Detectives and Abductive Reasoning

Sherlock Holmes is often thought to engage in deductive reasoning. He even says so himself. However, Ivar Fahsing points out in an article on how to think like a detective that what Sherlock did was actually abductive reasoning (in contrast to deductive or inductive reasoning). This surprised me since, even though I am somewhat versed in logical analysis, I was not consciously aware that there is a word for this form of reasoning.

From Wikipedia: “Abductive reasoning (also called abduction,[1] abductive inference,[1] or retroduction[2]) is a form of logical inference formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century. It starts with an observation or set of observations and then seeks to find the simplest and most likely conclusion from the observations. This process, unlike deductive reasoning, yields a plausible conclusion but does not positively verify it. Abductive conclusions are thus qualified as having a remnant of uncertainty or doubt, which is expressed in retreat terms such as “best available” or “most likely”. One can understand abductive reasoning as inference to the best explanation,[3] although not all usages of the terms abduction and inference to the best explanation are exactly equivalent.[4][5]” (End from Wikipedia.)

I good example given by Fahsing is medical diagnosis. A good doctor will collect data on symptoms and consider many different diagnoses and look for the diagnosis that best fits the symptoms. You don’t start with an assumption of what the health problem is and look for symptoms to support it. Bringing in any form of bias or ignoring a symptom is potentially deadly.

What struck me about this reasoning method and most of Fahsing’s article was how it is a variant of what skeptics and scientists do. This is illustrated by the ABC principle presented by Fahsing:

  • Assume nothing
  • Believe nothing
  • Challenge and check everything

This is an excellent description of starting from doubt. I often describe doubters and skeptics as making decisions based on reason and evidence. Skeptics are wont to say they challenge (or doubt) everything. This effectively requires starting with a blank slate that contains no assumptions. The collection of evidence and the use of reason is how you check everything. This process leads to working conclusions.

When I think of deductive logic I generally think in terms of formal proof. Starting with a well-defined set of assumptions, rules of logic are applied so as to systematically show how a conclusion must follow from the assumptions. Inductive logic is kind of in-between deductive and abductive reasoning. Induction uses rules of logic, but can start with premises not assumed or known to be true. So it seems to me that inductive reasoning is sometimes used in abductive reasoning although I think intuition based on experience plays are large role as well. But in the sense that a conclusion obtained abductively is not considered to be “proven”, deductive reasoning is not truly part of abduction.

The concept of “inference to the best explanation” is quite precisely the foundation of science and is consistent with my philosophical foundation of modelism. I don’t think there is any choice but to assume that I exist and that something other than I exists. But beyond that, the model which I develop as a consequence of input though my senses is a less than perfect representation of objective reality. My subjective model is the best fit of my sensory input that I’ve been able to infer. Similarly, this is how science works. If new evidence shows up that doesn’t fit the current scientific model, the model is adjusted to fit this new evidence.

This leads to the question of when do we claim to “know” something to be true? A detective works within the context of a legal system. In the U.S. there is the concept that a verdict has to be found “beyond a reasonable doubt.” It is certainly possible to go down the rabbit hole of defining “reasonable doubt”, but consider that this criterion is regularly and successfully applied in court rooms. It isn’t impossible to come up with an acceptable definition – at least in specific cases. (Unfortunately, even though this criterion is the best we seem to have been able to come up with, it still doesn’t always lead to the correct conclusion.)

I think “reasonable doubt” is a useful criterion for science and daily living as well. For example, I think most people consider the existence of gravity beyond a reasonable doubt. But perhaps surprising to some, science has ways of quantifying doubt and even “reasonable” doubt.  I’ve discussed the fact that every measurement has an error. The quantification of this error effectively quantifies doubt. In statistics, the acceptable level of error is identified by applying a limit to the p-factor. (Of course, and more kudos to science, the applied limit and even the value of using the p-factor is under debate.) Other quantified limits relate to the number of sigmas (or standard deviations) or the number of nines (the number of decimal places in a measurement’s error that are 9’s).

