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An adaptability limit to climate change due to heat stress
Despite the uncertainty in future climate-change impacts, it is often assumed that humans would be able to adapt to any possible warming. Here we argue that heat stress imposes a robust upper limit to such adaptation. Peak heat stress, quantified by the wet-bulb temperature TW, is surprisingly similar across diverse climates today. TW never exceeds 31 °C. Any exceedence of 35 °C for extended periods should induce hyperthermia in humans and other mammals, as dissipation of metabolic heat becomes impossible. While this never happens now, it would begin to occur with global-mean warming of about 7 °C, calling the habitability of some regions into question. With 11–12 °C warming, such regions would spread to encompass the majority of the human population as currently distributed. Eventual warmings of 12 °C are possible from fossil fuel burning. One implication is that recent estimates of the costs of unmitigated climate change are too low unless the range of possible warming can somehow be narrowed. Heat stress also may help explain trends in the mammalian fossil record.

Trajectories of the Earth System in the Anthropocene:
We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a “Hothouse Earth” pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be.
study  org:nat  environment  climate-change  humanity  existence  risk  futurism  estimate  physics  thermo  prediction  temperature  nature  walls  civilization  flexibility  rigidity  embodied  multi  manifolds  plots  equilibrium  phase-transition  oscillation  comparison  complex-systems  earth 
august 2018 by nhaliday
Ultimate fate of the universe - Wikipedia
The fate of the universe is determined by its density. The preponderance of evidence to date, based on measurements of the rate of expansion and the mass density, favors a universe that will continue to expand indefinitely, resulting in the "Big Freeze" scenario below.[8] However, observations are not conclusive, and alternative models are still possible.[9]

Big Freeze or heat death
Main articles: Future of an expanding universe and Heat death of the universe
The Big Freeze is a scenario under which continued expansion results in a universe that asymptotically approaches absolute zero temperature.[10] This scenario, in combination with the Big Rip scenario, is currently gaining ground as the most important hypothesis.[11] It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry. With a positive cosmological constant, it could also occur in a closed universe. In this scenario, stars are expected to form normally for 1012 to 1014 (1–100 trillion) years, but eventually the supply of gas needed for star formation will be exhausted. As existing stars run out of fuel and cease to shine, the universe will slowly and inexorably grow darker. Eventually black holes will dominate the universe, which themselves will disappear over time as they emit Hawking radiation.[12] Over infinite time, there would be a spontaneous entropy decrease by the Poincaré recurrence theorem, thermal fluctuations,[13][14] and the fluctuation theorem.[15][16]

A related scenario is heat death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed and there are no gradients—which are needed to sustain information processing, one form of which is life. The heat death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.[17]
physics  big-picture  world  space  long-short-run  futurism  singularity  wiki  reference  article  nibble  thermo  temperature  entropy-like  order-disorder  death  nihil  bio  complex-systems  cybernetics  increase-decrease  trends  computation  local-global  prediction  time  spatial  spreading  density  distribution  manifolds  geometry  janus 
april 2018 by nhaliday
orbit - Best approximation for Sun's trajectory around galactic center? - Astronomy Stack Exchange
The Sun orbits in the Galactic potential. The motion is complex; it takes about 230 million years to make a circuit with an orbital speed of around 220 km/s, but at the same time it oscillates up and down with respect to the Galactic plane every ∼70∼70 million years and also wobbles in and out every ∼150∼150 million years (this is called epicyclic motion). The spatial amplitudes of these oscillations are around 100 pc vertically and 300 pc in the radial direction inwards and outwards around an average orbital radius (I am unable to locate a precise figure for the latter).
nibble  q-n-a  overflow  space  oscillation  time  cycles  spatial  trivia  manifolds 
december 2017 by nhaliday
[1509.02504] Electric charge in hyperbolic motion: The early history and other geometrical aspects
We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material points are replaced by infinitesimal length elements.

SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay:
nibble  preprint  papers  org:mat  physics  electromag  relativity  exposition  history  mostly-modern  pre-ww2  science  the-trenches  discovery  intricacy  classic  explanation  einstein  giants  plots  manifolds  article  multi  liner-notes  org:junk  org:edu  absolute-relative 
november 2017 by nhaliday
Hyperbolic angle - Wikipedia
A unit circle {\displaystyle x^{2}+y^{2}=1} x^2 + y^2 = 1 has a circular sector with an area half of the circular angle in radians. Analogously, a unit hyperbola {\displaystyle x^{2}-y^{2}=1} {\displaystyle x^{2}-y^{2}=1} has a hyperbolic sector with an area half of the hyperbolic angle.
nibble  math  trivia  wiki  reference  physics  relativity  concept  atoms  geometry  ground-up  characterization  measure  definition  plots  calculation  nitty-gritty  direction  metrics  manifolds 
november 2017 by nhaliday
gn.general topology - Pair of curves joining opposite corners of a square must intersect---proof? - MathOverflow
In his 'Ordinary Differential Equations' (sec. 1.2) V.I. Arnold says "... every pair of curves in the square joining different pairs of opposite corners must intersect".

