As I did at the end of 2013, 2014 & 2015, so I do again here at the end of 2017 to recount some travel experiences, which I don’t normally write about here. I did not post anything about my travels at the end of 2016, so this years post will cover my travels from 2016 and 2017. I need not give the setup again for the premise of such entries and see my blog from the end of 2013: Travels of Spocklogic. The notable travels from 2016 & 2017 (travel blogs I finished or made additions to) include:

That’s the summary for 2016 & 2017. For the previous years travels, I include the links here for convenience, but all blog links can be found in the “Browse Blog Posts” at the top of the page.

Travels of Spocklogic
Travels of Spocklogic II
Travels of Spocklogic III

All in all, it was a good couple of years in travel with a visit to France in early 2016, visits to Sicily and Central Italy in the summer of 2016, and a trip to the Shenandoah region of Virginia in the fall of 2016. For this later blog on Shenandoah, I included a couple of other trips there with one from 2000 and another from 2005. Over the years, since I have lived in the state of Virginia, I have visited this area of the state maybe a dozen or so times, but I don’t have photos for all the visits there, and just the years 2000, 2005 and 2016. I also have a Virginia blog called “Virginia Perspectives” covering 1990-present that is a mix of travel & slice of life. The year 2017 consisted of a road trip to New England in the early summer and a trip to Brazil in late summer, my first trip to South America, making it my 5th continent to visit. There is also another blog I made on Places in Passing, which consists of entries regarding places I mentioned in passing, but did not write about in great detail. I have plans to fill in the narratives, but for now the entries display  photos and a reference link to a blog where the place was mentioned.

For a complete collection of blogs, one can always visit Spocklogic’s Travel Blogs at TravBuddy.

Best wishes for the New Year in 2018!



Nobel Prize Medals

The Nobel Prize is perhaps the most prestigious and well known award and given each year for Physics, Chemistry, Physiology or Medicine, Literature, Peace and Economic Sciences. The award for Economic Sciences, established in 1968, is not one of the original prizes established in 1895 through Alfred Nobel’s Will. It is technically called The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel, though common called the Nobel Prize in Economics as the process, criteria and award ceremony are done in the same way as the other Nobel Prizes. This prize in Economics has been a source of controversy for a variety of reasons. Nevertheless it is still a Real Nobel Prize just like the others. The announcements for the Nobel Prize are made during October and the ceremony is held in Stockholm, Sweden during December. Each recipient must deliver a Nobel Prize Lecture within six months of the official ceremony to receive the prize money.

The establishment of the Nobel Prize stems from the last will and testament of Alfred Nobel, signed on November 27, 1895 at the Swedish-Norwegian Club in Paris. Alfred Nobel died on December 10, 1896 from a stroke due to a long lasting heart ailment. When the will was read it caused quite a controversy as the majority of his wealth was left to the establishment of “prizes to those who, during the preceding year, shall have conferred the greatest benefit to mankind,” as the will stipulated, and outlined the five equal parts: (physics, chemistry, physiology or medicine, literature, peace) and the awarding bodies. Alfred Nobel’s fortune he left was over 31 million Swedish Kroner, which In today’s dollars, accounting for inflation, would have been about 265 million dollars. It was a vast fortune at the time, and one of the largest in the world, accrued through Nobel’s many patents and companies. Alfred Nobel’s life as a chemist, engineer and industrialist led to some 355 patents, but is most famously known as the inventor of dynamite. Today the assets are worth almost twice this amount, around 443 million dollars, managed by the Nobel Foundation.

The first Nobel Prizes were not awarded until 1901, some five years after Alfred Nobel’s death. Though Nobel never married and had no children, his extended relatives contested the will and the named prize-awarding bodies initially were reluctant to comply with the will as they were not consulted. It was also criticized by by the King of Sweden at the time, Oscar II, and other Swedish leaders in the belief that the assets could be used to help Sweden rather than dispersing them to the world through a prize. It was complicated by the fact that Alfred Nobel left the assets to executors and awarding bodies for which a foundation had to be created with everybody on board. This in itself was not an easy task, but the Nobel Foundation was eventually founded on June 29, 1900. The following year the first Nobel Prizes were awarded.

