Eikonal Blog


Denialism of science

  • Denialism (WikiPedia) – http://en.wikipedia.org/wiki/Denialism
    • In human behavior, denialism is exhibited by individuals choosing to deny reality as a way to avoid dealing with an uncomfortable truth. … “[It] is the refusal to accept an empirically verifiable reality. It is an essentially irrational action that withholds validation of a historical experience or event”. … group denialism [is defined] as “when an entire segment of society, often struggling with the trauma of change, turns away from reality in favor of a more comfortable lie.”
    • In science, denialism has been defined as the rejection of basic concepts that are undisputed and well-supported parts of the scientific consensus on a topic in favor of ideas that are both radical and controversial. … It has been proposed that the various forms of denialism have the common feature of the rejection of overwhelming evidence and the generation of a controversy through attempts to deny that a consensus exists. … A common example is Young Earth creationism and its dispute with the evolutionary theory.


  • “How To Convince Conservative Christians That Global Warming Is Real” by Chris Mooney (Mother Jones; 2014.05.02) – http://www.motherjones.com/environment/2014/05/inquiring-minds-katharine-hayhoe-faith-climate
    • Millions of Americans are evangelical Christians. Climate scientist Katharine Hayhoe is persuading them that our planet is in peril.
    • “Years of Living Dangerously Premiere Full Episode” – https://www.youtube.com/watch?v=brvhCnYvxQQ
  • “Most Americans doubt Big Bang, not too sure about evolution, climate change – survey” By Rik Myslewski (The Register; 2014.04.21) – http://www.theregister.co.uk/2014/04/21/most_americans_doubt_big_bang_not_too_sure_about_evolution_climate_change_survey/
    • Science no match for religion, politics, business interests


  • “AP-GfK Poll: Big Bang a big question for most Americans” (AP-Gfk; 2014.04.21) – http://ap-gfkpoll.com/featured/findings-from-our-latest-poll-2
    • Few Americans question that smoking causes cancer. But they express bigger doubts as concepts that scientists consider to be truths get further from our own experiences and the present time … Americans have more skepticism than confidence in global warming, the age of the Earth and evolution and have the most trouble believing a Big Bang created the universe 13.8 billion years ago….
    • Just 4 percent doubt that smoking causes cancer, 6 percent question whether mental illness is a medical condition that affects the brain and 8 percent are skeptical there’s a genetic code inside our cells. More – 15 percent – have doubts about the safety and efficacy of childhood vaccines …
    • About 4 in 10 say they are not too confident or outright disbelieve that the earth is warming, mostly a result of man-made heat-trapping gases, that the Earth is 4.5 billion years old or that life on Earth evolved through a process of natural selection, though most were at least somewhat confident in each of those concepts. But a narrow majority – 51 percent – questions the Big Bang theory …
    • “Science ignorance is pervasive in our society, and these attitudes are reinforced when some of our leaders are openly antagonistic to established facts,”…
    • The poll highlights “the iron triangle of science, religion and politics,” … And scientists know they’ve got the shakiest leg in the triangle….
    • To the public “most often values and beliefs trump science” when they conflict, … … Political values were closely tied to views on science in the poll, with Democrats more apt than Republicans to express confidence in evolution, the Big Bang, the age of the Earth and climate change….
    • Religious values are similarly important… Confidence in evolution, the Big Bang, the age of the Earth and climate change decline sharply as faith in a supreme being rises, according to the poll. Likewise, those who regularly attend religious services or are evangelical Christians express much greater doubts about scientific concepts they may see as contradictory to their faith … “When you are putting up facts against faith, facts can’t argue against faith,” … “It makes sense now that science would have made no headway because faith is untestable.” …
    • Beyond religious belief, views on science may be tied to what we see with our own eyes. The closer an issue is to our bodies and the less complicated, the easier it is for people to believe, …
    • Marsha Brooks, a 59-year-old nanny who lives in Washington, D.C., said she’s certain smoking causes cancer because she saw her mother, aunts and uncles, all smokers, die of cancer … But when it comes to the universe beginning with a Big Bang or the Earth being about 4.5 billion years old, she has doubts. …
    • Jorge Delarosa, a 39-year-old architect from Bridgewater, N.J., pointed to a warm 2012 without a winter and said, “I feel the change. There must be a reason.” But when it came to Earth’s beginnings 4.5 billion years ago, he has doubts simply because “I wasn’t there.”…
    • Experience and faith aren’t the only things affecting people’s views on science. … “the force of concerted campaigns to discredit scientific fact” as a more striking factor, citing significant interest groups – political, business and religious – campaigning against scientific truths on vaccines, climate change and evolution….
    • … sometimes science wins out even against well-financed and loud opposition, as with smoking. Widespread belief that smoking causes cancer “has come about because of very public, very focused public health campaigns,” … [also, what is very encouraging is] the public’s acceptance that mental illness is a brain disease, something few believed 25 years ago, before just such a campaign.
  • “Why climate deniers are winning: The twisted psychology that overwhelms scientific consensus” by Paul Rosenberg (The Salon; 2014.04.19) – http://www.salon.com/2014/04/19/why_climate_deniers_are_winning_the_twisted_psychology_that_overwhelms_scientific_consensus/
    • There’s a reason why overwhelming evidence hasn’t spurred public action against global warming
    • “The reason ‘consensus’ has not appeared to work in society at large to date isn’t because it’s ineffective – it’s because there is a well-funded counter-movement out there that takes every opportunity to mislead the public into thinking that there isn’t a consensus,”
  • “How politics makes us stupid” by Ezra Klein (Vox; 2014.04.06) – http://www.vox.com/2014/4/6/5556462/brain-dead-how-politics-makes-us-stupid

Older articles

  • “How Do You Get People to Give a Damn About Climate Change?” by Chris Mooney (Mother Jones; 2013.10.18) – http://www.motherjones.com/environment/2013/10/inquiring-minds-kahan-lewandowsky-communicate-climate
    • Experts have come a long way in figuring out which messages can successfully open minds and move public opinion. There’s just one problem: They disagree about whether the message everyone’s using actually works.
  • “Scientific uncertainty and climate change: Part I. Uncertainty and unabated emissions” by Stephan Lewandowsky, James S. Risbey, Michael Smithson, Ben R. Newell, John Hunter (Springer) – http://link.springer.com/article/10.1007/s10584-014-1082-7
    • Uncertainty forms an integral part of climate science, and it is often used to argue against mitigative action. This article presents an analysis of uncertainty in climate sensitivity that is robust to a range of assumptions. We show that increasing uncertainty is necessarily associated with greater expected damages from warming, provided the function relating warming to damages is convex. This constraint is unaffected by subjective or cultural risk-perception factors, it is unlikely to be overcome by the discount rate, and it is independent of the presumed magnitude of climate sensitivity. The analysis also extends to “second-order” uncertainty; that is, situations in which experts disagree. Greater disagreement among experts increases the likelihood that the risk of exceeding a global temperature threshold is greater. Likewise, increasing uncertainty requires increasingly greater protective measures against sea level rise. This constraint derives directly from the statistical properties of extreme values. We conclude that any appeal to uncertainty compels a stronger, rather than weaker, concern about unabated warming than in the absence of uncertainty.
  • “Scientific uncertainty and climate change: Part II. Uncertainty and mitigation” by Stephan Lewandowsky, James S. Risbey, Michael Smithson, Ben R. Newell (Springer) – http://link.springer.com/article/10.1007/s10584-014-1083-6
    • In public debate surrounding climate change, scientific uncertainty is often cited in connection with arguments against mitigative action. This article examines the role of uncertainty about future climate change in determining the likely success or failure of mitigative action. We show by Monte Carlo simulation that greater uncertainty translates into a greater likelihood that mitigation efforts will fail to limit global warming to a target (e.g., 2 °C). The effect of uncertainty can be reduced by limiting greenhouse gas emissions. Taken together with the fact that greater uncertainty also increases the potential damages arising from unabated emissions (Lewandowsky et al. 2014), any appeal to uncertainty implies a stronger, rather than weaker, need to cut greenhouse gas emissions than in the absence of uncertainty.
  • “The pivotal role of perceived scientific consensus in acceptance of science” by Stephan Lewandowsky, Gilles E. Gignac, Samuel Vaughan (Nature Climate Change 3, 399-404 (2013); doi:10.1038/nclimate1720; 2012.10.28) – http://www.nature.com/nclimate/journal/v3/n4/full/nclimate1720.html
    • Although most experts agree that CO2 emissions are causing anthropogenic global warming (AGW), public concern has been declining. One reason for this decline is the ‘manufacture of doubt’ by political and vested interests, which often challenge the existence of the scientific consensus. The role of perceived consensus in shaping public opinion is therefore of considerable interest: in particular, it is unknown whether consensus determines people’s beliefs causally. It is also unclear whether perception of consensus can override people’s ‘worldviews’, which are known to foster rejection of AGW. Study 1 shows that acceptance of several scientific propositions-from HIV/AIDS to AGW-is captured by a common factor that is correlated with another factor that captures perceived scientific consensus. Study 2 reveals a causal role of perceived consensus by showing that acceptance of AGW increases when consensus is highlighted. Consensus information also neutralizes the effect of worldview.