In general, thinking of starting from doubt and science as detective work is spot on.

(The cover image does not require a credit, but here’s where I got it from: Pixabay.)

Ask culture vs. guess culture

This came to my attention from BdiJ. The following was an easy cut and paste way for me to provide the basic concept (from The Atlantic):

Let’s say your husband or wife has a friend who will be coming to your city for two weeks on business. This friend writes to you and your spouse, asking if you can put him up while he’s in town. Has this person committed a gross violation of etiquette? Whether you answer yes or no may speak to whether you’re an Asker or a Guesser–the two personality types described in a three-year-old [at the time] Web comment that has lately taken on a second life as a full-on blog meme.

On January 16, 2007, Andrea Donderi responded to an Ask MetaFilter post that dealt with a houseguest-related situation like the one described above. Donderi’s take on the situation is as elegant as it is provocative. Basically, she says, there are two types of people in the world:

“This is a classic case of Ask Culture meets Guess Culture. In some families, you grow up with the expectation that it’s OK to ask for anything at all, but you gotta realize you might get no for an answer. This is Ask Culture.

In Guess Culture, you avoid putting a request into words unless you’re pretty sure the answer will be yes. Guess Culture depends on a tight net of shared expectations. A key skill is putting out delicate feelers. If you do this with enough subtlety, you won’t even have to make the request directly; you’ll get an offer. Even then, the offer may be genuine or pro forma; it takes yet more skill and delicacy to discern whether you should accept.”

(End of excerpt from The Atlantic.)

A search on this comes up with quite a few hits but it appears that the 2007 post is what started the conversation. I found looking through the discussions interesting. First, a lot of people (including myself) find the existence of names for these cultures to be extremely helpful. Second, there are some people that have adamant opinions about this. There were quite a few people that think directly asking to stay was rude. There was at least one opinion that guess culture is out-and-out wrong. I will explore this through two lenses: gift giving and dating. Both of these illustrate that guess culture permeates our society – even amongst ask culture people.

There are at least two phrases that are a direct result of guess culture: “regifting” and “It’s the thought that counts.” BdiJ and I have a no-surprises rule. It is, perhaps, most applicable to the “gift” of a surprise party. We both consider openness and honesty to be extremely important. Throwing a surprise party inherently requires lying – even if it’s lying by omission. And, personally, I think it is rude to assume I will drop everything to participate in your surprise activity. But this rule also applies to gift giving in general. I’m constantly trying to keep the amount of stuff I have to a minimum. Getting presents that I don’t want doesn’t help. That doesn’t mean I don’t want any presents. But I want to be asked about a present before it’s bought. Acceptance can be on an individual basis or on an ongoing basis. I collect marbles. If BdiJ is somewhere and sees a marble I might like, she calls me to ask. On the other hand, she knows I always like to get (unscented) flowers. Wouldn’t it be nice if you only got things you wanted? Isn’t the need for the term “regifting” rather absurd? Isn’t it even more absurd that it is traditionally embarrassing to be caught regifting? How much thought has really gone into a gift if the person doesn’t actually want it? Unless you really know that someone would like a particular gift, wouldn’t it be more thoughtful to ask them first?

Something that immediately came to my mind when reading about these cultures is a phrase that I originally read in The Ethical Slut by Janet W. Hardy in reference to asking about sexual activities: “It is always okay to ask, if it is always okay to say no.” This is an explicit description of ask culture. To me, this seems like a very good philosophy. It encourages communication and honesty. It also normalizes rejection; it says up-front that there is a possibility someone will say no and that it is okay for this to happen. So let’s look at how ask philosophy is so not part of societal norms – especially for women.

There is a distinctly sexist attitude that it is not okay for women to ask men out or to ask a man to marry them. (Fortunately this is changing, albeit not fast enough.) This social taboo is so strong it led to the concept of Sadie Hawkins Day which is the idea that a special day (or social event) has to be declared in order for it to be okay for a woman to ask a man out. Yuck!