Table of Nobel Prize Awardees Data (1986-2016)

There has been some debate about race and gender disparity in the Nobel Laureates, specifically with regards to women and minorities (non-Caucasian), and also religious persuasion. The statistics do indeed look very disparaging when taking the total span of years the original Nobel Prizes have been around (1901 to present), but this should not be a surprise given the society of the 20th century and that social progress for women and minorities only advanced later in the century. So, looking at a 30 year span (a generation) from 1986-2016 is perhaps more indicative of current trends. The data show (no surprise) that Caucasian’s by far lead the pack in winning percentage (80%), followed by Jewish (36%), Asian (18%), Women (14%), Black (5%) and Hispanic (4%). See the tabulated data for a breakdown by award. The only award that is fairly evenly distributed is the Nobel Peace Prize. There are a couple of points here that are relevant:

  1. ) The first is who the nominators are, that is, what is the gender , cultural diversity, and/or racial distribution of those making the nominations for the Nobel Prize. A more balanced distribution could help remedy this problem. Historically (1901-1966) the distribution of nominees looks very much like that of the nominators. Data is only available up to 1966 because the Nobel Foundation has a 50 Year Secrecy Rule that states: “The Committee does not itself announce the names of nominees, neither to the media nor to the candidates themselves. In so far as certain names crop up in the advance speculations as to who will be awarded any given year’s Prize, this is either sheer guesswork or information put out by the person or persons behind the nomination. Information in the Nobel Committee’s nomination database is not made public until after fifty years”.
  2. ) The second point concerns the centers of research themselves, which tend to be in the United States and Europe for the most part, which is mostly Caucasian, and in Asia to some extent. This is a matter of resources and opportunity, and it’s just a fact of the world that places with stable governments, freedom, and equal opportunity afford scientists prosperity in their work. This is the result of geopolitical situations, but with some gender and racial aspects to it as well that can not be ignored.

Nobel Prize Nominators and Nominees (1901-1966). Source:

With those issues covered, there is also debate over the relevance and adaptation to changing times of the Nobel Prize in today’s world. It is argued that, at least for the fields of science, the approach has changed since the inception of the Nobel Prize. No longer do scientists work in private, toiling away in private for years on theory or experiment to produce great discoveries, but that science is more a community effort now with colleagues cooperating together, hosts of graduate students participating, and laboratories lending their resources for cutting edge experimentation. Although there are a number of Nobel Prize Awarded Organizations, they are all for the Nobel Peace Prize, and this has not been the case with other Nobel Prize awards. There is nothing prohibiting this, in say physics, but it is just never done. There are good arguments that it is time to consider this. A good example is the Nobel Prize in Physics 2017, which was awarded “for decisive contributions to the LIGO detector and the observation of gravitational waves“. What is LIGO, you may ask? The acronym stands for Laser Interferometer Gravitational-Wave Observatory, constructed between 1994-2002, until it became operational on August 23, 2002. That is 15 years of operation between 2002-2017, but overall there have been decades of work, theoretically and experimentally, regarding gravitational waves involving hundreds (if not thousands) of scientists. In the end, the Nobel Prize in Physics for 2017 was given to just three people. Some articles published in early October 2017 address this further:

The Atlantic: The Absurdity of the Nobel Prize
Scientific American: It’s Time to Rethink the Nobel Prizes
Slate: The Nobel Prizes Should Reward Science, Not Scientists

The Nobel Foundation Statues state that “In no case may a prize amount be divided between more than three persons.”, but goes on to say, “Each prize-awarding body shall be competent to decide whether the prize it is entitled to award may be conferred upon an institution or association”. From 1901-2017, a total of 27 Nobel Prizes have been awarded to organizations, but all of them have been for the Nobel Peace Prize. So, there you have it, the prize-awarding bodies for the sciences are free to choose an organization for the award, but they never do. The Nobel Foundation is very steeped in its history and tradition, but seemingly very resistant to change, which is why some see it as an antiquated body unwilling to overhauling the Nobel Prizes in keeping up with modern times. Regardless, there is some legality in all this. This is tied to the will of Alfred Nobel and subsequent establishment of the Nobel Foundation, however, some flexibility could be exercised in interpretation of the legal underpinnings.