Filed under: education, health, mind & brain, society — Tags: , , , — sandokan65 @ 09:26
  • Poverty @WikiPedia – http://en.wikipedia.org/wiki/Poverty
    • Poverty is general scarcity or dearth, or the state of one who lacks a certain amount of material possessions or money.
  • “Your Brain on Poverty: Why Poor People Seem to Make Bad Decisions (And why their “bad” decisions might be more rational than you’d think.)” by Derek Thompson (The Atlantic; 2013.11.22) – http://www.theatlantic.com/business/archive/2013/11/your-brain-on-poverty-why-poor-people-seem-to-make-bad-decisions/281780/
  • “This Is Why Poor People’s Bad Decisions Make Perfect Sense” by Linda Tirado (The Huffington Post; 2013.11.22) – http://www.huffingtonpost.com/linda-tirado/why-poor-peoples-bad-decisions-make-perfect-sense_b_4326233.html
  • “Why I Make Terrible Decisions, or, poverty thoughts” by Killermar (2013.11.22) – http://killermartinis.kinja.com/why-i-make-terrible-decisions-or-poverty-thoughts-1450123558
  • “The High Cost of Not Having Enough” by Emily Badger (The Atlantic > Cities; 2013.09.04) – http://www.theatlanticcities.com/jobs-and-economy/2013/09/high-cost-not-having-enough/6759/
  • “How Poverty Taxes the Brain” by Emily Badger (The Atlantic > Cities; 2013.08.29) – http://www.theatlanticcities.com/jobs-and-economy/2013/08/how-poverty-taxes-brain/6716/
  • “Poverty Impedes Cognitive Function” by Anandi Mani1, Sendhil Mullainathan, Eldar Shafir and Jiaying Zhao (Science; 2013.08.30; Vol. 341 no. 6149 pp. 976-980) – http://www.sciencemag.org/content/341/6149/976.abstract
    • Burden of Poverty: Lacking money or time can lead one to make poorer decisions, possibly because poverty imposes a cognitive load that saps attention and reduces effort. Mani et al. (p. 976; see the Perspective by Vohs) gathered evidence from shoppers in a New Jersey mall and from farmers in Tamil Nadu, India. They found that considering a projected financial decision, such as how to pay for a car repair, affects people’s performance on unrelated spatial and reasoning tasks. Lower-income individuals performed poorly if the repairs were expensive but did fine if the cost was low, whereas higher-income individuals performed well in both conditions, as if the projected financial burden imposed no cognitive pressure. Similarly, the sugarcane farmers from Tamil Nadu performed these tasks better after harvest than before.
    • Abstract: The poor often behave in less capable ways, which can further perpetuate poverty. We hypothesize that poverty directly impedes cognitive function and present two studies that test this hypothesis. First, we experimentally induced thoughts about finances and found that this reduces cognitive performance among poor but not in well-off participants. Second, we examined the cognitive function of farmers over the planting cycle. We found that the same farmer shows diminished cognitive performance before harvest, when poor, as compared with after harvest, when rich. This cannot be explained by differences in time available, nutrition, or work effort. Nor can it be explained with stress: Although farmers do show more stress before harvest, that does not account for diminished cognitive performance. Instead, it appears that poverty itself reduces cognitive capacity. We suggest that this is because poverty-related concerns consume mental resources, leaving less for other tasks. These data provide a previously unexamined perspective and help explain a spectrum of behaviors among the poor. We discuss some implications for poverty policy.


Peopling of Americas

Filed under: anthropology, evolution, geneaology, history, past — Tags: , , — sandokan65 @ 10:43


  • “Discoveries Challenge Beliefs on Humans’ Arrival in the Americas” by Simon Rommero (The New York Times; 2014.03.27) – http://www.nytimes.com/2014/03/28/world/americas/discoveries-challenge-beliefs-on-humans-arrival-in-the-americas.html?_r=0
    • Researchers here say they have unearthed stone tools proving that humans reached what is now northeast Brazil as early as 22,000 years ago. Their discovery adds to the growing body of research upending a prevailing belief of 20th-century archaeology in the United States known as the Clovis model, which holds that people first arrived in the Americas from Asia about 13,000 years ago.
    • More recently, numerous findings have challenged that narrative. In Texas, archaeologists said in 2011 that they had found projectile points showing that hunter-gatherers had reached another site, known as Buttermilk Creek, as early as 15,500 years ago. Similarly, analysis of human DNA found at an Oregon cave determined that humans were there 14,000 years ago.

      But it is in South America, thousands of miles from the New Mexico site where the Clovis spear points were discovered, where archaeologists are putting forward some of the most profound challenges to the Clovis-first theory.

      Paleontologists in Uruguay published findings in November suggesting that humans hunted giant sloths there about 30,000 years ago. All the way in southern Chile, Tom D. Dillehay, an anthropologist at Vanderbilt University, has shown that humans lived at a coastal site called Monte Verde as early as 14,800 years ago.

    • In what may be another blow to the Clovis model of humans’ coming from northeast Asia, molecular geneticists showed last year that the Botocudo indigenous people living in southeastern Brazil in the late 1800s shared gene sequences commonly found among Pacific Islanders from Polynesia.
  • “Native Americans Descend From Ancient Montana Boy” (Science; 2014.02.12) – http://news.sciencemag.org/archaeology/2014/02/native-americans-descend-ancient-montana-boy


