lochlannach

The brachistochrone
This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.
If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?
Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.
Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.

The brachistochrone

This animation is about one of the most significant problems in the history of mathematics: the brachistochrone challenge.

If a ball is to roll down a ramp which connects two points, what must be the shape of the ramp’s curve be, such that the descent time is a minimum?

Intuition says that it should be a straight line. That would minimize the distance, but the minimum time happens when the ramp curve is the one shown: a cycloid.

Johann Bernoulli posed the problem to the mathematicians of Europe in 1696, and ultimately, several found the solution. However, a new branch of mathematics, calculus of variations, had to be invented to deal with such problems. Today, calculus of variations is vital in quantum mechanics and other fields.

science-of-noise
[…] the main trick of science is to really think of something: the shape of clouds and their occasional sharp bottom edges at the same altitude everywhere in the sky; the formation of the dewdrop on a leaf; the origin of a name or a word—Shakespeare, say, or “philanthropic”; the reason for human social customs—the incest taboo, for example; how it is that a lens in sunlight can make paper burn; how a “walking stick” got to look so much like a twig; why the Moon seems to follow us as we walk; what prevents us from digging a hole down to the center of the Earth; what the definition is of “down” on a spherical Earth; how it is possible for the body to convert yesterday’s lunch into today’s muscle and sinew; or how far is up—does the universe go on forever, or if it does not, is there any meaning to the question of what lies on the other side?
historical-nonfiction
historical-nonfiction:

This man helped create analytic philosophy and was one of the 1900s’ premier logicians, and you probably don’t know who he is. Meet Bertrand Russell, a British philosopher, logician, mathematician, historian, socialist, pacifist and social critic. He co-authored Principia Mathematica, an attempt to show all mathematics derive from a well-defined set of axioms. His philosophical essay “On Denoting” has been considered a “paradigm of philosophy.” Both works influence a variety of fields today, including mathematics, linguistics, and logic. 

historical-nonfiction:

This man helped create analytic philosophy and was one of the 1900s’ premier logicians, and you probably don’t know who he is. Meet Bertrand Russell, a British philosopher, logician, mathematician, historian, socialist, pacifist and social critic. He co-authored Principia Mathematica, an attempt to show all mathematics derive from a well-defined set of axioms. His philosophical essay “On Denoting” has been considered a “paradigm of philosophy.” Both works influence a variety of fields today, including mathematics, linguistics, and logic. 

science-of-noise
science-of-noise:

fuckyeahsouthasia:

ifartsparkswithkaty:

Value of Pi, written in Sanskrit by Arya Bhatta.
(X)

Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata I (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta.

Transliteration of Sanskrit (mostly for self-reference, but if y’all wanna know):
Caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṣṭistathā sahasrāṇām, ayutadvayaviṣkambhasyāsanno dṛttapariṇāḥ.

science-of-noise:

fuckyeahsouthasia:

ifartsparkswithkaty:

Value of Pi, written in Sanskrit by Arya Bhatta.

(X)

Aryabhata (Sanskritआर्यभटIASTĀryabhaṭa) or Aryabhata I (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta.

Transliteration of Sanskrit (mostly for self-reference, but if y’all wanna know):

Caturadhikaṃ śatamaṣṭaguṇaṃ dvāṣaṭistathā sahasrāṇām, ayutadvayaviṣkambhasyāsanno dṛttapariṇāḥ.

science-of-noise
we-are-star-stuff:

Alan Turing was born on 23 June, 1912, in London. His father was in the Indian Civil Service and Turing’s parents lived in India until his father’s retirement in 1926. Turing and his brother stayed with friends and relatives in England. Turing studied mathematics at Cambridge University, and subsequently taught there, working in the burgeoning world of quantum mechanics. It was at Cambridge that he developed the proof which states that automatic computation cannot solve all mathematical problems. This concept, also known as the Turing machine, is considered the basis for the modern theory of computation.
In 1936, Turing went to Princeton University in America, returning to England in 1938. He began to work secretly part-time for the British cryptanalytic department, the Government Code and Cypher School. On the outbreak of war he took up full-time work at its headquarters, Bletchley Park.
Here he played a vital role in deciphering the messages encrypted by the German Enigma machine, which provided vital intelligence for the Allies. He took the lead in a team that designed a machine known as a bombe that successfully decoded German messages. He became a well-known and rather eccentric figure at Bletchley.
After the war, Turing turned his thoughts to the development of a machine that would logically process information. He worked first for the National Physical Laboratory (1945-1948). His plans were dismissed by his colleagues and the lab lost out on being the first to design a digital computer. It is thought that Turing’s blueprint would have secured them the honour, as his machine was capable of computation speeds higher than the others. In 1949, he went to Manchester University where he directed the computing laboratory and developed a body of work that helped to form the basis for the field of artificial intelligence. In 1951 he was elected a fellow of the Royal Society.
In 1952, Turing was arrested and tried for homosexuality, then a criminal offence. To avoid prison, he accepted injections of oestrogen for a year, which were intended to neutralise his libido. In that era, homosexuals were considered a security risk as they were open to blackmail. Turing’s security clearance was withdrawn, meaning he could no longer work for GCHQ, the post-war successor to Bletchley Park.
He committed suicide on 7 June, 1954. [x]