It is perhaps time for the Nobel Foundation to consider addressing some issues regarding gender and race for the Nobel awards overall, as well and inclusiveness in science with regards to the more collaborative approach of science in modern times. Tradition and historical continuity have their place, but there is something to be said about changing with the times as well. Such an approach does not have to diminish the credibility and prestige of the prizes, but may afford them wider appeal and make them less susceptible to criticism from various opponents. As it stands, it is what it is for now and something to celebrate in the context of which the Nobel Prizes are awarded.

Nobel Prize Facts. Source:

Facts about the Nobel Prize:

The Nobel Prize is an international award given by the Nobel Foundation in Sweden.
The Nobel Prize consists of a medal, a personal diploma, and a cash award.
The Nobel Prize can not be awarded posthumously.
The Nobel Prize is awarded without consent of the recipient.
The Nobel Prize may be awarded to no more than 3 recipients for each prize.
The Nobel Prize can be awarded to organizations.
The Nobel prizes can not be appealed.
The Nobel Prize votes are usually announced as unanimous. (* see note below)
The Nobel Prize winners are announced in October.
The Nobel Prize recipient is called a Nobel Laureate.

*Note: The Committees seek to achieve unanimity in its selection of Nobel Laureate’s. On the rare occasions when this proves impossible, the selection is decided by a simple majority vote.

The official website for the Nobel Prize,, is a wealth of information to explore. Another site,, is also worth looking at.

Some further links of interest for reference or further reading:

National Geographic: Nobel Prizes 2017:Facts About the Secretive Process and Peculiar Past
Fortune: Why the Nobel Prize Payout is Shrinking
New Republic: What Happened to the Nobel Prize in Literature?
Atlantic: The Political Slant of the Nobel Prize in Economics
Live Science: Nobel Prize in Physics: 1901-Present
New York Times: Alfred Nobel and the Prize That Almost Didn’t Happen
New York Review of Books: Satre on the Nobel Prize
Stats: Evolution of National Nobel Prize Shares in the 20th Century
Forbes: American Leadership in Science, Measured in Nobel Prizes [Infographic]
Business Insider: Here’s a Beautiful Visualization of Nobel Prizes By Country Since 1901
The Guardian: Nobel Peace Prize Winners – The full list
Britannica: Nobel Prize


Keep on Trekkin

As I did at the end of 2013 & 2014, so I do again here at the end of 2015 to recount some travel experiences, which I don’t normally write about here. I need not give the whole setup again for the premise of such entries and see my blog from the end of 2013: Travels of Spocklogic. The notables this year (travel blogs I finished or made additions to) include:


Feature - Washington DC-1




That’s the summary for 2015. Some are carry overs from 2014, but I finished the blogs in 2015, after my last post on travels (see: Travels of Spocklogic II) in December 2014 or earlier if I made additions. As I alluded to in recent entries, I will take a break from this Cogito Ergo blog for a while in 2016. I’ve had 20 years of internet exposure and been blogging for 10 years (see: 20 Years of Internet and Mapping the Internet). I hope to return again with a fresh perspective down the line. There’s plenty to explore in the Cogito Ergo blog archives until then (see the link to: Browse Blog Posts). Best wishes for the New Year 2016! See you in the future…



The controversy surrounding the Patriots deflated footballs in the AFC Championship game on Jan. 18, 2015 has made some headlines in the news, and raised some physics questions. There has been talk of the ideal gas law, guage pressure vs. absolute pressure and relative temperature vs. absolute temperature. So, I take this as an opportunity to explain some of what all this means if you have followed it or have an interest in this. Lets begin with the NFL rule book stating:

The ball shall be made up of an inflated (12 1/2 to 13 1/2 pounds) urethane bladder enclosed in a pebble grained, leather case (natural tan color) without corrugations of any kind. It shall have the form of a prolate spheroid and the size and weight shall be: long axis, 11 to 11 1/4 inches; long circumference, 28 to 28 1/2 inches; short circumference, 21 to 21 1/4 inches; weight, 14 to 15 ounces.