  • “DNA reveals details of the peopling of the Americas” by Tina Hesman Saey (Science news; 2013.11.21) – https://www.sciencenews.org/article/dna-reveals-details-peopling-americas
    • Migrants came in three distinct waves that interbred once in the New World
    • About 15,000 to 18,000 years ago, the first migrant wave spilled from Asia down the Pacific coast and then pushed inland, eventually peopling the land from “the tip of South America all the way to Hudson Bay,” says Andrew Kitchen, a genetic anthropologist at the University of Iowa who was not involved in the new research. That first migrant wave contained the ancestors of all South and Central American tribes, and North Americans, too. But something different was going on in North America, an international team of researchers has discovered.
    • A second wave of migration probably left Siberia only a couple thousand years after the first wave. Instead of trickling down the coast, the second group slipped through an ice-free corridor running from Alaska into what is now southern Canada, the team found. The second wave never made it south of the present-day United States. The mixture of first-wave and second-wave genetic signatures in some Native Americans today indicates that the newcomers and existing populations interbred.
    • A third wave of migration started around 4,000 years ago in Alaska and swept mostly eastward across Canada.
    • Previous studies of human migration into the Americas have sometimes focused on two types of languages that emerged among the tribes: the Na-Dene language family, including Navajo, Apache and Tlingit, and non-Na-Dene languages, including Algonquin, Ojibwe and Chippewa. Scientists had thought the language groups reflected genetic separation, with the second wave being restricted to the Na-Dene language family. But Torroni and his colleagues discovered that second-wave genetic marks occurred in people who spoke languages from both groups. The finding suggests that the languages developed after the people arrived, and gives a more dynamic picture of what was happening in eastern North America, says Kitchen.
  • “DNA testing on 24,000-year-old skeleton reveals that Native Americans could have EUROPEAN origins” by Ellie Zolfagharifard (MailOnline; 2013.11.21) – http://www.dailymail.co.uk/sciencetech/article-2511172/DNA-testing-24-000-year-old-skeleton-reveals-Native-Americans-EUROPEAN-origins.html
    • The genome of the four-year-old boy is the oldest sequenced to date
    • DNA from the remains, discovered in Siberia in the 1920s, are thought to contain a third of Native American ancestry’s gene pool
    • Interestingly, the boy showed no similarities with populations in East Asia
  • “Ancient Bone of 24,000-Year-Old Siberian Youth Shows Native Americans had West Eurasian Origins” by Kathleen Lee (Science World Report; 2013.11.21) – http://www.scienceworldreport.com/articles/11072/20131121/ancient-bone-of-24-000-year-old-siberian-youth-shows-native-americans-had-west-eurasian-origins.htm
  • “DNA indicates Eurasian roots for Native Americans, new study says” by Meeri Kim (The Washington Post; 2013.11.20) – http://www.washingtonpost.com/national/health-science/fossil-indicates-eurasian-roots-for-native-americans/2013/11/20/2777ac24-51fa-11e3-a7f0-b790929232e1_story.html
  • “24,000-Year-Old Body Shows Kinship to Europeans and American Indians” by NICHOLAS WADE (The New York Times; 2013.11.20) – http://www.nytimes.com/2013/11/21/science/two-surprises-in-dna-of-boy-found-buried-in-siberia.html
  • “”Great Surprise”—Native Americans Have West Eurasian Origins” by Brian Handwerk (National Geographic; 2013.11.20) – http://news.nationalgeographic.com/news/2013/11/131120-science-native-american-people-migration-siberia-genetics
    • Oldest human genome reveals less of an East Asian ancestry than thought.
    • Nearly one-third of Native American genes come from west Eurasian people linked to the Middle East and Europe, rather than entirely from East Asians as previously thought, according to a newly sequenced genome.
  • “Upper Palaeolithic Siberian genome reveals dual ancestry of Native Americans” (Nature; 2013.11.20) – http://www.nature.com/nature/journal/vaop/ncurrent/full/nature12736.html
    • Abstract: The origins of the First Americans remain contentious. Although Native Americans seem to be genetically most closely related to east Asians1, 2, 3, there is no consensus with regard to which specific Old World populations they are closest to4, 5, 6, 7, 8. Here we sequence the draft genome of an approximately 24,000-year-old individual (MA-1), from Mal’ta in south-central Siberia9, to an average depth of 1×. To our knowledge this is the oldest anatomically modern human genome reported to date. The MA-1 mitochondrial genome belongs to haplogroup U, which has also been found at high frequency among Upper Palaeolithic and Mesolithic European hunter-gatherers10, 11, 12, and the Y chromosome of MA-1 is basal to modern-day western Eurasians and near the root of most Native American lineages5. Similarly, we find autosomal evidence that MA-1 is basal to modern-day western Eurasians and genetically closely related to modern-day Native Americans, with no close affinity to east Asians. This suggests that populations related to contemporary western Eurasians had a more north-easterly distribution 24,000 years ago than commonly thought. Furthermore, we estimate that 14 to 38% of Native American ancestry may originate through gene flow from this ancient population. This is likely to have occurred after the divergence of Native American ancestors from east Asian ancestors, but before the diversification of Native American populations in the New World. Gene flow from the MA-1 lineage into Native American ancestors could explain why several crania from the First Americans have been reported as bearing morphological characteristics that do not resemble those of east Asians2, 13. Sequencing of another south-central Siberian, Afontova Gora-2 dating to approximately 17,000 years ago14, revealed similar autosomal genetic signatures as MA-1, suggesting that the region was continuously occupied by humans throughout the Last Glacial Maximum. Our findings reveal that western Eurasian genetic signatures in modern-day Native Americans derive not only from post-Columbian admixture, as commonly thought, but also from a mixed ancestry of the First Americans.
  • “Disputed finds put humans in South America 22,000 years ago” by Bruce Bower (*Science News; 2013.04.20) – https://www.sciencenews.org/article/disputed-finds-put-humans-south-america-22000-years-ago
    • Brazilian site may have been home to people before the Clovis hunters
    • C. Lahaye et al. Human occupation in South America by 20,000 BC: The Toca da Tira Peia site, Piaui, Brazil. Journal of Archaeological Science. Doi: 10.1016/j.jas.2013.02.019.



  • “Stone tools cut swathe through Clovis history” by Matt Kaplan (nature; 2011.03.24) – http://www.nature.com/news/2011/110324/full/news.2011.185.html
    • Dig uncovers previously unknown North American culture.
    • The long-standing idea that the Clovis people of ancient North America were the first tool-using humans on the continent 13,200 years ago is being overturned by the discovery of human artefacts in a Texan creek bed that are even older.


Near-Death Experiences

Filed under: mind & brain — Tags: , — sandokan65 @ 09:17


Applied graph theory (“Social Networks Analysis”)


Graph theory:

  • nodes and edges
  • degree = number of edges for a given node
  • isolated nodes
  • connected nodes
  • hub = well connected node
  • Scale-free networks = average number of nodes stays constant
  • preferential attachment:
    • the fraction of nodes with k edges: p(k) \sim k^{-\gamma}
    • a long tail distribution
  • Degree of distribution

SNAs on YouTube

Six degrees of separation, Small Worlds, Kevin Bacon metric, Erdos metric, etc


Authors and Sites


  • “Power laws, Pareto distributions and Zipf’s law” by M.E.J. Newman (arXiv) – http://arxiv.org/abs/cond-mat/0412004
    • When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people’s personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.
    • more papers by M.E.J. Newman at arXiv – arxiv.org/find/cond-mat/1/au:+Newman_M/0/1/0/all/0/1


Generating functions

Recently I have been rereading the Herbert S. Wilf’s free online book Generatingfunctionologyhttp://www.math.upenn.edu/~wilf/DownldGF.html. It is choke-full of interesting results.


For a number series {\bf a} :\equiv \{a_n|n\in\{0,\infty\}\} one defines following generating functions (GFs):

  • Ordinary Power Series GF (OPSGF): OPSGF[a](x) :\equiv \sum_{n=0}^\infty a_n x^n   \leftrightarrow_{opsgf} {\bf a};
  • Exponential Series GF (EGF): EGF[a](x) :\equiv \sum_{n=0}^\infty a_n \frac{x^n}{n!} \leftrightarrow_{egf} {\bf a};
  • Dirichlet GF (DGF): DGF(x;s) :\equiv \sum_n \frac{a_n}{n^s} x^n \leftrightarrow_{dgf} {\bf a};
  • Lambert GF (LGF): LGF(x) :\equiv \sum_n \frac{a_n}{1-x^n} x^n \leftrightarrow_{lgf} {\bf a};
  • Bell GF (BGF): BGF(x;s) :\equiv \sum_n a_{p^n} x^n \leftrightarrow_{bgf} {\bf a};
  • Poisson GF (PGF): PGF(x;s) :\equiv \sum_n \frac{a_n}{n!} x^n e^{-x} = e^{-x} EGF(x) \leftrightarrow_{pgf} {\bf a};

Simple results

  • \{a_n=n\}  \leftrightarrow_{opsgf} f(x) = \frac{x}{(1-x)^2}.
  • \{a_n=n^2\} \leftrightarrow_{opsgf} f(x) = \frac{x(x+1)}{(1-x)^3}.
  • \{a_n=b^n\}  \leftrightarrow_{opsgf} f(x) = \frac{1}{1-b x}.
  • \{a_n=n\}  \leftrightarrow_{egf} f(x) = x e^{x}.
  • \{a_n=n^2\}  \leftrightarrow_{egf} f(x) = x(x+1)e^{x}.
  • \{a_n=b^n\}  \leftrightarrow_{egf} f(x) = e^{b x}.
  • For Fibonacci numbers \{F_n|F_{n+1} = F_n + F_{n-1} | f_0 = F_1 = 1\} one has: OPSGF(x) = \frac{x}{1-x-x^2}, leading to F_n = \frac{r_+^n-(r_-^n}{\sqrt{5}} (r_\pm = \frac{1\pm\sqrt{5}}{2}).
  • \{a_n|a_{n+1}=2 a_n + 1| a_0=0\}  \leftrightarrow_{opsgf} OPSGF = \frac{x}{(1-x)(1-2x)} = \frac{1}{1-2x} - \frac{1}{1-x}; which leads to a_n=2^n - 1.
  • For a_{n+1} = 2 a_n + n, $alatex _0=1$ one has: OPSGF = \frac{2}{1-2x} - \frac1{(1-x)^2} leading to
    a_n = 2^{n-1} - n - 1.

