a priori’ (in the Kant’s sense) to furnish the foundation of mathematical physics.
Archimedes was proud of computing the volume of a sphere exactly
Archimedes invented a kind of integration, and used it to demonstrate (rigorously) the volume of the sphere. As illustrated below, the idea is easy to understand. However, Archimedes was a very careful mathematician, so he used the idea of inner and outer measures (see supplement to 3.1) to determine the areas and volumes rigorously. This level of rigor was never reached until Cauchy. That is, for 2000 years
human-beings never cared for mathematical precision. The lesson we must learn is that the best part of our culture can be lost very easily, unless majority of the people understand the cultural value and know at least the core ideas intuitively.
1.5 Air density and plane take-off
The Carboniferous and Permian oxygen level increase; the oxygen level probably rose to a
maximum value of ca 0.3 atm during the Carboniferous before returning to its present value.
This high oxygen phase 375-275 MaBP is very likely to be due to the land plant proliferation
(R. A. Berner, ``Atmospheric oxygen over Phanerozoic time," Proc. Nat. Acad. Sci. 96, 10995
(1999). Subsequent cooling might be due to the decrease of green house gas.). This caused
gigantism in several arthropod groups, and the body-size increase of primitive reptiles. The
emergence of shelled egg-laying animals may have been the result of high oxygen pressure.
<< Legacy of hyperoxic phase >>
The biotic effect of this hyperoxic phase is summarized in
J. B. Graham, R. Dudley, N. M. Aguilar and C. Gans, ``Implication of the late Paleozoic
oxygen pulse for physiology and evolution." Nature 375, 117 (1995). O2 level may have
reached a max of 35% and then dropped during Permian to 15% (cf. PAL = 21%). Since
the N2 pressure was about the same as PAL, the air density was 21% greater under 35% O2.
This would favorably influence the evolution of insect flight (cf [4.5]).
Not only insects [6] but gigantism for bryozoans, foraminiferans, rugose corals and brachiopods
was observed.
Greater atmospheric density elevated wind stress, but oxygen-dependent biosynthesis of
lignin facilitated thicker support structures.
Breathing hyperoxic air reduces the ratio of evaporative water loss to oxygen uptake, and
thus increases aerial gas exchange efficiency.
<<Hotter air means planes need more speed to take off>>
[Five Things for your new day (Good Morning from CNN) June 29, 2017.] The heat is on out West, where it's so hot that American Airlines has canceled about 50 flights in and out of Phoenix as the temperature there hit 118 degrees. Hotter air means planes need more speed (and more runway) to
take off. Las Vegas may see its highest temperature ever recorded, while temperatures today
in Phoenix (119 degrees) and Death Valley, California (127 degrees) will be scorching, as well.
