God, Mathematics and Psychology: Are they all one?

This discussion focuses on psychology and the philosophy of mathematics and will contribute nothing to mathematical thought. Its aim is to introduce mathematics as a creation of psychology. Sophisticated, complex and ever evolving, but nevertheless psychology.

Mathematics translates patterns into reducible parts. These parts form theorems—incremental reasoning based on a chain of formal proofs—that conform to logic but operate beyond logic. Mathematicians argue that these patterns are universal and real and that the interconnecting system of reducible parts is what constitutes mathematics—a language of spatial positioning, geometry, numbers, volume, movement and patterns. These are complex patterns that lead to complex theorems.

Sometimes these patterns exist in reality and prove useful in terms of predicting physical events in the universe and sometimes they are the perfect embodiment of a cognitive world--true forms that exist primarily in our imagination, such as the perfect circle. Sometimes the theorems relate to patterns that are solely--as far as we know, or yet--in the realm of a group of mathematicians’ imagination. Although mathematics is not set-up, by mathematicians, to explain our reality, there is however a symbiotic relationship, in that proofs can come from within the physical experimental world.

The basis for elevating mathematics to more than just a complex system of creating theorems is the role that mathematics was given by Pythagoras (6th Century BC).  Pythagoras believed that numbers were not only the way to truth, but truth itself. That mathematics not only described the work of god, but was the way that god worked. This belief, that mathematics holds an intrinsic truth remains with mathematicians today. They believe that mathematics is the language of the gods. And that is a problem if you do not believe in god or in an over-ridding principle of existence--none that we can understand anyway. Science is by definition both atheist and agnostic despite what individual scientists believe. Most mathematicians behave as deist who believe that God created the universe but that natural laws determine how the universe plays out. This is a Epicurean (341–270 BC) belief that the gods are too busy to deal with the day-to-day running of the universe but they set it in motion using mathematics.

Mathematicians therefore argue that mathematics is a higher order that is found in reality. But there are no examples of such proofs. Mathematicians argue that they are more discoverers rather than inventors. But this dichotomy also seems false. Mathematicians seem to do both, most often at the same time.  The British philosopher Michael Dummett suggests that mathematical theorems are prodded into existence--he uses the term probing (Dummett, 1964). Using the analogy of the game of chess where, “It is commonly supposed … that the game of chess is an abstract entity” (Dummett, 1973). But there is certainly a sense in which the game would not have existed were it not for the mental activity of human beings. It is a delusion to believe that just because we find a pleasing pattern, a game that resonates across cultures, that the reason it is pleasing is because there is a god behind it. But mathematicians argue that chess, or theorems are not entirely products of our minds since there must already be something there to prod. But the obverse argument is equally true that mathematical “truths” are entirely dependent on us since we need to prod them to bring them into existence.

The same is true for language, art, music and other “Third World” constructs—these are incrementally evolving systems and form one of Karl Popper’s ontological tools (Carr, 1977). Third World is where the system that is developed exists beyond the creator. Language is an excellent example, although Third World also includes abstract objects such as scientific theories, stories, myths, tools, social institutions, and works of art. Language is incremental and ever evolving, and is used to help us communicate reality. Within this Third World, language as with mathematics, is also argued to be both discovered or invented.

Theory of language development has oscillated between two schools of thought.  One school that argues that language is culture-bound, known as Descriptivists. And on the other side is the argument that promotes language as part of our biological makeup, known as the Generativists. As a Generativist, Chomsky (1980: p134) phrased it eloquently when he said that, “we do not really learn language; rather, grammar grows in the mind”.  The analogy between formal mathematical systems and human languages is not a new or novel idea. In fact such formal language theory have already been established in its modern form by Noam Chomsky in an attempt to systematically investigate the computational basis of not just human language but has become applicable to a variety of rule-governed system across multiple domains--computer programs, music, visual patterns, animal vocalizations, RNA structure and even dance (Fitch & Friederici, 2012). This symbiotic relationship exists across all Third World constructs: mathematics and music, music and art, art and language and all other permutations. As with mathematics, we refine language with time. Future generations build upon language and mathematics and the only constraint seems to be our psychology.  Mathematics similarly has this incremental nature. The last sentence of a talk given by Fine on mathematics  “The only constraint is our imagination and what we find appropriate or pleasing.”  (Fine, 2012: p27).  What we find appropriate and pleasing is where the psychology comes in and our clue to the inception of mathematics and the description of our psychology.

