Some insights into mathematicians

Keywords: social awkwardness, handedness, learning modes, conversation, methods of thinking

I’m one of the fortunate people that have always had a direction in my life (as well as to have the ability to pursue that direction). When I set off for college, there was absolutely no doubt that I would major in math. By the time I graduated I was very comfortable with calling myself a mathematician. Over the decades I have realized that being a mathematician isn’t just a hobby or vocation, it is truly a part of who I am.

I’ve been reading a book on the philosophy of mathematics. One part of one of the essays talks about characteristics of mathematicians. There were three specific characteristics that especially rang true for me; things that I’ve known about myself that I never thought about being common, if not universal, characteristics of mathematicians.

First, I have always had a difficult time with telling left from right. An example occurred in driver’s ed. At the time, passing driver’s education allowed me to get my driver’s license at 16 ½ instead of 17. So I signed up right away (unlike younger generations who are not so anxious to get driver’s licenses). At the end of the course, the instructor had the students drive around the neighborhoods where the DMV tests were usually taken. Three times in a row, my instructor told me to take a right and I took a left. He suggested I not do that during the actual test. Here is what A.V. Borovik says in Humanizing Mathematics and Its Philosophy:

“I collected hundreds of mathematicians’ testimonies about difficulties they experienced in their earliest encounters with mathematics. … The most frequent specific difficulty was telling the left from the right – for lack of logical distinction between the two.”

Let me expand on this. It is not possible to define left and right without pointing. It is necessary to define them in their relation to the direction a person is facing. The problem is that left and right are logically interchangeable, the assignment is arbitrary, and they are symmetrical opposites. This is illustrated by the handedness of molecules (their chirality). Life tends to be based on left handed amino acids while plant sugars (our food) tend to be right handed. We can’t metabolize left handed food. So, if all the right handed food became left handed, we’d be in trouble. But, if all left handed molecules became right handed and all right handed molecules became left handed, there would be no difference in the way anything interacted with each other. Everything would be just fine. The handedness is arbitrary. Because of this arbitrariness – that there is no “logical distinction between the two” – to this day I have to very consciously think about left and right.

Second, a few decades ago I was introduced to a theory that espoused seven modes of learning. (My understanding is that the basic concept that people learn differently holds up, but that the modes identified and other aspects of that specific theory do not.) So I asked myself what my mode of learning is. I settled on geometric and graph theoretic (which are not any of the original seven). I think in terms of objects and the relations between them. My doctoral dissertation reflects this in that it can be described as combinatorial geometry. (See the Art Gallery Theorem for a simple introduction.)

Borovik provides a quick summary of an MRI study (emphasizing that it is only a single study): “Our results suggest high level mathematical thinking makes minimal use of language areas and instead recruits circuits initially involved in space and number (Amalric and Dehane 2016).” Again, this is only one study, but this resonated with my personal concept of geometric learning. It is something different than audio, visual, or verbal activities of the mind.

Third, I know that I take longer than average to respond to comments during person-to-person conversations. I remember a study that looked at the length of the pause between when someone stops talking on the telephone and the other person speaks. In other words, how long is an uncomfortable silence in a conversation? What I remember is that the average pause is about 3 seconds. I figure mine is closer to 4 or 6. This was something I had to express to my girlfriend, whose average length of pause is probably closer to 1 or 2 seconds. I need to be given time to respond before the next part of the conversation ensues. Borovik describes the way mathematicians interact with each other face-to-face. Part of that interaction “includes pauses (for a lay observer, very strange and awkwardly timed) for absorption of thought…”

These insights are probably more awesome to me than many other people. But I think most people find knowing they are not alone to be comforting. Further, and more importantly, being consciously aware of personal characteristics, especially ones that create social awkwardness, can be very useful. It can allow for a dialog to help both yourself and other people develop more pleasant interactions.

(Note: the blog featured image of a man thinking about math is from the Job Monkey Blog.)

Metrology Part II – How do I measure thee? Let me count the ways.

Keywords: measure, measurement, ISO, SI, units, derived units, metrology

I’ve had various discussions about science where people have made statements like, “That can’t be measured” and “Science can’t tell us anything about that.” Since I have yet to be presented with a well-defined concept that science is not capable of analyzing (vs. necessarily already having analyzed) I feel such statements need to be addressed. This is the second in a series about metrology – the science of measurement.

In Metrology is not about the weather. Part I – How to weigh a potato, I introduced the most important thing to know about a measurement: there is always an error in both accuracy and precision. I then outlined the traceability of measurement standards from the International Organization for Standardization (ISO) to a produce scale used to weight a potato. The final section discussed how the formalization of measurement error is also a formalization of my three philosophical foundations discussed in Am I a figment of your imagination?  In this installment, I will further explore the ISO standards and introduce the formal definition of a measure, which allows expansion beyond ISO based measurements. This will establish a foundation for further blogs on the relation between measurement and science.

SI Base Units and Their Derivatives

All physical measurements in the modern world derive from the International System of Units (SI). (The ISO coordinates the SI standard.) These are a set of seven physical units such as the second and the meter. I’ve copied the detailed but concise  review of the basics from Wikipedia below, but first, here are some key points:

  1. There are seven base units: second, metre, kilogram, ampere, kelvin, mole, and candela.
  2. The base units are used to define derived units which are combinations of the base units. (Some of these have standard names.)
  3. The SI defines prefixes, such as the somewhat familiar “mega“, “giga”, “milli”, and “nano.” These allow easy description of orders of magnitude. Is it a billion of or a billionth of?

