anyone who’s been following this blog knows that we’re highly susceptible to popular memes
You know what feels really amazing? Mutual love and respect. Lol who would have thought
Type of Spirals: A spiral is a curve in the plane or in the space, which runs around a centre in a special way.
Different spirals follow. Most of them are produced by formulas:The radius r(t) and the angle t are proportional for the simplest spiral, the spiral of Archimedes. Therefore the equation is:
(3) Polar equation: r(t) = at [a is constant].
From this follows
(2) Parameter form: x(t) = at cos(t), y(t) = at sin(t),
(1) Central equation: x²+y² = a²[arc tan (y/x)]².
You can make a spiral by two motions of a point: There is a uniform motion in a fixed direction and a motion in a circle with constant speed. Both motions start at the same point.
(1) The uniform motion on the left moves a point to the right. - There are nine snapshots.
(2) The motion with a constant angular velocity moves the point on a spiral at the same time. - There is a point every 8th turn.
(3) A spiral as a curve comes, if you draw the point at every turn(Image).
Figure 1: (1) Archimedean spiral - (2) Equiangular Spiral (Logarithmic Spiral, Bernoulli’s Spiral).
Figure 2 : (1) Clothoide (Cornu Spiral) - (2) Golden spiral (Fibonacci number).
More Spirals: If you replace the term r(t)=at of the Archimedean spiral by other terms, you get a number of new spirals. There are six spirals, which you can describe with the functions f(x)=x^a [a=2,1/2,-1/2,-1] and f(x)=exp(x), f(x)=ln(x). You distinguish two groups depending on how the parameter t grows from 0.
Figure 4: If the absolute modulus of a function r(t) is increasing, the spirals run from inside to outside and go above all limits. The spiral 1 is called parabolic spiral or Fermat’s spiral.
Figure 5: If the absolute modulus of a function r(t) is decreasing, the spirals run from outside to inside. They generally run to the centre, but they don’t reach it. There is a pole. Spiral 2 is called the Lituus (crooked staff).
Figure 7: Spirals Made of Line Segments.
Source: Spirals by Jürgen Köller.
See more on Wikipedia: Spiral, Archimedean spiral, Cornu spiral, Fermat’s spiral, Hyperbolic spiral, Lituus, Logarithmic spiral,
Fibonacci spiral, Golden spiral, Rhumb line, Ulam spiral,
Hermann Heights Monument, Hermannsdenkmal.
The first hint that the worlds of child welfare and neuroscience could be unified was a 2005 study by Moshe Szyf and his colleagues at McGill University, which showed that rat pups raised by abusive mothers had epigenetic changes in a gene that helps rats—and humans—manage stress. This gene, called NR3C1, had a few extra methyl groups stuck to it: tiny quartets of carbon and hydrogen atoms that stick to DNA and derail the cellular machinery that translates genes into proteins. A methylated gene is still there, but it’s muted.
Scientists knew that things like drugs or radiation could turn genes off in this way, but Szyf’s experiment, Pollak says, “was the first demonstration that something like parenting, parental care, was flipping the switch.” A few studies in humans also hinted that trauma might be turning this stress-management gene off, but there wasn’t any direct evidence in children. That’s what Pollak was determined to find.
So Pollak’s staff recruited those kids and their parents and walked the kids from the lab to a local hospital to get their blood drawn. When they checked each kid’s DNA, they saw that, in the children with a history of abuse, NR3C1 was methylated, just as it had been in the rats—in fact, at the very same sites. That, Pollak thought, was remarkable. “It gives us a real window into understanding why people that are abused as children sort of have these lifelong problems.”
NR3C1 codes for a receptor that senses a hormone called cortisol. “Cortisol is something that we produce in an emergency,” Pollak explains. That’s because it prepares you to respond to a threat: when cortisol from the adrenal gland is sent flowing into the bloodstream, it ramps up blood sugar for a quick burst of energy, dials down energy-draining processes like digestion, growth, and immune function, and can reduce bleeding and inflammation if you’re injured. Gunnar points out that, for children in abusive homes, who are in threatening situations every day, having more cortisol floating around isn’t necessarily bad—at first. “You may need to remain vigilant more often. You may need to flip into vigilant state more easily. That’s keeping you alive under harsh conditions, but it’s also making it really hard for you to function.”
Normally, cortisol molecules dock in receptors that are coded for by NR3C1 in the brain and white blood cells, which signals the body to calm down and return to its normal operating mode, and revives the immune system. But if NR3C1 is methylated, the body won’t be able to produce enough receptors, hobbling its ability to regulate stress. The body can still produce cortisol, but without enough receptors, Pollak says, there’s nothing to reign in the heightened state. “It’s the brake that’s not working.”
When the body can’t signal itself to calm down, the short term results are kids who, Pollak says, are “on alert all the time.” They often misinterpret innocent behavior as threatening; they can be aggressive, and they struggle with change. The long-term results are the chronic psychological problems like anxiety and depression and chronic physical problems like heart disease and type II diabetes, which often surface years later in victims of childhood abuse.