Countdown to Math Anxiety

Countdown to Math Anxiety

Scott Bradley Gerhardt

Oregon State University

Author Note

Scott Bradley Gerhardt, Department of Psychology, Oregon State University

Correspondence to this article should be sent to Scott Gerhardt, Department of Psychology, Oregon State University, Corvallis, Oregon, 97331. E-mail: gerhards@onid.orst.edu

Abstract

There exist multi-national concerns about levels of competency in mathematical knowledge gained by pupils in schools; inevitably the spotlight has fallen on teachers, yet some children react as if wired by nature against mathematics and for math anxiety (Ashcraft, 2002). This research investigated the potential relationship (based on behavioral psychology’s principles of operant conditioning (Skinner, 1938; 1953), conditioned responses (Pavlov, 1927), and stimulus generalization (Watson, 1920)) between math anxiety and those whose parents issued a countdown procedure to extinguish unwanted behavior.  The sample population included 49 male respondents, 45 female respondents, and one participant who did not respond at all. The average age was 29.8.  The hypothesis tested was that a parental countdown procedure primed and conditioned people for math anxiety.  Of the 52 people who did report receiving a countdown procedure as a behavior extinguishment technique, 29, or 55.8%, also reported math anxiety.  Of the 43 people who did not report receiving a countdown procedure as a behavior extinguishment technique two, or 4.65%, also reported math anxiety.  The self report inventories were distributed via the internet’s multiplicity of channels that is online links.

Countdown to Math Anxiety

Many economic, sociological, cultural, and psychological theories have been postulated to try and assist educators in motivating, empowering, and emboldening students, and advancing pedagogy (Freire, 1968). Theories of classical (Pavlov, 1927), operant (Skinner, 1953), and respondent (Pear & Eldridge, 1984) conditioning are not new ideas; the three ideas evolved through psychological behavioral science in that order. STEM, Science Technology Engineering and Mathematics, are abstractions that share many commonalities, mathematics being one of the core issues restraining many otherwise intelligent people from meeting their life goals.  At first the connection between behaviorism and mathematics is not clear, until teaching and learning are added to the paradigm of their relationship.

Mathematics and intelligence are helpful and necessary in logic, reasoning, problem-solving, and computation inherent in modern scientific endeavors.  Fear and anxiety responses tend to mask and inhibit implementation of metacognitive processes necessary to elucidate solutions (Legg & Locke, 2009). Anxiety is a common experience and a reaction to a stimulus. From Pavlov’s dogs (1927), to Watson’s Little Albert, to Skinner’s operant conditioning (1938; 1953), thru respondent conditioning (Pear & Eldridge, 1984), the dynamic mechanical nature of behaviorism is a clear causational function deterministically fusing stimuli and response forward through time; uniquely similar to reciprocal determinism (Bandura, 1986).

Anxiety is a common experience and can be a reaction to a stimulus.  From Pavlov’s dogs to Watson’s Little Albert to Skinner’s operant conditioning to respondent conditioning the dynamic mechanical nature of behaviorism is a clear causational function deterministically fusing stimuli and response through time forward.  The experiment examined the practical applications of conditioning by exploring if any correlation exists between categorical variables defined as individuals who self report math anxiety and as individuals having experienced counting as an extinction technique implemented by an authority figure as a child.

Behaviorism

The terms classical conditioning termed by Nobel Prize winning scientist Ivan Pavlov (1927) who happened upon conditioning quite by accident while studying salivary glands and their role in breaking down food via digestion for absorption into the blood.  Pavlov (1927) began by observing: “I started to record all the eternal stimuli falling on the animal at the time its reflex reaction was manifested… at the same time recording all changes in the reaction of the animal.” At first, the only reaction was the ordinary salivary reflex. When an experimenter put food into a dog’s mouth, it salivated.  But after a while, the animal would salivate before receiving food.  By observing the “external stimuli falling on the animal,” Pavlov was able to see what triggered these secretions.  Pavlov noticed that the smell or sight of food elicited secretions.  Pavlov (1927) concluded two distinct reflexes: the inborn, unconditional reflexes and the acquired conditional reflex.  This is important in defining the variable of a countdown procedure, and its recalled presence.

The Little Albert case study experiment (Watson, 1920) illustrated the empirical evidence of classical conditioning in humans.  The same study proved to be exemplary for stimulus generalization.  John B. Watson (1920), after observing kids at play, was prompted to investigate the relationship of loud noises and fear.  He set out to prove that classical conditioning could condition a human child to respond with anxiety and fear to an otherwise benign stimulus.  The study proved successful much to Albert’s loss.  This research endeavors to examine a similar relationship between a “countdown” trigger presented to children as a way to elicit extinction of an undesirable behavior by authority that later manifests as ‘math anxiety’.  The generalization of the countdown stimulus can be different for each and every individual participant.  If behaviorism is the path, (for the hypothesis investigated) the beginning is the countdown and the destination is the math anxiety.  The paths are different for everyone as they chose their response, which in turn determines the next stimuli.  This research did not investigate individual pathways; rather it searched for those who had completed a journey.

The term operant conditioning was termed by B.F. Skinner. Skinner (1938; 1953) identified four operant procedures, two that strengthen behavior, (positive and negative reinforcement) and two that weaken behavior, (positive and negative punishment) juxtaposed and orthogonally arranged in a 2X2 matrix just like the data in table 1 collected from this research. 

Punishment, the procedure of providing consequences for a behavior that reduces the frequency of that behavior (Skinner, 1953).  Applying behaviorism to pedagogy Catania (1998) proved a procedure must have three characteristics to qualify as punishment, the procedure must have a consequence, a decrease in strength (occur less often) and the latter must be a function of the prior; which is to say it is iterative.  The punishment and its consequences are often referred to as punishers.  Catania's fourth edition of Learning (1998) is a comprehensive and authoritative account of learning from a behavioral perspective. Bridging the separate literatures on animal learning and basic behavioral processes with research on human language, cognition, and memory, Catania employs an internally consistent approach to reasoning that convincingly illustrates that even the most complex types of human learning can be addressed from a radical behavioral approach. Relevant topics include equivalence classes for responses and stimuli, conditioned reinforcement, relational frame theory (the emergence of higher order, generalized classes of symbolic behavior), remembering early childhood events, applications of differential reinforcement, and selection of the capacity to learn.  This applies to the ‘countdown’ as negative reinforcement of the anxiety felt while experiencing the disapproval of authority, and its latter association with math anxiety.  Reinforcement is the procedure of providing consequences for a behavior that increase or maintains the rate of afore mentioned behavior.  The positive reinforcement is the response followed by the appearance of, or an increase in the intensity of, a stimulus.  This stimulus, called a positive reinforcer, is ordinarily something the organism seeks.  Skinner (1953) later noted “the only defining characteristic of a reinforcing stimulus is that it reinforces”.  This is to say, a reinforcer is defined by its effect on the behavior it follows. With negative reinforcement, a response is strengthened by the removal of, or a decrease in the intensity of, a stimulus.  This stimulus, called a negative reinforcer, is generally that which an organism is averse to; similar to punishment, yet different.   This continued elucidation of possible pathways does not delineate individual pathways; it merely aims to determine if further investigation is warranted.