Define [x^n]f(x) as the coefficient next to x^n in power series f(x). Examples and properties:

  • [x^n] e^x = \frac1{n!},
  • [x^n] \frac1{1-ax} = a^n,
  • [x^n] (1+x)^s = \binom{s}{n},
  • [x^n] \{x^m f(x)\} = [x^{n-m}] f(x),
  • [\lambda x^n] f(x) = \frac1{\lambda} [x^n]f(x),
  • \left[\frac{x^n}{n!}\right] e^x = 1.

For binomial coeficients:

  • \sum_{k=0}^{\infty} \binom{n}{k} x^k = (1+x)^n,
  • \sum_{n=0}^{\infty} \binom{n}{k} y^n = \frac{y^k}{(1-y)^{k+1}},
  • \binom{n}{k} = [x^k y^n] \frac1{1 - y (1+x)}.

Some orthogonal polynomials:

  • Tchebitshev polynomials generating function: \sum_{n=0}^\infty \frac{z^n}{n!} T_n(x) = e^{zx}\cos(z\sqrt{1-x^2}).
  • Legendre polynomials generating function: \frac1{(1-2tz+z^2)^{\frac12}} = \sum_{n=0}^\infty P_n(t)z^n.
  • Generating function for associated Legendre polynomials: (1-2tc+t^2)^{\alpha} = |1-t e^{i\theta}|^{2\alpha} = \sum_{n=0}^\infty t^n P_n^{\alpha}(c).

Dirichlet series generating functions

  • For a_n=1: DGF = \zeta(s).
  • For a_n=\mu(n) (the Moebius function): DGF = \frac1{\zeta(s)}.
  • For a_n=d(n)=\sigma_0(n) (the zeroth-order divisor function): DGF = \zeta(s)^2.
  • For a_n=\sigma_k(n) (the kth-order divisor function): DGF = \zeta(s)\zeta(s-k).
  • For a_n=\phi(n) (the totient function): DGF = \frac{\zeta(s-1)}{\zeta(s)}.
  • For a_n=H(n) (the number of ordered factorizations): DGF = \frac{1}{2 - \zeta(s)}.
  • For a_n=\frac12 [1-(-1)^n]: DGF = \lambda(s) (the Dirichlet lambda function).

Moebius inversion formula:

  • If two DGF series A(s) and B(s) have coefficient relation a_n = \sum_{d|n} b_d, then A(s) = B(s) \zeta(s), and b_n = \sum_{d|n} \mu\left(\frac{n}{d}\right) a_d.
  • If a_n = \sum_{d|n} b_d, then b_n = \sum_{d|n} \mu\left(\frac{n}{d}\right) a_d.


Pretty little tables

Filed under: mathematics, number theory, puzzles — Tags: , — sandokan65 @ 14:59

Recently I have seen in an math forum this:

    Wonder #1

and just a few days later this one, too:

    Wonders 1-4

Pretty little tables, aren’t they? How could they be so regular? Can they be generalized somehow?

Answers are: yes, you will see, and yes.

Wonder #1

Let’s first take a look at the first table:

Table 1
  • 1 \times 8 + 1 = 9,
  • 12 \times 8 + 2 = 98,
  • 123 \times 8 + 3 = 987,
  • 1,234 \times 8 + 4 = 9,876,
  • 12,345 \times 8 + 5 = 98,765,
  • 123,456 \times 8 + 6 = 987,654,
  • 1,234,567 \times 8 + 7 = 9,876,543,
  • 12,345,678 \times 8 + 8 = 98,765,432,
  • 123,456,789 \times 8 + 9 = 987,654,321,

In order to understand it one has to work not with the specific numbers (digits), but with their abstract representations. For this, we will work with a number system of base B (\in {\Bbb N}), which in the orginal tables is B=10. Then we can rewrite several first members of the Table 1 as follows:

  • 1 \cdot B^0 \times (B-2) + 1 = (B-1) B^0,
  • (1 \cdot B^1 + 2 B^0) \times (B-2) + 2 = (B-1) B^1 + (B-2)B^0,
  • (1 \cdot B^2 + 2 B^1 + 3 B^0) \times (B-2) + 3 = (B-1)B^2 + (B-2)B^1 + (B-3)B^0,
  • etc

Ok, we see some regularity here. To proceed further, rewrite the n^{th} row of that table in the form a mathematical equation y_n :\equiv x_n \cdot \hbox{some number} + \hbox{some other number}, transforming the first beautifully looking number (x_n) into second beautifully looking number y_n.

Here the series \{x_n\} is:

  • x_1 = 1_B = 1\times B^0,
  • x_2 = 12_B = 1\times B^1 + 2 \times B^0,
  • x_3 = 123_B = 1\times B^2 + 2 \times B^1 + 3 \times B^0,
  • x_n = 123...n_B = 1\times B^{n-1} + 2 \times B^{n-2} + \cdots + n \times B^0 = \sum_{k=1}^n k B^{n-k}.
    A side note:
    Note that x_n =  \sum_{s=0}^{n-1} (n-s) B^s. It can be explicitly summarized as follows:

      x_ n = (n- B \partial_B) \sum_{s=0}^{n-1} B^s = (n-B\partial_B) \frac{B^n-1}{B-1} = \frac{B(B^n-1)-n(B-1)}{(B-1)^2}.

    For example, for B=10 that formula yields x_n = \frac{10(10^n-1)-9n}{81}: x_1 = 1, x_2 = 12, …, x_5 = 12345, etc.

Let’s go back to the main line of discussion.

Now we are interested in the following derivative series y_n :\equiv x_n \cdot (B-2) + n. The straightforward manipulation leads to the anticipated result:

    y_ n = B^n + \sum_{s=1}^{n-1} (s+1-n)B^s - n
    = (B-1)B^{n-1} + B^{n-1} + \sum_{s=1}^{n-2} (s+1-n)B^s - n
    = (B-1)B^{n-1} + (B-2) B^{n-2} + \sum_{s=1}^{n-3} (s+1-n)B^s - n


    = \sum_{r=1}^{m} (B-r)B^{n-r} + B^{n-m} + \sum_{s=1}^{n-m-1} (s+1-n)B^s - n


    = \sum_{r=1}^{n-2} (B-r)B^{n-r} + B^{2} + \sum_{s=1}^{1} (s+1-n)B^s - n
    = \sum_{r=1}^{n-2} (B-r)B^{n-r} + B^{2} + (2-n)B^1 - n
    = \sum_{r=1}^{n-1} (B-r)B^{n-r} + B^{1} - n
    = \sum_{r=1}^{n} (B-r)B^{n-r}.

i.e. y_n = (B-1)(B-2)...(B-n+2)(B-n+1)(B-n)_B. The initial pyramid of simple results holds for every base B.

Example: for B=5 we have x_n = \frac{5(5^n-1)-4n}{16}, so x_1 = \frac{5\cdot 4 - 4 \cdot 1}{16} = 1, x_2 = \frac{5\cdot 24 - 4 \cdot 2}{16} = 7_{10} = 12_5, etc. Then, for example y_2 = x_2 \cdot 3 + 2 = 7\cdot 3 + 2 = 21 + 2 = 23_{10} = 43_5.

Wonder #2

Let’s look at the Table 2:

Table 2
  • 1 \times 9 + 2 = 11,
  • 12 \times 9 + 3 = 111,
  • 123 \times 9 + 4 = 1,111,
  • 1,234 \times 9 + 5 = 11,111,
  • 12,345 \times 9 + 6 = 111,111,
  • 123,456 \times 9 + 7 = 1,111,111,
  • 1,234,567 \times 9 + 8 = 11,111,111,
  • 12,345,678 \times 9 + 9 = 111,111,111,
  • 123,456,789 \times 9 + 10 = 1,111,111,111,

Here the first (i.e. the independent) variable x_n is the exactly same as the one used for Table 1. The second (i.e. the dependent) variable z_n is new one, determined by defining equation:

    x_n = \sum_{s=0}^{n-1}(n-s)B^s,

Then, using steps similar to these used in analysis of the Table 1, we get:

    z_n :\equiv x_b \cdot (B-1) + (n+1) =
    = \sum_{s=0}^{n-1} (n-s) B^{s+1} - \sum_{s=0}^{n-1} (n-s) B^s + (n+1) =
    = \sum_{s=1}^{n} (n+1-s) B^{s} - \sum_{s=0}^{n-1} (n-s) B^s + (n+1) =
    = B^n + \sum_{s=1}^{n-1} (n+1-s - n +s) B^{s} - n + (n+1) =
    = B^n + \sum_{s=1}^{n-1} B^{s} +1 =
    = \sum_{s=0}^{n} B^{s} =
    = 1\cdots 1_B,

where there are (n+1) copies of digit 1.