From Wikipedia:

“The International System of Units (SI, abbreviated from the French Système international (d’unités)) is the modern form of the metric system. It is the only system of measurement with an official status in nearly every country in the world. It comprises a coherent system of units of measurement starting with seven base units, which are the second (the unit of time with the symbol s), metre (length, m), kilogram (mass, kg), ampere (electric current, A), kelvin (thermodynamic temperature, K), mole (amount of substance, mol), and candela (luminous intensity, cd). The system allows for an unlimited number of additional units, called derived units, which can always be represented as products of powers of the base units.[Note 1] Twenty-two derived units have been provided with special names and symbols.[Note 2] The seven base units and the 22 derived units with special names and symbols may be used in combination to express other derived units,[Note 3] which are adopted to facilitate measurement of diverse quantities. The SI system also provides twenty prefixes to the unit names and unit symbols that may be used when specifying power-of-ten (i.e. decimal) multiples and sub-multiples of SI units. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves.”

(End from Wikipedia)

Considering there are only seven base units, the concept of derived units is pretty important. A derived unit is just a combination of base units such as miles per gallon or pounds per square inch. Derived units can be really complex. For example, the unit of electrical conductance, the siemens (S), is defined as s3A2/kgm2. But you can literally combine any or all of the base units, raise each of them to any power (positive or negative) and have yourself a lovely time trying to figure out what it measures. (As it says above, this allows for an infinite number of possible units.)

An interesting type of derived unit is the “unitless” measure. A commonly known example is Mach number, which is the ratio of the speed of an object to the speed of sound. Technically the unit of Mach is (meters per second) / (meters per second). But, in the sense that units can “cancel” the way numerators and denominators can, the resulting unit appears to be nonexistent – thus, “unitless.” Something that is not universally understood is that Mach number changes with atmospheric pressure (or, more generally, with the density of the material the sound is traveling through). That is, Mach number is not the equivalent of speed or velocity. Many of us have been told the heuristic of counting seconds between a flash of lightning and the resulting thunder to figure out how far away the lightning was. (The five second per mile heuristic translates to roughly Mach 1-million.) But this is based on the speed of sound at the atmospheric pressure found at sea level. Trick question: what’s the Mach number of a vehicle traveling in space? Sound doesn’t propagate in a vacuum, so the denominator in the calculation of Mach is 0. So the answer is Mach infinity. (A fun fact is that the space shuttles used to enter the atmosphere at about Mach 26; infinite to 26 in the blink of an eye!)

Another important aspect of units is conversion, like between meters and feet. (Some people may remember the Mars landing disaster that happened because this conversion wasn’t done.) Such conversions are merely mathematical so that they are not any different than a rose by any other name. Which unit you use is mere preference. In my experience, for some reason, metrologists tend to prefer furlongs per fortnight instead of miles per hour.

It’s also important to understand that the same unit name can be defined differently. For example there is the imperial ton as well as the metric ton. An interesting historic example is the cubit which has been defined to be many different lengths. And, of course, units are not always well defined, as when the foot was (supposedly) based on the length of the king’s foot. But that’s why we have standards.

Units in Abstract and the Generalized (Mathematical) Definition of Measure

Some metrologists would probably end the discussion of measure with the SI units and their derivatives. But it doesn’t take much thought about “units” to realize that there are plenty of things we use as units that don’t seem to be based on the SI units. The phrase, “you can’t compare apples and oranges” is effectively saying that apples and oranges are two different units. A way of discussing this is in terms of a generalized definition of measure. This definition is pretty straight forward, so I’ll start with it and then elucidate. From Wikipedia:

“In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume.”

Focus on the relation of “set” and “unit.” We might have a bunch of apples in front of us. We have a set of apples. We can pull out a subset of 5 apples. In this context, the unit of measure is “apple”. The size, or measure, of the subset is 5. You can substitute “unicorn” or any other object for “apple” and have it act as a unit. As such, the SI units are a subset of the more general concept of measure. You can stand on a plot (set) of land and measure its area in square meters.

The International System of Quantities and ISO/IEC 80000 are a generalized standard of quantities. The SI units are derivable from this standard, but the quantities defined by this standard go beyond the SI units. For example, there are information technology units such as bit and byte.

The reason I bring these quantities up is to emphasize that the definition of measure allows for a very broad range of measurements. All you have to do is define a set of things (such as apples) and establish a way of assigning sizes to subsets. (Of course, there are mathematical conditions required on how you assign the sizes as described in the Wikipedia article.) For future discussion, I want to point out that the SI units, including their derivatives, are the only physical units. I will call all other units “conceptual.” For example, bits and bytes are electromagnetically instantiated on disks, but you can’t really hold a bit or byte in your hand – they are conceptual. There are plenty of units other than those in the ISO standard, such as apples and unicorns. These also fall into the categories of physical and conceptual. In future blogs on metrology, I will discuss the relationship between conceptual and physical units in order to distinguish what types of units represent measurements of physical objects.