Conditioned reinforcers, or secondary reinforcers, are those who acquire their power by having been paired with other reinforcers (Skinner, 1953).  An example is provided by Zimmerman (1957), who sounded a buzzer for two seconds before giving thirsty rats water.  After the buzzer and water had been paired in this way several times, Zimmerman put a lever into the rat’s chamber.  Each time the rat pressed the lever, the buzzer sounded.  The rat soon learned to press the lever, even when lever pressing never produced water as the buzzer had become a conditioned reinforcer. A secondary reinforcer, punishment, or conditioned reflex is those reinforcers that are dependent on their association with other reinforcers or punishments (Zimmerman, 1957).  This research aims to explore the possibility that an acquired conditional reflex exists as a “countdown” stimulus first presented in youth as a behavior extinguishment technique implemented by authority that leads to math anxiety later in life.  Specifically this would occur in a natural treatment throughout the lifespan of the participant through various institutional settings, following and temporally coinciding with the countdown administration in youth.

Reciprocal Determinism is the idea that behavior is determined and/or controlled by individual cognitive processes, and by environment through external social stimulus events.  Its basis transforms individual behavior by allowing subjective thought processes transparency as contrasted with cognitive, environmental and external social stimulus events similar to experiencing a countdown procedure to extinguish unwanted behavior.  The specific instance manifests the transformation in individuals as math anxiety, hardly a desired effect.  The theory set forth by Albert Bandura postulates that individual behavior can be conditioned through awareness of consequences, which impact the environment to impact ego and the recursive stimulus response chain containing the ego, within the environment and external social stimulus.  Such that a person’s behavior, once influenced, continues to be self-reinforced by behavior that both influences and is influenced by personal factors, relational frame theory, and the social environment.  This is also evident in Catania’s selection of the capacity to learn as individuals pursue passions, not what individuals have been aversively conditioned against.  Actions do not have direction as affected by repercussions; rather behavior is complicated and cannot be limited to environmental and individual means.  This behavioral phenomenon consists of environmental and individual elements woven together in function and to function; exemplified in this research as the different and varied cognitive behavioral paths that gathered people with math anxiety in one place, and people without math anxiety in another.  

            The present study was conducted to examine the relationship between the use of a countdown procedure in childhood, as a way to decrease undesirable behavior, and math anxiety.  The hypothesis for this study was developed based on the theories of conditioning (classical, operant and operant-respondent), stimulus generalization (Watson, 1920), and reciprocal determinism (Bandura, 1986).  Hypothesis 1: If a participant self reports on the inventory that they remember an authority figure using a countdown procedure to extinguish undesirable behaviors in their childhood; they will be more likely to also self report having math anxiety than those participants that do not self report remembering the use of a countdown procedure in childhood.  The research’s initial premise was based on behavioral psychologies principles of operant conditioning and stimulus generalization; operant conditioning was measured as and represented by a higher incidence of math anxiety in the population of people who had been exposed to a generalize-able stimulus identified as a parental or authoritative issued countdown procedure implemented to extinguish unwanted behavior during the individuals in the sample population’s youth, as self reported by the individual participants of the study. 

Method

This experiment examined practical applications of conditioning via exploration of relationships that exist between categorical variables defined as individuals who self report math anxiety and as individuals having experienced mathematically related extinction techniques implemented by an authority figure as a child. The study included what has classically been referred to as deception by misleading with relationships of world view, life experience, and upbringing. This was done to mitigate false memories prompted by the self inventory due to negative or positive consequences inherent in the recall algorithm of replying to the self report by balancing negative, neutral and positive stimuli of the inventory, thereby burying the true goal/data within neutral and random yet relative concepts.  There was deception present in the informed consent and dissemination material so as to avoid any internal and external validity issues that may arise. Studies on how negative emotion cause false memories were used to account for memory processes that are measured in the conjoint recognition paradigm (Brainerd, Stein, Silveria, Rohenkohl, & Reyna, 2008).  False memory was operationalized as recollection rejection, phantom recollection, false acceptance of similarity judgment and response bias.  While true memory was recognized by identity judgment, correct similarity judgment, and response bias acceptance was used for verbatim, gist, and verbatim plus gist questions (which were not explicitly listed in the article). There were four findings about how valence affects false memory, true memory and response bias; all were applied to the research conducted concerning math anxiety and any conditioning that may exist in perpetuating it. 

Participants

Of the 95 participants 94 self reported, that there were 49 male respondents, 45 female respondents, and one participant who did not respond; an average age of 29.8.  The Population was a slightly left shifted Gaussian distribution.  The race/ethnicity portion of the questionnaire was left blank and without instruction, there were six people who left this space blank.  79 people self-reported Caucasian or White; two people self reported Middle-Eastern decent, one Native American, one Creole and another Cajun; and five from Eastern Asian: Japanese, Korean, Chinese, Singapore, and Thai.  Participants were all able to read, write and respond in English, were willing volunteers, and were limited to the population with internet access.  An overwhelming majority would be demographically categorized as white college students and white Midwestern WASP’s.

Materials

Informed consent, demographic information gathering, and a series of three self report inventories, and debrief were conceived of, generated, and loaded into and onto the survey monkey software as a service (SaaS) website.  The informed consent deceived participants into thinking and believing the three self report inventories were gathering information concerning worldview, life experience, and upbringing.  A tabulation of the materials used, arranged in a matrix organization, are displayed in appendices A, B, & C.  The survey is located at this link: http://www.surveymonkey.com/s/LWDRPLB. 

Procedure

The study was conducted via Survey Monkey as a self report inventory.  The Inventories were distributed via an online link to Survey Monkey and were made available on the Facebook, twitter, tumblr, blogspot, read write web, and wordpress of the researcher.  The survey link was also disseminated by an email sent out to the fall 2011CEM 342 Estimating II class and to the fall 2011 PSY 301 section eleven class both through blackboard website of Oregon State University Corvallis Campus in Oregon and through the email of Nyla Gerhardt, the researcher’s mother; the email forward is still accumulating data.  Participants were initially informed that it was a survey exploring relationships of world view, perception, and upbringing.  This was done to mitigate false memories, negative, or positive consequences inherent in filling out the self report inventory by balancing negative neutral and positive stimuli and burying the true data in with related ideas.

For procedural, visuospatial, timing and other possible references the survey is located at: http://www.surveymonkey.com/s/LWDRPLB.  Participants clicked on the link to open it in their web browser and follow the instructions presented as they are presented until the time they chose not to.  The initial informed consent is part of the deception and frame of reference manipulation as shown first on the first screen.  The second screen is for the data entry of self reported demographic information.  The next three screens were matrix self report inventories balanced across positive, negative, and neutral salience and valence (Brainerd, 2008), to ensure valid and reliable data recall.   

