nhaliday + dynamical   33

Stability of the Solar System - Wikipedia
The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have been stable when historically observed, and will be in the short term, their weak gravitational effects on one another can add up in unpredictable ways. For this reason (among others) the Solar System is chaotic,[1] and even the most precise long-term models for the orbital motion of the Solar System are not valid over more than a few tens of millions of years.[2]

The Solar System is stable in human terms, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and the Earth's orbit will be relatively stable.[4]

Since Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, Vladimir Arnold and Jürgen Moser) have searched for evidence for the stability of the planetary motions, and this quest led to many mathematical developments, and several successive 'proofs' of stability of the Solar System.[5]

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The planets' orbits are chaotic over longer timescales, such that the whole Solar System possesses a Lyapunov time in the range of 2–230 million years.[3] In all cases this means that the position of a planet along its orbit ultimately becomes impossible to predict with any certainty (so, for example, the timing of winter and summer become uncertain), but in some cases the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more—or less—elliptical.[7]

Is the Solar System Stable?: https://www.ias.edu/ideas/2011/tremaine-solar-system

Is the Solar System Stable?: https://arxiv.org/abs/1209.5996
nibble  wiki  reference  article  physics  mechanics  space  gravity  flux-stasis  uncertainty  robust  perturbation  math  dynamical  math.DS  volo-avolo  multi  org:edu  org:inst  papers  preprint  time  data  org:mat 
november 2017 by nhaliday
rotational dynamics - Why do non-rigid bodies try to increase their moment of inertia? - Physics Stack Exchange
This happens to isolated rotating system that is not a rigid body.

Inside such a body (for example, steel chain in free fall) the parts move relatively to each other and there is internal friction that dissipates kinetic energy of the system, while angular momentum is conserved. The dissipation goes on until the parts stop moving with respect to each other, so body rotates as a rigid body, even if it is not rigid by constitution.

The rotating state of the body that has the lowest kinetic energy for given angular momentum is that in which the body has the greatest moment of inertia (with respect to center of mass). For example, a long chain thrown into free fall will twist and turn until it is all straight and rotating as rigid body.

...

If LL is constant (net torque of external forces acting on the system is zero) and the constitution and initial conditions allow it, the system's dissipation will work to diminish energy until it has the minimum value, which happens for maximum IaIa possible.
nibble  q-n-a  overflow  physics  mechanics  tidbits  spatial  rigidity  flexibility  invariance  direction  stylized-facts  dynamical  volo-avolo  street-fighting  yoga 
august 2017 by nhaliday
gravity - Gravitational collapse and free fall time (spherical, pressure-free) - Physics Stack Exchange
the parenthetical regarding Gauss's law just involves noting a shell of radius r + symmetry (so single parameter determines field along shell)
nibble  q-n-a  overflow  physics  mechanics  gravity  tidbits  time  phase-transition  symmetry  differential  identity  dynamical 
august 2017 by nhaliday
The Rise and Fall of Cognitive Control - Behavioral Scientist
The results highlight the downsides of controlled processing. Within a population, controlled processing may—rather than ensuring undeterred progress—usher in short-sighted, irrational, and detrimental behavior, ultimately leading to population collapse. This is because the innovations produced by controlled processing benefit everyone, even those who do not act with control. Thus, by making non-controlled agents better off, these innovations erode the initial advantage of controlled behavior. This results in the demise of control and the rise of lack-of-control. In turn, this eventually leads to a return to poor decision making and the breakdown of the welfare-enhancing innovations, possibly accelerated and exacerbated by the presence of the enabling technologies themselves. Our models therefore help to explain societal cycles whereby periods of rationality and forethought are followed by plunges back into irrationality and short-sightedness.

