Cryptography and the Landauer Limit

Sunday, July 5, 2009

In Hollywood, decrypting encrypted data is a simple matter of handing it off to a government lab or wunderkind and coming back in a few hours.

However, even if we were lenient toward Hollywood's fanciful views on computing power, there is another limitation which hackers are unlikely to get the better of: energy.

To bruteforce the decryption to AES-256 encrypted harddrive (commonly available for purchase) would require more energy than exists in the entire solar system. Even if you converted the sun and all the planets into pure energy, you would still come up short.

This is due to Landauer's principle. For a computational operation in which 1 bit of logical information is lost, the amount of entropy generated is at least k ln 2, and so the energy that must eventually be emitted to the environment is E ≥ kT ln 2. (k is the Boltzman constant and T is the temperature of the computer). For AES-256, 2^256 bits must be computed, which is quite a lot!

Possible remedy to this limitation may lie in the future development of reversible computing. If no information is erased, computation may be achieved which is thermodynamically reversible, and require no release of heat. The caveat is that this requires remembering previous states of the system, and must have available the memory necessary to do so.


Tuesday, June 9, 2009

The wild ancestors of the carrot are likely to have come from Afghanistan, which remains the centre of diversity of the wild carrot. Specimens of the eastern carrot that survive to the present day are commonly purple or yellow, and often have branched roots. The purple colour common in these carrots comes from anthocyanin pigments.

The western carrot emerged in the Netherlands in the 17th century, its orange colour making it popular in those countries as an emblem of the House of Orange and the struggle for Dutch independence. The orange colour results from abundant carotenes in these cultivars. Selective breeding over the centuries has reduced bitterness, increased sweetness, and minimized the woody core.

In early use, carrots were grown for their aromatic leaves and seeds, not their roots. Some relatives of the carrot are still grown for these, such as parsley, fennel, dill and cumin. The first mention of the root in classical sources is in the 1st century CE.

Massive overconsumption of carrots can cause hypercarotenemia, a condition in which the skin turns orange.

The urban legend that says eating large amounts of carrots will allow one to see in the dark developed from stories of British gunners in World War II who were able to shoot down German planes in the darkness of night. The legend arose during the Battle of Britain when the Royal Air Force circulated a story about their pilots' carrot consumption as an attempt to cover up the use of radar technologies in engaging enemy planes. It reinforced existing German folklore and helped to encourage Britons—looking to improve their night vision during the blackouts—to grow and eat the vegetable.

The Vegetable Improvement Center at Texas A&M University has developed a purple-skinned, orange-fleshed carrot, the BetaSweet (also known as the Maroon Carrot), containing substances which help prevent cancer. The high β-carotene content gives the carrot its maroon shade.

WWI and a three millenia old strategy

Monday, May 25, 2009

Spach, John Thom, "Allenby And The Last Crusade," MILITARY HISTORY,
March, 1996, 741 Miller Dr. SE, Suite D-2, Suite 300, Leesburg, VA

On February 13, 1918, the 60th Division took over the Deir Ibu Obed-Ras es Suffa-Hezmeh Line from the 53rd Division, and on the next day, operational orders were issued for an attack on Jericho with the object of driving the enemy across the Jordan River. Before the main attack could take place, it was necessary to straighten out the Brit ish line by capturing a small village in the hands of the Turks and directly in front of the 180th Brigade. The village was named Mukhmas, or Michmash.

A frontal assault was decided upon. Supported by artillery and machine guns, the brigade was to move down into the valley separating the two lines and at dawn it would storm up the other side, in the face of the enemy fire. The plan would entail some casualties, but those were deemed unavoidable. Orders were issued, and then the troops got what rest they could.

In his bivouac, by the light of a candle, Major Gilbert read his Bible. When the raid was first discussed, the name Michmash had sounded vaguely familiar, although he could not quite place it. Just as he was about to put out his candle, he thought he would try one more time to find the name. At last he found what he was searching for in 1st Samuel, chapters 13 and 14: "And Saul and Jonathan, his son, and the people that were present with them, abode in Gibeah: but the Philistines encamped in Michmash.

"Now it came to pass upon a day that Jonathan, the son of Saul, said unto the young man that bare his armor, 'Come and let us go over to the Philistines' garrison, that is on the other side,' but he told not his father. . . . And the people knew not that Jonathan was gone.