The third screen begins and consists of what is counted as the sixth ‘question’ formed as a fill in the blank framed as “I am” followed by a matrix inventory of nine items on the Y-axis: listening, math, job, public speaking, writing, school, being myself, reading, getting lost; the participant self identifies weather they are good, acceptable, or bad at these items along the X-axis, or a combination such that the three choices can generate eight different codings and six different scorings.  The specific scoring and coding instructions are listed in the coding and scoring instructions.  For this round of this research the third screen and sixth question is present primarily to neutralize priming effects or false memory while staying consistent with the overall deception explained in the informed consent, no variables are currently operationalized from this screen of the survey.  

The fourth screen and seventh question posed as a fill in the blank of “I feel” is another matrix inventory of eleven different participant feelings along the Y-axis and two responses on the X-axis either positive or negative for the presence of the feeling investigated.  Each variable was chosen contingent on its positive, negative, or neutral valence (Brainerd, 2008) in order to balance them; with context identified as part of the condition and emotional response presented with two choices that can be scored four different ways.  For this round of this research the majority of the information on the fourth screen and contained in the seventh question is present primarily to neutralize priming effects or false memory while staying consistent with the overall deception explained in the informed consent.  The only variable operationalized was the fifth line on this screen where participants could self-report their feelings of math anxiety, contained in question seven of the survey for this round of this research.

Screen five is the last matrix inventory framed by the fill in the blank question of “I remember” with eleven different memories along the Y-axis that again have two choices on the X-axis either remember or remember not, four possible codings, and four possible scorings. The memories vary in intensity, context, situation, and other forms of variance.  The specific scoring and coding instructions are listed in the coding and scoring instructions.  For this round of this research the fifth screen and eighth question is present primarily to neutralize priming effects or false memory while staying consistent with the overall deception explained in the informed consent.  The only variable operationalized was the eighth line on this screen contained in question eight of the survey for this round of this research.   Multiple variables were presented to increase the probability that the two variables the research pursues were valid, reliable, and did not suffer from random sampling error by dividing it among and across variables that were not operationalized, this time.  Using multiple variables was also advantageous and congruent with the balancing of saliency and valence (Brainerd, 2008). 

The final screen is the debriefing form.  The debriefing form was used to inform the participants of the true nature of the research, inventories, and demographic information.  Then volunteers are done, and free to leave the terminal, if they haven’t already. 

Results

From the 95 participants, 94 reported their sex on the inventory.  The sample consisted of 49 male participants, 45 female participants, and one participant whom abstained from answering; there was no unusual distribution across the data set.  The sample population had a mean age of 29.8 years old. The population was a slightly left shifted Gaussian distribution.  The race/ethnicity portion of the questionnaire was left blank and without instruction, there were six people who left this space blank.  Seventy-nine people self-reported being Caucasian or White; two people self reported being of Middle-Eastern decent, one Native American, one Creole and another one Cajun; and five from Eastern Asian: Japanese, Korean, Chinese, Singapore, and Thai.  The Null hypothesis was that math anxiety is socio economic, cultural, linguistic, biological, or of other non- cognitive behavioral nature.  Contrasted with the hypothesis to be tested was that parental countdown procedure primed and condition people for math anxiety.  Of the 52 people who reported receiving a countdown procedure as a behavior extinguishment technique, 29, or 55.8%, also reported math anxiety (Table 1).  Of the 43 people who did not report receiving a countdown as a behavior extinguishment technique, 2, or 4.65% also reported math anxiety (Table 1).  This is more than a tenfold differential multiplier. The Null hypothesis was rejected twice; once by the CHI-square test of c² (1, N = 95), p < 0.001; providing grounds for further research (see Figure 1).  And the null hypothesis was checked with a two tailed T-test conducted using the rates of 4.65% and 55.8% from between the two groups who did not receive the countdown, and those who did receive the countdown.  This reduced the possibility of type I or Type II errors by increasing the degrees of freedom resulting in t(93) = 3.43, p < 0.01.

Discussion

None of the demographic information collected was relevant in terms of deviating from what may be considered a null hypothesis, although it could be noted that the population is overwhelmingly Caucasian.  The hypothesis that there was a correlation and causation, is and was supported dually through the research conducted investigating the correlation of self reported math anxiety and the self reported presence of an authoritative countdown procedure in youth by the CHI squared test results from table 1 and figure 1.  A two tailed T-test was also conducted using the rates of the two groups reduce the possibility of type I or Type II errors by increasing the degrees of freedom and comparing the rate of incidence of math anxiety as displayed in table 2 and figure 2.  Using the two tailed T-test essentially reduces the 2x2 factorial design to a 1x2 matrix in order to compare the incidence rates.  The other supporting column of the overarching research is built upon the foundations of behaviorism as a pathway.

This experiment examined practical applications of conditioning via exploration of relationships that exist between categorical variables defined as individuals who self report math anxiety and as individuals having experienced mathematically related extinction techniques implemented by an authority figure as a child. The study included what has classically been referred to as deception by misleading with relationships of world view, life experience, and upbringing. This was done to mitigate false memories prompted by the self inventory due to negative or positive consequences inherent in the recall algorithm of replying to the self report by balancing negative, neutral and positive stimuli of the inventory, thereby burying the true goal/data within neutral and random yet relative concepts; based upon valence research (Brainerd, 2008).

Respondent behaviors are those that are reflexive and occur automatically to previous stimuli and are generally and typically referred to as involuntary (Pear, 1984).  Who can salivate, blush, laugh or cry on command. Some method actors and improvisationalists may appear to do so after they have learned how or expressed the ability.  Operant behavior (Skinner, 1953) is controlled by consequences and is sometimes referred to as voluntary.  When asked to do so some can readily sit, stand, walk, and talk, whisper, and so on.  This is in contrast to conditioned reflexive responses which can involve smooth muscles and glands that are important to the functioning of internal bodily processes such as relaxation prior to sleep or arousal to a threatening situation; like a math test.  Respondent and operant conditioning procedures appear to influence two different kinds of behaviors (Pear & Eldridge, 1984).

The Little Albert case study experiment (Watson, 1920), illustrated the empirical evidence of classical conditioning in humans.  The same study proved to be exemplary for stimulus generalization.  Stimulus generalization refers to the natural procedure of reinforcing responses in the presence of a stimulus or situation and the effect of the response becoming more probable in the presence of another stimulus or situation (Watson, 1920). This specific research investigated the possibility of generalization of numbers, mathematics, and related ideas.  And this grouping of ideas as possible stimulus generalizations from initial classical and operant conditioning presented in the countdown procedure as not only a source of priming, but also as the frame for the introduction of a new idea on a piece of the mind otherwise known as the impressionable tabula rasa; the portion of the mind apart from nature where nurture is to be placed in a child’s mind. 