Before moving on, I want to address one of the technical requirements for a measure. A measure is a function onto the real numbers. That is, to formally state the size of a subset is to provide a number. In Part I of this metrology series I point out that the eyeball is the most common measurement device. But the eyeball rarely constructs a number during its measurement. This illustrates the difference between “in practice” and “in theory”. In practice we don’t need to know the numeric size of something to know whether it will go through a door. But in theory we could quantify it if we need to.

Analyzing Sets of Measurements (aka Statistics)

I’m not going to go into statistics very much, but it is an important aspect of analyzing measurements. A single measurement can be useful, but it’s by grouping sets of measurements that give us deeper understanding.  Roughly speaking, data is grouped across space or time or both. How many gorillas are there at a moment in time and where are they? How has their population changed over time? What are the demographics of a particular issue and how has that changed?

One of the main ways of analyzing sets of data is to determine their distribution curve (more properly called their probability distribution). The standard bell curve is probably the most well-known. But there are lots of other distributions. After determining the distribution, there are lots of analyses that can be done on the data: determining mean, median, standard deviation, and many more complicated characteristics. It is also possible to take many sets of data, each with their own distribution, and combine them. My first point is that the level of analysis can get very sophisticated and such techniques provide deeper insights than individual measurements. My second point is that these analyses are ultimately based on individual physical measurements. My third point is that the complexity of analysis is what sometimes leads to the famous expression about types of lies.

Summary and Looking Ahead

I started with the SI base units and then provided the formal generalized definition of measure and its relation to unit. This illustrated the broad nature of “measure”. Along the way, I mentioned that some units measure physical objects while others are conceptual. In future metrology blogs I will discuss how to tell when a unit relates to a physical object. This will aid in discussing what science is and, in particular, in demonstrating that the so called “soft” social sciences are not only sciences, but that they are physical sciences.

Solstice Banner Fundraiser Closeout

I want to thank everyone that donated to the Solstice Banner. I received enough donations to pay for this year’s installation. It is very validating to me that so many people have supported this project.

I started displaying the banner because a Jesus banner had been displayed annually. I felt that the secular community should be represented and I also felt it was worth reminding people that not everyone is Christian. But my opinion, as well as that of the Freedom From Religion Foundation (FFRF), is that the public square is not the appropriate place for religious promotion. I have always said that I would stop displaying mine if they stopped displaying theirs. Well, the Jesus banner was not up this year. So, I will not be displaying the Solstice banner in 2021. If Jesus returns in 2021, I’ll follow up in 2022.

FFRF has been very supportive of this effort. They have provided the $500,000 liability insurance each year. They also provided the online donation mechanism in 2018 and 2020 and some funding the first year. Although I did not run a funding campaign in 2019, I had a few donations that year. If you’re interested, all told during the three years of display, including the costs to make the banner, my out of pocket expenses have been $155 out of a total of $1691 in expenses.

Thanks for the support!


Metrology is not about the weather. Part I – How to weigh a potato

Keywords: philosophy of science, measurement, ISO, NIST, standards, accuracy, precision, philosophical foundations

When someone buys a pound of potatoes, how do they know it weighs one pound? A likely answer is that the produce scale said it was. But that assumes the scale is accurate. Is it? And how do we know? The answer to this question can be found in the science of measurement – metrology (in contrast to meteorology). This is the first in a series of posts that will talk about metrology and its uses.

I’ve had various discussions about science where people have made statements like, “That can’t be measured” and “Science can’t tell us anything about that.” Since I have yet to be presented with a well-defined concept that science is not capable of analyzing (vs. necessarily already having done so) I feel such statements need to be addressed.

The motto of an organization I used to work for is: “Without data there is no test.” The organization was involved in acquiring test data to evaluate complex systems. The objective was to provide legal certification that the systems met specifications. Such legal certification cannot be documented without well measured and analyzed data. This is a practical application of measurement, of metrology. But the model applies to all of science. There is no science without experimentation. There is no experimentation without measurement data. To understand what science is, does, and can tell us, we need to understand what a measurement is and what information measurements provide. This post is, then, one part of a response to statements about what science can and cannot do.

The first two sections of this post provide a slightly technical introduction to measurement. The third section gets into how measurement relates to my philosophical foundations. If you’re more interested in the philosophical aspect, you could skip to there and decide if you need to review the technical stuff. On the other hand, if you’ve never considered the basic question of how we know we have a pound of potatoes, you might be interested in an overview of this fascinating field of study.  

Accuracy and Precision

In essence, a measurement tells us the static state of an object. But what exactly does a scale tell us when we weigh a potato? The key issue is that every measurement has an error. The best we can do is to say that the potato weighs one pound plus or minus some error. The figure illustrates that a measurement error has two parts: accuracy and precision.

The concise description of this from Wikipedia is: “Accuracy is the proximity of measurement results to the true value; precision is the degree to which repeated (or reproducible) measurements under unchanged conditions show the same results.”

Wikipedia has an excellent detailed discussion that I’m not going to repeat here but I’ll walk through the basics with an example. It is convenient to consider the reference value in the figure as the “true” value of what we’re measuring. (There is a technical reason for calling it a “reference” rather a “true” value.) This may very well be exactly one pound, but we can never know for sure. All we can know is that there is some distance, the accuracy, between what we measured and the “true” value. Precision can be thought of as how many calibration lines there are on the scale. Does it measure to a tenth of a pound? To a thousandth? The curve above the word precision in the diagram represents the fact that, every time you measure something – even the same potato on the same scale – the scale will give you a slightly different answer. (This is a fundamental limitation of technology and our ability to use it. Since there is a portion of the scale that moves, any slight difference in many factors – even air pressure – can change where the moving part settles.) Thus the curve represents the distribution of repeated measurements. The center of that curve is the most likely instance of any of those measurements.