As a guide, we have to go back to earlier (and more simple) mathematics to understand this principle of “pleasing.” Pythagoras and music is the basis for a convergence between mathematics and psychology.  Pythagoras (6th century BC) observed that when the blacksmith struck his anvil, different notes were produced according to the weight of the hammer. He later discovered that the ratio of the length of two strings determines the octave "that the chief musical intervals are expressible in simple mathematical ratios between the first four integers" (Kirk & Raven, 1964: p.229). Thus, the "Octave=2:1, fifth=3:2, fourth=4:3" (p.230). These ratios harmonize, meaning that are pleasing both to the mind and to the ear. Although this mathematical system breaks down the higher we go up the scale, there was a solution by adjusting the ratio of the fifth so that it is commensurable with seven octaves. Seven octaves is 128:1, or 27. John Stillwell (2006) argues that "equal semitones" or "equal temperament" (p.21), was developed almost simultaneously in China and the Netherlnds, by Zhu Zaiyu (Chu Tsai-yü) in 1584 (during the Ming Dynasty and by the Simon Steven in 1585 and by (Ross, 2001). But the point is that a mathematical rule was developed on the basis of a harmony that we humans find pleasing.

In nature, all sounds are the same. The creator of the universe created all acoustics, all sounds are perfect. Nature cannot discriminate among them since they are all necessary and useful. As such, selecting harmonics is psychological rather than godlike. We like the separation of scales because we can psychologically compartmentalize the sound. We are creatures of order and consistency and prefer to have distinct and distinguishable sounds. In reality there is no such thing as harmonics, we look for it as humans because it is pleasing.

Such psychological preferences are automatic and require no processing and thinking on our part. This automation can be easily be disrupted by playing a tone that is ostensibly ever increasing or decreasing without end. Such a tone was developed by Roger Shepard and consists of a superposition of sine waves separated by octaves. This creates the auditory illusion of a tone that continually ascends or descends in pitch, yet remaining constant.

Not only does the Shepard Tone create dissonance because we find it difficult to understand, it also creates uneasiness as a result of this dissonance. This perceived auditory dissonance causes emotional uneasiness.  We become uncomfortable when we cannot pigeon hole our perception. We need sounds that are at a prescribed distance from each other that make perception easier. Pythagoras defined the first mathematical rule for auditory perception, the definition of an octave that pleases our psychology for order and form. The fact that both European and Chinese figured this out at the same time indicates that the perception of octave generalizes across linguistic and auditory differences (for more auditory illusions see Deutsch, 2011). These psychological requirements, codified into mathematics are also found true for vision.

We like to see things in “chunks.” Mathematics was the earliest discipline to reflect this psychological need by inventing the number “one.” This basis of an “entity” forms the upside down pyramid of mathematics. Without a “one” there is no mathematics. But there are problems with the number one. There is a point at which a “one” cannot be defined mathematically, or where it fails to conform to some particular way, such as differentiability. This singularity--which is proving to be so problematic for mathematicians in explaining quantum physics for example--is only a problem for mathematicians, because an entity of “one” is the perfect creation of our mind and not nature. In fact the only way that quantum physics can explain superposition, entanglement and other quantum mechanics is by removing the “one” from the theorem. By removing the parenthesis around “one” quantum physics can be better explained, although then we have to readdress our psychology and the reliance on our perception of separate entities. From a psychological point this can be easier achieved rather than forcing quantum physics to conform to psychology.

History has been here before. Pythagoras--having traced the hand of god in how music is constructed--thought that each of the seven planets produced particular notes depending on its orbit around the earth. This was Musica Mundana and for Pythagorians, different musical modes have different effects on the person who hears them. Taking this a step further, the mathematician Boethius (480-524 AD) explained that the soul and the body are subject to the same laws of proportion that govern music and the cosmos itself. As the Italian semiotician Umberto Eco observed we are happiest when we conform to these laws because "we love similarity, but hate and resent dissimilarity" (Eco, 2002; p31).