By “pounds” it is assumed this means “pounds per square inch” or psi. However, this term refers to a guage pressure, so the actual pressure is really guage pressure + atmospheric pressure. To understand this remember that the pressure measured with a guage, such as you would with a tire, indicates pressure relative to the atmospheric pressure. Scientists often speak of atmospheres of pressure or atm and define Standard Temperature and Pressure for sea level at 273.15 K as 1 atm = 101325 Pa, or 14.69595 psi. (Note: Pa is another pressure unit called the Pascal and K is a temperature unit called Kelvin). So, consider 1 atm of pressure inside some container, that is, there is the same pressure inside the container as outside of it. Taking a gauge will not show 1 atm, but zero atm, since the pressure in the container is just the same as the pressure outside. This means that relative to the outside there is pressure in the container and it is in balance or equilibrium. This is the meaning of gauge pressure. Now, absolute pressure is technically more accurate when speaking of pressure as it is the force that some gas is applying to the container surface area, by virtue of the fact that on the order of 1E23 molecules are bouncing around off each other and the container wall because of thermal stimulation (heat), a form of kinetic energy.


Heat is not the same thing as temperature, though they are related to each other. Heat is a form of energy that flows from a hotter substance to a colder one, which have higher and lower temperatures, respectively. So, there must be a temperature difference for heat to flow. Consider our container again, and it has a certain amount of heat associated with it, which can be probed by measuring the temperature. Another container made of a different substance may have more heat associated with it but still measure the same temperature, because the second container has more mass. Anyway, that’s the concept, and wanted to get that out of the was to talk about temperature specifically. Temperature scales we commonly use everyday to speak about the weather are measurements relative to some reference value. In the Celsius scale, for example, the reference value is the freezing point of water, or 0 °C. Fahrenheit uses 32 °F as the freezing point for peculiar scientific historical reasons. All measurements are made relative to these reference values, for example in speaking of above or below freezing. The Celsius scale and the Fahrenheit scales are relative temperature scales and can have both positive and negative numbers. This is not so with an Absolute temperature scale, which has only have positive numbers. The Kelvin scale and the Rankine scale are absolute temperature scales. The Rankine scale, in which the degree intervals are equal to those of the Fahrenheit scale and in which Rankine (R) equals −459.7° Fahrenheit. The Kelvin scale, in which the degree intervals are equal to those of the Celsius scale and in which absolute zero is 0 degrees Kelvin and the triple point of water has the value of approximately 273 degrees Kelvin (K). The triple point is the temperature and pressure where the three phases of a substance (solid, liquid and gas) are in equilibrium. The triple point of water, 273.16 K at a pressure of 611.2 Pa, is chosen basis of Kelvin definition.


I explained all this (more than you the reader maybe wanted to know) because it is important to understand the difference between relative measurements and absolute measurements. This is important in scientific discussions describing values of things like pressure and temperature. So, we now have a better feel for things like gauge pressure vs absolute pressure and relative temperature versus absolute temperature. This allows discussion of the Ideal Gas Law that has been in the news. A good description of an ‘ideal gas’ is as follows: “An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other.” The Ideal Gas Law is characterized by three variables: absolute pressure (P), volume (V), and absolute temperature (T) and written as:

PV = nRT

where n = number of moles of the gas, with each mole (abbreviated as mol) containing 6.02214129 × 1023 atoms or molecules, known as Avogadro’s number. R is the gas constant (known as universal or ideal gas constant) universal  having a value of 8.314  J/K-mol or 10.731  ft3 -psi -lb/R-mol. As will be seen, we won’t need these constants, but just note them for reference. The utility of this equation is that one can hold any variable constant and see how the others change. In the case we want to examine, our container is a football, and we can tentatively take the volume to be constant and see how the pressure changes with a known temperature change.