Every measuring device has a limited accuracy and precision due to limits in manufacturing. Accuracy can be corrected mathematically by a calibration curve. Whereas precision mostly requires better manufacturing of the device – more calibration lines on the scale. Calibration curves can be very simple. If the scale always weighs a half pound light then the calibration curve is applied by adding half a pound to each measurement. (This is done mechanically on older, spring based, scales with a dial at the top of the scale.) On the other hand, calibration scales can be very complex. There was a recent announcement of potential signs of life on Venus. The result was from a spectrographic analysis of the composition of Venus’ atmosphere. Now, a measurement of a spectrograph is a curve rather than a single number. It provides a value for each frequency in the spectrum being measured. There are a lot of things that cause error in measuring such a curve: changes in the atmosphere, interference between the sensor and the atmosphere, etc. In order to tease out these errors, a complex calibration curve was used (this might be called filtering). I doubt if I remember the details exactly, but I read it was something like a 12th order curve. Such curves change dramatically with small perturbations. The complexity of this filtering calibration curve was one of the concerns as to the validity of the result. (I haven’t followed up with what the current status is on this.)

International Standards and Traceability

So how do I know that the scale I put the potato on is accurate enough? How do I know it’s not always off by ½ a pound? The answer is that someone calibrates it against a known standard. They physically place a one pound weight on the scale and check the result. But you then have to ask how we know that the weight itself is one pound. The answer is that there is a series of calibrations that provide a chain of traceability starting with the set of standards defined by the International Organization for Standardization (ISO). There used to be a physical object that had a mass of 1 kilogram by definition. This object would be used to calibrate the most accurate scales. These scales would then be used to calibrate other physical objects and on down the chain from scales to weights to scales to weights until you get to the potato. The international standards have, however, moved from artifacts (a physical object massing a kilogram) to intrinsic standards (mathematically based on fundamental constants). The kilogram is now defined in terms of the second and the meter. So, anyone with the right equipment can determine a kilogram. In practice, there are national level standards labs (such as the National Institute of Standards and Technology, NIST, in the U.S.) that calibrate from international standards. Then there are primary standards labs that calibrate from NIST. There are also sometimes secondary or tertiary labs. Working down this chain you ultimately reach the scale at the produce store that weighs the potato.

The accuracy of devices get less and less as the cost goes down and the devices get further and further from the ISO standard. Ultimately, as long as the produce scale is “accurate enough” the store and customer are happy. The way we know it is accurate enough is through standards traceability.

Relation to three philosophical foundations

There is a common saying among metrologists that “the most common measurement device is the eyeball.” This maxim provides a direct link between measurement and the third of the three philosophical foundations I discuss in Am I a figment of your imagination?  

  1. Cogito, ergo sum (I think therefore I am),
  2. Something exists besides self (objective reality),
  3. Sensory perceptions interpret, rather than capture, reality (modelism).

Our senses are the foundational source of our understanding of objective reality; our senses measure. Even further, the scenario of measuring, along with the understanding that every measurement has an error, formalizes much of the three foundations. It is “I” that doing the measuring. I am measuring something in objective reality. This measurement interprets, rather than captures, an aspect of reality due to some level of inaccuracy and imprecision. It is the measurement, not objective reality, which we incorporate into our model.

The fact that every measurement has an error applies especially to eyeballs and our other senses. The level of accuracy of our senses is good enough for a great deal of what we do during the day, but our senses can also be completely fooled. Optical illusions are a good example, especially at the level of professional stage magic. Some of the reasons stage magic “works” is due to the limits of our senses. To illustrate an example of why magic uses misdirection, hold your hand out at arms distance. The physical optical sensor in your eye is only capable of sensing an area about the size of your thumbnail at that distance. That is, at any given instant of time, you only see a tiny portion of the scenery – a tiny portion about the size of your thumbnail. Add to this the fact that the eye looks at very few spots in the scenery per second. When you envision a room or some scenic view, most of what you “see” in your mind is a construction made up from very sparse data. If you aren’t looking directly at something at the time it happens, you literally don’t see it. That’s why magicians misdirect you. Another example is that the hand is literally faster than the eye. I once had a magician demonstrate that he could do a card maneuver without my being able to see it. He purposely didn’t use misdirection and let me look directly at his hand. He repeated the move and slowly increased the speed until I couldn’t see him do it.

[Please remember that stage magic is trickery. (I really appreciate Penn & Teller being adamant about this. During their shows they emphatically say that anyone telling you they are performing real magic is a scammer.) I was at a magic show in Las Vegas [not Penn & Teller] once where I saw the assistant that had “disappeared” climb up into the box that they suddenly “appeared” in. But that was because I was very close to the stage on the far right hand side. I was in one of the least susceptible positions, the box was maybe ten feet from me at eye level, and I was consciously trying to see something like that. And even then, it was maybe a second of opportunity.]

The eyeball maxim also captures the point that a measurement doesn’t have to be quantified in the sense of being reduced to a number. You don’t have to know that a door is 32 inches wide or the exact width of some object to know that the object will fit through the door. Sometimes it’s necessary to quantify such measurements, but not always. We use measuring instruments when we need more accuracy or precision than our eyeballs or other senses can provide. We also use instrumentation to help us decide if our senses have been completely fooled.