This is not the first time that mathematicians thought they have touched the hand of god, neither will it be the last time. But what Pythagoras touched is our psychology. By focusing on pleasing patterns, similarities, and order, mathematicians are exploring the foundations of our psyche. And to do this they had to build rules and “common notions” that bind all these thoughts into a coherent language that translates into mathematics. For example if we take Euclid (4th Century BC) five "common notions” as defined in The Elements:

•  Things that are equal to the same thing are also equal to one another

•  If equals are added to equals, then the wholes are equal

•  If equals are subtracted from equals, then the remainders are equal

•  Things that coincide with one another are equal to one another

•  The whole is greater than the part.

There is an unambiguous relationship with classic Euclidian mathematics and Gestalt psychology. Gestalt psychology has rules that mirror these Euclidian common notions (Lagopoulos & Boklund-Lagopoulou, 1992). But there have been further developments. The prolific Swiss psychologist Jean Piaget (1896–1980) while investigating children’s conception of space discovered highly abstract mathematical structures in the child’s primordial conception of space.  He argues that the further development of geometric space should not be understood as reflecting the capacity of the child’s developing physiological functions, but as a product of the child’s interaction with the world. The child constantly builds up specific structures of perception and reorganizes spatial conception. Accordingly, Euclid’s elements and the topological properties of shapes have their origin neither in the world nor in the history of sciences, but in cognitive schemes that we build up in our daily interaction with objects.

The same understanding—that there are mathematical structure embedded in our cognitive processes—precludes the need for either mathematical or language. These theorems exist independent because that is how the brain is structured. A good example of this pre-mathematics and pre-linguistic ability is provided by a tribe that does not have a concept of numbers in its language. Dan Everett’s description of the Pirahã language of the southern Amazon basin exposes the tangled relationship between mathematical constructs and our cognitive capacity (Everett 2012). The Pirahã language has no clause subordination (e.g. after, because, if) at all, indeed it has no grammatical embedding of any kind, and it has no quantifier words (e.g. many, few, none); and it has no number words at all (e.g. one, two, many).  But they can still count and perform quit complex mathematical comparisons despite the lack of linguistic structure. The main deficit is that they cannot memorize these functions. So they can perform mathematical functions only for the immediate situation. In Popperian terms, they do not have a Third World construct of mathematics to enable them to retain an abstract representation of numbers which mathematicians, through their use of mathematical language can. And mathematicians have created this language, this mathematics where “one” forms the foundation.

Mathematics however has evolved and built upon this concept of “one.” It would be naïve to assume that mathematics has stood still as a discipline. Although the early conception of “one” is very restrictive number, in which ‘number’ means ‘natural number’ mathematics evolved to adopt a less restrictive conception of “one” in which it means ‘integer’; then meaning rationals; then reals, and then complex numbers. With such creations, there is a more nuanced appreciation of the finite interpretations of “one”. In psychology we might distinguish a human being (aka one), and then talk about aggregate or composite features such as family, community, or head, eyes, nose (reals), and then complex numbers such becoming a millionaire, getting divorced, losing a limb, becoming blind (complex numbers.) Mathematics has not extended the domain of numbers, but liberalized what we mean by ‘number’ and as a collinearity what we mean by “one.” Our presumption that there is a single number “one” and that, in extending the number system we simply add and perform “functions” to the numbers that were already there is not what mathematics has become. There are as many number “ones” as there are types of numbers. But by redefining the meaning we are creating a new definition of “one”. One that is less suspect to investigation and study, and bears less of a relationship with anything tangible (Fine, 2012).