Nice. Easy.

Wonder #3

Table 3
  • 9 \times 9 + 7 = 88,
  • 98 \times 9 + 6 = 888,
  • 987 \times 9 + 5 = 8,888,
  • 9,876 \times 9 + 4 = 88,888,
  • 98,765 \times 9 + 3 = 888,888,
  • 987,654 \times 9 + 2 = 8,888,888,
  • 9,876,543 \times 9 + 1 = 88,888,888,
  • 98,765,432 \times 9 + 0 = 888,888,888,

That series of relations has form v_n = u_n \cdot 9 + (8-n) where the dependent variable is
v_n = \underbrace{8\cdots8}_{n+1} in the normal decimal system (B=10).

For general basis B this generalizes to the:
v_n = u_n \cdot (B-1) + (B - n -2). Here the independent variable u_n is

    u_n = \sum_{k=1}^n (B-k) B^{n-k} =
    = \sum_{s=0}^{n-1} (B- n -s) B^s =
    = (B - n + B \partial_B) \sum_{s=0}^{n-1}B^s =
    = (B - n + B \partial_B)\frac{B^n-1}{B-1} =
    = \frac{B(B-2)(B^n-1)+n (B-1)}{(B-1)^2}.


    v_ n :\equiv u_n (B-1) + (B-n-2) =
    = (B-1) B^n - \sum_{s=1}^{n-1} B^s - 2 =
    = (B-2) B^n + (B-1) B^{n-1} - \sum_{s=1}^{n-2} B^s - 2 =
    = (B-2) B^n + (B-2) B^{n-1} + (B-1)B^{n-2} - \sum_{s=1}^{n-3} B^s - 2 =


    = (B-2) B^n + \cdots + (B-2) B^{n-m+1} + (B-1)B^{n-m} - \sum_{s=1}^{n-m-1} B^s - 2 =


    = (B-2) B^n + \cdots + (B-2) B^{3} + (B-1)B^{2} - B^1 - 2 =
    = (B-2) B^n + \cdots + (B-2) B^{3} + (B-2)B^{2} + B^2 - B^1 - 2 =
    = (B-2) B^n + \cdots + (B-2) B^{2} + (B-1)B^{1} - 2 =
    = (B-2) B^n + \cdots + (B-2) B^{1} + B - 2 =
    = \sum_{r=0}^{n} (B-2) B^r.

For B=10 that covers all examples in the Table 3.

Note: Even more, we can add two more members to it, corresponding to n=9 and n=10:

  • u_9 = 987,654,321 corresponds to v_9 = x_9 \cdot 9 + (-1) = 8,888,888,888,
  • u_{10} = 9,876,543,210 corresponds to v_{10} = x_{10} \cdot 9 + (-2) = 88,888,888,888.

Also, the u_0=0 provides one more line, which is prepended to this more complete table 3:

Table 3*
  • 0 \times 9 + 8 = 8,
  • 9 \times 9 + 7 = 88,
  • 98 \times 9 + 6 = 888,
  • 987 \times 9 + 5 = 8,888,
  • 9,876 \times 9 + 4 = 88,888,
  • 98,765 \times 9 + 3 = 888,888,
  • 987,654 \times 9 + 2 = 8,888,888,
  • 9,876,543 \times 9 + 1 = 88,888,888,
  • 98,765,432 \times 9 + 0 = 888,888,888,
  • 987,654,321 \times 9 - 1  = 8,888,888,888,
  • 9,876,543,210 \times 9 - 2  = 88,888,888,888.

Wonder #4

Table 4
  • 1^2 = 1,
  • 11^2 = 121,
  • 111^2 = 12,321,
  • 1,111^2 = 1,234,321,
  • 11,111^2 = 123,454,321,
  • 111,111^2 = 1,2345,654,321,
  • 1,111,111^2 = 1,234,567,654,321,
  • 11,111,111^2 = 123,456,787,654,321,
  • 111,111,111^2 = 12,345,678,987,654,321.

Here the independent variable is

    p_n :\equiv 1\cdot B^{n} + 1\cdot B^{n-1} + \cdots + 1\cdot B^0 = \sum_{i=0}^n B^i = \frac{B^{n+1}-1}{B-1}.

The resulting variable is

    r_n :\equiv p_n^2 = \sum_{i=0}^n \sum_{j=0}^n B^{i+j} =
    = \sum_{k=0}^{2n} (\sum_{i=0}^n \sum_{j=0}^n \delta_{i+j,k}) B^k.

Now the sum in brackets can be transformed as follows:

    \sum_{i=0}^n \sum_{j=0}^n \delta_{i+j,k} = \sum_{i=0}^n  \Theta(0 \le  k-i \le n) =
    = \sum_{i=0}^n \Theta(k-n \le i \le k) =  \sum_{i=\hbox{max}(0,k-n)}^{\hbox{min}(n,k)} 1 =
    = \hbox{min}(n,k) - \hbox{max}(0,k-n) + 1 = *

which has three posible simplifications:

  • * = k - 0 + 1 = k + 1 for k < n,
  • * = n + 1 for k = n,
  • * = n - (k-n) + 1 = 2n - k + 1 for k > n.

So, now we can write the final form for r_n as following:

    r_n = \sum_{k=0}^{n-1} (k+1) B^k + (n+1) B^n + \sum_{k=n+1}^{2n} (2n-k+1) B^k =
    = 1\cdot B^0 + 2\cdot B^1 + 3\cdot B^2 + \cdots + (n+1) B^n + \cdots 2\cdot B^{2n-1} + 1\cdot B^{2n} =
    = 123\cdots(n+1)\cdots321_B.

That is it.

Note that one can get some regularities for degrees higher than 2. For example, for degree 3 one has:

    1^3 = 1
    11^3 = 1,331
    111^3 = 135,531

    1,111^3 = 13,577,531
    11,111^3 = 1,357,997,531
    111,111^3 = 135,79b,b97,531
    1,111,111^3 = 13,579,bdd,b97,531


    {\underbrace{1\cdots1}_{[B'/2]+1}}^3 = 1357\cdots B'B'\cdots 7531.

up to the last member (of that series) where the two central digits are the highest single-digit number B' allowed in the number system of base B (i.e. B'=B-2 if B is odd, and B'=B-1 if B is even).

Note: Here a = 10_{10}, b = 11_{10}, c = 12_{10}, d = 13_{10}, e = 14_{10}, f = 15_{10}, g = 16_{10}, h = 17_{10}, i = 18_{10}, etc.

For the degree 4 the similar pyramid/table is:

    1^4 = 1
    11^4 = 14,641
    111^4 = 1,48a,841

    1,111^4 = 1,48a,cec,841


Here one can also work some more (and I did not do that work yet) to establish which is the last member of that table (as a function of the base B), and what is the innermost digit in that last member.
This could be a homework for you. 🙂

For the degree 5:

    1^5 = 1
    11^5 = 15885
    111^5 = 15ciic51


Similar here: More simple math wonders – https://eikonal.wordpress.com/2012/03/14/more-simple-math-wonders/ | Mental calculation of cube root of a six-digit number – https://eikonal.wordpress.com/2010/01/14/mental-calculation-of-cube-root-of-a-two-digit-number/ | Squares with just two different decimal digits – https://eikonal.wordpress.com/2010/01/05/squares-with-just-two-different-decimal-digits/ | Number theory finite concidental sums – https://eikonal.wordpress.com/2010/01/05/number-theory-finite-considental-sums/


Skills acquisition


Related: On importance of practice – https://eikonal.wordpress.com/2011/01/11/on-importance-of-practice/


Life writing


Sites, People


Reality of wave function in quantum mechanics

Filed under: physics, Quantum mechanics — Tags: , , — sandokan65 @ 15:39

Asperger’s syndrome, Autism, ASD


Lambert W function

Filed under: mathematics — Tags: — sandokan65 @ 13:38

Definition: A function W: {\mathbb C} \rightarrow {\mathbb C} defined by W(z) e^{W(z)} = z is named the Lambert W-function.