More importantly, there are strong historical and religious traditions that it is not okay for a woman to say no. Saudi Arabia is known for its guardian laws regarding women. In the extreme case – and still practiced in much of that country – a women cannot even leave the house unless they are accompanied by a male relative. But it doesn’t stop there. Even if it isn’t universally enforced, according to Islamic law refusing to have sex with your husband is reason for divorce. This can include being thrown onto the street penniless. (I became aware of this through the well-documented book Why I am not a Muslim by Ibn Warraq.) There are similar guardian laws in the Old Testament. Women in the Old Testament are treated like slaves having to be under the control of a man. An extreme case of this is Deuteronomy 22:28-29 where a woman is supposed to marry her rapist. (Biblical apologists often argue that this passage doesn’t actually say this. My response to these arguments is that a passage that can even remotely be interpreted this way is abhorrent. Also, Jesus explicitly said he didn’t come to overturn the old laws (Mathew 5: 17-18)). Another example is that it was only in 1976 that Nebraska became the first state to recognize that a husband could rape his wife. It was only in 1993 that all 50 states did. On a personal level, I know someone that, when she was young, thought that going on a date required her to have sex if the man asked for it.

This attitude continues today. Consider that we have had to popularize the phrase “no means no” and its affirmative counterpart “yes means yes” (active vs. passive consent). Men need to viscerally internalize the second half of the ask philosophy. It should always be okay for a woman to say no. Too many women have been abused simply for turning a man down or for making it known that even trivial come-ons or physical complements are not welcome. There is a discussion group called something like I’m a nice guy, you fucking bitch. It is mostly posts of anonymized screen shots from online dating interactions. A man is all gushy and nice about wanting to meet someone and the moment they are turned down the response turns nasty. The fact that there are multiple discussion groups for this type of behavior is evidence of how common men turn to abuse when turned down. (There is plenty of other evidence.) Men need to stop doing this – now!

Even nice guys need to understand that there are enough men (not all men, but enough men) that don’t except no as an answer. This is why women have to be so cautious with every man until an individual man proves they are safe to be around. For example, don’t be insulted if a woman doesn’t want to be picked up at their house on a first date or wants the first date to be short and somewhere safe. It’s okay to offer to pay for a date, but if you insist after the woman says no, you are engaging in dominating and abusive behavior. Don’t make physical complements, even about clothing, unless you know a woman well or are in a dating situation. Even if you think you’re just being nice, these actions can make a woman start worrying about potential future abuse. Such caution is a necessity based on evidence. Don’t make it about you if you’re not the abusive type. Making it about you makes you one of the abusive men.

An important aspect of ask culture, perhaps especially in dating, is immediate acceptance of the refusal. There may be times, such as during negotiations or planning sessions, where pursuing the reason behind saying no is appropriate, but generally speaking it is okay for the reason to be “I don’t want to.” Especially if you don’t know someone, are only casual acquaintances, or just happen to` work together, there is no obligation for someone to explain themselves.

Guess culture proponents apparently think directly asking for something is rude. Part of this argument seems to be that saying no is also rude. Some of the guess culture defendants basically said you have to come up with a lie to justify why you’re saying no. Seriously? It’s better to lie than be upfront? This is the same reasoning that forces women to stop, smile, and politely respond to a random comment from a strange man rather than simply ignoring them or honestly telling them their attention is not welcome.

I would be quite surprised if any negotiator, mediator, or relationship counselor did not consider clear, open, and honest communication to be essential to resolving conflict. If there is anything that’s come out of the #Metoo movement it’s that, in the context of sex, clear communication is absolutely critical. The guess culture effectively promotes the opposite. I ask people in the guess culture to recognize the potential for confusion and harm their culture creates. There shouldn’t be any guessing that “It should always be okay to ask and it should always be okay to say no.