https://static1.squarespace.com/static/51ed234ae4b0867e2385d879/t/595fac998419c208a6d99796/1499442499093/Cyclical-Population-Dynamics.pdf
Psychologists, neuroscientists, and economists often conceptualize decisions as arising from processes that lie along a continuum from automatic (i.e., “hardwired” or overlearned, but relatively inflexible) to controlled (less efficient and effortful, but more flexible). Control is central to human cognition, and plays a key role in our ability to modify the world to suit our needs. Given its advantages, reliance on controlled processing may seem predestined to increase within the population over time. Here, we examine whether this is so by introducing an evolutionary game theoretic model of agents that vary in their use of automatic versus controlled processes, and in which cognitive processing modifies the environment in which the agents interact. We find that, under a wide range of parameters and model assumptions, cycles emerge in which the prevalence of each type of processing in the population oscillates between 2 extremes. Rather than inexorably increasing, the emergence of control often creates conditions that lead to its own demise by allowing automaticity to also flourish, thereby undermining the progress made by the initial emergence of controlled processing. We speculate that this observation may have relevance for understanding similar cycles across human history, and may lend insight into some of the circumstances and challenges currently faced by our species.
econotariat  economics  political-econ  policy  decision-making  behavioral-econ  psychology  cog-psych  cycles  oscillation  unintended-consequences  anthropology  broad-econ  cultural-dynamics  tradeoffs  cost-benefit  rot  dysgenics  study  summary  multi  EGT  dynamical  volo-avolo  self-control  discipline  the-monster  pdf  error  rationality  info-dynamics  bounded-cognition  hive-mind  iq  intelligence  order-disorder  risk  microfoundations  science-anxiety  big-picture  hari-seldon  cybernetics 
july 2017 by nhaliday
Evolution of sexual asymmetry | BMC Evolutionary Biology | Full Text
Background
The clear dominance of two-gender sex in recent species is a notorious puzzle of evolutionary theory. It has at least two layers: besides the most fundamental and challenging question why sex exists at all, the other part of the problem is equally perplexing but much less studied. Why do most sexual organisms use a binary mating system? Even if sex confers an evolutionary advantage (through whatever genetic mechanism), why does it manifest that advantage in two, and exactly two, genders (or mating types)? Why not just one, and why not more than two?

Results
Assuming that sex carries an inherent fitness advantage over pure clonal multiplication, we attempt to give a feasible solution to the problem of the evolution of dimorphic sexual asymmetry as opposed to monomorphic symmetry by using a spatial (cellular automaton) model and its non-spatial (mean-field) approximation. Based on a comparison of the spatial model to the mean-field approximation we suggest that spatial population structure must have played a significant role in the evolution of mating types, due to the largely clonal (self-aggregated) spatial distribution of gamete types, which is plausible in aquatic habitats for physical reasons, and appears to facilitate the evolution of a binary mating system.

Conclusions
Under broad ecological and genetic conditions the cellular automaton predicts selective removal from the population of supposedly primitive gametes that are able to mate with their own type, whereas the non-spatial model admits coexistence of the primitive type and the mating types. Thus we offer a basically ecological solution to a theoretical problem that earlier models based on random gamete encounters had failed to resolve.

Having sex, yes, but with whom? Inferences from fungi on the evolution of anisogamy and mating types: http://onlinelibrary.wiley.com/doi/10.1111/j.1469-185X.2010.00153.x/full
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march 2017 by nhaliday
Religion, fertility and genes: a dual inheritance model | Proceedings of the Royal Society of London B: Biological Sciences
The paper considers the effect of religious defections and exogamy on the religious and genetic composition of society. Defections reduce the ultimate share of the population with religious allegiance and slow down the spread of the religiosity gene. However, provided the fertility differential persists, and people with a religious allegiance mate mainly with people like themselves, the religiosity gene will eventually predominate despite a high rate of defection. This is an example of ‘cultural hitch-hiking’, whereby a gene spreads because it is able to hitch a ride with a high-fitness cultural practice.
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march 2017 by nhaliday
Discovering Limits to Growth | Do the Math
https://en.wikipedia.org/wiki/The_Limits_to_Growth
http://www.unz.com/akarlin/review-limits-to-growth-meadows/
https://foundational-research.org/the-future-of-growth-near-zero-growth-rates/
One may of course be skeptical that this general trend will also apply to the growth of our technology and economy at large, as innovation seems to continually postpone our clash with the ceiling, yet it seems inescapable that it must. For in light of what we know about physics, we can conclude that exponential growth of the kinds we see today, in technology in particular and in our economy more generally, must come to an end, and do so relatively soon.
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march 2017 by nhaliday
Social Epistasis Amplifies the Fitness Costs of Deleterious Mutations, Engendering Rapid Fitness Decline Among Modernized Populations | SpringerLink
- Michael A. Woodley

We argue that in social species, interorganismal gene-gene interactions, which in previous literatures have been termed social epistasis, allow genomes carrying deleterious mutations to reduce via group-level pleiotropy the fitness of others, including noncarriers. This fitness reduction occurs by way of degradation of group-level processes that optimize the reproductive ecology of a population for intergroup competition through, among other mechanisms, suppression of free-riding.