Even though our senses can sometimes be very inaccurate, it is pretty awesome that are senses can also sometimes be very precise, especially with training. Someone with perfect pitch can tell what note a sound is. If that person also knows how to translate the standard notes to their frequencies, it’s possible they can tell the pitch of a tone to an error of a few hertz. I once played a note on my saxophone using a fingering for a non-note (a nonstandard fingering that would create a nonstandard tone) and had my cousin identify it as a note between two standard notes. Some mechanics or hardware store workers can look at a nut or screw and have a damn good chance of telling you its measurements. One of the awesome examples I remember has to do with mothers and their babies. A study found that most mothers can identify their baby simply by brushing the child’s cheek. That’s awesome!

A final philosophical note is that this series of posts on metrology fills in details for Is there anything supernatural? Measurement plays an important part in that discussion. I provided a very brief discussion and said I’d probably post about measurement later. Here it is.

Systemic racism: A concise history

Keywords: racism, war on drugs, inequity, incarceration

A friend pointed me to this 18 minute video by Phil Vischer the creator of Veggie Tales that very concisely overviews the history of how the U.S. got to the current point of social inequity. It starts with the end of slavery then continues through Jim Crow laws, segregation, redlining, the war on drugs, and incarceration rates. The video relates these to the fact that the average Black household income is 10% if the average white household income. This lower economic situation affects the ability of Blacks to get loans, pay for education, buy houses, etc. and thus perpetuates multigenerational inequity.

Although the video infers the effect of incarceration on income, it doesn’t do so explicitly. Having a record not only reduces family income during incarceration but also makes it harder to get a job or even to find a place to live. A significant factor in race based incarceration is drug possession (see the video for statistics.) I only recently came to realize how blatantly racist the war on drugs is. This racism goes back to the beginning of the 1900s when drug laws were being implemented, but here’s an explicit quote from someone that was “in the room” during the Nixon administration when the phrase “war on drugs” was popularized. As presented in an L.A. Times article:

[The war on drugs] “was authored by President Nixon not for reasons of health or science, but rather simple prejudice, according to Nixon’s domestic policy chief, John Ehrlichman.

“We knew we couldn’t make it illegal to be either against the war or black, but by getting the public to associate the hippies with marijuana and blacks with heroin, and then criminalizing both heavily, we could disrupt those communities,” he reportedly said 26 years ago in an interview that Harper’s Magazine published in 2016. “We could arrest their leaders, raid their homes, break up their meetings, and vilify them night after night on the evening news. Did we know we were lying about the drugs? Of course we did.”

One very minor criticism I have of the video is that it presents statistics without reference to studies. But it is intended to be brief and it’s harder to provide citations in this format.

The video is an awesome presentation of an extremely not awesome part of reality. It’s worth the time to watch.

Lucy Diggs Slowe

Keywords: women’s’ studies, civil rights, feminism, mea culpas

I came across Lucy Diggs Slowe in a N.Y. Times article Overlooked No More: Lucy Diggs Slowe, Scholar Who Persisted Against Racism and Sexism. From that article:

“She influenced broad campaigns for racial equality, feminism, personal freedom and peace activism. She made it a priority to create a separate women’s campus at Howard. And she developed the fortitude to take moral stands against oppressive authority. One such authority, Howard’s first Black president, was venomous in his refusal to grant her equal stature and comparable pay because of her gender. He dealt her only misery and insult.”

From Wikipedia:

“In 1922, Slowe was appointed the first Dean of Women at Howard University. She continued in that role for 15 years until her death. In addition, Slowe created and led two professional associations to support college administrators. Slowe was also a tennis champion, winning the national title of the American Tennis Association‘s first tournament in 1917, the first African-American woman to win a major sports title.”

Slowe was an awesome person that rose above the doubters, the misogynists, and the racists to demonstrate her abilities and to create ways to help other women do the same. As always, an online search provides more discussion of her.

The N.Y. Times article is “part of Overlooked, a series of obituaries about remarkable people whose deaths, beginning in 1851, went unreported in The Times.” Recognizing the snub of a single person like this isn’t on the same level as acknowledging things like the Holocaust, the Armenian genocide, or slavery, but this type of mea culpa is an important part of moving forward. It is difficult to change things without open recognition of the misdeeds of the past.

(There are many influential people in history that are not as well-known as they could be. Many such can arguably be said to have changed history because they doubted something and acted on that doubt. Slowe is someone I put in these categories.)

White supremacists on display in the capital

Keywords: racism, violence, white nationalism, insurrection, white identity

I am generally going to avoid politics in this blog, but this is only tangentially about politics. The storming of the Capital of the United States was not just by a mob, it was by a mob of white supremacists. FiveThirtyEight does an excellent job of discussing this in Storming The U.S. Capitol Was About Maintaining White Power In America so I don’t feel I need to add much. But, a key point is that FiveThirtyEight, being who they are, provides evidence to support their claim. This is not just an opinion. I don’t think the importance of this can be overstated.

Is there anything supernatural?

Keywords: philosophy of science, physical reality, philosophical foundations, nonphysical, god, ghosts, ch’i, chakras, soul, spirits, magic

There are lots of things that are said to be supernatural; things like ghosts, gods, and magic, to name a few. Can these things truly be supernatural?