Valence was balanced in the self report inventories based on two experiments.  Valence had a simple directional effect on false memory in both experiments.  Participants displayed more false memory for negative critical distracters than for neutral ones, and more false memory for neutral critical distracters than for positive ones (Brainerd, et al, 2008). Averaging over the experiments, the false memory increased from positive to negative valence was 1.38 standard deviations.  Secondly valence had the same directional effect on true memory with false memory increasing from positive to neutral to negative targets, although the effect was smaller at just .73 standard deviations.  Thirdly valence produced a qualitative shift in the net accuracy of memory as indexed by the difference between false memory values for targets versus critical distracters.  True memory exceeded false memory for items with positive and neutral valence, but not for items with negative valence.  Lastly, both the memory and the bias parameters in the signal detection analysis showed a coherent picture of valence effects.  Negative valence relative to positive or neutral valence elevated both true and false memory, while lowering response bias (Brainerd, et al, 2008).  Considering the negative salience of Math Anxiety and childhood punishment it was important to account for confounding factors prior to research to maintain internal validity of the self report inventories necessary to conduct the research efficiently.

What has traditionally been known as the quasiexperimental design was not used in this research; rather it was a natural treatment as quasi independent variables of countdown and math anxiety.  It is also a before and after design in that the memory of the countdown occurred temporally prior to the current frame of feeling math anxiety on math tests.  To some degree this nuance may cater to a younger population with higher memory function, limiting the sample population as the university sampling procedures did; also increasing validity of recall.  Before and after designs are very similar in their analysis before and after a treatment.  The treatment in this case was the administration of the countdown procedure to reduce and eliminate undesired behavior.  The reliability of this information is then called into question.  The answer is that it was accounted for to some degree in the balancing, modeling, and focus of the self report inventory administered.  This form of before and after design is the interrupted-time-series design often used to examine observations before and after a naturally occurring treatment.  A fact which has never been more true; given that it occurred before the experiment was conceived of in some cases.  The intriguing aspect of this distinction is that a truly natural treatment is only possible in a quasi-experimental design.  This quasi-experimental approach is very different from similarly structured simple two dimensional factorial experiment considerations in which variables are defined conceptually, operationally, and existentially a priori with groups formed by random assignment; as opposed to self organizing systems, networks, and convergent realities assessed by quasi-experiments and their truly infinite variability of contributing independent variables. 

At some point all the individuals in the study had a choice, as they still now have, to either accept or reject the frame imposed, the choice given, or decision of what to do in response to a stimulus.  From deciding what to do about the familiar frame obligated choice, and direction every single living person progresses through life, building their life by and in the moment. Constructivist theories acknowledge this experience of cultural exploration, of cultural differences; accordingly this research would be negligent to not note Hong et al. (2000) who framed quasi-experimental research in what has now been named constructivist theory.  Constructivist theory conceptualizes culture as the infinite blend of techniques, symbols, images, metaphors, procedures, practices, language and language use applied in, to, from, and for human life prevailing in a given group, civilization, community, niche, or society.  Constructivism is active in all participants as the pathway they chose in their response to their stimuli defines the path they take in behaviorism and fuses with the person to define the culture they identify with and eventually gravitate to.  People with math anxiety tend not to choose cultures, careers, or work where the typical response is that of anxiety.

Many threats exist to the countdown to math anxiety study conducted on the external level; specifically the innumerable confounding variables that may have conflicted, contradicted, or contributed to the measure of math anxiety, including the cultural influences of the parent or authoritarian principle caregiver.  A poor teacher, community, or period in an individual’s life coupled with bad timing could nullify all results; as could a culturally confined and biased sample that is 80% Caucasian.  Further constraining and possibly mitigating factors include over half of the survey responses came from one email forward via Nyla Gerhardt that may or may not be composed of overwhelmingly white Anglo-Saxon Protestant Midwestern plains dwellers; an email forward that is still gaining in terms of information and momentum.  The self report inventories gave no explicit or implicit direction, for it was assumed that previous experience would guide individual intuition.  At this time there is no meta-behavioral method to ensure validity or reliability of intuition, only distantly related meta-cognitive methodologies.  A longitudinal design would be better suited to assigned causalities although the research conducted provides grounds for the continued investigation of external factors, longitudinal, temporal, cross sequential, multi cultural, environmental, or otherwise.  The self report survey marketed as a survey was also limited to the people who would respond to such an inquiry via the internet.

Internal threats also exist, especially if the balancing or ordering of the extraneous variables used to balance salience is not actually as balanced as it may seem.  This could be especially true for suggestive participants or because of the motives of an adept researcher.  The instructions were not clear, or even present as recognized, until they were.  The use of technically transcendental writing similar to that of the American transcendental movement was also implemented.  Distributing the survey to a population of consisting half of college students towards the end of an Indian summer could affect data results; as could the economic tone or any number of factors. 

The self report survey disseminated through survey monkey was written in the first person to elicit introspection as opposed to the projection that maybe present in the use of second person pronouns, like ‘you’.  False acceptance of similarity may have affected the data based upon the arrangement, linguistics, and individual differences perceived from the self report inventory.  First Person was used in the form of the pronoun frame implemented as “I”.  Historically surveys, questionnaires, and data collection were limited to paper transactions where people would interact.  This existential frame of didactics, interaction, dualistic partnerships, multiple people, or other arrangements and dynamics led to the primary use of second person pronoun implementation on self report inventories and data gathering as framed by “you” and other consistent pronouns.  Whereas this inventory was to be sent out to individuals interfacing with a machine, a computer, in some form of human factor interaction; this opportunity was taken in an attempt to inspire introspection of being alone and framing in the first person in a self report inventory as opposed to didactic and reciprocal sharing that occurs in human interaction artifacts from past research in second person framing.

The initial deception was not so much deception as it was frame manipulation.  Upbringing, life experience, and world view are a large set.  Contained within that set are the identified variables of countdown procedure, as a form of upbringing, and math anxiety, as a form of life experience or worldview.  The first self report inventory located in Appendix A was the contained the most brevity.  Simplification allows the participant to grasp the initially sophisticated matrix design.  The first self report inventory’s initial frame is only three letters “I am”,  displayed in the upper left hand corner as is common practice for you and other readers and writers of English.  The next step in the mad libs matrix self report inventory was choosing “good”, “acceptable”, or “bad” at a noun that was displayed down the left justified y axis of the page.  “Good”, “acceptable”, or “bad” were presented orthogonally across the page below the initial frame.  Below this were the afore mentioned “at a noun’s” displayed down the side of the left justified y-axis of the page.  Participants were limited to people with internet access, which could read, and think through a matrix self report inventory similar to others they may have seen in the past.  Six surveys were not completed and were thrown out, participants may not have understood, some may have been voyeurs, or something else.  Regardless confusion and misunderstanding can be conflagrating variables in any study.  Participants essentially created nine structurally consistent and introspectively framed “I statements” as a self report.  On the next self report, presented in Appendix B, the frame was expanded and complexity was added throughout the balanced word salad selections. The material was presented in the same format although the initial frame on that page is “I feel” and it was not formatted to build a sentence as the previous self report inventory had been.  Feelings may be more complex so they were added as a way to build on the priming and learning from the first self report inventory, but was kept simple to make the tasks fast for the participants in order to diminish distractions or thoughts that could interfere with data collection that takes too much time.  This could also be a source of confusion for participants.  Once the participants mind was sufficiently primed for introspection by the format of the first two self report inventories the third and most complex sentence structures were presented in the third self report inventory. The third self report inventory is initially framed as “I remember” the format displayed in Appendix C does not contain consistent or similar sentence structure throughout the eleven sentence endings following either “Do remember” or “Do not remember”.  The difference is that the initial frame of “I remember” is disjuncted on the third self report inventory and is not used in the sentence as was the case with the first self report inventory.  This was done because the cognition framed by the language required a person to remember in the past and report in the present, for participants who noticed this difference this inventory may have been confusing.  In future studies a debrief that gathers data about the topic of disjuncted and separate yet consistent frames within the matrix structure of the self report inventory may prove insightful.  Especially given that participants may notice the differences between the different inventories, another potential distractions and source of variance in the data collection process.  Disjuncted was used to describe and reference cognition’s response to the written language perceived as an almost musical nature in thought, adverbially, colloquially, and as well as in terms of logic. 

