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Musical Prime Numbers in Base 7, from 2 to 20021 (4817 in Base 10) – Composition by Gennady Stolyarov II

Musical Prime Numbers in Base 7, from 2 to 20021 (4817 in Base 10) – Composition by Gennady Stolyarov II

Gennady Stolyarov II

You have never heard music quite like this before.

This is the musical expression, in Base 7, of every prime number from 2 to 20021 (4817 in Base 10). The video displays each prime number in Base 10 and Base 7, alongside the corresponding notation. It also presents the system for musically mapping the prime numbers, explains the rules for composing within this system, and discusses some of its possibilities.

This is not an entirely algorithmic composition, since the human-driven approach to splitting the notes representing each prime number enables the music to be as consonant as possible while adhering to the rules of the system. This work was composed by Gennady Stolyarov II between February 12 and March 4, 2021. It is played using the MuseScore 3.0 software. It is likely unplayable by a single human pianist, although two pianists might succeed in performing it.

Download the MP3 file of this composition here.

This composition and video may be freely reproduced using the Creative Commons Attribution Share-Alike International 4.0 License.

Remember to LIKE, FAVORITE, and SHARE this video in order to spread rational high culture to others.

See the index of Mr. Stolyarov’s compositions, all available for free download, here.



Elevated Fractal City III – Art by Gennady Stolyarov II

Elevated Fractal City III – Art by Gennady Stolyarov II

Elevated Fractal City III – by Gennady Stolyarov II

Note: Left-click on this image to get a full view of this digital work of fractal art.

“Elevated Fractal City III” depicts an angular, luminous outpost in the night on a befogged world. Even such less hospitable alien worlds will one day be colonized by our civilization, and the colonists will build their own amenities.

This digital artwork was created by Mr. Stolyarov in Apophysis, a free program that facilitates deliberate manipulation of randomly generated fractals into intelligible shapes.

This fractal is an extension of Mr. Stolyarov’s artistic style of Abstract Orderism, whose goal is the creation of abstract objects that are appealing by virtue of their geometric intricacy — a demonstration of the order that man can both discover in the universe and bring into existence through his own actions and applications of the laws of nature.

Fractal art is based on the idea of the spontaneous order – which is pivotal in economics, culture, and human civilization itself. Now, using computer technology, spontaneous orders can be harnessed in individual art works as well.

See the index of Mr. Stolyarov’s art works.

ECM Distributed Computing Project and Mr. Stolyarov Discover Factor for 279-Digit Number (“9” Surrounded by 139 Instances of “7” Per Side)

ECM Distributed Computing Project and Mr. Stolyarov Discover Factor for 279-Digit Number (“9” Surrounded by 139 Instances of “7” Per Side)

The New Renaissance Hat
G. Stolyarov II
November 21, 2012

I am pleased to report that a large prime factor for (7·10279+18·10139-7)/9 (visualized as a “9” surrounded by 139 instances of “7” on each side – for a total of  279 digits) was discovered on November 19, 2012, through my participation in the ECM distributed computing project (organized via Yoyo@home). This is the fourth discovery made on my computer via the ECM project (see posts about previous discoveries here and here).

The prime factor is a 53-digit number: 42684752427275029312252733896207947190538122452468697. I am credited with the discovery here and here.

I continue to be impressed by the potential of individual hyper-empowerment through distributed computing, and I encourage my readers to also donate their idle computer time to projects that attract their interest.

Factors for (141^141 + 142^142) and (148^148 + 149^149) Discovered by Mr. Stolyarov and ECM Distributed Computing Project

Factors for (141^141 + 142^142) and (148^148 + 149^149) Discovered by Mr. Stolyarov and ECM Distributed Computing Project

The New Renaissance Hat
G. Stolyarov II
August 28, 2012

Since the discovery in April 2012 of a factor for (118^67 + 67^118), I have continued to donate extensive computing resources to the ECM distributed computing project (organized via Yoyo@home). Today I am pleased to announce that two more large factors of even larger numbers have been discovered as a result of this endeavor. I am credited with the discoveries here. The following is now known:

● The number (141^141 + 142^142) (see long form here) has a 33-digit factor: 168,853,190,844,095,597,109,245,277,698,729.

● The number (148^148 + 149^149) (see long form here) has a 28-digit factor: 9,055,497,748,306,357,299,810,062,467.

To date, my computer has examined 2729 project workunits (each involving an attempt to factor a large number). I have thus far accumulated 528,533.42 BOINC credits for the ECM project.

The magnitudes involved are astounding, considering that the factors discovered are several hundred orders of magnitude less than the original numbers. As an example, (148^148 + 149^149) is equal to approximately 6.39 * 10^323. And yet our advancing technology is enabling us already to explore these immense quantities and derive meaningful conclusions regarding them.

