170
have ever approached a human-induced mass extinction by which to extrapolate
long-term adaptability for the one remaining Homo
32
, although the likelihood of
most other large vertebrates surviving many more generations under anthropocenic
conditions, is highly questionable. We witness countless forms of breaking polarities, splits, electron shifts, and unstable atoms with every conceivable composition
of positive and negative charges throughout the disciplines of cosmology, astronomy, astrophysics, chemistry, and research from quantum physics and electromagnetic research
33
.
We see countless instances of fundamental bifurcation points across the spectrum of mathematics (the Hopf Bifurcation, wherein an entire system becomes
unstable and then switches, for example, named after German mathematician Heinz
Hopf, 1894–1971), and have done so at least since the time of Hippasos (fifth century BCE), the Greek philosopher who appears to have first detected the existence
of irrational numbers. Legend has it that he drowned at sea as a result of the displeasure the Gods took in his discovery, which followed his contemplating the square
root of 2, or 1.41421356237309504880168872420969
807856967187537694807317667973789... The numbers move toward no closure, a cusp of infinite descent, as ever smaller natural numbers (integers, whole
numbers) are crammed into the incompletion, forever. Pi,π, as well as the famed
Euler Number (2.7182818284590452353602874713517… —pertaining to natural
logarithms) are other such irrational propositions. They cannot be written as simple
fractions, a hallmark of the mathematically irrational
34
, and mirror image of ecological paradox in practice, not mere theory.
2011.00214.x, https://www.ncbi.nlm.nih.gov/pubmed/25568035, Accessed April 1, 2019.
32 For in-depth discussion, see the Author’s book, The Hypothetical Species: Variables of Human
Evolution, Springer, New York, 2019.
33 See, for example, A&A 380, L5–L8 (2001) https://doi.org/10.1051/0004-6361:20011505 c ESO
2001 Astronomy & Astrophysics Zeeman-split opposite-polarity OH lines in sunspot spectra:
Resolution of a puzzle S. V. Berdyugina1 and S. K. Solanki, October 2001; http://www2.mps.mpg.
de/dokumente/publikationen/solanki/j129.pdf, Accessed March 26, 2019; See also, http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/zeeman.html, Accessed √March 26,2019; See also,
Song C, Phenix H, Abedi V, Scott M, Ingalls BP, et al. 2010, “Estimating the Stochastic Bifurcation
Structure of Cellular Networks,” PLoS Comput Biol 6(3): https://doi.org/10.1371/journal.
pcbi.1000699, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000699,
Accessed April 1, 2019; See also, Gregor F. Fussmann, Stephen P. Ellner, Kyle W. Shertzer, and
Nelson G. Hairston Jr. Crossing the Hopf Bifurcation in a Live Predator–Prey System. Science. 17
November 2000: 290 (5495), 1358–1360. https://doi.org/10.1126/science.290.5495.1358.
34 See Sir Thomas Little Heath’s work, A History of Greek Mathematics, Clarendon Press, Oxford,
UK, 1921.
18 A Cave at Taranga
have ever approached a human-induced mass extinction by which to extrapolate
long-term adaptability for the one remaining Homo
32
, although the likelihood of
most other large vertebrates surviving many more generations under anthropocenic
conditions, is highly questionable. We witness countless forms of breaking polarities, splits, electron shifts, and unstable atoms with every conceivable composition
of positive and negative charges throughout the disciplines of cosmology, astronomy, astrophysics, chemistry, and research from quantum physics and electromagnetic research
33
.
We see countless instances of fundamental bifurcation points across the spectrum of mathematics (the Hopf Bifurcation, wherein an entire system becomes
unstable and then switches, for example, named after German mathematician Heinz
Hopf, 1894–1971), and have done so at least since the time of Hippasos (fifth century BCE), the Greek philosopher who appears to have first detected the existence
of irrational numbers. Legend has it that he drowned at sea as a result of the displeasure the Gods took in his discovery, which followed his contemplating the square
root of 2, or 1.41421356237309504880168872420969
807856967187537694807317667973789... The numbers move toward no closure, a cusp of infinite descent, as ever smaller natural numbers (integers, whole
numbers) are crammed into the incompletion, forever. Pi,π, as well as the famed
Euler Number (2.7182818284590452353602874713517… —pertaining to natural
logarithms) are other such irrational propositions. They cannot be written as simple
fractions, a hallmark of the mathematically irrational
34
, and mirror image of ecological paradox in practice, not mere theory.
2011.00214.x, https://www.ncbi.nlm.nih.gov/pubmed/25568035, Accessed April 1, 2019.
32 For in-depth discussion, see the Author’s book, The Hypothetical Species: Variables of Human
Evolution, Springer, New York, 2019.
33 See, for example, A&A 380, L5–L8 (2001) https://doi.org/10.1051/0004-6361:20011505 c ESO
2001 Astronomy & Astrophysics Zeeman-split opposite-polarity OH lines in sunspot spectra:
Resolution of a puzzle S. V. Berdyugina1 and S. K. Solanki, October 2001; http://www2.mps.mpg.
de/dokumente/publikationen/solanki/j129.pdf, Accessed March 26, 2019; See also, http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/zeeman.html, Accessed √March 26,2019; See also,
Song C, Phenix H, Abedi V, Scott M, Ingalls BP, et al. 2010, “Estimating the Stochastic Bifurcation
Structure of Cellular Networks,” PLoS Comput Biol 6(3): https://doi.org/10.1371/journal.
pcbi.1000699, https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000699,
Accessed April 1, 2019; See also, Gregor F. Fussmann, Stephen P. Ellner, Kyle W. Shertzer, and
Nelson G. Hairston Jr. Crossing the Hopf Bifurcation in a Live Predator–Prey System. Science. 17
November 2000: 290 (5495), 1358–1360. https://doi.org/10.1126/science.290.5495.1358.
34 See Sir Thomas Little Heath’s work, A History of Greek Mathematics, Clarendon Press, Oxford,
UK, 1921.
18 A Cave at Taranga