We think in very complex ways that is still not understood, continues to be misrepresented and remains misunderstood. The human brain has more synaptic transmissions than we have stars in the universe. The capacity for human thought is immense. Clues are emerging that we think in very abstract ways that mirror the development of theorems in mathematics. Holographic theory of thinking is just one crude method of representing this universe of thought. It is plausible that mathematics could be a portal to understanding our psyche, our art and our behavior. We could learn our limitations, and our attributes and allow for the exploration of a process that we do not yet know and cannot know. We grow up developing our thinking as theorems--despite that in some cases our language does not accommodate such thinking--we still use innate mathematics to develop our sense of numbers and patterns. Mathematics is our way of thinking.  We simply grow out of it, as do mathematicians who simply grow out of being brilliant mathematicians and converge into cultural thought (language, roles and cultural morals.) Mathematicians have a short life of brilliance since their natural thought processes are eventually taken over by pragmatic concerns. Such is the final objective of our brain, survival in the real experiential world. Survival in a sentient world—a world dominated by feeling and experiencing. But mathematics can form the basis of formalizing theories of our thinking processes, mind sensations and feelings.  We need to see beyond the silos of disciplines and view our humanity as more than pitting humans against the hand of god, and simply see the hand of god as our own genius waiting to be acknowledged.

References

Carr B (1977). Popper's Third World. The Philosophical Quarterly Vol. 27, No. 108, pp. 214-226

Diana Deutsch Accessed 8/20/2015:: http://deutsch.ucsd.edu/psychology/pages.php?i=201)

Dummett M (1964) Bringing about the past. Philosophical Review 73: 338–59.

Eco U (2002). Art and beauty in the middle ages. Yale University Press.

Everett C (2012). A Closer Look at A Supposedly Anumeric Language 1. International Journal of American Linguistics, 78(4), 575-590.

Fine K (2012). Mathematics: Discovery of Invention? Think, 11, pp 11-27

Fitch WT & Friederici AD (2012). Artificial grammar learning meets formal language theory: an overview. Philosophical Transactions of the Royal Society B: Biological Sciences, 367(1598), 1933–1955. Accessed 8/20/2015: http://doi.org/10.1098/rstb.2012.0103

Hockenbury DH & Hockenbury SE (2006). Psychology. New York: Worth Publishers.

Kirk GS & Raven JE (1964). The Presocratic Philosophers, Cambridge University Press.

Lagopoulos, A. P., & Boklund-Lagopoulou, K. (1992). Meaning and geography: The social conception of the region in northern Greece (No. 104). Walter de Gruyter.

Ross KL (2011) Mathematics & Music, after Pythagoras. Accessed 8/20/2015: http://www.friesian.com/music.htm

Stillwell J (2006). Yearning for the impossible: The surprising truths of mathematics A. K. Peters, Ltd.

I am indebted to David Edwards, emeritus professor of mathematics from Georgia University for discussing with me the subtleties of some of these thoughts. Having such a knowledgeable and challenging adversary promoted the thinking of this argument and produced a much clearer thesis. However, all misrepresentations, deficiencies and shortfalls are purely my responsibilities.

© USA Copyrighted 2015 Mario D. Garrett 

Lost with Dementia

Patterns exist for people who get lost. Whether joggers, hikers, children, or those diagnosed with dementia, different groups exhibit different lost person behaviors. Knowing these patterns would help in finding them. Robert Koester's groundbreaking research has greatly expanded our understanding of “Lost Person Behavior” (Koester, 2008).  

This evolving line of inquiry  is becoming the bedrock for Search And Rescue (SAR) protocols. SAR  personnel consider variables such as behavioral profiles, activity, terrain, health, and personal characteristics to help predict the behavior of people who are declared lost. Koester has analyzed more than 50,000 cases world-wide to identify patterns of behavior that lost people tend to follow, including a special section for people with any variant of dementias—Koester’s specialty.

Older adults with dementia typically get lost through wandering behavior. Six in 10 people with dementia will wander—take off in an aimless way—becoming disoriented and perhaps not remembering their name, address, or their location.  Although effective programs exist in the United States—including MedicAlert®, Safe Return® Comfort Zone® and Comfort Zone Check-In®—the majority of people are not enrolled in such electronic tagging. Either they cannot afford the monthly premiums or they assume that they would never need such services. Due to America’s demographic changes, one thing is certain—people with dementia comprise an increasing concern for volunteer SAR teams, as well as state and federal agencies.