I’m not the first to come up with or present the types of arguments I’ll give below. But this is a critical foundational aspect of science that is useful for moving beyond doubt.  I want to emphasize that this discussion does not analyze whether or not these things exist. It analyzes one particular characteristic that is often given to these things: that they are supernatural.

In order to get very far, we’ll need a better term for what we’re talking about. The word “supernatural” is arguably an oxymoron. Can there truly be something that is not natural, that is beyond – super to – nature? We might alternatively ask: Is there something in the universe that is not natural? We sometimes use the word “artificial” in the sense of “made by humans” to mean “unnatural”. But this isn’t the sense we’re talking about here. We’re not using the term to imply that gods or ghosts are made by humans. In the grander sense of the term, everything in the universe (that is, everything) is natural.

So let us change the question to whether or not there is something that is not physical instead of supernatural. This is consistent with the use of the term “incorporeal” to describe ghosts and spirits. Such things are thought of as having no body, of being immaterial.

Arguably, using the term “nonphysical” increases the variety of things under discussion. For example, when I was studying chakras, I came across a statement that chakras exist in a “nonphysical dimension.” These, along with various “life energies” or “life forces”, such as ch’i, are often associated with medicinal practices and are thus often posed as involving the body more than the supernatural. Similarly, forms of extrasensory perception (ESP) such as telepathy or telekinesis are often posed as extensions of the mind more than as supernatural abilities. (This includes some science fiction stories that provide a fictional, “scientific”, reason for their existence.) There are myriad other examples.

The next step, of course, is to have an understanding of what “physical” means. Indeed we need a clear definition of “physical.” I’ll use our bodies as a foundation for this definition. But I’ll also link the definition to my three philosophical foundations discussed in Am I a figment of your imagination?

  1. Cogito, ergo sum (I think therefore I am),
  2. Something exists besides self (objective reality),
  3. Sensory perceptions interpret, rather than capture, reality (modelism).

I hope that few people would argue that we exist only as thought. I hope that most people would admit we are beings of flesh and blood. A body of flesh and blood is a physical body – by definition. Further, our senses, being part of our physical body, are – by definition – physical senses. As physical senses they can sense nothing but physical reality – again, by definition. When we speak, our larynx and mouth modulate sound waves that propagate by physically moving air molecules. When we see something, it is via photons hitting our retinas. When necessary, we can look to biochemistry and physics to understand that our physical body and the physical world are made of molecules and atoms or, more generally, that the universe is made up of the full array of particles in the Standard Model of physics. But for the sake of this discussion, it is important to realize that the definition of “physical” is founded in our bodies and its interaction with objective reality. Particles are just experimentally based refinements to the model that this definition is a part of. It is, perhaps, also useful to realize that this definition is consistent with the definition of “physical” used by science and, in particular, by physics.

It is certainly possible for the word “physical” to be defined in other ways. And people are wont to do so; people commonly engage in what I call Whac-a-mole arguments (which are more formally referenced as moving the goal posts.) If there is a reason to do so, other definitions can be compared to my definition for elucidation. But I argue that any definition of “physical” must include the physicality of our bodies – the physicality of flesh and blood – or else it references a completely different concept then what I am talking about here.

I will likely write a post discussing measurability in more detail, but the concept is an important part of this discussion, so here are a few comments. To measure something in physical reality is to measure either a static characteristic of an object or a change of state of an object. We might measure the static volume of an object or its change of position in space. We might measure a static temperature or the change of temperature as something cools. (As part of our model, measurements always have an error and never measure reality exactly.) Our senses work by making physical measurements (although their accuracy is always in question). We hear by measuring the frequency of sound waves as they move air molecules. We see by measuring the color and intensity of photons. We also extend the range and accuracy of our senses through technological instrumentation, such as yardsticks and the Large Hadron Collider. These are extensions of our senses in that the measurements of these devices are ultimately incorporated into our minds via our physical senses.

This brings us to the definition of a physical “force.” Any force that makes a measurable change to a part of the physical world is a physical force – by definition. There is a sense in which we don’t really measure the physical forces per se; we measure the changes they produce on physical objects. We measure the force of gravity by how it affects dropped objects. We measure the electromagnetic force by its effect on electrons. Physics has identified four forces: gravity, electromagnetism, the weak nuclear force, and the strong nuclear force. If we happened to measure a change in a physical object that could not be accounted for by the combination of these four forces, we would have identified another physical force. There is currently no evidence of a fifth force, but for the sake of this discussion, let us assume the possibility.

We’re now ready to start addressing the question of whether something can be nonphysical.

I’ll use god as an example to illustrate the main argument. Assume god tells me something and I speak to someone about what god said. Because my speaking is a physical act, somewhere between god and my larynx, god had to have made a change in my physical body. To be clear, the assumption is that I am saying something that I would not have said, would not have known about, if god hadn’t interacted with me. For emphasis, I’ll work back along the trail. We know speech moves physical air molecules. We know that this air motion is created by our lungs and modulated by the motion of muscles in our mouth and throat. Does god have one hand on my throat and another on my lungs physically controlling my speech? Well, the assumption is that I am consciously aware of what god told me. Just as we know that the blood we bleed when we are cut has a function related to the maintenance of our body, we know that the neurons in our brain have functions related to muscle control and consciousness. So, we can work our way back along the nerves that control my mouth muscles to my brain. We know that our brains work, in part, via the firing of neurons. For the sake of discussion, let’s assume that the way god told me something was by controlling electrons as they moved down my neurons. For the sake of imagery, assume god has a teeny tiny little hammer and god is sitting in our brain whacking electrons as they go by. Such changes to the motions of these electrons – physical particles – would be measurably separable from the effects of other known physical forces. For emphasis: it doesn’t matter how far we have to go on our journey from the larynx, or how minute a change to my body we attribute to god, if god speaks to me, it requires a physical, measurable, change in my body. By definition this would make god a physical force.