Derivatives of numbers

Filed under: mathematics, number theory — Tags: , , — sandokan65 @ 23:45


  • p'=1 for every prime number p
  • (a b)' = a' b + a b' (Leibnitz rule) for every two natural numbers a, b \in {\Bbb N}


  • 1' = 0.
  • (p^n)' = n \cdot p^{n-1}
  • for any natural number n=  \prod_{i=1}{k} {p_i}^{n_i} one has n' = n \sum_{i=1}^{k} \frac{n_i}{p_i}.
    • Eg: 40' = (2^3 \cdot 5)' = 3 \cdot 2^2 \cdot 5 + 2^3 = 68.
  • in general (a+b)' \ne a' + b'
  • \left(\frac{a}{b}\right)' = \frac{a' b - a b'}{b^2}
  • (p^p)' = p^p for any prime number p is equivalent of the exponential function’s property that its derivative is itself.
  • If n = p^p \cdot m for prime p and natural m>1, then n' = p^p (m+m') > n, n^{(k)} \ge n+k, and \lim_{k\rightarrow \infty} n^{(k)} = \infty.
  • For infinitely many natural numbers n there exist suitable k s/t n^{(k)}=0
  • Ufnarovski and Åhlander give following conjecture: for every natural n, as we observe its derivatives n^{(k)} (as k grows to infinity), the limit will be either 0, \infty, or n itself (if n=p^p for some prime p).
  • If n'=0, then n=1.
  • If n'=1, then n = p (for all possible primes).


  • “Deriving the Structure of Numbers” by Ivars Peterson (Ivars Peterson’s MathTrek) – http://www.maa.org/mathland/mathtrek_03_22_04.html
  • “How to differentiate a number” by Ufnarovski, V., and B. Åhlander (Journal of Integer Sequences 6; 2003.09.17) – http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.html
      Abstract: We define the derivative of an integer to be the map sending every prime to 1 and satisfying the Leibnitz rule. The aim of the article is to consider the basic properties of this map and to show how to generalize the notion to the case of rational and arbitrary real numbers. We make some conjectures and find some connections with Goldbach’s Conjecture and the Twin Prime Conjecture. Finally, we solve the easiest associated differential equations and calculate the generating function.
  • “Investigations of the number derivative” by Linda Westrick – http://web.mit.edu/lwest/www/intmain.pdf


Collatz conjecture


  • “When the multiverse and many-worlds collide” by Justin Mullins (The New Scientist; 2011.06.01) – http://www.newscientist.com/article/mg21028154.200-when-the-multiverse-and-manyworlds-collide.html
  • “Are Many Worlds and the Multiverse the Same Idea?” by Sean Carroll (Cosmic Variance blog at Discover Magazine; ) – http://blogs.discovermagazine.com/cosmicvariance/2011/05/26/are-many-worlds-and-the-multiverse-the-same-idea/
  • “Physical Theories, Eternal Inflation, and Quantum Universe” by Yasunori Nomura (arXiv.org > hep-th > arXiv:1104.2324v2 [hep-th])- http://arxiv.org/abs/1104.2324
      Abstract: We present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We show that the entire multiverse is described purely from the viewpoint of a single “observer,” who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is “gauge invariant,” i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a theory of “initial conditions” for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal “mega-multiverse,” in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox, the Boltzmann brain problem, and a peculiar “end” of time.
  • “The Multiverse Interpretation of Quantum Mechanics” by Raphael Bousso and Leonard Susskind (arXiv.org > hep-th > arXiv:1105.3796v1 [hep-th]) – http://arxiv.org/abs/1105.3796
      Abstract: We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.
      Decoherence – the modern version of wave-function collapse – is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the “environment”. In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event. However, if one restricts to the causal diamond – the largest region that can be causally probed – then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry.
      We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in “hats” (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.



Distraction-Free Tools


Microsoft office foolies


Intelligence in Earth’s nonhuman life



  • “Complex thinking goes beyond primates: Dolphins understand zero, elephants rescue each other” by Seth Borenstein (Winnipeg Free Press; 2012.06.24) – http://www.winnipegfreepress.com/arts-and-life/life/sci_tech/complex-thinking-goes-beyond-primates-dolphins-understand-zero-elephants-rescue-each-other-160191285.html
    • Dolphins understand concept of “zero”. Can do everything that chimpanzees and bonobos can do. Likely have personalities.
    • Animal intelligence “is not a linear thing,” said Duke University researcher Brian Hare, who studies bonobos, which are one of man’s closest relatives, and dogs, which are not. “Think of it like a toolbox,” he said. “Some species have an amazing hammer. Some species have an amazing screwdriver.”
    • Elephants work cooperatively, solving problems faster than chimps.
  • “Line blurs between man, animal: Monkeys do math, baboons seem to read, orangutans plan ahead” by Seth Borenstein (Winnipeg Free Press; 2012.06.24) – http://www.winnipegfreepress.com/arts-and-life/life/sci_tech/line-blurs-between-man-animal-monkeys-do-math-baboons-seem-to-read-orangutans-plan-ahead-160191235.html
    • Some of the shifts in scientific understanding of animals are leading to ethical debates. When Emory University researcher Lori Marino in 2001 co-wrote a groundbreaking study on dolphins recognizing themselves in mirrors, proving they have a sense of self similar to humans, she had a revelation. “The more you learn about them, the more you realize that they do have the capacity and characteristics that we think of as a person,” Marino said. “I think it’s impossible to ignore the ethical implications of these kinds of findings.”





Mammals: Primates

Mammals: Elephants

Mammals: Cetaceans (dolphins, whales, …)

  • “Talk with a dolphin via underwater translation machine” by MacGregor Campbell (New Scientist – issue 2811; 2011.05.09) – http://www.newscientist.com/article/mg21028115.400-talk-with-a-dolphin-via-underwater-translation-machine.html
  • “Intelligence of Dolphins: Ethical and Policy Implications” – http://aaas.confex.com/aaas/2010/webprogram/Session1526.html
      Charter: The dolphin brain has a large cerebral cortex and a substantial amount of associational neocortex. Most anatomical ratios that assess cognitive capacity place it second only to the human brain. More important, recent research in marine science has revealed that dolphins have a remarkable degree of cognitive and affective sophistication. For example, dolphins can recognize their image in a mirror as a reflection of themselves — a finding that indicates self-awareness similar to that seen in higher primates and elephants. These and other studies, which have found that dolphins are also capable of advanced cognitive abilities such as problem-solving, artificial language comprehension, and complex social behavior, indicate that dolphins are far more intellectually and emotionally sophisticated than previously thought. Considerable research indicates that they are significantly different from fish and other marine species, and this research has significance for commercial policy and practice. This symposium will present the scientific findings and explore their ethical and policy implications.
    • Lori Marino (Emory University): Anatomical Basis of Dolphin Intelligence – http://aaas.confex.com/aaas/2010/webprogram/Paper1487.html
        Many modern dolphin brains are significantly larger than our own and second in mass to the human brain when corrected for body size. Despite evolving along a different neuroanatomical trajectory than human brains, cetacean brains exhibit several features that are correlated with complex intelligence, including a large expanse of neocortical volume that is more convoluted than our own, extensive insular and cingulate regions, and highly differentiated cellular regions.
        These characteristics of dolphin brains are consistent with current behavioral evidence. In this presentation I will discuss the neuroanatomical basis of complex intelligence in dolphins, how the neuroanatomy provides evidence for psychological continuity between humans and dolphins, and the profound implications for the ethics of human-dolphin interactions. Specifically, I will focus on the growing worldwide industry of capturing and confining dolphins for amusement in marine park shows, “swim-with-dolphin” and “dolphin-assisted therapy” facilities. Our current knowledge of dolphin brain complexity and intelligence suggests that these practices are potentially psychologically harmful to dolphins and present a misinformed picture of their natural intellectual capacities.
    • Diana Reiss (Hunter College of the City University of New York): Self-Awareness and Dolphins – http://aaas.confex.com/aaas/2010/webprogram/Paper1488.html
        Bottlenose dolphins are highly social mammals with large and complex brains. Studies conducted in the field and aquaria have provided increasing evidence for the dolphin’s cognitive-social prowess, revealing that dolphins are cultural animals – much of their behavior is learned and passed down through generations.
        They have demonstrated the capacity for mirror-self recognition (MSR), a hallmark of a level of self-awareness, previously thought to be restricted to humans but also shared by the great apes, elephants and magpies. Despite profound differences in neuroanatomical characteristics and evolutionary histories dolphins, primates (human and great apes), and elephants show striking parallels in both the progression of behavioral stages and actual responses to a mirror providing compelling evidence for convergent cognitive evolution. MSR may index an increased self-other distinction that also underlies the social complexity and altruistic tendencies shared among these species.
        Can our scientific knowledge be used to influence international policy decisions and ethical considerations of the treatment of dolphins? Do scientific facts translate and transcend cultural boundaries? In the dolphin drive hunts in Japan, there are no restrictions on capture or killing methods of the highly sentient dolphin and other small whales. The killing methods fail to meet even the most minimal requirements used in U.S. laboratories and slaughterhouses. Scientists are making the argument on the basis of the scientific evidence that the drive hunts are unjustifiable and indefensible in that they inflict pain and suffering on animals that are intelligent, sentient, socially complex and have capacity to experience pain and suffering.
    • Thomas I. White (Loyola Marymount University): Ethical Implications of Dolphin Intelligence: Dolphins as Nonhuman Persons – http://aaas.confex.com/aaas/2010/webprogram/Paper1489.html
        The scientific research on dolphin intelligence suggests that dolphins are “nonhuman persons.” (Like humans, dolphins appear to be self-conscious,
        unique individuals [with distinctive personalities, memories and a sense of self] who are vulnerable to a wide range of physical and emotional pain and harm, and who have the power to reflect upon and choose their actions.) At the same time, fundamental differences between humans and dolphins have also surfaced. (The dolphin brain has an older architecture than the human brain, and dolphin and human brains have features not found in the other. Dolphins possess a sense that humans lack [echolocation]. Humans and dolphins have profoundly different evolutionary histories.) This juxtaposition of important similarities and differences has significant ethical implications.
        The similarities suggest that dolphins qualify for moral standing as individuals-and, therefore, are entitled to treatment of a particular sort. The differences, however, suggest that species-specific standards may apply when it comes to determining something as basic as “harm.” The policy implications are considerable. For example, certain human fishing practices are indefensible and would need to change. (Over 300,000 cetaceans are thought to die annually around the world as a result of fisheries by-catch. Thousands more typically die in the annual Japanese drive hunts.) Similarly, changes would need to be made regarding the hundreds of captive dolphins currently used in entertainment facilities. The economic, political and diplomatic challenges in ending ethically problematic practices, however, are daunting and multi-faceted. Unfortunately, humans have a poor track record for recognizing the rights and interests even of members of our own species once they’ve been dubbed “inferior.” Meaningful change in human/dolphin interaction, then, is likely to unfold slowly. Yet developing an interspecies ethic could mark a significant turning point in the relationship between humans and other intelligent beings on the planet.
  • “Non-human Persons” by petchary (Petchary blog) – http://petchary.wordpress.com/2011/01/02/non-human-persons/ – dog knows more worlds (over 1000) that a two-years old.