For SAR teams all dementias are treated the same. Koester & Stooksbury (1995) reported that when normal older adults got lost they traveled on average a greater straight-line distance (2.56 km) from the Point Last Seen (PLS) than older adults (in this case older than 40 years of age) with dementia (0.88 km). Although statistics indicate greater variability of distance traveled among dementia patients,here are some outliers where some might only travel a short distance while others travel greater distances (one in ten travel an average of 52 miles). Surprisingly, age did not emerge as an important consideration in how people with dementia behave when they get lost.

Dementia patients generally leave their own residence or nursing home and start traveling along roads. The patient is usually located (in 89% of cases) within one mile (1.2 km) of the PLS.  If the patients were not on a road (14%), they were usually found in a creek/drainage (28%), and/or caught in briars/bushes (33%).

The majority of patients succumb to the environment. One in five dementia patients (42 cases in this study) were found deceased due to hypothermia, dehydration, or drowning. No fatalities were found among dementia patients when they were located within 24 hours. If they were not found within this 24-hour window, half of dementia patients were likely to be found dead.

Consequently, searches for dementia patients are considered urgent and require an aggressive SAR response. Koester highlights that the diagnosis of dementia is important to elicit urgency. However, he also points out that most primary care physicians fail to administer cognitive status tests, and therefore only correctly identify 58% of the cases as possible dementia. This is particularly true of patients who become lost in wilderness and rural settings, who often belong to disadvantaged socioeconomic groups and who receive minimal health care. Not knowing that the lost person has dementia diminishes the search’s urgency, with potentially detrimental effects.

A key hypothesis  among SAR responders when looking for lost dementia patients is referred to as the “path of least resistance.”  This theory states that when people with dementia start wandering they tend to follow terrain that provides less resistance (down rather than uphill, roads rather than meandering paths, or railway tracks rather than steps).

A considerable number (28%) of dementia patients were found in drainages or creeks—indicating that they most likely walked downhill—supporting the path of least resistance hypothesis. Another 33% of the patients appear to have become stuck in thick brush or briars. This insight is important because untrained searchers, or searchers working at night often avoid looking into brush or briars because most people tend to try to make themselves visible. Getting stopped in drainages, creeks, brush and briars  support research indicating that lost patients with dementia are traveling a path of least  resistance until they reach an insurmountable barrier.

Because prevention is the best cure, reducing wandering becomes the best first line of defense. A personal care plan that reduces agitation and depression will help minimize wandering. Because people with dementia tend to leave few clues when they are lost and often do not respond to shouts or voice-based searching, getting expert help as early as possible is crucial. Knowing how to look for lost people with dementia requires an urgency that only expert help can provide.

Local dementia organizations counsel families that when someone with dementia goes missing, SAR efforts should be initiated immediately. Ninety-four percent of people who wander are found within 1.5 miles of where they disappeared. After the family and/or caregivers search the immediate area for no more than 15 minutes, they should call "911" and report to the police that a person with dementia—a vulnerable adult—is missing. Reporting parties should provide enough detail, including any places nearby that might have been important in childhood for the missing person.  Reports should include information on fears or phobias that the person might have, and what medications they are on.  A Missing Person Report should be filed so that police will also initiate a search.

In addition, even if a concerned party is not enrolled in a locator program, they should file a report with MedicAlert+ Alzheimer's Association Safe Return at 1-800-625-3780.  First responders are often trained to check this resource when they locate a missing person with dementia. Additional help can be accessed from the Alzheimer's Association 24/7 Helpline, 1-800-272-3900, which provides information and support to those who need assistance.Getting help as fast as possible might be the strategy that saves the lives of lost people with dementia.

Further Reading:

Perkins D & Roberts P (2000). Search Management for the Initial Response Incident Commander 2000. ERI International Inc. 

Twardy CR, Koester R & Gatt R (2006). Missing Person Behaviour An Australian Study Final Report to the Australian National SAR Council. Accessed online: http://www.esf.com.au/documents/reports/RobertGatt2002VicPol.pdf (link is external)

Koester RJ & Stooksbury DE (1999). Behavioral profile of wandering Alzheimer’s patients.  Wilderness and Environmental Medicine, 6,34-43 (1995)

Koester RJ (2008) Lost Person Behavior: A Search and Rescue Guide on Where to Look - for Land, Air and Water. Dbs Productions; Spi edition.