Ghosts illustrate the concept of a supposedly incorporeal entity measurably affecting the physical world. Ghosts are purportedly seen or heard through our eyes or ears. The purported rattling and shaking produced by ghosts are physical phenomena and thus ghosts cannot be nonphysical.

This same argument applies to souls and things like animistic spirits of trees. If the soul in any way influences our physical body or a spirit inhabits and affects a tree, it would have to do so via a physical force. Similarly, if some life force animates our bodies, it would have to do so by affecting our physical bodies in some measurable way.

I’ll now move away from the image of god with a little hammer in our head by considering telekinesis (moving objects with our minds) or magic in the form of casting spells (or in the form of its cousin, prayer). These tend to be presented as something happening at a distance; that there is physical separation between the person and the object being affected. Let’s assume a person is doing something that causes an effect on some object. Let’s say, either through telekinesis or through spell casting, that a rock is lifted. On the rock side, we are back to a measurable effect that we could isolate out from gravity. But there is also the action of the person – whether it is waving their hands in a spell or just thinking really hard about lifting the rock. These are measurable actions – either the motion of the hands or neurons firing as part of a conscious act. That is, there are two measurable and linked effects involved in the lifting of the rock. This makes these abilities part of physical reality.

Let’s also discuss “dimensions” since, for example, chakras have been said to exist in a nonphysical dimension (which they can’t because they supposedly affect our physical bodies.) Various forms of string theory posit more than the four dimensions of space-time (10, 11, and 26 in particular.) So, even physicists are willing to discuss extra dimensions. But the key point here is that, if they exist (and there is currently no evidence that they do) they are physical dimensions. They would be extensions of our current four dimensional model and would have measureable affects. Sometimes the word “dimension” is used to discuss “alternate” universes or realities. Science fiction and fantasy like to use the trope of “portals,” “gates,” or “doorways” into these alternate places. But, once again, if there is a doorway, it provides a physical connection to those alternate dimensions.

Finally, I’ll discuss things that people really want to believe have transcendental origins: love and other emotions. Many people don’t want to think that love is only a physical response. Well, we’re already capable of measuring some emotions in terms of their electrochemical presence in our bodies (although not very easily and not with any level of accuracy). Even further, I’ll point out that people in love (especially newly discovered love) can sometimes be identified by sight – without fancy equipment. Many of us have looked at a couple and thought to ourselves, “They’re in love.” For another example, anger is often visibly noticeable. These, again, are physical measurements made by our physical senses. I want to emphasize that this in no way diminishes the beauty of love. Love exists and produces one of the most exquisite feelings we feel. That love is “only” electrochemical doesn’t change these facts.

In summary, anything that affects the physical world and, in particular, produces (by whatever means) a conscious awareness of its existence in our physical bodies, is necessarily a physical force or object. Otherwise it couldn’t interact with the physical world or our bodies or our minds. These facts are true by definition. Harking back to my original definition of “physical”, to deny this definition is to deny that we have flesh and blood bodies. In conclusion: there is nothing nonphysical or supernatural.

There is a technicality regarding this conclusion. It is imaginable that there is something which we cannot measure because it is not connected to the part of the universe we occupy. Perhaps we are in one isolated bubble in a multiverse sea of bubbles. Well, we will never know if this is true because if there are segments of reality that are completely, physically, disconnected from us – that our physical bodies (or current or future instruments) cannot sense– there is zero chance of knowing anything about them.

There is another concept in the category of things that might exist but are not measurable: an observer. I’ll use an observer soul as a focus. I’ve already noted that if the soul in any way controls or influences the body, it is physical. But it might be that the soul is simply an observer, an archiver of our life, something that acts as a memory storage device. (This is an important aspect of souls. If the soul does not have any memory of who I was then how is it in any way a continuation of “me?”) We often observe people without them knowing it. So, it is imaginable that there is something observing us without our knowing. (Of course, the question of mechanism comes into play. The analogy thus falls apart in that we see people via physical photons. But let’s ignore mechanism for this discussion.) This is no different than the situation of a bubble universe. If something is only an observer that in no way interacts with us in a measurable way, we, again, have zero chance of knowing anything about it.

As I said at the beginning, this argument does not address the existence of things like gods or ghosts. I will likely post other arguments against their existence, but I want to strongly emphasize that the purpose of this post is to discuss a single characteristic often attributed to these things. This post only argues that there is nothing nonphysical, nothing supernatural. That is, if gods or magic or whatever exist, then they are physical objects or forces. As physical entities, they are measurable. This means they can be analyzed by the scientific method because what science does is analyze data obtained via measurement.