Once mitigating factors such as false memory were neutralized the simple investigation of a 2x2 factorial design concerning math anxiety becomes much easier.  Conditioning was measured as what was presented and represented by a larger score for the operationalized independent variable presented at line eight of question eight “I remember…” my parents issuing a countdown when I was naughty” represented as and measured as a response of the stimulus for conditioning being scored and coded as listed previously in the scoring coding instructions.  The conditioned response represented by a larger score for the operationalized dependent variable presented at line five of question seven “I feel math anxiety on math tests” represented as and measured as a condition of the response from conditioning.  All other materials are present primarily to neutralize sources of error variance specific to this study such as priming, false memory, and participant manipulation, while increasing internal and external validity. 

Backward chaining (Myerson, 1997) is a commonly used technique both in the rearing of children, the education of mathematics, and game theory.  Backward chaining is a method for establishing a chain, (a behavioral chain in this instance) in which the last step of the chain is taught or modeled first.  Then the nest available step is linked to the last and previous step, and so on until the chain is learned.  In both mathematics and behaviorism the goal behavior and necessary solution are synonymous as the starting point for backward chaining.  The unfortunate coincidence found in this study elucidated the confounding nature present in the harmonics of sociocultural phenomenon; where different behavioral paths (individuals given momentum by the countdown eliciting the self reported state of math anxiety) delivered unwitting individuals to where they now stand.

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Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety.  Journal for Research in Mathematical Education, 21, 33-46.

Hong, Y. ~Y., Morris, M. W., Chiu, C. ~Y., & Benet-Martinez, V. (2000). Multicultural minds: A dynamic constructivist approach to culture and cognition. American Psychologist, 55, 709-720.

Legg, A. M., Locke, L. J. (2009). Math performance and its relationship to math anxiety and metacognition. North American Journal of Psychology, 11, 471-485.

Myerson, R.B. (1997) Game Theory: Analysis of Conflict: Cambridge Massachusetts, Harvard University Press

Pavlov, I. P. (1927). Conditioned Reflexes: New York, NY: Dover Publications.

Pear, J. J., Eldridge, G.D. (1984). The Operant–respondent distinction: Future directions. Journal of the Experimental Analysis of Behavior, 42, 453-467.

Skinner, B. F. (1938). The Behavior of Organisms:  New York, NY: Appleton-Century-Crofts.

Skinner, B. F. (1953). Science and Human Behavior: Oxford, England: Macmillan.

Watson, J. B. (1920). Conditioned emotional reactions.  Journal of Experimental Psychology, 3, 1-15.

Zimmerman, D. W. (1957). Durable secondary reinforcement: Method and Theory.  Psychological Review, 64, 373-383.

Table 1

Numerical Measurement of Responses

Raw data	math anxiety	no math anxiety
countdown	29	23
no countdown	2	41
total	31	64
scored data	math anxiety	no math anxiety
countdown	261	69
no countdown	6	41
total	267	110

Table 2

Percentage of positive math anxiety presence from affirmative and negative presence of countdown procedure, or rate of incidence of math anxiety between groups

	Countdown	No Countdown
Math Anxiety	4.65%	55.8%

Figure 1

Figure 1. Numerical Results of Self report Inventory (In number of responses per condition) The Null hypothesis was rejected by the CHI-square test of c² (1, N=95), p<0.001; providing grounds for further research.

Figure 2

Figure 2. Incidence of Math Anxiety between countdown condition groups in percentage of sample population. Null hypothesis was reject by T-test of t(93) = 3.43, p < 0.01.
Appendix A

I am…
	Good	Acceptable	Bad
At listening
At math
At my job
At public speaking
At writing
At school
At being myself
At reading
At getting lost

Appendix B

I feel…
	Agree	Disagree
Apathetic towards punishment
Nervous before public speaking
Like dancing when I hear music
Lost when looking at maps
Math anxiety on math tests
Like getting married someday?
Happy when I’m winning!
Average, sometimes
Afraid of being alone
Blessed

Appendix C

I remember…
	Do remember	Do not remember
Going on fishing trips as a family
Getting in trouble at school
Daydreaming
Waiting in lines with people
Getting hurt: pulled muscles, broken bones, cut, physical pain of some sort
Feeling loved
Learning from mistakes others have made or I witnessed
My parents issuing a countdown when I was in trouble
My parents rewarding me when I did something good
Wanting to run away, or actually running away
Sunrises and Sunsets

Legalism and Legalese: Analog to Digital Conversion?

Originally posted August 10th 2012

My name is Scott Gerhardt.  I am not a lawyer and neither is Stephanie (the woman to whom I am married). I do not call her 'my wife' because 'my' is a possessive pronoun and I do not consider her to be my possession, I consider her presence a gift; although she does refer to me as "my husband", but I digress...  

I have argued and won cases in court over property law issues as the plaintiff and have argued and won cases as a defendant. But the other day an odd legal issue passed us by and I would feel doubly derelict and negligent in allowing it to occur without sharing the possibilities and processes for the benefit of you, the reader.  As Maya Angelou has been quoted as saying: “There is no greater agony than bearing an untold story inside you.”  Stephanie and I co-wrote this blog post from my perspective, just for a sense of consistent context, content, and clarity.


The hearing or arraignment happens as the first court appearance which is all the further Stephanie made it before pleading no contest. After the first appearance the process can take many directions, dependant on what happens, how the law is or is not interpreted, pleas, and the judge’s decision. I did not go to court with my wife because I consider Stephanie to be a capable, cognizant, confident person who I have faith in and trust.
Stephanie was in court for having expired tags and what the officer on the scene considered not proof of insurance. We had no money for registration or for printer ink to produce proof, or for the fines levied. Stephanie is and was resourceful enough to use her smart phone to access the servers at GEICO; providing a digital proof of insurance that I consider not only more difficult to forge but which is more current than any insurance card. If this wasn’t the case then: Why do the police have access to double check with their squad car communication equipment laptops, and intranets? 