Before proceeding, let’s review the scenario that transpired in Foxborough, MA on the afternoon and early evening of Jan 18, 2015 before and during the AFC championship game between the New England Patriots and the Indianapolis Colts. The timeline of events can be found here – Timeline: Key Deflategate events probed in Wells Report. Key events needed for calculations are that footballs were checked at 3:45 pm and found to be at or above the minimum 12.5 psi gauge pressure, though they were not recorded. At 8:28 pm during halftime, the footballs are retested and found to be below psi specifications. The exact measurements of the under inflated footballs can be found here – Finally, the halftime PSI numbers are known. A couple of additional pieces of information are needed: (1) the temperature at which the footballs were and the atmospheric pressure in Foxborough at that time and (2) the field temperature and atmospheric pressure when the footballs were taken off the field. Data is available about the weather conditions and can be found here – Foxborough Weather Conditions (Jan. 18, 2015). This is actually data from Norwood, MA about 20 miles away from Foxborough. Only a guess can be made of the locker room temperature (say 70° F or 294.26 K) before the game, but the atmospheric pressure was approximately 29.9 Hg (or 14.686 psi) from the weather data. During halftime the temperature was approximately 50° F (or 283.15 K) and the atmospheric pressure at 29.6 Hg (or 14.538 psi). We have the needed data now for some calculations on all the footballs, but let’s play with the ideal gas law, and assume a constant volume for the football at time 1 (3:45 pm) and time 2 (8:35 pm), that is V1 = V2 and

P{_1}V = nRT{_1}

P{_2}V = nRT{_2}

Combining these equations, V, n and R cancel out and we are left with:

P{_2} = {{T_2}\over{T_1}}P{_1}

I ran the numbers, correcting gauge pressure to absolute pressure from the weather data and using the Kelvin scale temperatures, for both alternate referee measurements (Piroleau and Blakeman). Initial minimum pressure was assumed to be 12.5 psi and 13.0 psi for the Patriots and Colts footballs, respectibvely, at T =294.26 K and atmospheric pressure of 14.686 psi (with absolute pressure being 27.186 psi), while final temperature was 283.15 K with an atmospheric pressure of 14.538 psi. The results for the final absolute pressure on the 11 Patriots footballs and 4 colts footballs are:


Patriots Footballs, based on initial pressure of 12.5 psi


Colts Footballs, based on initial pressure of 13.0 psi


Taking the average of the two alternate referees measurements, gas law results and difference between the them, results in the following:

Patriots: Initial pressure = 27.186, average halftime measured pressure = 25.836, gas theory pressure = 26.10, average ∆P = -0.324
Colts: Initial pressure = 27.686, average halftime measured pressure = 27.069, gas theory pressure = 26.64, average ∆P = 0.429

This means that the actual alternate referee measurements and the gas law agree to within 0.324 psi with the actual measurement for the Patriots footballs, being slightly lower than what the gas law would predict, while they agree to within 0.429 psi for the Colts footballs, being slightly higher than what the gas law would predict . Said in another way this is only about 0.32 to 0.43 in 27, or approximately 1.2 to 1.5% difference in measurement and theory. The total average pressure drop, gas law aside, for Patriots footballs is 1.35 psi and for Colts footballs is 0.617. Both teams show an average drop in pressure, so something happened to both teams footballs that caused them to measure lower pressure. With that said, it is also curious that Prioleau’s measurements are consistently higher than Blakeman’s measurements for Patriots footballs, while Prioleau’s measurements are consistently lower than Blakeman’s measurements for Colts footballs. I don’t understand this unless they switched gauges between measurement of Patriots and Colts footballs. This appears to be the case. There are a lot of unknowns here: Initial pressures of the footballs before the game were never recorded, the initial temperature in each locker room is not known, the time between when the footballs were taken off the field and when they were measured is not precisely known, and the football pressures at games end were presumably not measured. In addition, only 4 Colts footballs were measured because referees ran out of time according to the Wells Report, implying the Colts footballs were measured after the Patriots footballs, which may have given them more time to warm up. What was the time gap from officials going from the Patriots to Colts locker room? All we really know is that halftime was around 13.5 minutes, where measurements and reinflation took place.