© USA Copyrighted 2015 Mario D. Garrett

Legal Consequences of Dementia

In most states, dementia is a reportable disease. Since 1988 physicians in California are required by law to report patients with dementia to their local health departments, information that is then shared with the Department of Motor Vehicles (DMV). Similar to sexually transmitted diseases, infections, and food borne illnesses, dementia is reported to both state and federal agencies. Unlike transmittable diseases however, the diagnosis and reporting of dementia initiates a cavalcade of medical, financial and legal consequences that might strip you of some of your rights as a citizen.
If you are diagnosed with dementia the first thing that you will notice is that the DMV informs you that you need your driving skills to be re-examined—if you are lucky and your physicians indicated that you have mild rather than severe dementia which in the eyes of the DMV renders you unsafe to drive and you automatically lose your license.  Statistically drivers with dementia are eight times more likely to be involved in a car accident. The DMV will schedule a meeting for you to meet with one of their driving instructors to determine your level of awareness, cognitive processes, and perception. Failure to pass these tests will results in your driving privilege being revoked. But if this meeting goes well then you will be scheduled for a special drive test, which includes vision screening. If you are successful at this test as well, then your license might be re-issued but it might come with some restrictions (driving at night driving on certain routes). From here on you will be reevaluated usually every 6 months or less. If the tests are unsatisfactory, you will lose your license.  This loss will jeopardize your ability to work and provide for your dependents, restrict your social participation, diminish your involvement in personal interests, and severely curtail participating in community activities.
The second metamorphosis will involve your relationship with your bank. Banks are catching up slowly to the consequences of dementia both in terms of financial abuse and mismanagement of accounts. Banks are however blind to the diagnosis unless your diagnosis is reported by your spouse, business partner, or family. If you owe a lot of debt, own or manage or a company with a board of directors then it is likely that knowledge of your diagnosis will change your status dramatically. At this stage you can be declared incompetent and treated as such. But you might also be tricked into buying or investing in low-interest or volatile stocks/shares, or sign over assets by your bank or lawyer. Although rare, bankers and lawyers have been found guilty of such abuses. Especially when banks are actively trying to sell new policies, you might be an attractive customer to them despite your diminished capacity. Bankers cannot judge your capacity, and in most cases will not assume that you are incompetent, unless it is to their determent. Whether you like it or not, your spouse or family will become more important to you. Not only because they are privy to your diagnosis but because they can also determine your legal standing. They can submit legal motion to declare you incompetent and take over your estate and business dealings.
A diagnosis of dementia is life changing. In the eye of a personal storm there are important legal and financial questions. In a complex legal field that is evolving, your best bet is to access professional legal advice as soon as possible.   Legal Aid Society, the local Area Agency on Aging, or the Alzheimer's Association might be able to provide you with the names of attorneys practicing in your area who deal with these issues. The obvious start should be determining your eligibility for Medicaid, investigating long-term care insurance, writing a living will and assigning a durable power of attorney for health care.

https://stocksnap.io/photo/6D2BBBEF99
Source: https://stocksnap.io/photo/6D2BBBEF99
For those that have assets,, gather your wills and trusts, prior tax returns, health and life insurance policies, pension information, deeds, mortgage/s, bank accounts (and PIN numbers), and information on other financial investments including ownership of property. Discuss the benefits and implications of transferring assets. If you do not have family or friends that can manage your accounts or business there are fiduciary agents who are certified to do this work for you. In some states you can prepare all your documents and then have them applied at a later period when your diagnosis become more severe. For those who have no or few assets, it is important to realize that you still need help with living arrangements and health directives.
In some cases, especially among people with extensive wealth, the strategy is not to get the diagnosis of dementia in the first place. They either go abroad where mandatory reporting is non-existent, or they go to a private physician and present a different identity. There are obfuscations from the patient as well. The central kingpin in all this is the family practitioner. His or her determination will guide bankers, lawyers and fiduciary agents. This is why a relationship with your primary care physician is important because he or she can help you coordinate and in some cases maneuver this complex medical and legal field.

© USA Copyrighted 2015 Mario D. Garrett