Furthermore ORS 742.447 was enacted into law by the Legislative Assembly but was not added to or made a part of ORS chapter 742 or any series therein by legislative action requiring a 'card form' of insurance proof. 
ORS 806.011 Insurance card required; rules. An unexpired card issued as provided in ORS 742.447, or other current proof of compliance with financial or future responsibility requirements approved by rule by the Oregon Department of Transportation, shall be carried in each motor vehicle that is operating in this state and that is not exempt from compliance with financial or future responsibility requirements. Failure of the driver of a motor vehicle to show a valid card or other proof of compliance when asked to do so by a police officer is reasonable grounds for the officer to believe that the person is operating the vehicle in violation of ORS 806.010 was violated although 806.012 was not violated.  The judgement as to what constitutes 'other proof of compliance' was delegated to ODOT, their lack of action has allowed jurisdiction to fall to the officers of the peace on patrol.

There is a gray space for digital proof that is fulfilled under the letter of the law despite not being directly addressed by the statute.  ORS 806.011 Insurance card required; rules. An unexpired card issued as provided in ORS 742.447, or other current proof of compliance with financial or future responsibility requirements approved by rule by the Department of Transportation, shall be carried in each motor vehicle that is operating in this state and that is not exempt from compliance with financial or future responsibility requirements. Failure of the driver of a motor vehicle to show a valid card or other proof of compliance when asked to do so by a police officer is reasonable grounds for the officer to believe that the person is operating the vehicle in violation of ORS 806.010.  Therefore ORS 806.010 was violated although 806.012 was not violated. ORS 806.012 was what was written on the ticket.  From these facts it could be considered that there is a gray space for digital proof that is fulfilled under the letter of the law despite not being directly addressed by the statute. 

Don’t get me wrong, I acknowledge the necessity of society and civilization to enforce subscription to insurance companies in order to protect each and every one of us from each other fostering a culture capable of supporting mutual faith and trust. I also acknowledge the security provided by digital means to ensure that insurance is carried by al drivers. These facts are structured so as to also acknowledge that the officer on the scene who stopped Stephanie knew she had insurance but chose to write her up under ORS 806.012. ORS 806.012 does not specify what proof of insurance is or is not other than being current, which digital proof always is. 
I thought I had conveyed this idea to Stephanie clearly, but in her misunderstanding of both the ticket and the court process, led to her pleading no contest. Stephanie claims the judge also did not allow her to show that we had since printed proof of insurance and that vehicle had been registered. Both tasks our children partook in to help them learn how to function on their own someday. Paxton is still proud of putting the registrations stickers on the license plate.

The problem now is that despite my belief, and the courts belief that Stephanie knew what to do, why, and how; she plead no contest. Stephanie is book smart, and I assumed we watched law and order because she knew what was going on. She graduated Magna Cum Laude in three years with a degree in psychology from WOU. But she did not understand what was happening and now we have over $450.00 in fines.  Stephanie explains what happened as this:
 “The ticket that I received was for having expired tags and not carrying proof of insurance. I attempted to show the officer my phone with the insurance information on it but he refused to look at it. Instead he told me that he had written me a ticket for the two things, but that the insurance was a correctable violation. He informed me that I could take the ticket and this piece of paper (which he tossed at me along with my license and registration) to the police station with my printed proof of insurance and the fine would be dismissed and I would have to pay $35. Scott and I both went down to the police station to talk to them about my digital proof, and got nowhere. We did not even have the $35 to pay for the ticket to be dismissed. Now, in my previous experience with traffic court, I had witnessed such “correctable violations” be dismissed in court with no fees, so I thought that would be my answer. I decided to plead no contest because while I was not guilty, I also did not want to contest the charge because I believed that the judge would see that I had printed the proof and would dismiss it. That is not what happened. She asked me if I had gotten insurance, and I told her that I had always had insurance, and that I was currently holding the printed proof that the officer was asking for. She did not allow me to say anything further, and instead imposed close to the maximum penalty even though I have a very clean driving record. I realize now the implications of pleading no contest, however at the time I did not have a clue. I left the courthouse feeling sick to my stomach knowing that I was now responsible for fines that I knew my family can not afford to pay, and for something that I did not do wrong in the first place.”  

Personally, I was excited that the possible legal interpretations and distinctions that could be made to improve the function of legalism, simplify procedures for officers of the peace, and improve citizens’ lives by simplifying processes/procedures/policies. I failed my wife and the people of the community I live in by not communicating the problem with my wife. We discussed the solution and I assumed this meant Stephanie understood the problem. But when faced with the problem in court she panicked and now the people who are truly punished are our children.


UPDATE:  GEICO and Oregon's legislature have made some unanimous changes, other states might follow.

The Value of the Philosophy of Science

Not everyone can be an expert in biology, computer science, chemistry, electrical engineering, genetics, kinesiology, medicine,  physics, psychiatry, whatever, or zoology (in alphabetical order), but we could all benefit from a general grasp of various scientific ideologies, their epistemology's, and philosophies.   The published journals, papers (peer reviewed and otherwise), and general treatises which record and recapitulate the progress of human thought concerning explanation are open not only to those residing in Olympus, nor are they reserved for academically trained readers, but such communications are for all of us.  The works of Aristotle, Spinoza’s Ethics, and even Wittgenstein’s Tractus are less readable now than when they were written.  The Proceedings of the Royal Society’s literature are as obtuse to many as when Pepys, Dryden, and Evelyn were fellows.  In consequence, there have grown up two classes of writings that are needed more now than ever before, on which a non-scientific reader has to rely on for wisdom, understanding, and discernment.  For any of us there are works of popular science where theoretical advances are explained in a way crafted to avoid technicalities; and for students of philosophy there are books and articles on logic in which the nature and problems of some sciences are discussed as deduction and induction based upon application of the scientific method.

Many of these books discuss first the premise of logic, applications of set theory, number theory, grammar, causality, Boolean algebra, Lie algebra, Voronoi diagrams, Venn diagrams, algorithms, calculus, statistics, and many other tools.  Whether the results of the sciences are true or only highly probable, the uniformity of nature, the accumulation of confirming instances, Mill’s methods, and the probability-calculus form the basis of most laws, theories, and expositions.  But to anyone with practical experience of science there is a curious, almost mystical, air of unreality concerning the appearance of the results.  Lucid, erudite, and carefully framed as the ideological structures might be yet somehow missing the universal mark of the absolute.  It is not that the statements are untrue fallacies, but rather that they appear irrelevant when taken out of context. The hypothesis (null and otherwise) that are impeccably written with eloquent mathematics and rational discussion are often perceived as having no application or bearing on everyday life.  Not since the discovery of fire has a scientific idea’s application and conflagration been instantly apparent.  Meanwhile the actual methods of rhetoric employed are rarely examined.  For example, writers such as Kuhn, Poincare, and Hickey recognize that one must not take too much for granted.  Several years before Einstein developed his relativity theory the mathematician Poincare postulated a non-Euclidean physical space and claimed that physicists had two choices.  Either to accept non-Euclidean geometry as a description of physical space or they can preserve Euclidean geometry for the description of physical space by adopting new physical laws stating that all solid bodies undergo certain contractions and expansions as later noted by thermodynamics and other sciences, and that light does not travel in straight lines.  Poincare maintained that physicists would always choose to preserve the Euclidean description of physical space, and would claim that any observed non-Euclidean deviations are due to the relative expansion or contraction of the instruments of measurement and to the deflection of light rays, no matter how miniscule, yet noticeable.  Einstein’s choice of the Riemannian geometry and physical laws for measurement were based on the resulting simplicity of the total system of established physics.  Relativity theory using Riemannian geometry greatly simplifies physical laws by the implementation of geodesics, such as the gravitation as a force is replaced by gravitation as a function of geometrical structure of curved space.     While many of us tend to assume some familiarity with the things that thinkers, scientists, or celebrities say and do glossing over the details that support the really intriguing philosophical points that follow.