"And between the passages by which Jonathan sought to go over to the Philistine garrison, there was a sharp rock on the one side, and a sharp rock on the other side: the name of one was Bozez, and the name of the other Seneh. The forefront of one was situated northward over against Michmash, and the other southward over against Gibeah. And Jonathan said to the young man that bare his armour. . . 'It may be that the Lord will work for us; for there is no restraint to the Lord to save by many or by few.'"

The major read on how Jonathan went through the pass of Michmash, between Bozez and Seneh, and climbed the hill with his armor-bearer following behind, until they came to a place high up, about "a half acre of land, which a yoke of oxen might plow," and the Philistines who were sleeping awoke, thought they were surrounded by the armies of Saul, and the "multitudes melted away" as they fled in disorder. Saul then attacked with his whole force of about six-hundred men. It was a great victory for him, and "so the Lord saved Israel that day and the battle passed
over into Bethaven."

"This pass, these rocky headlands and flat piece of ground are probably still there," Gilbert told himself. "Very little has changed in Palestine throughout the centuries." He woke General Watson and informed him of what he had found in the Bible. Together they read the story over again. Then Watson sent out scouts, who came back and reported finding the pass, thinly guarded by the Turks, with rock crags on either side--obviously Bozez and Seneh. Up in Michmash, the moonlight shone on a flat piece of ground just big enough for a team to plough.

Immediately, Watson decided to change the plan of attack. Instead of the whole brigade, one infantry company advanced in the dead of night along the pass of Michmash. The few Turks they met were quickly and silently dealt with. They passed between Bozez and Seneh, climbed the hillside and, just before dawn, found themselves on the flat piece of ground. When the Turkish soldiers awoke, they thought they were surrounded by several British armies and fled in disorder.

Every enemy soldier who had slept that night in Michmash was either killed or captured. After thousands of years, the tactics of Jonathan and Saul succeeded a second time.

The World's Strongest Acid

Sunday, May 24, 2009

The term superacid was originally coined by James Bryant Conant in 1927 to describe acids that were stronger than conventional mineral acids.

In 1994 the Nobel Prize in Chemistry was awarded to George A. Olah for his investigations of superacids and their use in the direct observation of carbocations. "Olah's magic acid," so-named for its ability to attack hydrocarbons, is prepared by mixing antimony pentafluoride (SbF5) and fluorosulfuric acid. The name was coined after one of Professor Olah's post-doctoral associates placed a candle in a sample of magic acid. The candle was dissolved, showing the ability of the acid to protonate hydrocarbons, which under normal acidic conditions do not protonate to any extent.

The strongest known superacid is fluoroantimonic acid (HSbF6), a mixture of hydrogen fluoride and antimony pentafluoride. It is rapidly and explosively decomposed by water, and reacts with virtually all known solvents.

Fluoroantimonic acid is approximately 2×1019 (20 quintillion) times stronger than pure sulfuric acid.

It all began with the aurochs.

Tuesday, April 21, 2009

The aurochs or urus (Bos primigenius) was a very large type of cattle that was prevalent in Europe until its extinction in 1627.

Aurochs are depicted in many Paleolithic European cave paintings such as those found at Lascaux and Livernon in France. Early carvings of the aurochs have also been found. The impressive and dangerous aurochs survived into the Iron Age in Anatolia and the Near East, and was worshipped throughout that area as a sacred animal, the Lunar Bull, associated with the Great Goddess and later with Mithras.

Aurochs had several features rarely seen in modern cattle, such as lyre-shaped horns set at a forward angle, a pale stripe down the spine, and sexual dimorphism of coat color. Males were black with a pale eel stripe or finching down the spine, while females and calves were reddish. Aurochs were also known to have very aggressive temperaments and killing one was seen as a great act of courage in ancient cultures. The size of the ancient aurochs was far larger than most modern cattle, approximately 2 metres (6.5 feet) at the shoulder, and weighing 1,000 kilograms (2,200 lbs).

According to the Paleontologisk Museum, University of Oslo, aurochs evolved in India some two million years ago, migrated into the Middle East and further into Asia, and reached Europe about 250,000 years ago.[10] They were once considered a distinct species from modern European cattle (Bos taurus), but more recent taxonomy has rejected this distinction. The South Asian domestic cattle, or zebu, descended from a different group of aurochs at the edge of the Thar Desert in India; this would explain zebu resistance to drought.

Domestication of the aurochs began in the southern Caucasus and northern Mesopotamia from about the 6th millennium BC, while genetic evidence suggests that aurochs were independently domesticated in northern Africa and in India.