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Fitness indicators theory (Houle 2000; Miller 2000) predicts that the behavioral and physiological condition of prospective partners strongly influences female mate choice in particular, as these constitute honest indicators of underlying genetic quality. Furthermore, as deleterious mutations are pleiotropic (i.e., they can influence the development of multiple traits simultaneously), they are a source of genetic correlation among diverse behavioral and physiological domains, yielding a latent general fitness factor( f ). This optimizes the efficiency of sexual selection, as selection for quality with respect to one domain will increase the probability of selection for quality “across the board” (Houle 2000; Miller 2000). If purifying selection is primarily cryptic—working by virtue of those lower in f simply being less successful in competition for mates and therefore producing fewer offspring relative to those higher in the factor—then considerably less reproductive failure is needed to solve the mutation load paradox (19% instead of 88% based on simulations in Leseque et al. 2012).

...

Theoretical work involving humans suggests a loss of intrinsic fitness of around 1% per generation in the populations of modernized countries (Lynch 2016; Muller 1950). Thus, these might yet be undergoing mutational meltdown, albeit very gradually (i.e., over the course of centuries)

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An interesting observation is that the fitness of the populations of modernized nations does appear to be rapidly decreasing—although not in a manner consonant with the direct action of deleterious mutations on the fitness of individuals (as per the mutation load paradox).

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Increased education has furthermore encouraged individuals to trade fertility against opportunities to enhance their social status and earning power, with the largest fitness losses occurring among those with high status who potentially carry fewer deleterious mutations (i.e., by virtue of possessing higher levels of traits that exhibit some sensitivity to mutation load, such as general intelligence; Spain et al. 2015; Woodley of Menie et al. 2016a). Hitherto not considered is the possibility that the demographic transition represents a potential change in the fitness characteristics of the group-level extended phenotype of modernized populations, indicating that there might exist pathways through which deleterious mutations that accumulate due to ecological mildness could pathologically alter fertility tradeoffs in ways that might account for the maladaptive aspects of the fertility transition (e.g., subreplacement fertility; Basten, Lutz and Scherbov, 2013).

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Cooperation, though offering significant fitness benefits to individual organisms and groups, involves some costs for cooperators in order to realize mutual gains for all parties. Free riders are individuals that benefit from cooperation without suffering any of the costs needed to sustain it. Hence, free riders enjoy a fitness advantage relative to cooperators via the former’s parasitism on the latter.

...

The balance of selection can alternate between the different levels depending on the sorts of selective challenges that a population encounters. For example, group selection may operate on human populations during times of intergroup conflict (i.e., warfare), whereas during times of peace, selection may tend to favor the fitness of individuals instead (Woodley and Figueredo 2013; Wilson 2002). A major factor that seems to permit group-level selection to be viable under certain ecological regimes is the existence of free-rider controls, i.e., features of the group’s social ecology that curb the reproductive fitness of the carriers of “selfish” genetic variants (MacDonald 1994; Wilson 2002).

...

High-status individuals participate in the generation and vertical cultural transmission of free-rider controls—these take the form of religious and ideological systems which make a virtue out of behaviors that overtly benefit the group, and a vice out of those that only favor individual-level fitness, via the promotion of ethnocentrism, martyrdom, and displays of commitment (MacDonald 1994, 2009, 2010; Wilson 2002). Humans are furthermore equipped with specialized mental adaptations for coordinating as part of a group, such as effortful control—the ability to override implicit behavioral drives via the use of explicit processing systems, which allow them to regulate their behavior based on what is optimal for the group (MacDonald 2008). The interaction between individuals of different degrees of status, i.e., those that generate and maintain cultural norms and those who are merely subject to them, therefore constitutes a form of social epistasis, as the complex patterns of interactions among genomes that characterize human culture have the effect of regulating both individual- and group-level (via the curbing of free-riding) fitness (MacDonald 2009, 2010).

Mutations that push the behavior of high-status individuals away from the promotion of group-selected norms may promote a breakdown of or otherwise alter these social epistatic interactions, causing dysregulation of the group’s reproductive ecology. Behavioral changes are furthermore a highly likely consequence of mutation accumulation, as “behavior” (construed broadly) is a large potential target for new mutations (Miller 2000; Lynch 2016) 1 owing to the fact that approximately 84% of all genes in the human genome are involved in some aspect of brain development and/or maintenance (Hawrylycz et al. 2012).

Consistent with the theorized role of group-level (cultural) regulatory processes in the maintenance of fitness optima, positive correlations exist between religiosity (a major freerider control; MacDonald 1994; Wilson 2002) and fertility, both at the individual differences and cross-cultural levels (Meisenberg 2011). Religiosity has declined in modernized nations—a process that has gone hand-in-hand with the rise of a values system called postmaterialism (Inglehart 1977), which is characterized by the proliferation of individualistic, secular, and antihierarchical values (Welzel 2013). The holding of these values is negatively associated with fertility, both at the individual level (when measured as political liberalism; Goldstone et al. 2011) and across time and cultures (Inglehart and Appel 1989). The rise of postmaterialist values is also associated with increasingly delayed onset of reproduction (Klien 1990) which directly increases the (population) mutation load.