This is an attitude that exposes each of us to cognitive biases, logical fallacies, or other dangers.  For if an individual has too simple an idea of what constitutes a statement, proof, or argument then philosophical inconsistencies occur that have no application other than humorous anecdotes ad absurdum.  If we are to take for granted that “opals and pearls are simply white” or that “Men do not require instruction” it could be concluded that appealing to such laws rest on the presupposition about the reliability of a subscription to gross generalization weekly.  But unless we are to see with clarity what the laws of nature are in practice who can decide the accuracy and precision of a proper conclusion?  The laws of nature cannot fit into the traditional array of logical categories with their corresponding criteria, leading to specialization in discussion within further refined sciences; ideological refining as an iterative and recursive process that also requires interdisciplinary communication to ensure compatibility, consistency, and validity for future applications.  Similarly anyone can think about the mechanics of causation and its place in modern sciences indefinitely, until it is noticed just how rarely the word ‘cause’ is employed in the scholarly works of professional researchers or scientists.  There is good reason for this rarity, a reason that if ignored is to divide reality from the philosophical discussion of scientific arguments.  

A student of philosophy benefits from an introductory education of the types of arguments, proof, and methods scientists employ in practice and how these are similar to those traditionally applied by theologians, logicians, and other orators.  To what degree are the examples in a logic book congruent with the practice of scientists, and what are the implications on the rest of us?  Are we to deconstruct these problems in a customary fashion and attempt to propound some novel solution; or are we to view the problems themselves as arising from naiveté conceptions that have existed since their inception.  How are we to conclude that an explanation is acceptable and therefore applicable?  What sort of impression must an expression perform to qualify on the level of Newton’s Second Law of Thermodynamics, or as a law of nature?  How does this differ from a proposed hypothesis?  Is the difference merely a matter of degrees of a confidence interval in the classes of a proposition, or is a distinction to drawn on other grounds?  And what role does mathematics play?  As for new entities in the sciences that are so often discussed: the Higgs-Boson, patented genes and their genetic markers, Quantum-computing, or what have you.  Are those things thought of as actually existing, and when are they explanatory devices?  These are all questions whose answers are easy to be mistaken about, unless we are to pay sufficient attention to the actual practices of scientists.  The rest of this writing will examine the features which must be pondered in order to settle some questions.

The difficulties that do arise between understanding, educational entrainment, and most individuals understanding on popular science are rather different.  Within this facsimile of an authentic scientific document there can be little to no doubt that what is discussed if rather different.  The cognates of various ideas are not only discrete, but are also fair game along with appearance, perception, cognition, behavior, communication, linguistics, humanities, mathematics, anthropology, agriculture, architecture, every and all other books, articles, and recapitulations on books of popular science that might otherwise be defined as rather different.  As for me, and my point of view there is no doubt that authentic science is simultaneously being discussed; but the terms by which these ideas are first presented are not as discrete nor as explanatory as first they might seem to a tailor.  There is a tendency for those philosophical writers within this field to explain to the readers only about the models, conceptions, and formulations, employed in a novel theory instead of first giving readers a firm anchor of facts of which the theories explanations are based and afterword illustrating to the reader the method by which the manner the theories fit the hierarchy of facts.  

Recall, for instance, the means by which Sir James Jeans and Sir Arthur Eddington took to spreading the non popular belief and thought that the theories of Physics based upon Isaac Newton, Leibniz, Spinoza, Descartes, Poincare, Copernicus, Bacon, Feynman, Einstein, Democritus, Socrates, Aristotle, Pythagoras, Sophocles, etc, etc, et, all of physics, modern, post modern, and everything else that will come to be.  Because too often those philosopher of science focused upon that which would otherwise be declared as comparatively inessential, what is introduced to the reader as predefined conceptions, particular models, or theories used to describe immanent phenomenon even when failing to do that which is essential, namely to elucidate the measurable and mathematical function of such adopted variable as they are derived into models, theoretical conceptions and the rest.  The well known two tables account is an established case in point much like an all you can eat buffet.   For a reader to acquiesce to Eddington’s multiplex understanding of ‘the two tables’ upon a surface that is understood as not only a tabletop defined as a case in point  “common-sense, solid table top”, which is also a scientific table top mostly consisting of empty space.  This recapitulation does not particularly assist a reader in the dubious task of what defines an atomic model which is more important to the sciences of explaining the chemical occurrences around us as it might be the atomic theory of matter.  The entirety of such models is to explain that which could not other there unto be explained by traditional models.  Cut off from the phenomenon of the model one can only be mislead, raising further unreal and needless conceptions about what might happen when the tea-tray that supports it is set down.  The same also goes regrettably for those pretty pictures of electron clouds encompassing our mind of atoms like bees which might hum about a blank center in a cathedral, the pictures of your brain as an anagram of our universe, depictions of your white and gray matter as a network of computers and their entwined connections, and rest.  Regrettably in can be said, because we as literary devices certainly have value, and if we were not left to stand on our own feet we might have value, unfortunately that value is defined by the very limitations of the language implemented to transfer such ideas via a written word.  The same also goes for the written word which acts as a searchlight in the darkness, picking up there a pinnacle, a chimney, and in a distance an attic window; the detail illuminated is dazzlingly commensurate even while everything surrounding is caste into even greater obscurity until we are all distracted from the overall proportions with which we have been beautifully presented. 

This is not the worst of which happens when assaulted by the human nature of appearances, appurtenances, reality, awareness, and perception.  At times an attempt to popularize a physical theory might even result in unpopularizing it, for one might ask if it is not reverse psychology if it does not work. As things are elucidation generally operates as a searchlight through the darkness of human knowledge.  For instance blue Jeans relied on finding a happy analogy  which would by itself bring home to its readers the chief features of Einstein’s general theory of relativity. And how did he invite them to think of our universe?  As the three dimensional surface of a four dimensional balloon? As the lack of condensation of anti-matter on the domain wall of  a spinor Bose-Einstein optical lattice? The mislead layperson who had been acculturated to use the word surface for two dimensional things alone, now found themselves instructed to visualize what had otherwise been contradictory.  So it was no wonder that many who agreed to Jeans’ calling the universe a mysterious one; A spectrum of mystification balanced by the confusion idea of unnecessary nothing.  There is no reason that the principles of the Theory of Relativity should not be explained in the terms of an ordinary reader who can make something of Einstein.  Oddly enough, Einstein does this very well.  But Jeans’ method defeated its own end.  Via reduction Jean defeated method by deconstructing the subject and object into that which is too easy and to do with a simile, metaphor, and allegory what no literary device alone can do, to lead many readers to conclude that what you are reading is utterly incomprehensible, thus this should now be set aside as not for you, the reader.  But then how ought you now know as such?