we-are-star-stuff:

Alan Turing was born on 23 June, 1912, in London. His father was in the Indian Civil Service and Turing’s parents lived in India until his father’s retirement in 1926. Turing and his brother stayed with friends and relatives in England. Turing studied mathematics at Cambridge University, and subsequently taught there, working in the burgeoning world of quantum mechanics. It was at Cambridge that he developed the proof which states that automatic computation cannot solve all mathematical problems. This concept, also known as the Turing machine, is considered the basis for the modern theory of computation.

In 1936, Turing went to Princeton University in America, returning to England in 1938. He began to work secretly part-time for the British cryptanalytic department, the Government Code and Cypher School. On the outbreak of war he took up full-time work at its headquarters, Bletchley Park.

Here he played a vital role in deciphering the messages encrypted by the German Enigma machine, which provided vital intelligence for the Allies. He took the lead in a team that designed a machine known as a bombe that successfully decoded German messages. He became a well-known and rather eccentric figure at Bletchley.

After the war, Turing turned his thoughts to the development of a machine that would logically process information. He worked first for the National Physical Laboratory (1945-1948). His plans were dismissed by his colleagues and the lab lost out on being the first to design a digital computer. It is thought that Turing’s blueprint would have secured them the honour, as his machine was capable of computation speeds higher than the others. In 1949, he went to Manchester University where he directed the computing laboratory and developed a body of work that helped to form the basis for the field of artificial intelligence. In 1951 he was elected a fellow of the Royal Society.

In 1952, Turing was arrested and tried for homosexuality, then a criminal offence. To avoid prison, he accepted injections of oestrogen for a year, which were intended to neutralise his libido. In that era, homosexuals were considered a security risk as they were open to blackmail. Turing’s security clearance was withdrawn, meaning he could no longer work for GCHQ, the post-war successor to Bletchley Park.

He committed suicide on 7 June, 1954. [x]

image

anottershambles
fireandwonder:

ladieslovescience:

femmerenaissance:

Vera Rubin (b. 1928)

When Vera Cooper Rubin told her high school physics teacher that she’d been accepted to Vassar, he said, “That’s great. As long as you stay away from science, it should be okay.”
Rubin graduated Phi Beta Kappa in 1948, the only astronomy major in her class at Vassar, and went on to receive her master’s from Cornell in 1950 (after being turned away by Princeton because they did not allow women in their astronomy program) and her Ph.D. from Georgetown in 1954. Now a senior researcher at the Carnegie Institute’s Department of Terrestrial Magnetism, Rubin is credited with proving the existence of “dark matter,” or nonluminous mass, and forever altering our notions of the universe. She did so by gathering irrefutable evidence to persuade the astronomical community that galaxies spin at a faster speed than Newton’s Universal Law of Gravitation allows. As a result of this finding, astronomers conceded that the universe must be filled with more material than they can see. 
Rubin made a name for herself not only as an astronomer but also as a woman pioneer; she fought through severe criticisms of her work to eventually be elected to the National Academy of Sciences (at the time, only three women astronomers were members) and to win the highest American award in science, the National Medal of Science. Her master’s thesis, presented to a 1950 meeting of the American Astronomical Society, met with severe criticism, and her doctoral thesis was essentially ignored, though her conclusions were later validated. “Fame is fleeting,” Rubin said when she was elected to the National Academy of Sciences. “My numbers mean more to me than my name. If astronomers are still using my data years from now, that’s my greatest compliment.”


 Sources:
1. http://innovators.vassar.edu/innovator.html?id=68; http://science.vassar.edu/women/
2. http://dspace.mit.edu/handle/1721.1/45424

A+ YES. Fabulous ladies getting it DONE.
LLS

do you realize how many scifi stories she is indirectly responsible for?  She discovered the inspiration for Dust in The Golden Compass.

fireandwonder:

ladieslovescience:

femmerenaissance:

Vera Rubin (b. 1928)


When Vera Cooper Rubin told her high school physics teacher that she’d been accepted to Vassar, he said, “That’s great. As long as you stay away from science, it should be okay.”

