How is it that Beethoven, who is celebrated as one of the most significant composers of all time, wrote many of his most beloved songs while going deaf? The answer lies in the math behind his music. Using the “Moonlight Sonata”, we can begin to understand the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.

The standard piano octave consists of 13 keys, each separated by a half step. A standard major or minor scale uses 8 of these keys with 5 whole step intervals and 2 half step ones.

The first half of measure 50 of “Moonlight Sonata” consists of three notes in D major, separated by intervals called thirds that skip over the next note in the scale. By stacking the notes first, third, and fifth notes – D, F sharp, and A – we get a harmonic pattern known as a triad.

But, these aren’t just arbitrary magic numbers. Rather, they represent the mathematical relationship between the pitch frequencies of different notes, which form a geometric series. The stacking of these three frequencies creates ‘consonance’, which sounds naturally pleasant to our ears. Examining Beethoven’s use of both consonance and dissonance can help us begin to understand how he added the unquantifiable elements of emotion and creativity to the certainty of mathematics.

Animation by Qa’ed Mai

Via Ratak Monodosico.

Posted at Gates of Vienna:

I think that the take-down happened in international waters. The Iranians would have known to the minute when the boats were leaving Kuwait, and their probable course to Bahrain, so an intercept would be simple. They know our ROE would be “Do not shoot EVER unless you are fired upon first. PERIOD!!!”

So, if the Iranians jam our boats so they cannot communicate, and then swoop in close, it’s almost a guaranteed outcome. They KNOW we won’t shoot first! So by coming in closer and closer with weapons aimed at our sailors, overwhelming them with numbers at point-blank, then on loudspeaker they say, “Step away from your weapons or we will slaughter you!” At that point, it’s a fait accompli. Once our sailors step back from their guns, it’s over. Next, “Take off your jackets and weapons” etc, until they are in t-shirts only. Then “Kneel down!”

Step by step they get their way, based on a deep understanding of our ROE and our responses at every stage. Once they have control of our boats, they can drive them to Farsi Island, and remove every single GPS device, radar, cell phone etc. Then, there can be no proof of where the attack happened. And worst of all, Obama and Kerry are happy to go along with the lie, in order not to upset the nuclear deal applecart.

Matthew Bracken comments on a Rick Moran American Thinker post:

I rarely pull out my dusty old trident, but in this case, here goes. I was a Navy SEAL officer in the 1980s, and this kind of operation (transiting small boats in foreign waters) was our bread and butter. Today, these boats both not only had radar, but multiple GPS devices, including chart plotters that place your boat’s icon right on the chart. The claim by Iran that the USN boats “strayed into Iranian waters” is complete bull$#it.

For an open-water transit between nations, the course is studied and planned in advance by the leaders of the Riverine Squadron, with specific attention given to staying wide and clear of any hostile nation’s claimed territorial waters. The boats are given a complete mechanical check before departure, and they have sufficient fuel to accomplish their mission plus extra. If, for some unexplainable and rare circumstance one boat broke down, the other would tow it, that’s why two boats go on these trips and not one! It’s called “self-rescue” and it’s SOP.

This entire situation is in my area of expertise. I can state with complete confidence that both Iran and our own State Department are lying. The boats did not enter Iranian waters. They were overtaken in international waters by Iranian patrol boats that were so superior in both speed and firepower that it became a “hands up!” situation, with automatic cannons in the 40mm to 76mm range pointed at them point-blank. Surrender, hands up, or be blown out of the water. I assume that the Iranians had an English speaker on a loudspeaker to make the demand. This takedown was no accident or coincidence, it was a planned slap across America’s face.

Just watch. The released sailors will be ordered not to say a word about the incident, and the Iranians will have taken every GPS device, chart-plotter etc off the boats, so that we will not be able to prove where our boats were taken.

The “strayed into Iranian waters” story being put out by Iran and our groveling and appeasing State Dept. is utter and complete BS from one end to the other.

Ben Shapiro observes that the rest of us understand exactly what Ted Cruz was talking about.

The media of New York City playing dumb on “New York values” while they look down their noses at the rest of the country is the height of ridiculousness.

Mark Twain knew what New York values were: “All men in New York insult you–there seem to be no exceptions. There are exceptions of course–have been–but they are probably dead. I am speaking of all persons there who are clothed in a little brief authority.” That was in 1885. Nothing has changed.

New Yorkers are famous for being rude, socially liberal, in favor of big government, in favor of social leftism – and most of all, convinced of their own superiority. This is why everyone hates Yankees fans.

