Growth of the early Internet, node by node

Network diagrams are a popular way of visualizing social and corporate relationships. Network theory has been used to model telecommunications performance and especially, the Internet. Communications networks increase in value as the number of connections increases. Metcalfe’s Law attempts to quantify the increased value.

Optimizing Metcalfe’s Law

For a network with n members, Metcalfe’s Law posits that the total value of that network is proportional to n * (n-1). Metcalfe’s Law as applied to the Internet, and even to the telephone network, is only valid if all connections have equal value. This is incorrect. Some internet connections are hardly used and contribute limited value. Of course, there are reasons to connect everyone that are not based on monetary value! Rural electrification is an example.

Andrew Odlyzko’s article about Metcalfe’s Law (IEEE Spectrum, 2006) was written with a keen awareness of the 2000 dotcom bubble. Odlyzko demonstrated how Metcalfe’s Law’s applicability could be limited by the equal value assumption, among others. I read it, and wondered: What is the Internet’s optimal number of nodes and connections? When did the value of a larger Internet network start diminishing?

At some point, ISPs (Internet Service Providers) stopped charging users for access, as the business of delivering content became more valuable than providing greater network connectivity. AOL charged for service until 2002 or so.

I thought it would be helpful to begin with a timeline of Internet growth, by number of sites connected and corresponding events, as a starting point for determining incremental value. I searched for a streamlined history, but the best that I could find is provided by The Computer History Museum, and it isn’t quite linear. It also has a lot of technical detail that isn’t relevant for verifying Metcalfe’s Law. I decided to construct a timeline of dates and nodes, from which connectivity can be determined. I am writing this partly for myself, for reference purposes. (I don’t know how to value connectivity, not yet.)

In the beginning

In the beginning, the Internet had only two nodes. It was called the ARPANET. (more…)

Published in: on November 25, 2016 at 6:41 am  Comments (3)  
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Oil prices and OPEC influence

Light, sweet crude is the most desirable grade of crude oil because it requires minimal refining while producing the most gasoline. This chart is useful when considering geopolitical risk and commodities prices, as it illustrates where the “best” oil is.

Comparison of oil types by country

Oil types by country (click image to view full-sized)

The chart was produced by the U.S. Department of Energy in 2012. Perhaps that is why West Texas Intermediate (WTI) crude is not listed, as the U.S. was not an oil exporting nation until recently, under President Obama’s administration, although we are not a net oil exporter.


The Organization of Petroleum Exporting Countries has had varying levels of power since its founding in 1960 and heyday in the 1970s. Saudi Arabia has always been the controlling producer in the cartel. OPEC’s objective is to control oil price by either freezing production or cutting production.

Iran is an OPEC member. (more…)

Published in: on March 4, 2016 at 2:31 am  Comments (2)  
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Cornucopia of mathematics

This image was originally developed as the focal point of the Math Awareness Month poster of April 2000. The theme was “Math Spans All Dimensions”. It was too lovely to be retired, and appeared again at TFBCON2003.

Dimension Cornucopia via TFBCON2003

According to the artist, Brown University professor Thomas Banchoff, it is suffused with joy, just as I had hoped!

It begins with mere points, then a curve that flares into a spiral and eventually a colorful 3-d cornucopia of mathematical plenty:

…suggesting the possibility of further dimensions yet to come.

Professor Banchoff’s art work has even graced some book covers, including this one, written by my favorite statistician.

Published in: on February 27, 2015 at 12:33 am  Comments (2)  

The EPA is not the Federal Reserve of oil markets

Energy market pricing behavior seems contrary to the relationship between supply and demand. The oddly behaving RIN market is an intermediate factor that influences gasoline prices for automobiles. RIN (Renewable Identification Numbers) should be decreasing. Instead, they are too high.

Bio-fuel pricing anomaly

RIN establish compliance with standards for non-fossil fuel usage, specifically, for corn-based ethanol as a blend in gasoline. In 2007, legislation was passed to encourage greater use of ethanol. The percentage requirement of ethanol is set by the EPA. It increases annually, and is calculated at an aggregate level, measured volumetrically, over all U.S. domestic consumption.

My favorite energy blog, Platt’s Oil Barrel, featured a guest post* by former Special Assistant to President Obama and Senior Director for Energy and Climate Change of the National Security Council Jason Bordoff, explaining anomalous RIN price behavior, and what the EPA is doing about it. He noted two reasons for the seemingly anomalous pricing.