Based on this analysis the conclusion would be (from a scientific point of view) that the footballs were not tampered with and pressure differences are partly explained by the Ideal Gas Law. Hooray for physics! The footballs were re-inflated at halftime, but it doesn’t see that anybody bothered to measure them again at the end of the game. Nevertheless, the Wells Report seems to reject the Patriots explanation using physics. The scientific analysis of “Exponent”, the consulting firm used in the Wells report, seems thorough. However, the Wells Report may have cherry picked what they wanted from the scientific report by Exponent to phrase what they wanted to say. A key statement in the Wells Report is: “Exponent concluded that, within the range of likely game conditions and circumstances studied, they could identify no set of credible environmental or physical factors that completely accounts for the Patriots halftime measurements or for the additional loss in air pressure exhibited by the Patriots game balls, as compared to the loss in air.” True, but both teams footballs lost pressure when measured at halftime, and the Patriots footballs measured 0.733 psi lower in lost pressure than the Colts footballs, according to my analysis. The Wells Report makes this to be ~ 0.7 psi. Interestingly, the difference in pressure of the footballs explained by the Ideal Gas Law -0.324 for the patriots and 0.429 for the Colts, an absolute difference of 0.753 psi. The point is that both teams have a pressure discrepancy that has to be explained by something. Instead, the Wells Report states, “According to our scientific consultants, however, the reduction in pressure of the Patriots game balls cannot be explained completely by basic scientific principles, such as the Ideal Gas Law, based on the circumstances and conditions likely to have been present on the day of the AFC Championship Game.” So, what about the reduction in pressure of the Colts footballs? What is that explained by? This is not thorough, unbiased science as presented in the Wells report. Somebody should scrutinize the Wells Report more, as it’s full of assumptions and goes so far as to say science does not explain the Patriots footballs pressure drop. If true then by the same token, what has caused the pressure drop in Colts footballs, and science must not be able to explain that either?

Well, the NFL punishment has been doled out and it seems more about Patriots lack of cooperation in the investigation now, or more specifically, Tom Brady’s participation. I can’t say I blame him for not cooperating in today’s hypersensitive society where every little detail is scrutinized and people are presumed guilty until proven innocent. Maybe the Patriots real flaw is a culture of trying to gain a competitive edge without actually breaking any rules. It’s a grey line on morality, but part of sports, past and present. Some of the ways players try to get an edge up seem based more on psychology or physiology than physics. Athletes will be athletes and rely on brawn more than brains most of the time. Coaches or managers on the other hand often know more than they admit to, but it’s like protecting the commander in chief and players do that as they should. Maybe the Patriots did tamper with the footballs, but maybe they didn’t – it’s a stretch at best (without complete data) to conclude they did. To single out Tom Brady just seems unfair to me. He seems an honest guy and others say that of him too. His character is at stake here and I hope he come out on top in challenging the Wells Report!


Enough said, and here are some facts about footballs:

The NFL rule says it must be a prolate spheroid. It has a volume V = {4\over 3}{\pi}{a^2}c , where a is half the length of the long axis and b is half the length of the short axis, called the major and minor axes, respectively. Since 1959, the inch has been defined and internationally accepted as being equivalent to 25.4mm, so with 1″ = 2.54 cm,  an NFL regulation football is 27.94 to 28.575 cm along the long axis (giving b = 13.97 to 14.2875 cm) and 53.34 to 53.975 cm around the short circumference, which requires using the formula for circumference = 2{\pi}r (giving a = 8.489 to 8.59 cm). Using these numbers in the formula for an oblate spheroid to be V = 4216.95 to 4416.02 cm3 (or 257.33 to 269.48 square inches).

A football weight is 14 to 15 ounces. With 1 ounce = 28.349 gm, a football is 396.886 to 425.235 gm. It is generally assumed that the air in a fully inflated football accounts for only about 10 grams of its mass. Is this true? Assuming a gauge pressure of 13 psi (89632 Pa) at standard temperature and pressure (T = 273.15 K and P = 101325 Pa = 14.69595 psi) gives the absolute pressure of the football to be and knowing the volume of a football in addition to the molecular weight of O = 15.9994 and  molecular weight of N = 14.0067, we can figure it out. By weight, dry air contains 23.2% O2 and 75.47% N2 by weight, which accounts for 98.67% of the weight of air. The actual major constituents of air are shown below:

Gas Ratio compared to Dry Air (%) Molecular Mass
M –
Chemical Symbol Boiling Point
By volume By weight (K) (oC)
Oxygen 20.95 23.20 32.00 O2 90.2 -182.95
Nitrogen 78.09 75.47 28.02 N2 77.4 -195.79
Carbon Dioxide 0.03 0.046 44.01 CO2 194.7 -78.5
Hydrogen 0.00005 ~ 0 2.02 H2 20.3 -252.87
Argon 0.933 1.28 39.94 Ar 84.2 -186
Neon 0.0018 0.0012 20.18 Ne 27.2 -246
Helium 0.0005 0.00007 4.00 He 4.2 -269
Krypton 0.0001 0.0003 83.8 Kr 119.8 -153.4
Xenon 9 10-6 0.00004 131.29 Xe 165.1 -108.1