Wall Street Math – Article by Douglas French

Wall Street Math – Article by Douglas French

The New Renaissance Hat
Douglas French
April 11, 2012

There’s plenty of blame for the financial crisis being spread around. Those on the left say Wall Street wasn’t regulated enough, while those on the right claim government mandates required lenders to make bad loans. The argument is made that the Federal Reserve was too loose, while the other side says Bernanke wasn’t loose enough. Some blame greed. Others blame Wall Street’s investment products. And then there’s mathematics.

Wall Street has become a numbers game played at high speed by powerful computers trading complex derivatives utilizing even more complex mathematical modeling. Writing for the Huffington Post, Théo Le Bret asks the reader to

Take the Black-Scholes equation, used to estimate the value of a derivative: it is actually no more than a partial differential equation of the financial derivative’s value, as a function of four variables, including time and “volatility” of the underlying asset (the derivative being a ‘bet’ on the future value of the asset). Differential equations are well-known to physicists, since such fundamental properties of nature as the wave equation or Schrodinger’s equation for quantum mechanics are given in the form of differential equations, and in physics their solutions seem to be very reliable: so why is this not always the case in finance?

Mr. Le Bret quotes Albert Einstein for his answer: “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”

Murray Rothbard put it another way:

In physics, the facts of nature are given to us. They may be broken down into their simple elements in the laboratory and their movements observed. On the other hand, we do not know the laws explaining the movements of physical particles; they are unmotivated.

Rothbard goes on to make the point that human action is motivated and thus economics is built on the basis of axioms. We can then deduce laws from these axioms, but, as Rothbard explains, “there are no simple elements of ‘facts’ in human action; the events of history are complex phenomena, which cannot ‘test’ anything.”

Using the models that work so well for physicists, mathematicians on Wall Street got it spectacularly wrong in the mortgage and derivatives markets, just as mathematical economists can never predict the future with any accuracy. Motivated human behavior cannot be modeled.

But the mathematicians or “quants” underscore all of Wall Street’s financial engineering, a process that takes a few pieces of paper and folds their attributes together to make new products, most times hoping to avoid taxes and regulation. Author Brendan Moynihan describes this engineering in his book Financial Origami: How the Wall Street Model Broke.

Origami is the traditional Japanese art of paper folding wherein amazing shapes and animals are created with just a few simple folds to a piece of paper. Moynihan cleverly extends the metaphor to the financial arena, pointing out that stocks, bonds, and insurance are pieces of paper simply folded by the Wall Street sales force into swaps, options, futures, derivatives of derivatives, and the like.

The author is adept at describing derivatives in terms a person can understand. Health-insurance premiums are a call option to have the insurance company pay for our medical care. Auto insurance premiums are like put options, allowing the insured to sell (put) his or her car, if it’s totaled, to the insurer at blue-book value.

Nobel Prize winners have played a big hand in the creation of derivatives. Milton Friedman’s paper on the need for futures markets in currencies paved the way for that market in 1971. But as Moynihan points out, it was Nixon’s shutting of the gold window that created the need to mitigate currency and inflation risk.

Nobel Laureate Myron Scholes was cocreator of the Black-Scholes-Merton option-pricing model. He and cowinner Robert Merton used their model to blow-up Long Term Capital Management.

But it was little-known economist David X. Li’s paper in the Journal of Fixed Income that would provide the intellectual foundation for Wall Street’s flurry into mortgages. “On Default Correlation: A Copula Function Approach” became “the academic study used to support Wall Street’s turning subprime mortgage pools into AAA-rated securities,” writes Moynihan. “By the time it was over, the Street would create 64,000 AAA-rated securities, even though only 12 companies in the world had that rating.”

Robert Stowe England, in his book Black Box Casino: How Wall Street’s Risky Shadow Banking Crashed Global Finance, says Li’s model “relied on the price history of credit default swaps against a given asset to determine the degree of correlation rather than rely on historical loan performance data.”

“People got very excited about the Gaussian copula because of its mathematical elegance,” says Nassim Nicholas Taleb, “but the thing never worked.” Taleb, the author of The Black Swan, claims any attempt to measure correlation based on past history to be “charlatanism.”

Subprime mortgages were bundled to become collateralized mortgage obligations (CMOs), which are a form of collateralized debt obligation(CDO). CDOs weren’t new; the first rated CDO was assembled by Michael Milken in 1987. But instead of a mixture of investment-grade and junk corporate bonds, in the housing bubble, CDOs were rated AAA based upon Li’s work.

Mr. England wryly points out, “A cynic might say that the CDO was invented to create a place to dump lower credit quality or junk bonds and hide them among better credits.”

England quotes Michael Lewis, author of The Big Short: “The CDO was, in effect, a credit laundering service for the residents of Lower Middle Class America.” For Wall Street it was a machine that “turned lead into gold.”