Part of my reason for this emphasis is to deflect arguments of “maybe science just hasn’t detected these things yet.” Such arguments from ignorance are irrelevant here. This discussion is about “in theory” vs. “in practice.” If there is a physical affect, then in theory we could develop techniques to measure it. Whether or not we have done so in practice is not part of this discussion. Understanding that the nature of reality is fundamentally physical and measurable is necessary for understanding the nature of science. The terms “supernatural” and “nonphysical” are red herrings we can discard as we analyze what is real and what is not.

An ironic aspect of this conclusion is that I started out by saying “supernatural” doesn’t mean “artificial” in the sense of “made by humans”. Well, since there is nothing supernatural, it turns out that anything claimed to be supernatural is just an artifice of human imagination.

(Update: I realized that I forgot to include credit for the ghostly image I used.

Just because it’s awesome: Advances in space exploration

Over the last year there have been some awesome accomplishments in space. A few examples (there are many others):

  1. Retrieval of subsurface asteroid samples to earth by Japan’s Hayabusa2.
  2. The return of lunar samples by China’s Chang’e 5.
  3. The transport of humans to space for the first time by a non-governmental agency, Space X.
  4. An unprecedented detailed image of a sunspot by the U.S. National Science Foundation’s Daniel K. Inouye Solar Telescope.

There are several forms of awe I experience from thinking about these achievements.

The complexity of retrieving rocks from objects in space is mind boggling. I mean this in the relatively literal sense that no one person can understand all the theoretical and engineering details necessary to accomplish this. Any one mind would be boggled to attempt it. The sense of awe here is increased by realizing how detailed our understanding of physics has to be to do this.

The transition of access to space from government to industry creates a sea of dreams that are closer to being implemented.

The expansion of knowledge is always a thrill to me. There are currently over two dozen space probes along with numerous earth based telescopes collecting data. (On the sad side, the Arecibo Observatory closed this year.)

As much as these individual accomplishments are awesome, I also find it awesome in an odd way. These accomplishments get significantly less coverage than space adventures of old. The awesomeness is the fact that going to space is becoming normal, even expected. What an accomplishment!

Liberation of doubt

Keywords: origin of morality, religious privilege, hate, good without god

I had another letter to the editor published in the Eugene, OR Register-Guard on Dec 17. It was in response to Michael Gerson (who writes for The Washington Post.) His column, Hope doesn’t depend on us, was published in the Register-Guard on Dec 9. My letter, as submitted, is provided below. However, because such letters are limited to 200 words, it is very concise and I think it is appropriate to provide some further discussion.

In the column, Gerson states “For me, doubt is like staring into an abyss.” This is the complete opposite of my view as evidenced by this blog. Gerson also states “Without a transcendent moral order, ideas such as good and evil, noble and ignoble, are pegged in mid-air.” He adds that hope comes from “Advent” and “is a delivery from elsewhere.” There is more along these lines.

Although Gerson doesn’t use the word “god”, his comments are a variant on a common theistic belief that morality derives from god. The contrapositive of this is that there can be no morality without god; the corollary is that atheists are intrinsically immoral. I use the analogy of anti-Semitism in my letter because it is generally acknowledged as hate. Saying that atheists are immoral simply because of their beliefs is no different in kind than saying Jews are.

This is not simply a philosophical distinction. The belief that “god equals good” combined with religious privilege has done, and continuous to do, real harm in the real world. People have been killed for being atheist. There are a half dozen or so countries where atheism is a capital offense. There are states where it is still technically illegal for an atheist to be a juror. I’ve met people that have lost their entire support structure, including someone that was kicked out of their house at age 16, for coming out as atheist in religious communities. People lose their family, their friends, and even their jobs for being atheist. More generally, the promotion of the U.S. as a Christian Nation (e.g., via Project Blitz) is a blatant attempt to reduce non-Christians to second class citizenry. Recent examples of legal harm in the name of religion include the Supreme Court rulings involving Hobby Lobby and the Little Sisters of the Poor. The history of religion relating to indigenous peoples, blacks, women, and slavery is horrendous.

I feel a need to preempt a potential response to this post. It is not unusual for people to think that, when I say promoting “god equals good” is a form of hate speech, I am engaging in a reverse form of hate speech. The difference is that I do not claim morality comes from some single external or higher source the denial of which implies the denial of morality. There are many religious people that act morally. But I believe they are epistemologically mistaken regarding where their morality comes from. I do not claim that this mistaken belief intrinsically implies they are immoral.

As submitted (published as Liberation of doubt):

Many people view doubt as a liberation rather than as the abyss Michael Gerson does (Dec 9). Doubt frees us to question and discover the world as it is rather than as viewed through the filter of faith and dogma. Such questioning has allowed science to reduce disease and poverty. There is no need for a “transcendent moral order” to understand good and evil or for nonreligious organizations, like Doctors Without Borders and those featured in the RG (Dec 9, p3A), to help others. Organizations like Innovations for Poverty Action provide hope through science based studies.

Understanding that purpose derives from love, friends, family, helping others, and protecting the environment requires no “revolt”. The acceptance of a “meaningless universe” gives extra meaning and importance to those things around us in the here and now.

Gerson’s implication that hope and morality require delivery from Advent or some mysterious “elsewhere” is a direct attack on the morality of atheists and others who obtain these from evidence, reason, and conscience. Gerson’s comments are directed at a population other than Jews, but they are a form of hate speech born of religious privilege that should be condemned as strongly as antisemitism is.

(End of published letter.)

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