Rubin graduated Phi Beta Kappa in 1948, the only astronomy major in her class at Vassar, and went on to receive her master’s from Cornell in 1950 (after being turned away by Princeton because they did not allow women in their astronomy program) and her Ph.D. from Georgetown in 1954. Now a senior researcher at the Carnegie Institute’s Department of Terrestrial Magnetism, Rubin is credited with proving the existence of “dark matter,” or nonluminous mass, and forever altering our notions of the universe. She did so by gathering irrefutable evidence to persuade the astronomical community that galaxies spin at a faster speed than Newton’s Universal Law of Gravitation allows. As a result of this finding, astronomers conceded that the universe must be filled with more material than they can see. 

Rubin made a name for herself not only as an astronomer but also as a woman pioneer; she fought through severe criticisms of her work to eventually be elected to the National Academy of Sciences (at the time, only three women astronomers were members) and to win the highest American award in science, the National Medal of Science. Her master’s thesis, presented to a 1950 meeting of the American Astronomical Society, met with severe criticism, and her doctoral thesis was essentially ignored, though her conclusions were later validated. “Fame is fleeting,” Rubin said when she was elected to the National Academy of Sciences. “My numbers mean more to me than my name. If astronomers are still using my data years from now, that’s my greatest compliment.”

 Sources:

1. http://innovators.vassar.edu/innovator.html?id=68; http://science.vassar.edu/women/

2. http://dspace.mit.edu/handle/1721.1/45424

A+ YES. Fabulous ladies getting it DONE.

LLS

do you realize how many scifi stories she is indirectly responsible for?  She discovered the inspiration for Dust in The Golden Compass.

starfoozle
kenobi-wan-obi:

Turbulent Black Holes Grow Fractal Skins As They Feed

Feeding black holes develop a fractal skin as they grow. That’s the conclusion of simulations that take advantage of a correlation between fluid dynamics and gravity.
"We showed that when you throw stuff into a black hole, the surface of the black hole responds like a fluid – and in particular, it can become turbulent," says Allan Adams at the Massachusetts Institute of Technology. "More precisely, the horizon itself becomes a fractal."
Fractals are mathematical sets that show self-similar patterns: zoom in on one part of a fractal drawing, like the famous Mandelbrot set, and the smaller portion will look nearly the same as the original image. Objects with fractal geometries show up all over nature, from clouds to the coast of England.
Adams and his colleagues have now found evidence that fractal behaviour occurs in an unexpected place: on the surface of a feeding black hole. Black holes grow by devouring matter that falls into them; the black hole at the centre of our galaxy is due to feast on a gas cloud later this year. But the details of how feeding black holes grow, and how this might affect their host galaxies, are still unknown.

kenobi-wan-obi:

Turbulent Black Holes Grow Fractal Skins As They Feed

Feeding black holes develop a fractal skin as they grow. That’s the conclusion of simulations that take advantage of a correlation between fluid dynamics and gravity.

"We showed that when you throw stuff into a black hole, the surface of the black hole responds like a fluid – and in particular, it can become turbulent," says Allan Adams at the Massachusetts Institute of Technology. "More precisely, the horizon itself becomes a fractal."

Fractals are mathematical sets that show self-similar patterns: zoom in on one part of a fractal drawing, like the famous Mandelbrot set, and the smaller portion will look nearly the same as the original image. Objects with fractal geometries show up all over nature, from clouds to the coast of England.

Adams and his colleagues have now found evidence that fractal behaviour occurs in an unexpected place: on the surface of a feeding black hole. Black holes grow by devouring matter that falls into them; the black hole at the centre of our galaxy is due to feast on a gas cloud later this year. But the details of how feeding black holes grow, and how this might affect their host galaxies, are still unknown.

fuckyeahsciencefiction

androidghost:

give this to me.

the-promised-wlan:

Foc.us: The first commercial tDCS headset that lets you safely overclock your brain

After an interminable wait, the first brain-boosting tDCS headset has finally received FCC approval and will begin shipping in the next few days. Dubbed the Foc.us, the headset jolts your prefrontal cortex with electricity, improving your focus, reaction time, and ability to learn new skills. The Foc.us is being targeted at gamers looking to improve their skillz, but tDCS has the potential to improve — or more accurately to overclock — almost every aspect of your life. »Continue Reading«