This might suggest that Jeans was merely careless, even if there was more to what than that.  For the fact that such writing picked up upon a point of writing which is redundant and is to the outsider is self-contradictory points to something which the average person must be told about the linguistics of speech as they might be applied to theories.  For when a theory is developed all kinds of phrases in ordinary life are devoid of meaning are given use, many familiar terms acquire fresh meanings, and a variety of new terms are introduced to serve the purpose of the theory.  A scientists, who learns their physics the hard way gradually becomes accustomed to implementing the novel technical terms and the everyday sounding phrases required to confer the source of condensation on a domain wall, or whatever even when less than half aware of what is really happening; as some professors born remark; the building of the languages of the sciences is not entirely a conscious process.  This has its consequence when a scientist has to explain a new theory to the lay person.  For then it is possible to unwittingly use in exposition terms and turns of phrase which can only be understood by those already familiar with the theory.  To the individual trained in the implementation of sophisticated geometry the phrase “three-dimensional surface” might no longer be a self-contradiction, but for those regurgitating it without appreciation to a non-mathematician it is an invitation to incomprehension.  And what happens to three dimensional surfaces like that which we live upon is equitable to invisible light and their constituents.  When scientific notions are being popularized it is necessary to explain the foci of such phrases, instead of making unexplained and untranslated use of them.  

To introduce a valued distinction is now of value.  For a communities adoption of a new theory involves a linguistic shift that can be distinguished between the account of the theory and the application of the new terminology in a participant language sense which is an account in the new terminology by which it is not used but is described by the voyeuristic nature of an onlooker’s language.  Supposing as Wittgenstein said in his ‘Tractus’ that “A physicist tells you that at last the discovery of how to see people in the dark, which no one had ever before known”.  Then you should not be surprised.  If Wittgenstein goes on to explain to you that the discovery of brainwave entrainment by means of gravitational induction is as ancient an idea as communication then you have a right to be surprised if you feel like it.  Then it is a different kind of surprise, not just a mental whirl, because before such a statement one may not just gape open after having been stretched but must ask: “What do you mean?”

An analogy will help to explain misconceptions that might follow if we were to attempt to popularize the physical sciences in such a way. When children are told stories at bedtime they are told about all kinds of people, not just rich and poor, white and black, beggars, and kings, but the more encompassing logically different people.  Some nights they are told stories from history, other nights ancient myths, sometimes legends, sometimes fables, sometimes they might even be accounts of we ourselves have done, other times accounts by contemporary authors.  Therefore when it comes to bedtime stories, this, Caesar, Cleopatra, Scheherazade, Heraclitus, Democritus, Achilles, Sisyphus, the boy who cried wolf, the man in the yellow hat, and Winnie the Pooh all appear at first sight to be on the same footing.  A clever child, no doubt, soon learns to spot from internal evidence what kind of story tonight's story is, and what sort of people its characters are, fabulous, legendary or historical,  But to begin with we must explain in asides what the logical status of each character and story is, saying, “No there aren’t really any talking animals: this is just a made up story”, or “yes, this really did happen, when my father was a boy.”  Unless the child is told these things in addition to the stories themselves, he might not know how to take them; and thus he might bet quite false ideas about the world into which he was born, about its history, its inhabitants, and the kinds of things he might encounter on any day as he turns the corner on the street.  If entertainment alone were needed, the story alone might do.  But the risks of misunderstanding are serious, and for real understanding more is always a requirement.

So in popular science: the average person is not merely ignorant of all the theories of science but is also unequipped to understand the terms in which a scientist will naturally begin to explain them.  To explain the sciences to the average person by giving the intrepid reader only potted theories and vivid analogies, without a good number of thoroughly confusing and logical asides, is like telling a child all of the sorts of stories we do tell children and not warning them as to the pitfalls, variations, and different inconsistencies therein.  Then no child will not know what weights to put on the various things that are said, which of the statements heard about the sciences are to be accepted at face value, and which narratives are misleading preponderances that are never to be met.

Perhaps the nub of the difficulty lies in that the popularizer has at least a double aim.  For most people would like to learn about the theories of the sciences in a language that is understandable; and most would like to learn this as Stephan Hawking has translated the universe “in a nutshell”.  These opposing ends of a spectrum are bound together as part of the same thing which are in practice a conflict.  For a major virtue of the language of the sciences is it conciseness.  It is always generally possible to say what a scientific theory amounts to without using the technical terms which scientists introduce to serve the purposes of the theory, although one can do so only by writing at very much greater length.  If the popularizer is to explain a theory in everyday terms and at the same time put it “in a nutshell”, something must first be sacrificed in terms of the technical accuracy of the premise.  Usually the logical asides are the first thing to go, and drastic cuts follow in the account of the phenomenon which the theory is introduced to explain.  What is even more important is just how much further along in the development of the idea the reader is when presented with the ‘explanation’.  As it is the reader might often be better off if simply left in the dark as far as the matter is concerned, due only to the simplification to the sharp point of Occam’s razor. Once this happens the everyday public individual is given no real entrance to the subject; for until they are told a good deal about the phenomena a real key is of little use if the beholden is unaware of what rooms it grants access to.  There is then no point to being told that Einstein has discovered the metaphorical key to the universe if we are not also informed as to what sort of thing counts as opening said door with said key.

However, something can be done to remedy such a state of affairs.  With the help of a few elementary examples it should be possible to show the common reader some of the more important ideas required regarding the logic of the physical sciences.  There is no reason for anyone to rest content with the ideological nature of the sciences are an inconsistent conglomeration of self-contradictions, like invisible electromagnetic phenomenon, three dimensional surfaces, and mysteries like the curvature of space.  When armed with the ability to ask questions all can penetrate behind the screen of appearance and reality to the living truth.  For the words of scientists are not always what they seem, and might be misleading if taken even slightly out of their original context.  The vital information is what sorts of questions should be asked if one is to garner a satisfactory understanding of a given theory; fortunately this is something which can be shown well with sophisticated and simple examples.  To illustrate what such questions are is the purpose of this writing you the reader are now engaged in perusing.  It will not require that you are capable of quoting the exact words of scientists so much as it necessitates the ability to notice the sort of things they do with the words they do employ.  As Einstein has said: “If you want to find out anything from the theoretical physicists about the methods they use, I advise you to stick closely to one principle: don’t pay attention to their words, fix your attention on their deeds.

This blog post is no different in aim, deed, or execution.  In fact this is merely an experimental foray into the metalinguistics of pronouns, and their subsequent psycholinguistic effects.    Thank you for your time, feedback, and complicit participation.