So, we can be a little more exact and include carbon dioxide (CO2) and argon (Ar) to account for 99.99% of air composition by weight. Adding the numbers scaled by weight fraction gives:

Molecular weight of air = (0.7547 x 28.02) + (.2320 x 32) + (.0128 x 39.94) + (.00046 x 44.01) = 29.1 g/mol

The volume of a football we know is 4216.95 to 4416.02 cm3 , so take V = 4316.5 cm3 as the average. Using the Ideal Gas Law we can calculate the number of moles of air in a football at standard temperature and pressure as: n = PV/RT = [(190957 Pa) x (0.0043165 m3)]/[(8.314  J/K-mol) x (273.15 K)] = 0.362 moles. Each mole has Avogadro’s number of 6.02214129 × 1023 molecules. With the molecular weight of air as 29.1 g/mol, we find that a football has and incredible 2.18 × 1023 air molecules (more that 2 billion billion) that add to approximately 10.5 gm. So, indeed it is true, and air only accounts for ~ 2.5% of its mass. We may conclude from this that the NFL source who reportedly told Kravitz (Bob Kravitz at WTHR in Indiana) that “officials took a ball out of play at one point and weighed it”, and would investigate the deflation of footballs by the Patriot’s, is sort of half-baked. Kravitz broke the story and posed it as possible cheating. That’s how these things start and take on a life of their own. Anyway, that’s all I have to say or share on this matter, and a wild one it is for sure. Here are some other links I can offer:

Patriots football pressure links for further reading:

1.) But What about the Ideal Gas Law?
2.) Can physics explain the deflation of NFL footballs (aka #DeflateGate)?
3.) Deflation Experiments Show Patriots May Have a Point After All
4.) Clearing Up the Air on DeflateGate
5.) Deflate-Gate: Could Weather have played a role in deflated balls?
6.) Science! One Way To Deflate a Football Without Even Touching It
7.) How to reduce the amount of air in a football without letting any air out
8.) Football Physics: The Science of Deflate Gate
9.) So the Patriots really were playing small ball

Physics links for further reading:

1.) Ideal Gas Law – Hyperphysics
2.) Gas law calculators – WebQC
3.) Humid Air and the Ideal Gas Law – The Engineering Toolbox
4.) Heat and Heat Vs. Temperature – Online Physics Tutorials
5.) Calculate mass of air in a tyre from pressure – Physics StackExchange

Other links for further reading:

1.) Science of Football
2.) NFL Football Weight Calculation
3.) Wells Report – pdf
4.) Patriots rebuttal to the Wells Report – website
5.) DeflateGate And The Softness Of The American Mind


As I did at the end of 2013, so I do again here at the end of 2014 to recount some travel experiences, which I don’t normally write about here. I need not give the whole setup again for the premise of such entries and see my blog from the end of 2013: Travels of Spocklogic. The notables this year are a couple of blogs I finished and some reviews that may be of interest:



That summarizes some travel selections for 2014. I did travel to Italy also in July 2014, and have some links to share for photo collections I put together for a special year in Erice to celebrate a 40th anniversary of the International School of Atomic and Molecular Spectroscopy (ISAMS):

Rino: 40 Year Erice Celebrations (2014) – Erice, Italy
2014 Erice Workshop: 30 July – August 5 – Erice, Italy
People (2014) – Erice, Italy
Places (2014)
– Erice, Italy

In addition, I traveled to China again this year in November 2014, but am still working on my travel blog for that, so it will have to wait until my 2015 account of my travels. I will make this type of entry something traditional at years end to cover where I have been and what I have done in travel ways. It’s all rather like the City on the Edge of Forever perhaps…




In the beginning there was an idea to share information and seeds of the internet were born sometime in the 1960’s. Segue to the early 1990’s and there is altavista & webcrawler for search engines, no advertisements and the start of the internet for everyone. There were modems that worked over the telephone line and squealed their functionality with signature precision. They were slow, but the internet didn’t need speed back then as it was mostly text based information. Then it all began to change: AOL, Friendster, Myspace, Facebook and the people didn’t really want information, they wanted to socialize. That was the real revolution of the internet.


