1729

1729

The number 1729 has an interesting story in mathematics involving the extraordinary Indian mathematician Srinivasa Ramanujan. G. H. Hardy accounts:

“I remember once going to see him (Ramanujan) when he was lying ill at Putney. I had ridden in taxi-cab No. 1729, and remarked that the number seemed to be rather a dull one, and that I hoped it was not an unfavourable omen. ‘No’, he replied, ‘it is a very interesting number; it is the smallest number expressible as the sum of two [positive] cubes in two different ways.’”

Ramanujan had a knack for numbers. Growing up in India at the turn of the 20th century, Ramanujan was largely self-taught. Over his short life time (aged 32), he independently developed nearly 4,000 results in mathematics. He kept his results (without proofs) in notebooks that modern mathematicians are still looking into this day. Nearly all of his results have been proven to be true and have driven research in number theory for the past century. Recently, one of Rumanujan’s results, previously unknown to mathematicians, was an important piece to a 2006 publication.

More at https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

More Posts from Philosophical-amoeba and Others

7 years ago
Rishi Coffin For A Commoner

Rishi coffin for a commoner

Second Intermediate Period, Dynasty 17, 1580–1550 B.C. (find spot unknown)

In Dynasty 17 a new type of coffin appeared in Thebes: anthropoid, but no longer conceived solely as an inner coffin, and resting on its back because of a change in funerary customs whereby the deceased was no longer laid on one side. The anthropoid coffin was to become the burial container of choice among royals and commoners alike. The earliest examples are decorated in paint with a feather pattern, and so they are known by the Arabic word for “feathered,” rishi. Carved from local sycamore because the Thebans no longer had access to imported cedar, all rishi coffins, royal or private, show the deceased wearing the royal nemes headdress. This example was clearly a stock item made for a commoner, for a blank space was left for the owner’s name to be inserted at the end of the vertical inscription on the lid (a conventional offering formula for the dead).

Great vulture’s wings envelop the legs and lower abdomen. Even the top of the headdress is decorated with a feather pattern so that the deceased appears as a human-headed bird according to the concept of the ba, or mobile spirit. The ba could travel to any place and transform itself into anything it desired. The face on the coffin is painted black, not to represent the unknown owner’s race but to reinforce his identification with Osiris. The flesh of the god of death and resurrection was often shown as black or green to signify the black silt that fertilized the land with each year’s Nile flood, and the new life in the form of green vegetation that it brought forth. Painted on the chest is a pectoral, or chest ornament, in the form of a vulture and cobra, symbols of Nekhbet and Wadjyt, the tutelary goddesses of Upper and Lower Egypt.

Source: Museum of Fine Arts Boston


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9 years ago
(Image Caption: If This Picture Makes You Feel Uncomfortable, You Feel Empathic Pain. This Sensation

(Image caption: If this picture makes you feel uncomfortable, you feel empathic pain. This sensation activates the same brain regions as real pain. © Kai Weinsziehr for MPG)

The anatomy of pain

Grimacing, we flinch when we see someone accidentally hit their thumb with a hammer. But is it really pain we feel? Researchers at the Max Planck Institute for Human Cognitive and Brain Sciences in Leipzig and other institutions have now proposed a new theory that describes pain as a multi-layered gradual event which consists of specific pain components, such as a burning sensation in the hand, and more general components, such as negative emotions. A comparison of the brain activation patterns during both experiences could clarify which components the empathic response shares with real pain. 

Imagine you’re driving a nail into a wall with a hammer and accidentally bang your finger. You would probably injure finger tissue, feel physical distress, focus all your attention on your injured finger and take care not to repeat the misfortune. All this describes physical and psychological manifestations of “pain” – specifically, so-called nociceptive pain experienced by your body, which is caused by the stimulation of pain receptors.

Now imagine that you see a friend injure him or herself in the same way. You would again literally wince and feel pain, empathetic pain in this case. Although you yourself have not sustained any injury, to some extent you would experience the same symptoms: You would feel anxiety; you may recoil to put distance between yourself and the source of the pain; and you would store information about the context of the experience in order to avoid pain in the future.

Activity in the brain

Previous studies have shown that the same brain structures – namely the anterior insula and the cingulate cortex – are activated, irrespective of whether the pain is personally experienced or empathetic. However, despite this congruence in the underlying activated areas of the brain, the extent to which the two forms of pain really are similar remains a matter of considerable controversy.

To help shed light on the matter, neuroscientists, including Tania Singer, Director at the Max Planck Institute for Human Cognitive and Brain Sciences in Leipzig, have now proposed a new theory: “We need to get away from this either-or question, whether the pain is genuine or not.”