(The cover picture is of Lil Abner where Sadie Hawkins Day originated. As far as I can tell the picture is a promo for a Columbia-Tristar movie.)

Metrology Part III – The “soft” sciences are harder than the “hard” sciences.

Keywords: measurement, metrology, reductionism, SI units, reality

Recap

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 third 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 Metrology Part II – How do I measure thee? Let me count the ways, I introduced the International System of Units (SI) including how an infinite number of units can be derived from the seven base units. I then introduced the formal generalized definition of a measure, which allows expansion beyond SI based units such as those of the International System of Quantities. Of relevance here, is the distinction between physical units and conceptual units (my terminology). I also briefly mentioned statistics as a methodology that analyzes sets of measurements.

In this installment I will argue that the so called “soft” sciences are still physical sciences. This includes discussing the difference between the types of measurements the different sciences use. This leads to a further generalization of units, culminating in a discussion of fictional units.

Hard and Soft Sciences

The so called “hard” sciences start with physics, chemistry, and biology and then cascade down through many an application such as geology, astronomy, and medicine. The so called soft sciences are usually related to things like society and psychology – the social sciences that look at the way people act and think. The term “soft” science is sometimes used because of the impression that they are less rigorous than the “hard” sciences. In the extreme case, some people don’t even consider them sciences at all. I will argue that they are, in fact, sciences, and that they can be rigorous. I will also argue that, contrary to popular belief, social sciences are, in essence, physical sciences since they measure functions of physical brains. In fact, the main difference between hard and soft sciences is that the soft sciences are much harder than the “hard” sciences. We’ve discovered the Higgs boson but we haven’t solved world hunger.

Some standard characteristics expected from science are peer review, reproducibility, and self-correction. Science results are expected to be written down, submitted for peer review for validation, and published for historical record. Ideally, such results are reproducible. That is, someone else performing the same study would get the same results. The next level is for related studies to validate a larger hypothesis. If there are inconsistencies in related studies, then the general results (possibly even specific results) are reexamined with the intent of revising the general hypothesis. This is the self-correcting nature of science. The Reproducibility Project by the Open Science Collaboration evidences these characteristics of science in the social sciences. The project identified the 100 most commonly cited papers in psychology and went about trying to reproduce them. The results are a good example of a half-empty-half-full debate. There were enough of the studies that could not be reproduced that some people are claiming there is a reproducibility “crisis”. However, considering that psychology was (arguably) first formalized as a science by Sigmund Freud circa 1900 – that is, it is less than 150 years old – I find it remarkable that there was a reasonable percentage of studies that held up to reproducibility. The Reproducibility Project directly implements the concept of self-correction.

Soft science measurement types

The essence of science is experimentation and measurement. In order to understand the soft sciences, it is necessary to realize that the types of measurements made are significantly different than those made by the hard sciences. (This might be why some soft science experiments are called “studies” rather than “experiments.”) One of the big differences is that psychological and sociological studies often collect data by asking people questions; we don’t usually pull out a yardstick to measure what people think or feel. (However, the ability to measure people’s inner thoughts is increasing. An interesting example is the Harvard Implicit Association Test which analyzes biases you might not know you have.) This can make such data collection seem “soft” since people change their mind, are not always conscious of how they feel about something, and out-and-out lie. But these are factors that are handled with increasing sophistication.

Within sociology, or any study of groups of people, the approach is to do statistical analysis across lots of people. Since people answer questions of the type “From 1 to 10 …” differently, the use of distributions and other statistical results are the appropriate presentation of the data. But this is really just a variant on the types of statistical methods that are used in many of the hard sciences. The much ballyhooed confirmation of the existence of the Higgs Boson is an example. The result is from analyzing many particle interactions to provide a statistical inference with a certain level of confidence. It might be argued that the error associated with the Higgs Boson are smaller than that often associated with sociological surveys, but the foundational methodology is not significantly different.