This is obvious geometrically but I was wondering how one could go about proving this rigorously. I have thought of a proof using Brouwer's Fixed Point Theorem which I describe below. I would greatly appreciate the group's comments on whether this proof is right and if a simpler proof is possible.


Since the full Jordan curve theorem is quite subtle, it might be worth pointing out that theorem in question reduces to the Jordan curve theorem for polygons, which is easier.

Suppose on the contrary that the curves A,BA,B joining opposite corners do not meet. Since A,BA,B are closed sets, their minimum distance apart is some ε>0ε>0. By compactness, each of A,BA,B can be partitioned into finitely many arcs, each of which lies in a disk of diameter <ε/3<ε/3. Then, by a homotopy inside each disk we can replace A,BA,B by polygonal paths A′,B′A′,B′ that join the opposite corners of the square and are still disjoint.

Also, we can replace A′,B′A′,B′ by simple polygonal paths A″,B″A″,B″ by omitting loops. Now we can close A″A″ to a polygon, and B″B″ goes from its "inside" to "outside" without meeting it, contrary to the Jordan curve theorem for polygons.

- John Stillwell
nibble  q-n-a  overflow  math  geometry  topology  tidbits  intricacy  intersection  proofs  gotchas  oly  mathtariat  fixed-point  math.AT  manifolds  intersection-connectedness 
october 2017 by nhaliday
Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution∗
We find that IPP capital entirely explains the observed decline of the US labor share, which otherwise is secularly constant over the past 65 years for structures and equipment capital. The labor share decline simply reflects the fact that the US economy is undergoing a transition toward a larger IPP sector.
The Fall of the Labor Share and the Rise of Superstar Firms:
The Decline of the U.S. Labor Share:
Table 2 has industry disaggregation
Estimating the U.S. labor share:

Why Workers Are Losing to Capitalists:
Automation and offshoring may be conspiring to reduce labor's share of income.
pdf  study  economics  growth-econ  econometrics  usa  data  empirical  analysis  labor  capital  econ-productivity  manifolds  magnitude  multi  world  🎩  piketty  econotariat  compensation  inequality  winner-take-all  org:ngo  org:davos  flexibility  distribution  stylized-facts  regularizer  hmm  history  mostly-modern  property-rights  arrows  invariance  industrial-org  trends  wonkish  roots  synthesis  market-power  efficiency  variance-components  business  database  org:gov  article  model-class  models  automation  nationalism-globalism  trade  news  org:mag  org:biz  org:bv  noahpinion  explanation  summary  methodology  density  polarization  map-territory  input-output 
july 2017 by nhaliday
Riemannian manifold - Wikipedia
In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real smooth manifold M equipped with an inner product {\displaystyle g_{p}} on the tangent space {\displaystyle T_{p}M} at each point {\displaystyle p} that varies smoothly from point to point in the sense that if X and Y are vector fields on M, then {\displaystyle p\mapsto g_{p}(X(p),Y(p))} is a smooth function. The family {\displaystyle g_{p}} of inner products is called a Riemannian metric (tensor). These terms are named after the German mathematician Bernhard Riemann. The study of Riemannian manifolds constitutes the subject called Riemannian geometry.

A Riemannian metric (tensor) makes it possible to define various geometric notions on a Riemannian manifold, such as angles, lengths of curves, areas (or volumes), curvature, gradients of functions and divergence of vector fields.
concept  definition  math  differential  geometry  manifolds  inner-product  norms  measure  nibble 
february 2017 by nhaliday
Deadweight loss - Wikipedia
Deadweight loss created by a binding price ceiling. Producer surplus is necessarily decreased, while consumer surplus may or may not increase; however the decrease in producer surplus must be greater than the increase (if any) in consumer surplus.
economics  concept  efficiency  markets  micro  metabuch  regulation  taxes  wiki  reference  models  things  manifolds  plots  supply-demand  intersection  intersection-connectedness 
february 2017 by nhaliday

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