There are wonderful things about New Yorkers, too. But when people say that someone is “New York” outside New York, everybody knows what they mean, just as if they say that someone is “Texas” outside Texas, everybody knows what they mean.

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Any Iowa Banker knows what Cruz meant.

But Ted Cruz got a much more important endorsement:

Navy video illustrates lots of weaponry and boasts that Riverine Command Boats “pack a punch.”

What exactly is a Riverine Command Boat?

Old Salt Blog has the answer:

The Riverine Command Boat (RCB) is a design based on the Swedish Combat Boat 90. It is a highly maneuverable water-jet powered shallow-draft vessel that can operate at speeds of up to 40 knots. The design has been adopted by navies around the world. The Swedish Navy has 150 of the boats in service while Mexico has 48, Norway 20 and Malaysia 12, the US 6 and the UK 4.

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How are they armed?

The Washington Post noted:

In a number of pictures released by the U.S. Navy, the boats are outfitted with a number of light, medium and heavy weapons including .50 caliber heavy machine guns and GAU-19 miniguns.

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Nate Hale asks the obvious questions.

[T]here are a few serious questions surrounding the incident that remain unanswered. The two patrol boats (actually, Swedish-built CB-90s) were transiting from Kuwait to Bahrain when one (or both) of the vessels suffered a mechanical breakdown. Eventually, the boats drifted into Iranian territorial waters near Farsi Island, where they were detained by members of Iran’s Revolutionary Guards Corps (IRGC).

The most direct route from Kuwait to Bahrain is along the western side of the Persian Gulf; Farsi Island is more centrally located. If the boats were following a direct route, they must have drifted for some time before reaching the Iranian-controlled island. If only one vessel was affected by the engineering casualty, why didn’t the second boat take it under tow? Why weren’t additional assets–including airpower–dispatched by 5th Fleet Headquarters in Bahrain? The presence of Navy helicopters and F/A-18s overhead might have caused the Iranians to think twice.

And what about distress calls from the CB-90s to Navy command elements? Early reports suggested the Navy “lost track” of its assets. Perhaps someone can explain why the vast surveillance assets of the United States Navy couldn’t maintain radio and/or radar contact with a pair of patrol boats–or provide warning of Iranian activity. Major surface combatants (along with airborne assets) give the Navy an impressive SIGINT capability on the high seas; assuming we were tracking Iranian activities, it would be nice to know what information commanders had as the episode unfolded and how it impacted their decision-making.

There are also issues involving the commander of the boat element, believed to be the junior officer who issued the on-camera apology. Why did he offer no resistance when the Iranians began boarding his craft. Article II of the U.S. Military Code of Conduct states “I will never surrender of my own free will. If in command, I will never surrender the members of my command while they have the means to resist.” A CB-90 is heavily armed, with .50-caliber machine guns, GAU-19 mini guns and individual weapons for the crew. Obviously, no officer wants to see his command slaughtered; on the other hand, would it have been possible for the crew to resist, particularly with air support?

It’s also worth asking about the level of involvement by senior officials in Washington. Press accounts suggest that Secretary of State John Kerry was involved in the earliest contacts with Iran and spoke with his counterpart in Tehran no long after the sailors were detained. That quick response suggests the White House and State received early notification of the incident (reflecting the desired level of coordination). But it also begs another essential question: were senior officials micro-managing the episode from Washington, and decided early on to avoid a confrontation with Tehran at all costs.

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Investors Business Daily calls for a congressional probe of the incident.

How can an advanced, ultra-agile U.S. combat boat suffer a “navigation error” that leads to a terrorist state capturing its sailors? Tehran just revealed military ineptitude warranting a congressional probe.

The Swedish-designed Combat Boat 90 can make the sharpest of turns at high speed, stop nearly on a dime, maneuver like magic and, with its Rolls-Royce jet-propulsion system, can speed along at over 45 miles an hour in rivers and shallow coastlines while transporting 18 amphibious troops.

But what good is any of that if it falls into enemy hands?

There is something fishy about how such a high-tech U.S. craft can “stray accidentally into Iranian waters due to a navigation error,” as Defense Secretary Ash Carter described it on Thursday to Univision. The Pentagon had previously claimed engine trouble for an incident that’s humiliated the U.S., as Iranian video showed to the world 10 American sailors on their knees at gunpoint.