The last recorded live aurochs, a female, died in 1627 in the Jaktorów Forest, Poland. The skull was later taken by the Swedish Army during the Swedish invasion of Poland (1655–1660) and is now the property of Livrustkammaren in Stockholm.

In the 1920s two German zoo directors, the brothers Heinz and Lutz Heck, attempted to breed the aurochs "back into existence" from the domestic cattle that were their descendants. Their plan was based on the concept that a species is not extinct as long as all its genes are still present in a living population. The result is the modern breed called Heck cattle, which bears an incomplete resemblance to the physiology of the wild aurochs.

The Siege of Tyre

Monday, April 20, 2009

The Siege of Tyre was orchestrated in 333 BC by Alexander the Great.

Alexander began with an engineering feat that shows the true extent of his brilliance; as he could not attack the city from sea, he built a kilometer-long causeway stretching out to the island on a natural land bridge no more than two meters deep. This allowed his artillery to get in range of the walls.

As the bridge approached the walls, however, the water became much deeper, and the combined attacks from the walls and Tyrian navy made construction nearly impossible. Therefore, Alexander constructed two towers 150 feet high and moved them to the end of the causeway.

Like most of Alexander’s siege towers, these were moving artillery platforms, with catapults on the top to clear defenders off of the walls, and ballista below to hurl rocks at the wall and attacking ships. The towers were made of wood, but were covered in rawhide to protect them from fire arrows.

Although these towers were possibly the largest of their kind ever made, the Tyrians quickly devised a counterattack. They used an old horse transport ship, filling it with dried branches, pitch, sulfur, and various other combustibles. They then hung cauldrons of oil from the masts, so that they would fall onto the deck once the masts burned through. They also weighed down the back of the ship so that the front rose above the water. They then lit it on fire and ran it up onto the causeway. The fire spread quickly, engulfing both towers and other siege equipment that had been brought up. The Tyrian ships swarmed the pier, destroying any siege equipment that hadn’t caught fire, and driving off Macedonian crews that were trying to put out the fires.

Alexander was convinced that he would not be able to take Tyre without a navy. However, the Persian navy returned to find their home cities under Alexander’s control. The Persians' allegiance to their cities allowed Alexander to command eighty ships. This coincided with the arrival of another hundred and twenty from Cyprus, which had heard of his victories and wished to join him. With the arrival of another twenty three ships, Alexander had two hundred and twenty three galleys under his command.

Alexander then sailed on Tyre and quickly blockaded both ports with his superior numbers. He had several of the slower galleys, and a few barges, refit with battering rams, the only known case of battering rams being used on ships. Finding that large underwater blocks of stone kept the rams from reaching the walls, Alexander had them removed by crane ships. The rams then anchored near the walls, but the Tyrians sent out ships and divers to cut the anchor cables. Alexander responded by replacing them with chains.

The Tyrians tried another brilliant counter attack. They noticed that Alexander returned to the mainland at the same time every afternoon for lunch, at the same time much of his navy did. They therefore attacked at this time, but found Alexander had skipped his afternoon nap, and was able to quickly counter the sortie.

Alexander started testing the wall at various points with his rams, until he made a small breach in the south end of the island. He then coordinated an attack across the breach with a bombardment from all sides by his navy. Once his troops forced their way into the city, they easily overtook the garrison, and quickly captured the city. Those citizens that took shelter in the temple of Herakles were pardoned by Alexander, including the king of Tyre. The others, some 30,000 people, were sold into slavery, both because of the length of the siege, and because the Tyrians had executed some captured sailors on the walls.

Banach-Tarski Paradox

Friday, April 17, 2009

First formulated in 1924, the Banach-Tarski paradox states that it is possible to decompose a ball into six pieces which can be reassembled by rigid motions to form two balls of the same size as the original. The number of pieces was subsequently reduced to five by Robinson (1947), although the pieces are extremely complicated. (Five pieces are minimal, although four pieces are sufficient as long as the single point at the center is neglected.) A generalization of this theorem is that any two bodies in that do not extend to infinity and each containing a ball of arbitrary size can be dissected into each other.

Of course, this doesn't actually work for everyday physical objects, because they are built up out of atoms, not an infinite continuum of points, but it does work for the idealized objects you are accustomed to studying in high-school geometry class!