Mammals: Carnivora (cats, dogs, …)

Aves (Birds)

Aves (Birds): Corvids [Corvidae]

  • Corvidae (WikiPedia) – http://en.wikipedia.org/wiki/Corvidae
  • “Rook reveal remarkable tool use” – http://vodpod.com/watch/1672586-rook-reveal-remarkable-tool-use
  • “Bird Tool Use Evolved for Better Grub, Literally” by Jennifer Viegas (Dicsovery News; 2010.09.16) – http://news.discovery.com/animals/bird-tool-use-evolved-for-better-grub-literally.html
  • “Ravens Reconcile after Aggressive Conflicts with Valuable Partners” by Orlaith N. Fraser, Thomas Bugnyar (PLoS; 2011.03.25) – http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0018118
      Reconciliation, a post-conflict affiliative interaction between former opponents, is an important mechanism for reducing the costs of aggressive conflict in primates and some other mammals as it may repair the opponents’ relationship and reduce post-conflict distress. Opponents who share a valuable relationship are expected to be more likely to reconcile as for such partners the benefits of relationship repair should outweigh the risk of renewed aggression. In birds, however, post-conflict behavior has thus far been marked by an apparent absence of reconciliation, suggested to result either from differing avian and mammalian strategies or because birds may not share valuable relationships with partners with whom they engage in aggressive conflict. Here, we demonstrate the occurrence of reconciliation in a group of captive subadult ravens (Corvus corax) and show that it is more likely to occur after conflicts between partners who share a valuable relationship. Furthermore, former opponents were less likely to engage in renewed aggression following reconciliation, suggesting that reconciliation repairs damage caused to their relationship by the preceding conflict. Our findings suggest not only that primate-like valuable relationships exist outside the pair bond in birds, but that such partners may employ the same mechanisms in birds as in primates to ensure that the benefits afforded by their relationships are maintained even when conflicts of interest escalate into aggression. These results provide further support for a convergent evolution of social strategies in avian and mammalian species.
  • “Angry Birds: Crows Never Forget Your Face” by Jennifer Viegas (Discovery News; 2011.06.28) – http://news.discovery.com/animals/angry-crows-memory-life-threatening-behavior-110628.html

    • Mess with a crow, and it will remember your face for over five years, research shows.
    • Crows remember the faces of “dangerous humans,” with the memories likely lasting for a bird’s lifetime.
    • Crows may scold people who threaten them, bringing in relatives and even strangers to mob the person.
    • The crows within mobs then indirectly learn about the person, so they too associate that individual’s face with danger and react accordingly.
    • “Others have shown that some crows make and use tools, forecast future events, understand what other animals know, and — in our case — learn from individual experience as well as by observing parents and peers,” Marzluff explained. “These are all advanced cognitive tasks shown by only a few animals.”
    • He suspects other social, long-lived species that live closely with humans might also share information in a similar manner. Possibilities include animals such as coyotes, raccoons, gulls, pigeons and rats. All could practice a combination of social and trial and error learning. The latter provides the most accurate information, but it is clearly riskier than indirect social learning.
  • “Crows are Feathered Engineers” by Gene Charleton (Discovery News; 2010.06.10) – http://news.discovery.com/tech/feathered-engineers.htmlCrows living in the jungles of New Caledonia use tools to solve problems.
  • “Feathered engineers” by Gene (Texas AM Engineering; 2010.06.02) – http://engineeringworks.tamu.edu/2010/feathered-engineers/
  • “Mirrors and Magpies” by fatfinch (The Fat Finch Bird Brain Blog; ) – http://fatfinch.wordpress.com/2008/08/20/mirrors-and-magpies/
  • “Self-Recognition in the Pica Pica (Magpie)?” (2008.08.19) – http://cognitivetrammeling.wordpress.com/2008/08/19/self-recognition-in-the-pica-pica/