Hitting the blend wall

Renewable Fuel Standards (RFS) were revised in 2007, based on the assumption that gasoline usage would increase over time. In fact, it has not done so, not consistently. Instead, it decreased during 2011-2013, yet the schedule of increasing amounts of ethanol has remained, as legislated. As a result, according to Bordoff, we are now hitting the “blend wall”, when blenders physically cannot put enough ethanol into the gas supply to comply with RFS law.

Bordoff identified a second reason:

broad-based skepticism in the market that EPA will use its waiver authority to avoid the blend wall—even though EPA just went to unusual lengths to signal precisely that it will.

Federal Reserve v. EPA: Powers and purpose

The bio-fuel situation bears an odd resemblance to the rational expectations based logic of monetary policy. It is difficult for the Federal Reserve to effectively signal to markets, e.g. the anticipated (and appropriate!) end of quantitative easing. The Federal Reserve System has taken measures to increase transparency. Fed Governors Bernanke and Yellen hold scheduled press conferences. Bernanke was the first Federal Reserve governor to do so. The Fed was audited by the GAO in 2012. Federal Open Markets Committee (FOMC) meeting notes are published and posted online.

The Fed also has the necessary tools to carry out monetary policy e.g. quantitative easing known as QE.

Despite all of the above, the “job creators” aren’t investing, and the Fed is now contemplating QE4. (more…)

Published in: on October 13, 2014 at 7:54 am  Comments (8)  
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Statistics comes to Swarthmore College

Some years ago, I studied mathematics and statistics. At that time, there was only one statistician among the mathematics department members, maybe the entire Swarthmore College faculty, Gudmund R. Iversen. He was my academic adviser. Professor Iversen was grey, tweedy and Norwegian. He always addressed me as Miss Kesselman, which helped alleviate my shyness at the time.

Professor Iversen got his PhD in statistics from Harvard University in 1969. I noticed only one other familiar name on that very short list of all Harvard Statistics PhD alumni: Columbia University political science and statistics professor Andrew Gelman PhD in 1990.

Lunch with Tufte

Professor Iversen had a group of colleagues, all statisticians from other academic institutions. They would visit Swarthmore to give lunchtime talks, or more typically, late Friday afternoon presentations to mathematical statistics students.

Diagram of Napoleon's Russian campaign by Minard

Napoleon’s March to Moscow. Charles J. Minard, 1869

I recall one particular guest statistician. Edward Tufte was on the faculty of Princeton University, and had recently written his first book, The Visual Display of Quantitative Information. The venue was a small private room in Sharples dining hall. I was one of maybe 20 attending. (more…)

Just a little bit more Bitcoin trouble

There has been so much tumult in bitcoin and cryptocurrency over the past few days! Interest and concern extends beyond online communities. Motives vary.

screenshot of bitcoin mining in Windows

Bitcoin miner GUI running Windows 7

Anonymous and decentralized

There are two conceptual pillars of trust that uphold bitcoin as being superior to fiat currency. (The fiat currency of reference is primarily the US dollar. Why? Because the US dollar is the world’s reserve currency, for now.)

The first is anonymity. US dollars held as cash are bearer instruments. Ownership and use is anonymous, but only until one wants to use them for commercial transactions of significant size as defined by anti-money laundering rules. Bitcoin does have some anonymity shortcomings, as transactions on the blockchain are actually pseudonymous, but there may be tractable remedies. Further details have been widely covered elsewhere.

The second conceptual pillar of bitcoin is decentralization. The US dollar is highly centralized. As ideological (but not market) confidence in the dollar diminishes, the appeal of an apolitical, alternative currency increases, especially one that is a fungible store of value.

All markets are game theoretic. Bitcoin is too.  I really wish we could ask Professor John Nash what he thinks of bitcoin! Nash wrote a pleasant, accessible article that described bitcoin-like currency, titled “Ideal Money” a few years ago.

I mention game theory because monopolists and cartels can assert control over bitcoin production. This is playing out right now.

Centralization of bitcoin

Currently, Bitcoin’s most acute concern is loss of decentralization. This is due to the documented, persistent existence of a 51% majority mining pool controlled by gHash is owned and operated by private entity gHash’s market dominant behavior was noted in March 2014, however the situation was transient. That has since changed. (more…)

Public school education

Not an autodidact

My only education-related experience has been passive, as a recipient. From kindergarten through 12th grade, I attended public schools in Las Cruces, New Mexico. I loved learning algebra, calculus, chemistry, English literature, French, U.S. history, physics, drafting, home economics, and orchestra. I find it difficult to learn from self-instructional materials. Learning by doing is effective, but requires some guidance.