The Internet (c. 2007)



The Internet (c. 2010)



The Internet (c. 2013)


Interesting from a certain viewpoint (don’t think physicality in the construction similar to the continents, but where you are and where you go to online based on the map designations). In this sense, it’s another travel dimension of sorts! It’s rather like the the maps you see in the Age of Discovery in the centuries past when men explored the world in sailing ships. The maps were crude at first but became more refined over time. There is a perspective here to be appreciated and that is the following: All things human begin from the fundamental to the advanced – that is how our species learns and understands. We seem to be better at this in some ways, especially technology, but not so good in other ways, especially getting along with each other.

A final comment: The internet is capable of breaking down barriers like class, religion and wealth and everyone can participate (in principle). The reality is that the human species does not use the brain it has developed and the instances of this are too numerous to mention in the thousands of years of civilization. Although Carl Sagan did not live to see the full potential of the internet age, I like what he had to say about humanity in general – The Frontier Is Everywhere:

We were hunters and foragers. The frontier was everywhere. We were bounded only by the earth, and the ocean, and the sky. The open road still softly calls. Our little terraqueous globe as the madhouse of those hundred thousand millions of worlds. We, who cannot even put our own planetary home in order, riven with rivalries and hatreds; are we to venture into space?

By the time we are ready to settle even the nearest other planetary systems, we will have changed. The simple passage of so many generations will have changed us; necessity will have changed us. We are… an adaptable species. It will not be we who reach Alpha Centauri and the other nearby stars. It will be a species very like us, but with more of our strengths, and fewer of our weaknesses; more confident, farseeing, capable and prudent.

For all our failings, despite our limitations and fallibilities, we humans are capable of greatness. What new wonders undreamt of in our time, will we have wrought in another generation, and another? How far will our nomadic species have wandered, by the end of the next century, and the next millennium?

Our remote descendants, safely arrayed on many worlds through the solar system, and beyond, will be unified, by their common heritage, by their regard for their home planet, and by the knowledge that, whatever other life may be, the only humans in all the universe, come from Earth. They will gaze up and strain to find the blue dot in their skies. They will marvel at how vulnerable the repository of all our potential once was, how perilous our infancy, how humble our beginnings, how many rivers we had to cross, before we found our way.

The internet 2007 –
The Internet 2010 –
The Internet 2013 –
Carl Sagan – The Pale Blue Dot




I don’t often write about my travels in this WordPress blog (Cogito Ergo) as I have another site for that (TravBuddy). In this year of 2013, I completed a number of travel blogs on that site that are worth noting and I give the links to them here. Mind you, I don’t know that any of my travel blogs are ever really completed. Each one is like a child I nurture and raise up, but always needs attention in future ways. Anyway, I suppose I list them here for my own reference and also to offer it to others who may be interested in my travels. There is some connection of the blogs, one to another in embedded personal ways, but are also self-contained. Here they are:




Spocklogic_Switzerland_Travel Blog.

Spocklogic_Germany_Travel Blog.



Some of these blogs have been posted for some years, and I either added to them, made them more complete, and/or formed connections between them. Some of them are entirely new in 2013. They do tell a story in total I suppose and maybe that’s why I decided to make a sort of review of the Travels of Spocklogic here. They were also all the blogs featured on TravBuddy for me this year. My Italy blog (L’Avventura Dell Italia) seems never-ending and I have some more work to do on it, but the majority of important events are there for the most part. The last one in this list, the blog on China, is something I am still working on too, but intend (or hope) to complete it before the end of 2013. I suppose this collection of blogs forms a personal journey of sorts that I tried to form this year regarding my life and relation to travel. When I finish the China blog, maybe I will know what I have been endeavoring to understand and ultimately discover in my life. It’s not a teaser, or cliffhanger, but maybe more a matter of what I will embrace. Sounds enigmatic I suppose, but not really. It’s my personal perspective, the choices I make and what is ultimately best for me in a world of possibilities…


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