As pointed out in Metrology Part I, a calibration trail is used to ensure the error of measurements of SI units. Social sciences don’t have a foundational standard equivalent to the intrinsic SI standards. But there are calibration methods just the same (even if practitioners wouldn’t use the term). The most basic error controls are simply to have large numbers of participants and to have appropriate diversity. Unfortunately, neither of these control factors has been implemented as well as they should have been. This is getting better. An example of improvement is the recognition that a lot of psychological studies have been done on college students. This has led to the acronym WIERD science (Western, Educated, Industrialized, Rich, and Democratic). Realistically, the description of this type of science should probably include white and male as well. But the growing awareness of this bias is another example of self-correction.

Another calibration method is the use of priming. This is when what immediately precedes a question can affect how someone answers a question.  I was introduced to this concept in the ‘70s as a freshman in college. We were asked to take what everyone called the “Carrot Test”. This is because you were asked multiple times whether or not you like your carrots raw or cooked. My understanding is that, although the basic idea of priming has held up, some of the original results and levels of influence have not. There is quite a science on how to write surveys to eliminate priming, leading or biased questions, and other potential flaws.

Finally, I’ll point out the A/B tests that have been done by social media (mentioned in the docudrama Social Dilemma). This is where algorithms on social media platforms have implemented two-option studies on people to see which option maximizes attention. This provides a calibration of psychological methods that allow changing behavior at a level never seen before.

Reduction to SI units

I’ve stated that all physical units are derivatives of the SI base units. So, if I want to claim that social sciences are physical sciences, it is necessary to reduce survey questions to SI units. The main argument is that brains are physical entities. Responses to surveys are a product of brain activity. I’ll use lie detectors as an example of this reduction since there is a popular image of someone taking a lie detector test.

One of the main tools used in lie detectors is an Electroencephalography (EEG). The cover photo is an example. (Note that current lie detection technology is not infallible which is why it cannot be used as legal evidence.) An EEG measures electrical activity (electron movement) of the brain. As such, the unit of measurement of an EEG is ultimately reducible to the ampere. In order to get the wavy lines there is also time (seconds) involved. Arguably volume (meters cubed) is involved since an EEG is of a particular brain. Thus, if necessary, you can reduce an EEG to some derived SI unit. A key point here is that a lie detector measures physical (SI) units and tells us something about a person’s thoughts and actions.

Although survey questions can be much more complicated than a yes or no answer, the basic principle still applies. With enough work and, realistically, more advanced science then we currently have, it would be possible to reduce the answer to a survey question to SI units. And the technology is getting closer. Some awesome examples are mind controlled prosthetics. But there has also been an experiment of technologically aided 3-way direct brain to brain communication. This requires reading what a person is thinking and writing that thought into someone else’s brain.

A key point here is that it is not necessary to formally reduce measurements to SI units in order for them to be useful. Even in the hard sciences, units of measure are usually referenced by special names rather than their specific SI equivalence.

Another key point is that it isn’t always necessary to make measurements at the molecular level to calculate a system’s properties. It is theoretically possible to calculate the miles per gallon of a car by analyzing its mass and the engine’s energy output based on molecular level analysis. But it isn’t practical and the result can be obtained by measuring the distance covered and the amount of fuel used. Similarly, there is no reason to look at a person at a molecular level in order to analyze their actions. If you want to know what someone thinks, a good place to start is by asking. (If only more people would do this outside of science, a lot of relationship problems might be more easily resolved.)

Physical, conceptual, and fictional units

I want to expand on, or generalize, the idea that it is not necessary to analyze everything at the molecular level in order for an analysis to be useful. This involves the idea of conceptual vs. physical units (again, these are my terms).