K-12 education

I perceive betrayal of public interest throughout the U.S.A., due to federal government educational policy. New York City is especially troubled. Exceptionally wealthy individuals with ZERO experience or training in education have decided that they know what is best for America’s children.

The 0.1% of the 0.1%

The Brookings Institute describes them as the 0.1% of 0.1% in assets. Assets held is a robust metric for gauging wealth. It is important to distinguish between wealth and income. Income fluctuates from year to year, even for the wealthy. Causes vary. Some have profound impact, such as significant reversals of fortune. Some are merely transitory, e.g. accounting losses reported in order to minimize impact of tax law changes. These 0.1% of 0.1% individuals choose to actively direct the projects that are beneficiaries of their philanthropy.

Philanthropy, education reform and charter schools

Most education reform activists, or perhaps investors, have no knowledge, nor experience in public school education. Rather, they are exceptionally capable leaders of global software conglomerates. Others have great prowess as hedge fund managers, venture capitalists or real-estate moguls. Several are Wal-Mart family scions. Education reformers who have children educate them at private schools like Philips Andover or Choate, yet they claim that charter school operators provide a superior education, compared to public schools in the U.S.A.

Comparison of charter and public ed chart

Statistically questionable comparison of charter versus public school performance via Wikipedia


Published in: on May 17, 2014 at 9:28 am  Comments (9)  
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The problem with randomness

How to generate random numbers from spam

dilbert comic strip 2001-10-25

Random number generators: The devil is in the details

I found SecurityDump’s WPRandom the other day:

Generating random numbers is pretty complicated if you need them for cryptographic algorithms. This software generates them based on spam comments…

It caught my eye as a sort of “spinning spam into RNG gold”, or more likely, PRNG (pseudo-random number generated) gold. Many WordPress blogs, whether self-hosted using or not, effectively use Akismet as a comment spam sieve. (more…)

Published in: on October 5, 2012 at 3:51 am  Comments (8)  
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SHODAN related infosec assortment

wiki defcon 2

The other Defcon

I never attended DEFCON, though it remains a dream I hope to realize one day, soon. It may soon become too logistically awkward due to increasing numbers of attendees.

Shodan is a remarkable search engine. Traditional search engines use “spiders” to crawl websites. Shodan culls data from ports. It was created by John Matherly in 2007. He continues to develop it.

Shodan is helpful for locating web server vulnerabilities. It is available as a free service, for up to 50 searches. Query syntax includes searches by country, host name, operating system and port. Shodan can search for software AND hardware. It has been acknowledged by mainstream media. The most prominent coverage was in early June, via The Washington Post, when Stuxnet received so much press attention.

Me and Shodan

Next is my Scribd infosec collection. It isn’t exclusively Shodan-related. This is why. (more…)

Published in: on June 13, 2012 at 9:24 pm  Comments (2)  
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Periodic Table Gallery

An exciting time for chemistry

Two new elements, flerovium Fl and livermoreium Lv have been approved for entry in the Periodic Table of the Elements! They were formerly known by blander names—ununquadium and ununhexium. In honor of the event, I assembled a gallery of periodic tables, but let me tell you more about the table first.

The chemical elements are arranged from top to bottom, in order of lowest to highest atomic number. (Atomic number is the same as the number of protons.) There are 118 elements. 98 are naturally occurring, and 14 occur naturally in decay chains of those 98, up to and including californium. The remaining six elements are lab synthesized.

timmurtaugh via Flickr

Periodic Tattoo

Why is it periodic?

Table rows are “periods” and table columns are “groups.” Some groups have specific names, e.g. the noble gases, occupying the last column on the right. Some rows do too, such as the lanthanides and actinides on the bottom two rows.

The table is also periodic because its inventor, Dmitri Mendeleev, intended for it to be updated periodically, as new elements are found. So Mendeleev’s design had a dual use: for describing how the elements relate to each other, as well as for inferring the properties of new and not yet found elements.

One scientific concept to rebuild civilization

The children’s Periodic Table on the U.S. EIA website has the basics. It links to Los Alamos National Lab’s (LANL) Periodic Table.

Photo of Los Alamos National Labs chemist with period table

Actinides at LANL

Here is a great quote from a recent LANL news story by David Hobart, Actinide Analytical Chemistry, History of the periodic table…and my history with it:

As the legendary physicist Richard Feynman put it, “If some universal catastrophe was to engulf the world and humankind could retain only one scientific concept to rebuild civilization, what would it be? The chemist’s answer is almost invariably the Periodic Table of the Elements.


Published in: on March 24, 2012 at 9:02 am  Comments (8)  
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