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One important factor behind the growth of the religiously unaffiliated is generational replacement, the gradual supplanting of older generations by newer ones. Among the youngest Millennials (those ages 18-22, who were minors in 2007 and thus not eligible to be interviewed in Pew Research Center surveys conducted that…
The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞. More sophisticated…
Name any event in history and you will find a star out there whose light gives you a glimpse of something happening during the year of that event. Provided you are not a very young child, somewhere up in the night sky you can find your personal birth star. Its light is a thermonuclear glow that heralds the year of…
But our unconscious feats of unweaving and weaving are greater even than this. Think what is happening when you listen to a whole orchestra. Imagine that, superimposed on a hundred instruments, your neighbour in the concert is whispering learned music criticism in your ear, others are coughing and, lamentably…
The spectrum depends upon light of different colours being slowed by different amounts: the refractive index of a given substance, say glass or water, is greater for blue light than for red. You could think of blue light as being a slower swimmer than red, getting tangled up in the undergrowth of atoms in glass or…
‘The achievement of the Kaminari-zoku implies that there are other spacetimes. Certainly other regions of the Universe beyond our causal horizon. If rational actors have evolved in them, they will have broken their Planck locks – or worse, evolved natively in an environment with no restrictions on computational…
[Motoo Kimura] has been the chief advocate of the neutral theory of evolution. The neutral theory says that, through the history of life from beginning to end, random statistical fluctuations have been more important than Darwinian selection in causing species to evolve. Evolution by random statistical fluctuation is…
It is time now to try to describe what a superstring really is. Here I run into the same difficulty which the geometer Euclid encountered 2,200 years ago. Euclid was trying to convey to his readers his idea of a geometrical point. For this purpose he gave his famous definition of a point: "A point is that which has no…
Astronomy affords the most extensive example of the connection of physical sciences. In it are combined the sciences of number and quantity, or rest and motion. In it we perceive the operation of a force which is mixed up with everything that exists in the heavens or on earth; which pervades every atom, rules the…
The theory is that numbers are self-organized around the smallest, most highly composite number, 12. The number 12 and many of its multiples (24, 36, 48, 60, etc.) are HCNs: highly composite numbers (with lots of divisors), which are extremely useful for measuring and proportions. Why are there 12 eggs in a carton, 12…
"Projections are essential for giving us information on long-term trends, but the timescale is beyond what many policy makers (and the public) consider to be relevant to their decision-making processes. Climate forecasts seek to address this issue by providing information on a shorter term (decadal) that can be used…
“Mathematics is not just a sequence of computations to be carried out by rote until your patience or stamina runs out—although it might seem that way from what you’ve been taught in courses called mathematics. Those integrals are to mathematics as weight training and calisthenics are to soccer. If you want to play…
no matter what the odds are at one point in spacetime probability materialize
Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is…
Big ideas are typically revealed via: • Core concepts (migration, function) • Focusing themes (good vs. evil) • Ongoing debate/issues (nature vs. nurture) • Illuminating paradox/problem (freedom vs. responsibility) • Organizing theory/principle (less is more) • Underlying assumption/perspectives (Occam’s Razor) • Key…
Synchronized with the northern winter solstice, the terran computational calendar began roughly*10 days before the UNIX Epoch. Each year is composed of 13 identical 28-day months, followed by a 'minimonth' that houses leap days (one most years and two every 4th but not 128th year) and leap seconds (issued by the IERS…
Each of our four theoretical traditions (Majoritarian Electoral Democracy, Economic Elite Domination, Majoritarian Interest Group Pluralism, and Biased Pluralism) emphasizes different sets of actors as critical in determining U.S. policy outcomes, and each tradition has engendered a large empirical literature that…
Mathematics is one of humanity’s great achievements. By enhancing the capabilities of the human mind, mathematics has facilitated the development of science, technology, engineering, business, and government. Mathematics is also an intellectual achievement of great sophistication and beauty that epitomizes the power…
Recognizing that no term captures completely all aspects of expertise, competence, knowledge, and facility in mathematics, we have chosen mathematical proficiency to capture what we think it means for anyone to learn mathematicssuccessfully. Mathematical proficiency, as we see it, has five strands: • conceptual…
Number is a rich, many-sided domain whose simplest forms are compre- hended by very young children and whose far reaches are still being explored by mathematicians. Proficiency with numbers and numerical operations is an important foundation for further education in mathematics and in fields that use mathematics…