In a previous post I said that “apple” is a unit. But, as a unit, it isn’t precise in the way an SI unit is. After all, no two apples have exactly the same volume, weight, and dimensions. Yet we have little problem recognizing an apple when we pick one up. The concept of apple is generic. A specific apple is an instantiation of the generic concept. A specific apple is the physical unit associated with the conceptual unit.  More abstract conceptual units are bits and bytes. You can’t really hold a bit in your hand. You can hold instantiations of bits in your hand in the sense that you can pick up a disk drive that has electromagnetic instances of bits. But these are only bits because of their interpretation as data. Unlike an instance of an apple, there is nothing inherent about a configuration of electrons that makes them a bit. Yet conceptually manipulating bits and instantiating them in computers has led to extremely useful results. Further generalizations and abstractions of units are numbers and math in general. You can’t hold a one or an equation in your hand. We don’t normally call numbers “units” but, in the context of this discussion, there isn’t any real distinction between numbers and bits. Numbers are instantiated in the same way as bits or apples. It just doesn’t make any difference what it’s two of – it can be two bits or two apples or two of anything.

My point is that conceptual units are very useful. The distinction I’m making between physical and conceptual units reflects the modelism of my three philosophical foundations I keep returning to. Bits and numbers are used to model objective reality. By conceptually manipulating the model, there is potential to learn more about objective reality, although the results of the manipulation have to be tested against objective reality. If the results hold up, then we might be able to manipulate objective reality through instantiations of those conceptual objects.

One last thing is to make a distinction between conceptual units and fictional units. We might think of “unicorn” as a conceptual unit in that there are many images of unicorns – unicorns are conceivable. But they are purely fictional since there are no instantiations of them. I want to emphasize that there is nothing wrong with contemplating fictional things. They can be very entertaining. That is, they can affect the real world by producing pleasure (and also pain). But too many people don’t seem to understand that just imagining something doesn’t make it real. And thinking that fictional things are real causes real harm in the real world. This is where science comes into play. Science helps us distinguish fiction from reality.

A skeptic, someone who doubts, tends to assume something is fictional until reason and evidence support its reality.

(The cover photo was taken from Wikipedia.)

An original meter

Keywords: meter, standards, metrology

In my post Metrology is not about the weather. Part I – How to weigh a potato, I mentioned that international standards used to be based on physical artifacts. I just came across this short article, The Last Original Standard Metre by Atlas Obscura. The cover picture is of one of the original such artifacts. (Picture credited to BridgetZoe [Atlas Obscura User].) I didn’t know that, “To define the meter, French astronomers Delambre and Méchain measured 10 millionths of the distance from the North Pole to the Equator through a Paris meridian.”

The nautical mile has a similar definition. It was historically defined as one minute (1/60 of a degree) of latitude along any line of longitude. If you don’t know, meridians (lines running from pole to pole) connect points with the same longitude.

Skeptical Inquirer Publication

Keywords: nonoverlapping magisteria, skepticism, publication, Skeptical Inquirer, Center for Inquiry. CSICON

I have an article “Is there a Philosophical Magisterium?” published in the current issue of the Skeptical Inquirer: The Magazine for Science and Reason, Vol. 45 No. 2 | March/April 2021.  My article is listed on the front cover. The Skeptical Inquirer is one of the leading skeptics magazines published by the Center for Inquiry (CFI). This organization’s origins are partly due to the late James Randi who was a famous magician, skeptic, and debunker.

The concept of nonoverlapping magisteria was introduced by Stephen Jay Gould. It is the idea that religion and science analyze different questions; that they occupy different magisteria. I started seeing this same idea applied more generally to philosophy and science. I was quite surprised to see Massimo Pigliucci’s promotion of this idea at CSICON 2018 (partly sponsored by CFI) during his presentation on “The Variety of Scientisms & the Limits of Science.

My article is mostly a response to Pigliucci. My main theme is that there is no well-defined concept that science cannot investigate. This doesn’t mean that science has necessarily investigated any particular concept, but that it could if it was of value to do so. A magisteria discussion is about “in theory” vs. “in practice.” The editor asked Pigliucci to write a response which is included in the current issue.