Instead, it should be seen as a complex interaction of multiple elements, which together form the complex experience we call “pain”. The elements include sensory processes, which determine, for example, where the pain stimulus was triggered: in the hand or in the foot? In addition, emotional processes, such as the negative feeling experienced during pain, also come into play. “The decisive point is that the individual processes can also play a role in other experiences, albeit in a different activation pattern,” Singer explains – for example, if someone tickles your hand or foot, or you see images of people suffering on television. Other processes, such as the stimulation of pain receptors, are probably highly specific to pain. The neuroscientists therefore propose comparing the elements of direct and empathetic pain: Which elements are shared and which, by contrast, are specific and unique to the each form of pain?

Areas process general components

A study that was published almost simultaneously by scientists from the Max Planck Institute for Human Cognitive and Brain Sciences and the University of Geneva has provided strong proof of this theory: They were able to demonstrate for the first time that during painful experiences the anterior insula region and the cingulate cortex process both general components, which also occur during other negative experiences such as disgust or indignation, and specific pain information – whether the pain is direct or empathic.

The general components signal that an experience is in fact unpleasant and not joyful. The specific information, in turn, tells us that pain – not disgust or indignation – is involved, and whether the pain is being experienced by you or someone else. “Both the nonspecific and the specific information are processed in parallel in the brain structures responsible for pain. But the activation patterns are different,” says Anita Tusche, also a neuroscientist at the Max Planck Institute in Leipzig and one of the authors of the study.

Thanks to the fact that our brain deals with these components in parallel, we can process various unpleasant experiences in a time-saving and energy-saving manner. At the same time, however, we are able register detailed information quickly, so that we know exactly what kind of unpleasant event has occurred – and whether it affects us directly or vicariously. “The fact that our brain processes pain and other unpleasant events simultaneously for the most part, no matter if they are experienced by us or someone else, is very important for social interactions,” Tusche says, “because it helps to us understand what others are experiencing.”


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7 years ago
12 Snipers From The Soviet 3rd Shock Army With 775 Confirmed Kills. Germany, May 4th 1945.

12 snipers from the Soviet 3rd Shock Army with 775 confirmed kills. Germany, May 4th 1945.

via reddit

Keep reading


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7 years ago
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House
The Christopher Robin Story Book From When We Were Very Young, Now We Are Six, Winnie The Pooh, The House

The Christopher Robin Story Book from When we were very young, Now we are six, Winnie the Pooh, The House at Pooh Corner by AA Milne Illustrated by Ernest H Shepard London Methuen & Co Ltd. First Edition 1929


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7 years ago
Science Fact Friday: Tetrodotoxin, Ft. A Small Gif Because I’m Avoiding My Real Obligations. Why Does

Science Fact Friday: Tetrodotoxin, ft. a small gif because I’m avoiding my real obligations. Why does tetrodotoxin not affect its host? More studies need to be done but at least a few species possess mutated sodium ion channels. The tetrodotoxin can’t interact efficiently with the altered channels.

Another interesting tidbit: Animals with tetrodotoxin can lose their toxicity in captivity. It is suspected that the animals accumulate the toxic bacteria as a side-effect of their diet. After several years of captivity on a tetrodotoxin-bacteria-free diet, the bacterial colonies living in the animals die, residual toxin is cleared from the system, and the animal is safe to handle.


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8 years ago
David Bowie (1947-2016) At Kyoto - Japan - 1980
David Bowie (1947-2016) At Kyoto - Japan - 1980
David Bowie (1947-2016) At Kyoto - Japan - 1980

David Bowie (1947-2016) at Kyoto - Japan - 1980

Photos by Sukita Masayoshi 鋤田 正義


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7 years ago
1.朝顔売り
1.朝顔売り
1.朝顔売り
1.朝顔売り

1.朝顔売り

2.西瓜売り

3.風鈴売り

4.金魚売り


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7 years ago
In 1992, A Man Named Wu Anai, Near A Chinese Village In Longyou County, Based On A Hunch, Began To Pump
In 1992, A Man Named Wu Anai, Near A Chinese Village In Longyou County, Based On A Hunch, Began To Pump
In 1992, A Man Named Wu Anai, Near A Chinese Village In Longyou County, Based On A Hunch, Began To Pump
In 1992, A Man Named Wu Anai, Near A Chinese Village In Longyou County, Based On A Hunch, Began To Pump

In 1992, a man named Wu Anai, near a Chinese village in Longyou County, based on a hunch, began to pump water out of a pond in his village. Anai believed the pond was not natural, nor was it infinitely deep as the local lore went, and he decided to prove it. He convinced some of his villagers and together they bought a water pump and began to siphon water out of the pond. After 17 days of pumping, the water level fell enough to reveal the flooded entrance to an ancient, man-made cave!