Aves (Birds): Parrots


Cephalopod: Squids, etc

  • Cephalopod intelligence (WikiPedia) http://en.wikipedia.org/wiki/Cephalopod_intelligence
  • This is probably a stretch (in domain of science-fiction), but it sounds like something that just could be the case. Is decoration of your nesting ground a sign of intelligence? Also, assuming that some ancient cephalopod indeed had this intelligence, then the questions is what happened to that intelligence during the following 50 millions of years? It looks like it had gone nowhere to be seen these days.
    • “The Revenge of the Imaginary Kraken” by Brian Switek (Wired; 2011.10.12) – http://www.wired.com/wiredscience/2011/10/the-revenge-of-the-imaginary-kraken/
    • “Gigantic KRAKEN fingered in prehistoric murder mystery – Prof reckons monster was also a Triassic Van Gogh” by Anna Leach (The Register; 2011.10.12) – http://www.theregister.co.uk/2011/10/12/kraken_killer/
        “The proposed Triassic kraken, which could have been the most intelligent invertebrate ever, arranged the vertebral discs in biserial patterns, with individual pieces nesting in a fitted fashion as if they were part of a puzzle. The arranged vertebrae resemble the pattern of sucker discs on a cephalopod tentacle, with each amphicoelous vertebra strongly resembling a coleoid sucker. Thus the tessellated vertebral disc pavement may represent the earliest known self‑portrait.”
    • “Ancient Krakens Making Self-Portraits?” (SlashDot; 2011.10.11) – http://science.slashdot.org/story/11/10/11/134240/ancient-krakens-making-self-portraits
        First time accepted submitter Sanoj writes “Strange patterns of ichthyosaur bones have been found on an ancient deep-water seabed. One paleontologist has put forward the theory that these could have been the work of giant cephalopods who were eating the swimming dinosaurs and then arranging the vertebrae to resemble their own tentacles [http://www.tgdaily.com/general-sciences-features/58953-triassic-kraken-may-have-created-self-portrait]. Sound far-fetched? Apparently, the modern octopus also does this.”
    • “The Giant, Prehistoric Squid That Ate Common Sense” by Brian Switek (Wired; 2011.10.10) – http://www.wired.com/wiredscience/2011/10/the-giant-prehistoric-squid-that-ate-common-sense/
    • “Smokin’ Kraken?” by Sarah Simpson(Discovery News; 2011.10.100) – http://news.discovery.com/earth/smokin-kraken-111011.html
    • “Triassic ‘Kraken’ may have created self-portrait” by Kate Taylor (TG Daily; 2011.10.10) – http://www.tgdaily.com/general-sciences-features/58953-triassic-kraken-may-have-created-self-portrait
    • “TRIASSIC KRAKEN: THE BERLIN ICHTHYOSAUR DEATH ASSEMBLAGE INTERPRETED AS A GIANT CEPHALOPOD MIDDEN” by Mark A.S. MCMENAMIN and Dianna L. SCHULTE MCMENAMIN (2011 GSA Annual Meeting in Minneapolis [9–12 October 2011]; Paper No. 120-3) – http://gsa.confex.com/gsa/2011AM/finalprogram/abstract_197227.htm
        The Luning Formation at Berlin‑Ichthyosaur State Park, Nevada, hosts a puzzling assemblage of at least 9 huge (≤14 m) juxtaposed ichthyosaurs (Shonisaurus popularis). Shonisaurs were cephalopod‑eating predators comparable to sperm whales (Physeter). Hypotheses presented to explain the apparent mass mortality at the site have included: tidal flat stranding, sudden burial by slope failure, and phytotoxin poisoning. Citing the wackestone matrix, J. A. Holger argued convincingly for a deeper water setting, but her phytotoxicity hypothesis cannot explain how so many came to rest at virtually the same spot. Skeletal articulation indicates that animals were deposited on the sea floor shortly after death. Currents or other factors placed them in a north‑south orientation. Adjacent skeletons display different taphonomic histories and degrees of disarticulation, ruling out catastrophic mass death, but allowing a scenario in which dead ichthyosaurs were sequentially transported to a sea floor midden. We hypothesize that the shonisaurs were killed and carried to the site by an enormous Triassic cephalopod, a “kraken,” with estimated length of approximately 30 m, twice that of the modern Colossal Squid Mesonychoteuthis. In this scenario, shonisaurs were ambushed by a Triassic kraken, drowned, and dumped on a midden like that of a modern octopus. Where vertebrae in the assemblage are disarticulated, disks are arranged in curious linear patterns with almost geometric regularity. Close fitting due to spinal ligament contraction is disproved by the juxtaposition of different-sized vertebrae from different parts of the vertebral column. The proposed Triassic kraken, which could have been the most intelligent invertebrate ever, arranged the vertebral discs in biserial patterns, with individual pieces nesting in a fitted fashion as if they were part of a puzzle. The arranged vertebrae resemble the pattern of sucker discs on a cephalopod tentacle, with each amphicoelous vertebra strongly resembling a coleoid sucker. Thus the tessellated vertebral disc pavement may represent the earliest known self‑portrait. The submarine contest between cephalopods and seagoing tetrapods has a long history. A Triassic kraken would have posed a deadly risk for shonisaurs as they dove in pursuit of their smaller cephalopod prey.
  • “Octopus Is First Invertebrate to Use Tools, Turning a Coconut Into Mobile Home (Video)”
    by Jaymi Heimbuch (TreeHugger; 2009.12.15) – http://www.treehugger.com/files/2009/12/octopus-is-first-invertabrate-to-use-tools-turning-a-coconut-into-mobile-home.php

Plan group intelligence

Bacteria group intelligence

Related here: Intelligence – https://eikonal.wordpress.com/2010/10/27/intelligence/.


Memetic diseases

Mass hysteria

  • “The Dark Side of the Placebo Effect: When Intense Belief Kills” by Alexis Madrigal (the Atlantic; 2011.09.14) – http://www.theatlantic.com/life/archive/2011/09/the-dark-side-of-the-placebo-effect-when-intense-belief-kills/245065/
      While people of all cultures experience sleep paralysis in similar ways, the specific form and intensity it takes varies from one group to the next …
      They died in their sleep one by one, thousands of miles from home. Their median age was 33. All but one — 116 of the 117 — were healthy men. Immigrants from southeast Asia, you could count the time most had spent on American soil in just months. At the peak of the deaths in the early 1980s, the death rate from this mysterious problem among the Hmong ethnic group was equivalent to the top five natural causes of death for other American men in their age group.

      Something was killing Hmong men in their sleep, and no one could figure out what it was. There was no obvious cause of death. None of them had been sick, physically. The men weren’t clustered all that tightly, geographically speaking. They were united by dislocation from Laos and a shared culture, but little else. Even House would have been stumped.

      Doctors gave the problem a name, the kind that reeks of defeat, a dragon label on the edge of the known medical world: Sudden Unexpected Nocturnal Death Syndrome. SUNDS. It didn’t do much in terms of diagnosis or treatment, but it was easier to track the periodic conferences dedicated to understanding the problem.

  • “What’s Causing ‘Mass Faintings’ at Cambodian Factories?” by Andrew Marshall (Time > World; 2011.09.20) – http://www.time.com/time/world/article/0,8599,2093516,00.html
      … In the past three months, at least 1,200 workers at seven garment and shoe factories have reported feeling dizzy, nauseated, exhausted or short of breath, and hundreds have been briefly hospitalized. No definitive explanation has yet been given for these so-called mass faintings. One baffled reporter described them as “unique to Cambodia.” (Read how companies are abandoning Chinese factories in search of cheaper options.)
      Hardly. It’s been almost 50 years since girls at a boarding school in Tanganyika (now Tanzania) were struck by an illness whose symptoms — fainting, nausea and helpless laughter — soon spread to other communities. Or consider the Pokémon contagion in 1997, when 12,000 Japanese children experienced fits, nausea and shortness of breath after watching a television cartoon. Sufferers of World Trade Center syndrome, meanwhile, blamed proximity to Ground Zero for coughs and other respiratory problems long after airborne contaminants posed any health threat.
      All these are examples of mass hysteria, a bizarre yet surprisingly common phenomenon that is increasingly recognized as a significant health and social problem. For centuries it has crossed cultures and religions, taking on different forms to keep pace with popular obsessions and fears. In our post-9/11 world, it thrives on the anxiety caused by terrorist attacks, nuclear radiation and environmental gloom. “At any one time there are probably hundreds of episodes happening all around the world,” says Simon Wessely, a psychology professor at the Institute of Psychiatry at King’s College London. “They just don’t normally get reported.”


More: Memetics – https://eikonal.wordpress.com/2010/04/13/memetics/



Filed under: anthropology, evolution, history, paleontology, past — Tags: , , — sandokan65 @ 10:44


Here at this blog: Human species interbreeding – https://eikonal.wordpress.com/2010/05/07/human-species-interbreading/

Astronomy & Astrophysics

Filed under: astronomy, cosmology, physics — sandokan65 @ 10:16


  • “Kepler May Uncover Numerous Ring Worlds” 9SlashDot; 2011.05.08) – http://science.slashdot.org/story/11/05/08/2230208/Kepler-May-Uncover-Numerous-Ring-Worlds
      “According to a new publication, NASA’s Kepler exoplanet-hunting space telescope may soon start discovering Saturn-like ringed alien worlds. So far, none have been positively identified, as Kepler has only detected exoplanets orbiting close to their parent stars; if these exoplanets have rings, they are most likely to have rings facing edge-on to their orbits, making them nearly impossible to detect. As more distant-orbiting exoplanets are detected, there’s more likelihood ringed worlds will be tilted, allowing Kepler to see them.”

Related here: Astronomic tables and calculators – https://eikonal.wordpress.com/2010/01/28/astronomic-tables-and-calculators/ | Solar planetary system – https://eikonal.wordpress.com/2011/02/17/solar-planetary-system/ | Inside black holes – https://eikonal.wordpress.com/2011/04/12/inside-black-holes/ | Physics Sites – https://eikonal.wordpress.com/2010/02/12/physics-sites/

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