A retired operations commander for the U.S. Navy’s Fifth Fleet in Bahrain, Christopher Harmer, told CNN the capture constituted “a severe failure,” charging that “either the naval leadership put these sailors in an impossible situation, or the sailors are professionally incompetent.” Harmer has researched the increased lethality of Iran’s submarine fleet for the Institute for the Study of War.

That one of the sailors would appear in an Iranian video apologizing may have actually violated the military’s Code of Conduct, which requires that a detainee give name, rank, serial number and age, but “evade answering further questions” and “make no oral or written statements disloyal” to his country “and its allies or harmful to their cause.”

Harmer told the Washington Times, “the U.S. Navy looks extraordinarily incompetent. … In its ability to transit boats without violating Iranian waters, they look incompetent to know how to deal with a mechanical malfunction, and now that they’ve been taken into custody, they’re apologizing.”

Harmer told CNN there was “no reason for a small vessel to be out that far and especially without escorting ships around it,” and “the Navy has to explain why you have small ships transiting 300 miles of open ocean.”

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Daily Mail:

A kickboxing champion dubbed the ‘hero of Cologne’ has told of how he fought off a gang of ‘drunken, lecherous Arabs’ who were terrifying two young women on New Year’s Eve.

Standing at seven foot tall and wielding 130kg of solid muscle, Ivan Jurcevic fought off the four sex attackers as they surrounded their young victims and groped them.

The towering doorman, 44, was working at a hotel overlooking Cologne square when the 1,000-strong sex mob Arab and North African men groped, attacked and robbed up 500 women.

Suddenly, two women appeared, begging him to protect them from a gang of men ‘who were harassing them’.

Speaking to MailOnline, Mr Jurcevic said: ‘There were four of them, young men in their 20s, speaking Arabic. They told me not to interfere, that the girls were “theirs”.

‘The girls looked like they worked in a bank, they were wearing jeans and coats, nothing provocative, they were really frightened. I told them to stand behind me.’

‘Then the loudest member of the gang came at me with a bottle so I kicked him in the chest and sent him flying. Another came at me so I slapped him across the face and he went over as well.

‘The leader drew his finger across his throat and told me he would be back to kill me. I stood my ground and they went on their way.’

The former kick-boxer, who has won five world championships, was arrested when he joined a vigilante patrol who took to the city centre on Sunday night.

Photo taken from the oil and gas platform south of Barrow Island late yesterday as severe Tropical Cyclone Narelle approached. The cyclone is now a category four storm packing winds to 230 km/hr. A viewer sent this photo to Nine News Darwin.

Daily Mail:

The cyclone was carrying a massive wall of red sand.

Philo contends that Professor Reynolds’ aperçu ought to be awarded the status of a law.

The government decides to try to increase the middle class by subsidizing things that middle class people have: If middle-class people go to college and own homes, then surely if more people go to college and own homes, we’ll have more middle-class people. But homeownership and college aren’t causes of middle-class status, they’re markers for possessing the kinds of traits — self-discipline, the ability to defer gratification, etc. — that let you enter, and stay, in the middle class. Subsidizing the markers doesn’t produce the traits; if anything, it undermines them.

I dub this Reynolds’ Law: “Subsidizing the markers of status doesn’t produce the character traits that result in that status; it undermines them.” It’s easy to see why. If people don’t need to defer gratification, work hard, etc., in order to achieve the status they desire, they’ll be less inclined to do those things. The greater the government subsidy, the greater the effect, and the more net harm produced.

This law is thus a relative to Murray’s third law in Losing Ground, the Law of Net Harm: “The less likely it is that the unwanted behavior will change voluntarily, the more likely it is that a program to induce change will cause net harm.” But Reynolds’ Law rests on a different and more secure foundation. It focuses on character as fundamental.

Since the time of Woodrow Wilson, Democrats—but not only Democrats—have fretted that the middle class is shrinking due to the power of large corporations, and that only government action to “level the playing field” can save the middle class. The “middle class is being more and more squeezed out by the processes which we have been taught to call processes of prosperity.” Obama? Hillary? No, that’s Woodrow Wilson in 1913 (The New Freedom). It’s striking to realize that progressives have been playing the same tune for a century, no matter what’s actually taking place in the economy—indeed, in the midst of the greatest expansion of affluence in the history of the world—with the same set of proffered solutions: greater government power, regulations, higher taxes, and subsidies for the markers of affluence.

Reynolds’ Law thus strikes at the heart of progressivism as a political ideology. Progressivism can’t deliver on its central promise. In fact, it’s guaranteed to make things worse in exactly that respect.