The cave has twenty-four rooms. There are pillars, staircases, and high ceilings over 30 meters (98 ft!) up. The work was done by humans, we know, because they left visible chisel marks in uniform bands of parallel groves. With over 30,000 square meters of space, all meticulously chiseled, this would have been a huge undertaking. Even if people were simply enlarging caves which already existed, it would still have required a lot of manpower working in a coordinated system for a long period of time.

Since the project would have been so large, it seems amazing that no record of it exists in China’s extensive written history. But there is not a word. Based on the cave alone, it is estimated to have been completed around 200 BCE, near the Qin Dynasty or Han Dynasties.


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7 years ago

Joan Beauchamp Procter: her best friend was a Komodo dragon and if that doesn’t entice you to read this, I don’t know what will

Joan Beauchamp Procter is a scientist every reptile enthusiast should admire.

Joan Beauchamp Procter: Her Best Friend Was A Komodo Dragon And If That Doesn’t Entice You To Read

Joan was an incredibly intelligent young woman who was chronically ill (and as a result of her chronic illness, physically disabled by her early thirties). Her health issues kept her from going to college, but that did not stop her from studying and keeping reptiles. She presented her first paper to the Zoological Society of London at the tender age of nineteen, and the society was so impressed that they hired her to help design their aquarium. In 1923, despite having no formal secondary education and despite being only 26 years old, she was hired as the London Zoo’s curator of reptiles. Now, that in and of itself is an awesome accomplishment, but Joan was absolutely not content to maintain the status quo. Nosiree, by the age of 26 Joan had already kept many exotic pets (including a crocodile!) and knew a thing or two about what needed to be done to improve their lives in captivity. So Joan got together with an architect, Edward Guy Dawber, and designed the world’s first building designed solely for the keeping of reptiles. She had some really, really great ideas. Her first big idea was to make the building differentially heated- different areas and enclosures would have different heat zones, instead of having the whole building heated to one warm temperature. She also set up aquarium lighting- the gallery itself was dark, with dim lights on individual enclosures to make things less stressful for the inhabitants. She also insisted on the use of special glass that didn’t filter out UVB. This meant that reptiles could synthesize vitamin D and prevented cases of MBD in her charges. 

Joan Beauchamp Procter: Her Best Friend Was A Komodo Dragon And If That Doesn’t Entice You To Read

But advances in enclosure design weren’t Joan’s only contribution to reptile keeping. She was also one of the first herpetologists to study albinism in snakes- she was the first to publish an identification how albinism manifests in reptile eyes differently than in mammal eyes, and stressed the importance of making accurate color plates of reptiles during life because study specimens often lose pigmentation. She also was really hands-on with many species, including crocodiles, large constrictors, and monitor lizards. Joan had this idea that if you socialize an animal and get it used to handling, then when you need to give it a vet checkup, things tend to go a lot better. This really hadn’t been done with reptiles before. She was able to identify many unstudied diseases, thanks to her patient handling of live specimens, and by being patient and going slow, she managed to get a lot of very large, dangerous creatures to trust her. One of them (that we know of) even came to like her- a Komodo dragon named Sumbawa. 

Joan Beauchamp Procter: Her Best Friend Was A Komodo Dragon And If That Doesn’t Entice You To Read

In 1928, two of the first Komodo dragons to be imported to Europe arrived at the London Zoo. One of them, named Sumbawa, came in with a nasty mouth infection. His first several months at the zoo were a steady stream of antibiotics and gentle care, and by the time he’d recovered enough for display, he had come to be tolerant of handling and human interaction. In particular, he seemed to be genuinely fond of Joan. She was their primary caretaker and wrote many of the first popular accounts of Komodo dragon behavior in captivity. While recognizing their lethal capacity, she also wrote about how smart they are and how inquisitive they could be. In her account published in The Wonders of Animal Life, she said that "they could no doubt kill one if they wished, or give a terrible bite" but also that they were “as tame as dogs and even seem to show affection.” To demonstrate this, she would take Sumbawa around on a leash and let zoo visitors interact with him. She would also hand-feed Sumbawa- pigeons and chickens were noted to be favorite food, as were eggs. 

Joan died in 1931 at the age of 34. By that time she was Doctor Procter, as the University of Chicago had awarded her an honorary doctorate. Until her death, she still remained active with the Zoological Society of London- and she was still in charge of her beloved reptiles. Towards the end of her life, Joan needed a wheelchair. But that didn’t stop her from hanging out with her giant lizard friend. Sumbawa would walk out in front of the wheelchair or beside it, still on leash- she’d steer him by touching his tail. At her death, she was one of the best-known and respected herpetologists in the world, and her innovative techniques helped shape the future of reptile care. 


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philosophical-amoeba - Lost in Space...
Lost in Space...

A reblog of nerdy and quirky stuff that pique my interest.

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