Thursday, April 16, 2009

Ethanethiol has a strongly disagreeable odor. The threshold for human detection is as low as one part in 2.8 billion parts of air. According to the 2000 edition of the Guinness Book Of World Records, ethanethiol is the "smelliest substance" in existence.

Ethanethiol is intentionally added to butane and propane to impart an easily noticed smell to these odorless fuels.

The Science of Made Up Substances

Wednesday, April 15, 2009

In 1667, Johann Joachim Becher published his Physical Education, which was the first mention of what would become the phlogiston theory.

The theory holds that all flammable materials contain phlogiston, a substance without colour, odour, taste, or mass that is liberated in burning. Once burned, the "dephlogisticated" substance was held to be in its "true" form, the calx.

In general, substances that burned in air were said to be rich in phlogiston; the fact that combustion soon ceased in an enclosed space was taken as clear-cut evidence that air had the capacity to absorb only a definite amount of phlogiston. When air had become completely phlogisticated it would no longer serve to support combustion of any material, nor would a metal heated in it yield a calx; nor could phlogisticated air support life, for the role of air in respiration was to remove the phlogiston from the body. Thus, phlogiston as first conceived was a sort of anti-oxygen.

Phlogiston remained the dominant theory until Antoine-Laurent Lavoisier showed that combustion requires a gas which has weight (oxygen), which could be measured by means of weighing closed vessels.

luminiferous aether

In Greek mythology, Aether is one of the Protogenoi, the first-born elemental gods. He is the personification of the "upper sky," space, and heaven, and the elemental god of the "Bright, Glowing, Upper Air." He is the pure upper air that the gods breathe, as opposed to the gloomy lower air of the Earth, which mortals breathe.

Plato's Timaeus posits the existence of a fifth element (corresponding to the fifth remaining Platonic solid, the dodecahedron) called quintessence, of which the cosmos and all celestial bodies are made.

Aristotle included aether in the system of the classical elements of Ionic philosophy as the "fifth element" (the quintessence), on the principle that the four terrestrial elements were subject to change and moved naturally in straight lines while no change had been observed in the celestial regions and the heavenly bodies moved in circles. In Aristotle's system aether had no qualities (was neither hot, cold, wet, or dry), was incapable of change (with the exception of change of place), and by its nature moved in circles.

In order to explain the properties of light, Newton's Opticks (1704) postulated an "Aethereal Medium" transmitting vibrations faster than light, by which light, when overtaken, is put into "Fits of easy Reflexion and easy Transmission", which caused refraction and diffraction.

Einstein's theories of relativity have since made the aether theory largely an irrelevancy.

A certain modification to the Aristotelian theory of motion preceded Galileo, in which motion was described as a transmission of "impetus." Objects would eventually run out of impetus, which explained why a thrown stone would eventually come back down.

dark matter
In astronomy and cosmology, dark matter is hypothetical matter that is undetectable by its emitted radiation, but whose presence can be inferred from gravitational effects on visible matter. Dark matter is postulated to explain the flat rotation curves of spiral galaxies and other evidence of "missing mass" in the universe. According to present observations of structures larger than galaxies, as well as Big Bang cosmology, dark matter and dark energy account for the vast majority of the mass in the observable universe.

energy and other quantities
While things like phlogiston may sound silly from our modern view, they are not that far off from contemporary beliefs. Dark matter has already been mentioned as one gap-filler in modern physics. But much more essential concepts such as "energy" perform the same role. It represents a quantity we use in certain bookkeeping on particles, but energy is not an essence that physicists have ever observed in its pure element (nor could they). The same goes for charge and other quantities. They serve us in the same role that phlogiston and impetus once served our predecessors: as a theoretical representation of how the state of objects changes.

The Oklo reactors

Tuesday, April 14, 2009

The first artificial nuclear reactor was built by Enrico Fermi and co-workers beneath the University of Chicago's football stadium and brought on line on December 2, 1942. This reactor, which produced several kilowatts of power, consisted of a pile of graphite blocks weighing 385 tons stacked in layers around a cubical array of 40 tons of uranium metal and uranium oxide.

But preceding this by billions of years is the Oklo reactor discovered in Gabon, Central Africa, in 1972. The sustained chain reaction of this naturally occurring uranium deposit was mediated by water, which would decelerate ambient neutrons to fission appropriate speeds, and boil away when the reaction became too hot. The length of reaction has been calculated as approximately two-and-a-half hours per interval.

While other Uranium deposits have sufficient fuel to create a reactor, only the Oklo deposits have had the neutron moderation necessary to become active.