Pathological Altruism

Some of the values embodied in postmaterialism have been linked to the pathological altruism phenomenon, i.e., forms of altruism that damage the intended recipients or givers of largesse (Oakley et al. 2012; Oakley 2013). Virtues associated with altruism such as kindness, fidelity, magnanimity, and heroism, along with quasi-moral traits associated with personality and mental health, may be under sexual selection and might therefore be sensitive, through the f factor, to the deleterious effects of accumulating mutations (Miller 2007).

...

Another form of pathologically altruistic behavior that Oakley (2013) documents is self-righteousness, which may be increasing, consistent with secular trend data indicating elevated levels of self-regarding behavior among Western populations (sometimes called the narcissism epidemic; Twenge and Campbell 2009). This sort of behavior constitutes a key component of the clever silly phenomenon in which the embrace of counterfactual beliefs is used to leverage social status via virtue signaling (e.g., the conflation of moral equality among individuals, sexes, and populations with biological equality) (Dutton and van der Linden 2015; Charlton 2009; Woodley 2010). There may be a greater number of influential persons inclined to disseminate such beliefs, in that the prevalence of phenotypes disposed toward egoistic behaviors may have increased in Western populations (per Twenge and coworkers’ research), and because egoists, specifically Machiavellians and narcissists, appear advantaged in the acquisition of elite societal stations (Spurk et al. 2015).

[Do Bad Guys Get Ahead or Fall Behind? Relationships of the Dark Triad of Personality With Objective and Subjective Career Success: http://sci-hub.tw/http://journals.sagepub.com/doi/abs/10.1177/1948550615609735

After controlling for other relevant variables (i.e., gender, age, job tenure, organization size, education, and work hours), narcissism was positively related to salary, Machiavellianism was positively related to leadership position and career satisfaction, and psychopathy was negatively related to all analyzed outcomes.]

...

By altering cultural norms, elite egoists may encourage the efflorescence of selfish behaviors against which some older and once highly influential cultural systems acted. For example, Christianity in various forms strongly promoted personal sacrifice for the good of groups and proscribed egoistic behaviors (Rubin 2015), but has declined significantly in terms of cultural power following modernization (Inglehart 1977). Thus, it is possible that a feedback loop exists wherein deleterious mutation accumulation raises population levels of egoism, either directly or indirectly, via the breakdown of developmental constraints on personality canalization; the resultantly greater number of egoists are then able to exploit relevant personality traits to attain positions of sociocultural influence; and through these … [more]
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march 2017 by nhaliday
Fundamental Theorems of Evolution: The American Naturalist: Vol 0, No 0
I suggest that the most fundamental theorem of evolution is the Price equation, both because of its simplicity and broad scope and because it can be used to derive four other familiar results that are similarly fundamental: Fisher’s average-excess equation, Robertson’s secondary theorem of natural selection, the breeder’s equation, and Fisher’s fundamental theorem. These derivations clarify both the relationships behind these results and their assumptions. Slightly less fundamental results include those for multivariate evolution and social selection. A key feature of fundamental theorems is that they have great simplicity and scope, which are often achieved by sacrificing perfect accuracy. Quantitative genetics has been more productive of fundamental theorems than population genetics, probably because its empirical focus on unknown genotypes freed it from the tyranny of detail and allowed it to focus on general issues.
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march 2017 by nhaliday
Give me your caffeinated, your well-off, your above-average yearning to get ahead – spottedtoad
Even though the mean has shifted only 0.2 standard deviations to the left, the % of the population that exceeds certain benchmarks has dropped considerably: there are only 58% as many people who exceed 1 standard deviation above the starting mean, 38% as many who exceed 2 standard deviations, and less than 25% as many who exceed 3 standard deviations as before the 30 years. This obviously influences the percentage of the population who can become competent government workers, or doctors or teachers or college professors or engineers.

this kinda argument always seems like concern trolling to me tho

see https://pinboard.in/u:nhaliday/b:2fc26306583e for some relevant calculations (need to take into account heritability too)

Brain Drain: Socio-Economic Impact on Indian Society: http://www.ijhssi.org/papers/v2(5)/version-3/C251217.pdf

https://spottedtoad.wordpress.com/2018/01/12/digging-your-way-out-of-a-hole/
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february 2017 by nhaliday
Information Geometry (Part 16) | Azimuth
While preparing this talk, I discovered a cool fact. I doubt it’s new, but I haven’t exactly seen it elsewhere. I came up with it while trying to give a precise and general statement of ‘Fisher’s fundamental theorem of natural selection’. I won’t start by explaining that theorem, since my version looks rather different than Fisher’s, and I came up with mine precisely because I had trouble understanding his. I’ll say a bit more about this at the end.