Wall Street’s CDO mania served to pump up investment-bank leverage. England explains that if level-3 securities were included (level-3 assets, which include CDOs, cannot be valued by using observable measures, such as market prices and models) then Bear Stearns sported leverage of 262 to 1 just before the crash. Lehman was close behind at 225, Morgan Stanley at 222, Citigroup at 212, and Goldman Sachs was levered at 200 to 1.

Leverage like that requires either perfection or eventual government bailout for survival.

The CDO market created the need for a way to bet against the CDOs and the credit-default-swap (CDS) market was born. Bundling the CDS together created synthetic CDOs. “With synthetic CDOs, Wall Street crossed over to The Matrix,” writes England, “a world where reality is simulated by computers.”

It’s England’s view that the CDO market “was the casino where the bets were placed. Wall Street became bigger and chancier than Las Vegas and Atlantic City combined — and more.” According to Richard Zabel, the total notional value of the entire CDS market was $45 trillion by the end of 2007, at the same time the bond and structured vehicle markets totaled only $25 trillion.

So the speculative portion of the CDS market was at least $20 trillion with speculators betting on the possibility of a credit event for securities not owned by either party. England does not see this as a good thing. It’s Mr. England’s view that credit default swaps concentrated risk in certain financial institutions, instead of disbursing risk.

In “Credit Default Swaps from the Viewpoint of Libertarian Property Rights and Contract Credit Default Swaps Theory,” published in Libertarian Papers, authors Thorsten Polleit and Jonathan Mariano contend, “The truth is that CDS provide investors with an efficient and effective instrument for exposing economically unsound and unsustainable fiat money regimes and the economic production structure it creates.”

Polleit and Mariano explain that credit default swaps make a borrower’s credit risk tradable. CDS is like an insurance policy written against the potential of a negative credit event. These derivatives, while being demonized by many observers, serve to increase “the disciplinary pressure on borrowers who are about to build up unsustainable debt levels to consolidate; or it makes borrowers who have become financially overstretched go into default.”

Mr. England concludes his book saying, “We need a way forward to a safer, sounder financial system where the power of sunlight on financial institutions and markets helps enable free market discipline to work its invisible hand for the good of all.”

Polleit and Mariano explain that it is the CDS market that provides that sunlight.

The panic of 2008 was the inevitable collapse of an increasingly rickety fiat-money and banking system — a system where the central bank attempts to direct and manipulate the nation’s investment and production with an eye to maximize employment. In a speech delivered to the Federal Reserve Bank of New York, Jim Grant told the central bankers that interest rates should convey information. “But the only information conveyed in a manipulated yield curve is what the Fed wants.”

Wall Street’s math wizards convinced the Masters of the Universe that their numbers don’t lie, believing they could model the Federal Reserve’s house-of-mirrors market. Maybe the numbers don’t lie, but the assumptions do.

Advising about mathematical economics, Rothbard wrote, “ignore the fancy welter of equations and look for the assumptions underneath. Invariably they are few in number, simple, and wrong.” The same could be said for Dr. Li’s model and Scholes’s model before him.

Until the era of unstable fiat-money regimes ends, the search for scapegoats will continue — because the crashes will never end.

Douglas French is president of the Mises Institute and author of Early Speculative Bubbles & Increases in the Money Supply and Walk Away: The Rise and Fall of the Home-Ownership Myth. He received his master’s degree in economics from the University of Nevada, Las Vegas, under Murray Rothbard with Professor Hans-Hermann Hoppe serving on his thesis committee. French teaches in the Mises Academy. See his tribute to Murray Rothbard. Send him mail. See Doug French’s article archives.

This article was published on and may be freely distributed, subject to a Creative Commons Attribution United States License, which requires that credit be given to the author.

ECM Distributed Computing Project and Mr. Stolyarov Discover Factor for 118^67 + 67^118

ECM Distributed Computing Project and Mr. Stolyarov Discover Factor for 118^67 + 67^118

The New Renaissance Hat
G. Stolyarov II
April 6, 2012

I am pleased to announce that my participation in the ECM distributed computing project (organized via Yoyo@home) has resulted in the discovery of a hitherto unknown factor for a large number. I am credited with the discovery here.

Did you know that the number 118^67 + 67^118 (see its long form here) has a multiplicative factor of 2091937057168244837833711997693707725557784572281 – a formidable 49-digit number?

Well, now you know, because of all the computing power I have devoted to the ECM project since late 2011. Finding such large factors of even larger numbers is a rarity. My computer had to examine 1546 project workunits (each involving an attempt to factor a large number) before finding one that resulted in a new discovery. I have thus far accumulated 277,345.88 BOINC credits for the ECM project.

ECM is a free distributed computing project that anyone can participate in. Its goal is to find factors for large numbers using the method of Elliptic Curve Factorization. It is highly rewarding to be able to devote otherwise idle resources to an endeavor for the convenient discovery of previously unknown truth.