Blog posts that expand on portions of this article (there will likely be more) include:

  1. Am I a figment of your imagination?
  2. Is there anything supernatural?
  3. Metrology is not about the weather. Part I – How to weigh a potato
  4. Metrology Part II – How do I measure thee? Let me count the ways.

The unhoused and their trash

Keywords: homeless, stress, mental health, housing first

A recent letter to the editor of the Eugene Register-Guard asked what I assume is a common question about the unhoused. Why, when they establish camps. do they allow trash to accumulate around them; why do they seem to “choose” to live in their trash? If you live in an area with a large unhoused population, such as Eugene, you’ve probably seen examples. BdiJ lived on the streets for seven years and has some insight into this. I helped her provide a response based on things she’s told me that was published in the RG on Feb 7, 2021. With a 200 word limit, it is very concise so I will present it and then discuss the issue more. Published as Housing first, trash will take care of itself:

“Marlene Pearson doesn’t understand why some unhoused “choose” to live amongst their trash (Letters, Jan 30). First, please remember that not every unhoused person disregards their trash. It only takes a few to trash a large area.

To live on the street can be to live in a constant state of trauma. Imagine living in a state of fight, flight, or freeze 24/7. Not knowing where your next meal is coming from, or where you’re going to sleep at night, can make it difficult to think about other issues. This extreme stress can, in essence, create a cognitive overload in the decision making parts of the brain. When living with this level of stress, trash may not have high enough priority to even think about, let alone make a choice about. Concern can be constantly about the next five minutes, not tomorrow.

This is part of why “housing first” is so important – even if it’s just a pallet house. Having a door that can be shut and locked can provide a biochemical calming of the brain that can allow for thinking about longer term issues – like what to do with the trash.”

(End of letter as submitted.)

If there is one idea to focus on it is that of living in a constant state of fight, flight, or freeze. Realistically, not every unhoused person is experiencing this and even individuals who do probably have moments of rest. But this state can easily become a foundation when you don’t know if you’re going to be told to move on or harassed by someone – potentially the police – at any moment. When you carry everything you consider valuable with you wherever you go, there can be a constant fear of losing something important. These are just some of the factors that can cause mental health issues among the unhoused whether or not they had any issues prior to losing their housing.

This is a level of stress I can only understand intellectually and not with a true visceral feeling. The closest I can come is due to helping out at the Egan Warming Center. (For those that don’t know, Egan is an awesome organization that provides a warm place to sleep in Eugene and Springfield, OR when the temperature drops below 30 degrees.) Because of Covid, this past season has required completely different logistics. BdiJ has been the transportation lead making sure people get to where they need to go. This year, that turned into her driving a shuttle around town (with me accompanying her for safety) picking people up and bringing them to the shelter. One of the people we picked up was camped in what many people would consider the type of trash pile under discussion. This person wanted to bring it all with them – it wasn’t trash to them! Unfortunately, there are limits to how much we can transport and this person had a difficult time deciding what to bring. What a conundrum to face: a warm place to sleep but at the risk of losing most of your belongings.

Another insight from BdiJ is using a trash pile to hide your valuables. People aren’t likely to look through a bunch of junk to see if you have something worth taking. The down side of this can be finding your valuables yourself.

Stepping back some, consider that living in your trash is not limited to the unhoused. And I’m not just talking about hoarders. Everyone has a different level of dirt tolerance. (This is a common point of conflict between roommates.) I once had a friend-of-a-friend who didn’t see the need to pick up their puppy’s poop on the living room floor during house training. (I only went to their house once.) It is only in the cases where hoarding pours into the yard or there is public notice of health concerns that an issue is made – and not always even then. So ask yourself and society, why do we treat the unhoused differently in this situation?

Finally, please remember that housing is only the first step. Helping people to get off the streets often requires continued support. Providing – and financing – case workers is a critical second step.

(The cover photo was found online and was attributed to king5.com.)

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!

Charles

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.

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