Here’s my version:
The square of the rate at which a population learns information is the variance of its fitness.
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february 2017 by nhaliday
mg.metric geometry - Pushing convex bodies together - MathOverflow
- volume of intersection of colliding, constant-velocity convex bodies is unimodal
- pf by Brunn-Minkowski inequality
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january 2017 by nhaliday
soft question - Thinking and Explaining - MathOverflow
- good question from Bill Thurston
- great answers by Terry Tao, fedja, Minhyong Kim, gowers, etc.

Terry Tao:
- symmetry as blurring/vibrating/wobbling, scale invariance
- anthropomorphization, adversarial perspective for estimates/inequalities/quantifiers, spending/economy

fedja walks through his though-process from another answer

Minhyong Kim: anthropology of mathematical philosophizing

Per Vognsen: normality as isotropy
comment: conjugate subgroup gHg^-1 ~ "H but somewhere else in G"

gowers: hidden things in basic mathematics/arithmetic
comment by Ryan Budney: x sin(x) via x -> (x, sin(x)), (x, y) -> xy
I kinda get what he's talking about but needed to use Mathematica to get the initial visualization down.
To remind myself later:
- xy can be easily visualized by juxtaposing the two parabolae x^2 and -x^2 diagonally
- x sin(x) can be visualized along that surface by moving your finger along the line (x, 0) but adding some oscillations in y direction according to sin(x)
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january 2017 by nhaliday
Noise: dinosaurs, syphilis, and all that | West Hunter
Generally speaking, I thought the paleontologists were a waste of space: innumerate, ignorant about evolution, and simply not very smart.

None of them seemed to understand that a sharp, short unpleasant event is better at causing a mass extinction, since it doesn’t give flora and fauna time to adapt.

Most seemed to think that gradual change caused by slow geological and erosion forces was ‘natural’, while extraterrestrial impact was not. But if you look at the Moon, or Mars, or the Kirkwood gaps in the asteroids, or think about the KAM theorem, it is apparent that Newtonian dynamics implies that orbits will be perturbed, and that sometimes there will be catastrophic cosmic collisions. Newtonian dynamics is as ‘natural’ as it gets: paleontologists not studying it in school and not having much math hardly makes it ‘unnatural’.

One of the more interesting general errors was not understanding how to to deal with noise – incorrect observations. There’s a lot of noise in the paleontological record. Dinosaur bones can be eroded and redeposited well after their life times – well after the extinction of all dinosaurs. The fossil record is patchy: if a species is rare, it can easily look as if it went extinct well before it actually did. This means that the data we have is never going to agree with a perfectly correct hypothesis – because some of the data is always wrong. Particularly true if the hypothesis is specific and falsifiable. If your hypothesis is vague and imprecise – not even wrong – it isn’t nearly as susceptible to noise. As far as I can tell, a lot of paleontologists [ along with everyone in the social sciences] think of of unfalsifiability as a strength.

Done Quickly: https://westhunt.wordpress.com/2011/12/03/done-quickly/
I’ve never seen anyone talk about it much, but when you think about mass extinctions, you also have to think about rates of change

You can think of a species occupying a point in a many-dimensional space, where each dimension represents some parameter that influences survival and/or reproduction: temperature, insolation, nutrient concentrations, oxygen partial pressure, toxin levels, yada yada yada. That point lies within a zone of habitability – the set of environmental conditions that the species can survive. Mass extinction occurs when environmental changes are so large that many species are outside their comfort zone.

The key point is that, with gradual change, species adapt. In just a few generations, you can see significant heritable responses to a new environment. Frogs have evolved much greater tolerance of acidification in 40 years (about 15 generations). Some plants in California have evolved much greater tolerance of copper in just 70 years.

As this happens, the boundaries of the comfort zone move. Extinctions occur when the rate of environmental change is greater than the rate of adaptation, or when the amount of environmental change exceeds the limit of feasible adaptation. There are such limits: bar-headed geese fly over Mt. Everest, where the oxygen partial pressure is about a third of that at sea level, but I’m pretty sure that no bird could survive on the Moon.

...

Paleontologists prefer gradualist explanations for mass extinctions, but they must be wrong, for the most part.
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september 2016 by nhaliday

bundles : abstract

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